// Numbas version: finer_feedback_settings
{"showstudentname": true, "timing": {"allowPause": true, "timedwarning": {"action": "none", "message": ""}, "timeout": {"action": "none", "message": ""}}, "metadata": {"licence": "Creative Commons Attribution-ShareAlike 4.0 International", "description": ""}, "navigation": {"browse": true, "reverse": true, "onleave": {"action": "none", "message": ""}, "showfrontpage": true, "allowregen": true, "preventleave": true, "startpassword": "", "showresultspage": "oncompletion"}, "duration": 0, "feedback": {"showactualmark": true, "intro": "", "allowrevealanswer": true, "showanswerstate": true, "advicethreshold": 0, "feedbackmessages": [], "showtotalmark": true, "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "never"}, "showQuestionGroupNames": true, "question_groups": [{"name": "Graphical Extensions", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questions": [{"name": "Josh's copy of Heating/phase change", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Tom Stallard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/841/"}, {"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}], "tags": [], "metadata": {"description": "<p>A random heating question, that randomly picks a material, and then heats it through either one or two phase changes, provides an example graph of the heating with scaled temperature ranges (though not with scaled latent and specific heats), and a table with the suitable constants.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "preamble": {"js": "", "css": ""}, "ungrouped_variables": [], "variable_groups": [{"variables": ["switcharoo_comment", "switcharoo_type", "phase_temp", "phase_latentheat"], "name": "switcharoo (phase type) values"}, {"variables": ["mass_string"], "name": "kg or g"}, {"variables": ["mat_string", "phase1_temp", "phase2_temp", "gas_heatcap", "phase1_latentheat", "liquid_heatcap", "phase2_latentheat", "solid_heatcap"], "name": "Material values"}, {"variables": ["solidheat", "fusionheat", "liquidheat", "vapourheat", "gasheat", "totalheat", "totalheat_m"], "name": "Energy"}, {"variables": ["st_string", "et_string"], "name": "K or C"}, {"variables": ["material_list", "solid_hc_list", "liquid_hc_list", "gas_hc_list", "fusion_lh_list", "vapour_lh_list", "fusion_temp_list", "vapour_temp_list"], "name": "Lists of values"}, {"variables": ["switcharoo", "wat_mat", "start_temp", "end_temp", "k_c_switch", "mass"], "name": "Random variables"}, {"variables": ["advice1", "advice2", "advice3", "advice4", "advice5"], "name": "advice"}], "functions": {"onestep": {"parameters": [], "language": "javascript", "type": "html", "definition": "// Takes variables\n\n// showing K or C?\nk_c = Numbas.jme.unwrapValue(scope.variables.k_c_switch);\n\nif (k_c = 0) {\n    var k_c_corr =0;\n    var k_c_str=\"K\";\n} else {\n     var k_c_corr =-273;\n    var k_c_str=\"<sup>o<sup>C\";\n}\n\n//Set values\nst = Numbas.jme.unwrapValue(scope.variables.start_temp)+k_c_corr;\net = Numbas.jme.unwrapValue(scope.variables.end_temp)+k_c_corr;\npt = Numbas.jme.unwrapValue(scope.variables.phase_temp)+k_c_corr;\n\n\n// The function provided by the JSXGraph extension wraps the board up in\n// a div tag so that it's easier to embed in the page.\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','300px',\n    {boundingBox: [-4,et+10,20,st-10],\n     axis: false,\n     showNavigation: false,\n     grid: false\n    });\n\n// div.board is the object created by JSXGraph, which you use to\n// manipulate elements\nvar board = div.board;\n\n\n\n// create the x-axis.\n//var xaxis = board.create('line',[[0,0],[1,0]], {strokeColor: 'black', fixed: true});\n//var xticks = board.create('ticks',[xaxis,20],{\n//  drawLabels: true,\n//  minorTicks: 0\n//});\n\n// create the y-axis\nvar yaxis = board.create('line',[[0,0],[0,1]], { strokeColor: 'black', fixed: true });\nvar yticks = board.create('ticks',[yaxis,parseInt((et-st)/50.)*10],{\ndrawZero:true,\ndrawLabels: true,\nlabel: {offset: [20, 0]},\nminorTicks: 0\n});\n\n//\n//slope 1\nvar slope1 = board.create('line',[[4,st],[((pt-st)/((pt-st)+(et-pt))*8)+4,pt]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar slope2 = board.create('line',[[((pt-st)/((pt-st)+(et-pt))*8)+4,pt],[16-((et-pt)/((pt-st)+(et-pt))*8),pt]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar slope3 = board.create('line',[[16-((et-pt)/((pt-st)+(et-pt))*8),pt],[16,et]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n\nvar dash1 = board.create('line',[[((pt-st)/((pt-st)+(et-pt))*8)+4,st-5],[((pt-st)/((pt-st)+(et-pt))*8)+4,et+5]], {dash:2, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar dash2 = board.create('line',[[16-((et-pt)/((pt-st)+(et-pt))*8),st-5],[16-((et-pt)/((pt-st)+(et-pt))*8),et+5]], {dash:2, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n\n\n//label the y-axis\n  var label = board.create('text',[-2,(et+st)/2,k_c_str]);\n\n\n// and return the container div\nreturn div;"}, "twostep": {"parameters": [], "language": "javascript", "type": "html", "definition": "// Takes variables\n\n// showing K or C?\nk_c = Numbas.jme.unwrapValue(scope.variables.k_c_switch);\n\nif (k_c = 0) {\n    var k_c_corr =0;\n    var k_c_str=\"K\";\n} else {\n     var k_c_corr =-273;\n    var k_c_str=\"<sup>o<sup>C\";\n}\n\n//Set values\nst = Numbas.jme.unwrapValue(scope.variables.start_temp)+k_c_corr;\net = Numbas.jme.unwrapValue(scope.variables.end_temp)+k_c_corr;\npt1 = Numbas.jme.unwrapValue(scope.variables.phase1_temp)+k_c_corr;\npt2 = Numbas.jme.unwrapValue(scope.variables.phase2_temp)+k_c_corr;\n\n\n// The function provided by the JSXGraph extension wraps the board up in\n// a div tag so that it's easier to embed in the page.\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','300px',\n    {boundingBox: [-5,et+(et-st)/10.,28,st-(et-st)/10.],\n     axis: false,\n     showNavigation: false,\n     grid: false\n    });\n\n// div.board is the object created by JSXGraph, which you use to\n// manipulate elements\nvar board = div.board;\n\n\n\n// create the x-axis.\n//var xaxis = board.create('line',[[0,0],[1,0]], {strokeColor: 'black', fixed: true});\n//var xticks = board.create('ticks',[xaxis,20],{\n//  drawLabels: true,\n//  minorTicks: 0\n//});\n\n// create the y-axis\n\nvar yaxis = board.create('line',[[0,0],[0,1]], { strokeColor: 'black', fixed: true });\nvar yticks = board.create('ticks',[yaxis,parseInt((et-st)/50.)*10],{\ndrawZero:true,\ndrawLabels: true,\nlabel: {offset: [20, 0]},\nminorTicks: 0\n});\n\n\n// full size of the five slopes\nvar allslope=(et-st);\nvar s1sz=(8*(pt1-st)/allslope);\nvar s3sz=(8*(pt2-pt1)/allslope);\nvar s5sz=(8*(et-pt2)/allslope);\n\n\n//\n//slope 1\nvar slope1 = board.create('line',[[4,st],[s1sz+4,pt1]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar slope2 = board.create('line',[[s1sz+4,pt1],[s1sz+8,pt1]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar slope3 = board.create('line',[[s1sz+8,pt1],[s1sz+s3sz+8,pt2]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar slope4 = board.create('line',[[s1sz+s3sz+8,pt2],[s1sz+s3sz+12,pt2]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar slope5 = board.create('line',[[s1sz+s3sz+12,pt2],[s1sz+s3sz+s5sz+12,et]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n\n//var slope6 = board.create('line',[[4,pt1],[20,pt2]], {dash:2,straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n\nvar dash1 = board.create('line',[[s1sz+4,st-10],[s1sz+4,et+10]], {dash:2, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar dash2 = board.create('line',[[s1sz+8,st-10],[s1sz+8,et+10]], {dash:2, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar dash3 = board.create('line',[[s1sz+s3sz+8,st-10],[s1sz+s3sz+8,et+10]], {dash:2, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar dash4 = board.create('line',[[s1sz+s3sz+12,st-10],[s1sz+s3sz+12,et+10]], {dash:2, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n\n\n//label the y-axis\n  var label = board.create('text',[-2,(et+st)/2,k_c_str]);\n\n\n// and 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"if(switcharoo<2,random(100..phase1_temp-10),random(phase1_temp+10..phase2_temp-10))"}, "advice3": {"description": "", "name": "advice3", "group": "advice", "templateType": "anything", "definition": "\"Heating the liquid: $Q = m \\\\times C_L \\\\times \\\\Delta T = \"+\nswitch(\n  switcharoo=0,mass+' \\\\times '+liquid_heatcap+\" \\\\times (\"+end_temp+\" - \"+phase1_temp+\")\",\n  switcharoo=1,mass+' \\\\times '+liquid_heatcap+\" \\\\times (\"+phase2_temp+\" - \"+phase1_temp+\")\",\n  switcharoo=2,mass+' \\\\times '+liquid_heatcap+\" \\\\times (\"+phase2_temp+\" - \"+start_temp+\")\"\n)\n+\"= {liquidheat} J$\""}, "end_temp": {"description": "", "name": "end_temp", "group": "Random variables", "templateType": "anything", "definition": "if(switcharoo>0,random(phase2_temp+10..phase2_temp+100),random(phase1_temp+10..phase2_temp-10))"}, "vapour_temp_list": {"description": "", "name": "vapour_temp_list", "group": "Lists of values", "templateType": "anything", "definition": "[373,630,2835,3243]"}, "switcharoo_comment": {"description": "", "name": "switcharoo_comment", "group": "switcharoo (phase type) values", "templateType": "list of strings", "definition": "[ \"solid_to_liquid\", \"solid_to_gas\", \"liquid_to_gas\" ]"}, "et_string": {"description": "", "name": "et_string", "group": "K or C", "templateType": "anything", "definition": "if(k_c_switch,end_temp+' K',(end_temp-273)+' \u00b0C') "}, "liquid_hc_list": {"description": "", "name": "liquid_hc_list", "group": "Lists of values", "templateType": "anything", "definition": "[4200,140,490,150]"}, "solid_hc_list": {"description": "", "name": "solid_hc_list", "group": "Lists of values", "templateType": "anything", "definition": "[2100,110,390,130]"}, "switcharoo_type": {"description": "", "name": "switcharoo_type", "group": "switcharoo (phase type) values", "templateType": "anything", "definition": "switcharoo_comment[switcharoo]"}, "phase2_temp": {"description": "", "name": "phase2_temp", "group": "Material values", "templateType": "anything", "definition": "vapour_temp_list[wat_mat]"}, "st_string": {"description": "", "name": "st_string", "group": "K or C", "templateType": "anything", "definition": "if(k_c_switch,start_temp+' K',(start_temp-273)+' \u00b0C') "}, "solidheat": {"description": "", "name": "solidheat", "group": "Energy", "templateType": "anything", "definition": "siground(if(switcharoo<2,mass*solid_heatcap*(phase1_temp-start_temp),0),6)"}, "advice4": {"description": "", "name": "advice4", "group": "advice", "templateType": "anything", "definition": "if(switcharoo=0,\" \",\"Vaporising the \"+Mat_string+\": $Q = m \\\\times L_H = \"+mass+\" \\\\times \"+phase2_latentheat+\" = \"+vapourheat+\" J$\")"}, "fusionheat": {"description": "", "name": "fusionheat", "group": "Energy", "templateType": "anything", "definition": "siground(if(switcharoo<2,mass*phase1_latentheat,0),6)"}, "wat_mat": {"description": "", "name": "wat_mat", "group": "Random variables", "templateType": "anything", "definition": "random(0..3)"}, "phase2_latentheat": {"description": "", "name": "phase2_latentheat", "group": "Material values", "templateType": "anything", "definition": "vapour_lh_list[wat_mat]"}, "advice1": {"description": "", "name": "advice1", "group": "advice", "templateType": "anything", "definition": "if(switcharoo=2,\" \",\"Heating the solid: $Q = m \\\\times C_S \\\\times \\\\Delta T = \"+mass+\" \\\\times \"+solid_heatcap+\" \\\\times (\"+phase1_temp+\"-\"+start_temp+\") = \"+solidheat+\" J $\")"}, "advice5": {"description": "", "name": "advice5", "group": "advice", "templateType": "anything", "definition": "if(switcharoo=0,\" \",\"Heating the gas: $Q = m \\\\times C_G \\\\times \\\\Delta T = \"+mass+\" \\\\times \"+gas_heatcap+\" (\"+end_temp+\"-\"+phase2_temp+\") = \"+gasheat+\" J$\")"}, "advice2": {"description": "", "name": "advice2", "group": "advice", "templateType": "anything", "definition": "if(switcharoo=2,\" \",\"Melting the \"+Mat_string+\": $Q = m \\\\times L_H = \"+mass+\" \\\\times \"+phase1_latentheat+\" = \"+fusionheat+\" J$\")"}, "mass": {"description": "", "name": "mass", "group": "Random variables", "templateType": "anything", "definition": "siground(if(random(0,1)=0,random(0.01..0.99#0.01),random(1.00..10.00#0.01)),3)"}, "phase_latentheat": {"description": "", "name": "phase_latentheat", "group": "switcharoo (phase type) values", "templateType": "anything", "definition": "switch(switcharoo=0,phase1_latentheat,switcharoo=2,phase2_latentheat,0)"}, "totalheat": {"description": "", "name": "totalheat", "group": "Energy", "templateType": "anything", "definition": "solidheat+fusionheat+liquidheat+vapourheat+gasheat"}, "liquid_heatcap": {"description": "", "name": "liquid_heatcap", "group": "Material values", "templateType": "anything", "definition": "liquid_hc_list[wat_mat]"}, "phase_temp": {"description": "", "name": "phase_temp", "group": "switcharoo (phase type) values", "templateType": "anything", "definition": "switch(switcharoo=0,phase1_temp,switcharoo=2,phase2_temp,0)"}, "fusion_lh_list": {"description": "", "name": "fusion_lh_list", "group": "Lists of values", "templateType": "anything", "definition": "[336000,11300,207000,63000]"}, "k_c_switch": {"description": "", "name": "k_c_switch", "group": "Random variables", "templateType": "anything", "definition": "random(0,1)"}, "gas_heatcap": {"description": "", "name": "gas_heatcap", "group": "Material values", "templateType": "anything", "definition": "gas_hc_list[wat_mat]"}, "material_list": {"description": "", "name": "material_list", "group": "Lists of values", "templateType": "anything", "definition": "['H<sub>2</sub>O','Mercury','Copper','Gold']"}, "fusion_temp_list": {"description": "", "name": "fusion_temp_list", "group": "Lists of values", "templateType": "anything", "definition": "[273,234,1357,1337]"}, "liquidheat": {"description": "", "name": "liquidheat", "group": "Energy", "templateType": "anything", "definition": "siground(switch(switcharoo=0,mass*liquid_heatcap*(end_temp-phase1_temp),switcharoo=1,mass*liquid_heatcap*(phase2_temp-phase1_temp),switcharoo=2,mass*liquid_heatcap*(phase2_temp-start_temp),0),6)"}, "solid_heatcap": {"description": "", "name": "solid_heatcap", "group": "Material values", "templateType": "anything", "definition": "solid_hc_list[wat_mat]"}, "gasheat": {"description": "", "name": "gasheat", "group": "Energy", "templateType": "anything", "definition": "siground(if(switcharoo>0,mass*gas_heatcap*(end_temp-phase2_temp),0),6)"}, "totalheat_m": {"description": "", "name": "totalheat_m", "group": "Energy", "templateType": "anything", "definition": "totalheat/10^6"}, "gas_hc_list": {"description": "", "name": "gas_hc_list", "group": "Lists of values", "templateType": "anything", "definition": "[2000,135,350,110]"}, "phase1_temp": {"description": "", "name": "phase1_temp", "group": "Material values", "templateType": "anything", "definition": "fusion_temp_list[wat_mat]"}, "vapour_lh_list": {"description": "", "name": "vapour_lh_list", "group": "Lists of values", "templateType": "anything", "definition": "[2260000,293000,4730000,1580000]"}, "mat_string": {"description": "", "name": "mat_string", "group": "Material values", "templateType": "anything", "definition": "material_list[wat_mat]"}}, "parts": [{"showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "choices": ["<p>Solid, Liquid</p>", "<p>Solid, Liquid, Gas</p>", "<p>Liquid, Gas</p>"], "type": "1_n_2", "displayType": "radiogroup", "prompt": "<p>What phases does the {mat_string} go through.</p>", "showCellAnswerState": true, "marks": 0, "showCorrectAnswer": true, "maxMarks": 0, "extendBaseMarkingAlgorithm": true, "shuffleChoices": false, "variableReplacements": [], "distractors": ["", "", ""], "minMarks": 0, "matrix": ["if(switcharoo=0,1,0)", "if(switcharoo=1,1,0)", "if(switcharoo=2,1,0)"], "scripts": {}, "customMarkingAlgorithm": "", "displayColumns": 0}, {"showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "choices": ["<p>Melting</p>", "<p>Melting,Vaporisation</p>", "<p>Vaporisation</p>"], "type": "1_n_2", "displayType": "radiogroup", "prompt": "<p>What phase changes does the {mat_string} go through.</p>", "showCellAnswerState": true, "marks": 0, "showCorrectAnswer": true, "maxMarks": 0, "extendBaseMarkingAlgorithm": true, "shuffleChoices": false, "variableReplacements": [], "distractors": ["", "", ""], "minMarks": 0, "matrix": ["if(switcharoo=0,1,0)", "if(switcharoo=1,1,0)", "if(switcharoo=2,1,0)"], "scripts": {}, "customMarkingAlgorithm": "", "displayColumns": 0}, {"extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "maxValue": "siground(totalheat_m,3)+siground(abs(totalheat_m/100),3)", "minValue": "siground(totalheat_m,3)-siground(abs(totalheat_m/100),3)", "marks": "1", "allowFractions": false, "type": "numberentry", "mustBeReduced": false, "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "prompt": "<p>Calculate the total heat absorbed by the {Mat_string} through this process in MJ to three significant figures.</p>", "showCorrectAnswer": false, "strictPrecision": true, "precision": "3", "correctAnswerFraction": false, "variableReplacements": [], "showPrecisionHint": false, "precisionMessage": "You have not given your answer to the correct precision.", "scripts": {}, "precisionType": "sigfig"}], "statement": "<p style=\"text-align: center;\"><strong>{mass_string} of {Mat_string} is heated from {st_string} to {et_string}, changing in temperature and phase.</strong></p>\n<p></p>\n<p>{if(switcharoo=1,twostep(),onestep())}</p>\n<table style=\"margin-left: auto; margin-right: auto;\" border=\"1\">\n<tbody>\n<tr>\n<td></td>\n<td>Solid specific heat</td>\n<td>Latent Heat of fusion</td>\n<td>Liquid specific heat</td>\n<td>Latent Heat of vapourisation</td>\n<td>Gaseous specific heat</td>\n<td>Fusion Temperature</td>\n<td>Vaporisation Temperature</td>\n</tr>\n<tr>\n<td>{Mat_string}</td>\n<td>{solid_heatcap} JK&lt;sup&gt;-1&lt;/sup&gt;kg&lt;sup&gt;-1&lt;/sup&gt;</td>\n<td>{phase1_latentheat} Jkg&lt;sup&gt;-1&lt;/sup&gt;</td>\n<td>{liquid_heatcap} JK&lt;sup&gt;-1&lt;/sup&gt;kg&lt;sup&gt;-1&lt;/sup&gt;</td>\n<td>{phase2_latentheat} Jkg&lt;sup&gt;-1&lt;/sup&gt;</td>\n<td>{gas_heatcap} JK&lt;sup&gt;-1&lt;/sup&gt;kg&lt;sup&gt;-1&lt;/sup&gt;</td>\n<td>{phase1_temp} K</td>\n<td>{phase2_temp} K</td>\n</tr>\n</tbody>\n</table>", "advice": "<p>{advice1}</p>\n<p>{advice2}</p>\n<p>{advice3}</p>\n<p>{advice4}</p>\n<p>{advice5}</p>\n<p></p>\n<p>Total Heat:</p>\n<p>{totalheat} J = {sigformat(totalheat/1000000,3)} MJ</p>"}, {"name": "Josh's copy of Block sliding down a frictionless slope (with graphic)", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Tom Stallard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/841/"}, {"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}], "rulesets": {}, "type": "question", "parts": [{"minValue": "FN-FN/100", "scripts": {}, "unitTests": [], "type": "numberentry", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "showFeedbackIcon": true, "marks": 1, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "maxValue": "FN+FN/100", "variableReplacements": [], "prompt": "<p>Find the normal reaction, $F_N$ between the block and the plane, in N to 3 decimal places.</p>", "mustBeReduced": false, "allowFractions": false, "notationStyles": ["plain", "en", "si-en"]}, {"minValue": "FP-FP/100", "scripts": {}, "unitTests": [], "type": "numberentry", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "showFeedbackIcon": true, "marks": 1, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "maxValue": "FP+FP/100", "variableReplacements": [], "prompt": "<p>Find the gravitational force on the block, parallel to the plane $F_P$, in N to 3 decimal places.</p>", "mustBeReduced": false, "allowFractions": false, "notationStyles": ["plain", "en", "si-en"]}, {"scripts": {}, "precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "marks": "1", "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "maxValue": "answer+answer/100", "type": "numberentry", "strictPrecision": false, "minValue": "answer-answer/100", "unitTests": [], "showPrecisionHint": false, "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "prompt": "<p>{a_string}, to 3 decimal places.</p>", "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "precisionPartialCredit": 0, "variableReplacements": [{"must_go_first": true, "variable": "FP", "part": "p1"}], "allowFractions": false, "mustBeReduced": false, "correctAnswerFraction": false, "precision": "3"}], "statement": "<p>{draw_block()}</p>\n<p>A block of mass {mass} kg slides down a frictionless plane which is inclined at an angle $\\theta$ = {theta}$^{\\circ}$ to the horizontal.</p>\n<p>The acceleration due to gravity is g={g} ms$^{-2}$.</p>", "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"g": {"templateType": "anything", "definition": "9.8", "description": "", "group": "constants", "name": "g"}, "FP": {"templateType": "anything", "definition": "siground(mass*g*sin(radians(theta)),3)", "description": "", "group": "calculated variables", "name": "FP"}, "a": {"templateType": "anything", "definition": "siground(random(1.1..5#0.1),2)", "description": "<p>The acceleration of the block down the slope.</p>", "group": "random variables", "name": "a"}, "mass": {"templateType": "anything", "definition": "siground(random(0.2..9.9#0.1),2)", "description": "<p>The mass of the block.</p>", "group": "random variables", "name": "mass"}, "theta": {"templateType": "randrange", "definition": "random(30..60#1)", "description": "<p>The angle of the slope.</p>", "group": "random variables", "name": "theta"}, "answer": {"templateType": "anything", "definition": "aa", "description": "", "group": "calculated variables", "name": "answer"}, "aa": {"templateType": "anything", "definition": "siground(FP/mass,3)", "description": "", "group": "calculated variables", "name": "aa"}, "FN": {"templateType": "anything", "definition": "siground(mass*g*cos(radians(theta)),3)", "description": "<p>The normal reaction force&nbsp;of the plane on the block</p>", "group": "calculated variables", "name": "FN"}, "a_string": {"templateType": "anything", "definition": "\"Calculate the acceration of the block in ms$^\\{-2\\}$\"", "description": "", "group": "calculated variables", "name": "a_string"}}, "tags": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>A block of given mass is sliding down the plane with a given acceration. Find the normal reaction force, the parallel force and the missing value of a and mu.</p>"}, "variable_groups": [{"variables": ["mass", "theta", "a"], "name": "random variables"}, {"variables": ["FN", "FP", "aa", "answer", "a_string"], "name": "calculated variables"}, {"variables": ["g"], "name": "constants"}], "advice": "<h4>a)</h4>\n<p>To find the normal reaction force $F_N$, we resolve the forces perpendicular to the plane.</p>\n<p>&nbsp;<br/>$F_N =$ mg cos $\\theta$,<br/>$F_N =$ {mass} $\\times$ {g} cos( {theta}$^{\\circ}$),<br/><br/></p>\n<p>And so the normal force $F_N$ is {fn} N.</p>\n<h4>b)</h4>\n<p>To find the force $F_P$ parallel to the plane, we resolve the forces parallel to the plane.</p>\n<p>&nbsp;<br/>$F_P =$ mg sin $\\theta$,<br/>$F_P =$ {mass} $\\times$ {g} sin ({theta}$^{\\circ}$),<br/><br/></p>\n<p>And so the parallel force $F_P$ is {fp} N.</p>\n<p></p>\n<p><strong>c)</strong></p>\n<p>To find the acceleration of the block, you must calculate divide the force down the slope by the mass.</p>\n<p>F=ma</p>\n<p>a = F{\"&lt;sub&gt;P&lt;/sub&gt;\"} / m</p>\n<p>a = {FP} / {mass}</p>\n<p>So, the acceration of the block is {answer} m/s&lt;sup&gt;-2&lt;/sup&gt;.</p>\n<p></p>", "preamble": {"js": "", "css": ""}, "functions": {"draw_block": {"parameters": [], "type": "html", "language": "javascript", "definition": "// Takes variables\n\n// showing K or C?\n//k_c = Numbas.jme.unwrapValue(scope.variables.k_c_switch);\n//\n//if (k_c = 0) {\n//    var k_c_corr =0;\n//    var k_c_str=\"K\";\n//} else {\n//     var k_c_corr =-273;\n//    var k_c_str=\"\u00b0C\";\n//}\n\n//Set values\ntheta = Numbas.jme.unwrapValue(scope.variables.theta);\nr_theta = theta * Math.PI / 180. \nm = Numbas.jme.unwrapValue(scope.variables.mass);\n//et = Numbas.jme.unwrapValue(scope.variables.end_temp)+k_c_corr;\n//pt1 = Numbas.jme.unwrapValue(scope.variables.phase1_temp)+k_c_corr;\n//pt2 = Numbas.jme.unwrapValue(scope.variables.phase2_temp)+k_c_corr;\n\n\n// The function provided by the JSXGraph extension wraps the board up in\n// a div tag so that it's easier to embed in the page.\nvar div = Numbas.extensions.jsxgraph.makeBoard('300px','260px',\n//{boundingBox: [-0.1,-0.1,1.,1.],\n    {boundingBox: [1.,0.8,-0.1,-0.1],\n     axis: false,\n     showNavigation: false,\n     grid: false\n    });\n\n// div.board is the object created by JSXGraph, which you use to\n// manipulate elements\nvar board = div.board;\n\n\n\n// create the x-axis.\n//var xaxis = board.create('line',[[0,0],[1,0]], {strokeColor: 'black', fixed: true});\n//var xticks = board.create('ticks',[xaxis,20],{\n//  drawLabels: true,\n//  minorTicks: 0\n//});\n\n// create the y-axis\n\n//var yaxis = board.create('line',[[0,0],[0,1]], { strokeColor: 'black', fixed: true });\n//var yticks = board.create('ticks',[yaxis,parseInt((et-st)/50.)*10],{\n//drawZero:true,\n//drawLabels: true,\n//label: {offset: [20, 0]},\n//minorTicks: 0\n//});\n\n\n// each line needs four coordinates start x,y and end x,y - these can then all be rotated\n\n// the slope itself\n\nvar l1_x1=0.\nvar l1_x2=0.9\nvar l1_y1=0.\nvar l1_y2=0.\n\n\t// the left edge of the box \n\nvar l2_x1=0.3\nvar l2_x2=0.3\nvar l2_y1=0\nvar l2_y2=0.2\n\n\t\t// the top edge of the box \n\nvar l3_x1=0.3\nvar l3_x2=0.6\nvar l3_y1=0.2\nvar l3_y2=0.2\n\t\t\t\n\t\t\t// the right edge of the box \n\nvar l4_x1=0.6\nvar l4_x2=0.6\nvar l4_y1=0.2\nvar l4_y2=0.\n\n//centre of the block\n\nvar c_x=0.45\nvar c_y=0.1\n\n//each line must be rotated by theta to get to the correct angle\n\n\n// the slope itself\n\nvar ql1_x1=l1_x1*Math.cos(r_theta)-l1_y1*Math.sin(r_theta)\nvar ql1_y1=l1_x1*Math.sin(r_theta)-l1_y1*Math.cos(r_theta)\nvar ql1_x2=l1_x2*Math.cos(r_theta)-l1_y2*Math.sin(r_theta)\nvar ql1_y2=l1_x2*Math.sin(r_theta)-l1_y2*Math.cos(r_theta)\n\n\t// the left edge of the box \n\nvar ql2_x1=l2_x1*Math.cos(r_theta)-l2_y1*Math.sin(r_theta)\nvar ql2_y1=l2_x1*Math.sin(r_theta)+l2_y1*Math.cos(r_theta)\nvar ql2_x2=l2_x2*Math.cos(r_theta)-l2_y2*Math.sin(r_theta)\nvar ql2_y2=l2_x2*Math.sin(r_theta)+l2_y2*Math.cos(r_theta)\n\n\t\t// the top edge of the box \n\nvar ql3_x1=l3_x1*Math.cos(r_theta)-l3_y1*Math.sin(r_theta)\nvar ql3_y1=l3_x1*Math.sin(r_theta)+l3_y1*Math.cos(r_theta)\nvar ql3_x2=l3_x2*Math.cos(r_theta)-l3_y2*Math.sin(r_theta)\nvar ql3_y2=l3_x2*Math.sin(r_theta)+l3_y2*Math.cos(r_theta)\n\t\t\t\n\t\t\t// the right edge of the box \n\nvar ql4_x1=l4_x1*Math.cos(r_theta)-l4_y1*Math.sin(r_theta)\nvar ql4_y1=l4_x1*Math.sin(r_theta)+l4_y1*Math.cos(r_theta)\nvar ql4_x2=l4_x2*Math.cos(r_theta)-l4_y2*Math.sin(r_theta)\nvar ql4_y2=l4_x2*Math.sin(r_theta)+l4_y2*Math.cos(r_theta)\n\n//centre of the box\n\nvar qc_x=c_x*Math.cos(r_theta)-c_y*Math.sin(r_theta)\nvar qc_y=c_x*Math.sin(r_theta)+c_y*Math.cos(r_theta)\n\n//var block = board.create('polygon',[ [0.3,0], [0.3,0.2] , [0.6,0.2] ,[0.6,0] ]  );\n\n//\n//slope 1\nvar line1 = board.create('line',[[l1_x1,l1_y1],[l1_x2,l1_y2]], {straightFirst:true, straightLast:true, strokeColor: 'black', fixed: true });\nvar line1b = board.create('line',[[ql1_x1,ql1_y1],[ql1_x2,ql1_y2]], {straightFirst:false, straightLast:true, strokeColor: 'black', fixed: true });\nvar line2 = board.create('line',[[ql2_x1,ql2_y1],[ql2_x2,ql2_y2]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar line3 = board.create('line',[[ql3_x1,ql3_y1],[ql3_x2,ql3_y2]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar line4 = board.create('line',[[ql4_x1,ql4_y1],[ql4_x2,ql4_y2]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n\n//var slope6 = board.create('line',[[4,pt1],[20,pt2]], {dash:2,straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n\n//var dash1 = board.create('line',[[s1sz+4,st-10],[s1sz+4,et+10]], {dash:2, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n//var dash2 = board.create('line',[[s1sz+8,st-10],[s1sz+8,et+10]], {dash:2, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n//var dash3 = board.create('line',[[s1sz+s3sz+8,st-10],[s1sz+s3sz+8,et+10]], {dash:2, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n//var dash4 = board.create('line',[[s1sz+s3sz+12,st-10],[s1sz+s3sz+12,et+10]], {dash:2, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n\n\n//label the y-axis\nvar label = board.create('text',[0.25,0.05,theta+'\\xB0'],{fontSize:20});\n\n//label the mass\nvar mass = board.create('text',[qc_x,qc_y, m.toFixed(1)+' kg'], {display:'internal',rotate:-theta,anchorX:'middle',anchorY:'middle',fontSize:18});\n\n\n//var tRot = board.create('transform', [6,0.1,0.15], {type:'rotate'})\n//tRot.bindTo(mass);\n//board.update();\n// and return the container div\nreturn div;"}}, "ungrouped_variables": []}, {"name": "nuExam12 - Vector Addition", "extensions": ["geogebra", "quantities", "weh"], "custom_part_types": [{"source": {"pk": 24, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/24/edit"}, "name": "Angle quantity", "short_name": "angle-quantity-from-reference", "description": "<p>Angle&nbsp;as a quantity in degrees.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['correct_quantity'])", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\ncorrect_scalar:\nscalar(correct_quantity)\n  \n\ncorrect_quantity:\nsettings['correct_quantity']\n\ncorrect_units:\nunits(correct_quantity)\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\njoin(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n\n\ngood_units:\ntry(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)\n\nstudent_quantity:\nswitch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)\n\nangle_in_range:\nif(settings['restrict_angle'], abs(student_scalar) <= 90, true)\n\nright:\nwithinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])\n\nclose:\nwithinTolerance(student_scalar, correct_scalar, settings['close'])", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)"}, {"name": "correct_scalar", "description": "", "definition": "scalar(correct_quantity)\n  "}, {"name": "correct_quantity", "description": "", "definition": "settings['correct_quantity']"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "", "definition": "join(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n"}, {"name": "good_units", "description": "", "definition": "try(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)"}, {"name": "student_quantity", "description": "", "definition": "switch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity)"}, {"name": "angle_in_range", "description": "", "definition": "if(settings['restrict_angle'], abs(student_scalar) <= 90, true)"}, {"name": "right", "description": "<p>Will check for correct sign elswhere.</p>", "definition": "withinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])"}, {"name": "close", "description": "<p>Must have correct sign to be close.</p>", "definition": "withinTolerance(student_scalar, correct_scalar, settings['close'])\n"}], "settings": [{"name": "correct_quantity", "label": "Correct Angle as quantity ", "help_url": "", "hint": "", "input_type": "code", "default_value": "qty(45,'deg')", "evaluate": true}, {"name": "right", "label": "Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.1", "evaluate": true}, {"name": "restrict_angle", "label": "Less than 90\u00b0", "help_url": "", "hint": "When checked, angle must be between -90&deg; and +90&deg;.", "input_type": "checkbox", "default_value": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units.", "input_type": "percent", "default_value": "75"}, {"name": "close", "label": " Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.5", "evaluate": true}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value without units.", "input_type": "percent", "default_value": "25"}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}], "preamble": {"js": "", "css": ""}, "functions": {"direction": {"language": "javascript", "type": "number", "parameters": [["v", "vector"]], "definition": "return Math.atan2(v[1],v[0])"}}, "variable_groups": [{"name": "Inputs", "variables": ["A", "B", "C", "alpha", "FA", "FB", "FC", "units", "debug"]}, {"name": "Outputs", "variables": ["ForceA", "beta", "gamma", "ForceB", "ForceC", "ForceR", "rho", "R", "angle_from_ref"]}], "variablesTest": {"maxRuns": 100, "condition": "B[0]<>C[0] and B[1]<>C[1] and abs(alpha-beta) >= 15 and abs(gamma-beta) >= 15 and  abs(gamma-alpha) >= 15"}, "tags": [], "ungrouped_variables": [], "rulesets": {}, "parts": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {}, "gaps": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "type": "engineering-answer", "settings": {"correctAnswer": "qty(forceA[0],units[1])", "C3": "25", "right": "0.2", "close": "1.0", "C2": "50", "C1": "75"}, "customMarkingAlgorithm": "", "marks": "2", "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "type": "engineering-answer", "settings": {"correctAnswer": "qty(forceA[1],units[1])", "C3": "25", "right": "0.2", "close": "1.0", "C2": "50", "C1": "75"}, "customMarkingAlgorithm": "", "marks": "2", "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "type": "engineering-answer", "settings": {"correctAnswer": "qty(forceB[0],units[1])", "C3": "25", "right": "0.2", "close": "1.0", "C2": "50", "C1": "75"}, "customMarkingAlgorithm": "", "marks": "2", "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "type": "engineering-answer", "settings": {"correctAnswer": "qty(forceB[1],units[1])", "C3": "25", "right": "0.2", "close": "1.0", "C2": "50", "C1": "75"}, "customMarkingAlgorithm": "", "marks": "2", "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "type": "engineering-answer", "settings": {"correctAnswer": "qty(forceC[0],units[1])", "C3": "25", "right": "0.2", "close": "1.0", "C2": "50", "C1": "75"}, "customMarkingAlgorithm": "", "marks": "2", "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "type": "engineering-answer", "settings": {"correctAnswer": "qty(forceC[1],units[1])", "C3": "25", "right": "0.2", "close": "1.0", "C2": "50", "C1": "75"}, "customMarkingAlgorithm": "", "marks": "2", "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}], "showCorrectAnswer": true, "type": "gapfill", "sortAnswers": false, "customMarkingAlgorithm": "", "prompt": "<p>Find the scalar components of the component forces <strong>A</strong>, <strong>B</strong>, and <strong>C</strong>.&nbsp;</p>\n<p>$A_x =$&nbsp;[[0]]&nbsp; $B_x =$&nbsp;[[2]]&nbsp; $C_x =$&nbsp;[[4]]</p>\n<p>$A_y =$&nbsp;[[1]]&nbsp; $B_y =$&nbsp;[[3]]&nbsp; $C_y =$&nbsp;[[5]]</p>", "marks": 0, "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {}, "gaps": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "type": "engineering-answer", "settings": {"correctAnswer": "qty(ForceR[0],units[1])", "C3": "25", "right": "0.2", "close": "1.0", "C2": "50", "C1": "75"}, "customMarkingAlgorithm": "", "marks": "2", "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "type": "engineering-answer", "settings": {"correctAnswer": "qty(ForceR[1],units[1])", "C3": "25", "right": "0.2", "close": "1.0", "C2": "50", "C1": "75"}, "customMarkingAlgorithm": "", "marks": "2", "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}], "showCorrectAnswer": true, "type": "gapfill", "sortAnswers": false, "customMarkingAlgorithm": "", "prompt": "<p>Sum the scalar components to get&nbsp;the scalar components of the resultant <strong>R</strong>.</p>\n<p>$R_x = \\Sigma F_x &nbsp;= A_x + B_x + C_x =$&nbsp;[[0]]&nbsp;</p>\n<p>$R_y = \\Sigma F_y &nbsp;= A_y + B_y + C_y =$ [[1]]&nbsp;&nbsp;</p>", "marks": 0, "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {}, "gaps": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "type": "engineering-answer", "settings": {"correctAnswer": "qty(R,units[1])", "C3": "25", "right": "0.2", "close": "1.0", "C2": "50", "C1": "75"}, "customMarkingAlgorithm": "", "marks": "2", "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {"mark": {"order": "after", "script": "index = Numbas.jme.unwrapValue(this.studentAnswerAsJME());\nangles = Numbas.jme.unwrapValue(Numbas.exam.currentQuestion.scope.getVariable('angle_from_ref'));\nans =  Qty(angles[index],'deg');\nthis.parentPart.gaps[2].settings.correct_quantity.value= ans;\nthis.markingComment(\"For your axis, the direction is \" +  ans.toPrec('0.1 deg') +'.');"}}, "showCorrectAnswer": true, "type": "drop-down-axis-reference", "settings": {"dummy": "'ignore'"}, "customMarkingAlgorithm": "", "marks": "0", "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "type": "angle-quantity-from-reference", "settings": {"correct_quantity": "qty(angle_from_ref[0],'deg')", "C3": "25", "restrict_angle": true, "right": "0.2", "close": "1.01", "C2": "50", "C1": "75"}, "customMarkingAlgorithm": "", "marks": "2", "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}], "showCorrectAnswer": true, "type": "gapfill", "sortAnswers": false, "customMarkingAlgorithm": "", "prompt": "<p>Resolve&nbsp;$R_x$ and $R_y$ to find the magnitude and direction of <strong>R</strong>.</p>\n<p>$R = \\sqrt{{R_x}^2 +{R_y}^2}$ =&nbsp;[[0]]&nbsp;</p>\n<p>&nbsp;$\\theta = \\tan^{-1}\\left(\\left|\\dfrac{R_y}{R_x}\\right| \\right)$ =&nbsp;[[2]]&nbsp; measured from the&nbsp;&nbsp;[[1]]</p>\n<p><span data-jme-visible=\"debug\">{angle_from_ref}</span></p>", "marks": 0, "useCustomName": false, "customName": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}], "variables": {"angle_from_ref": {"definition": "let(ang,rho,\n[if(ang>180,ang-360,ang),\nif(ang>270,ang-450,if(ang < -90,ang+270,ang-90)),\nif(ang>0,ang-180,ang+180),\nif(ang>90,ang-270,90+ang)])", "description": "", "templateType": "anything", "group": "Outputs", "name": "angle_from_ref"}, "FA": {"definition": "random(10..100#5)", "description": "<p>Magnitude of force A</p>", "templateType": "anything", "group": "Inputs", "name": "FA"}, "units": {"definition": "random(['cm','N'],['cm','N'],['cm','N'])", "description": "", "templateType": "anything", "group": "Inputs", "name": "units"}, "alpha": {"definition": "(random(-80..175#5 except[45,135,-45,80,100]))", "description": "<p>direction of force A</p>", "templateType": "anything", "group": "Inputs", "name": "alpha"}, "ForceR": {"definition": "ForceA+ForceB+ForceC", "description": "<p>Resultant as a vector</p>", "templateType": "anything", "group": "Outputs", "name": "ForceR"}, "A": {"definition": "vector(0,0)", "description": "<p>Position of point A</p>", "templateType": "anything", "group": "Inputs", "name": "A"}, "gamma": {"definition": "degrees(direction(vector(C[0]-A[0],C[1]-A[1])))", "description": "<p>Direction of force C in degrees</p>", "templateType": "anything", "group": "Outputs", "name": "gamma"}, "C": {"definition": "vector(random(1,-1)random(2..6),random(1,-1)random(2..6))", "description": "<p>Position of point C</p>", "templateType": "anything", "group": "Inputs", "name": "C"}, "ForceB": {"definition": "FB *( vector(cos(radians(beta)),sin(radians(beta))))", "description": "<p>Force B as a vector</p>", "templateType": "anything", "group": "Outputs", "name": "ForceB"}, "ForceA": {"definition": "FA *( vector(cos(radians(alpha)),sin(radians(alpha))))", "description": "<p>force A&nbsp;as a vector</p>", "templateType": "anything", "group": "Outputs", "name": "ForceA"}, "beta": {"definition": "degrees(direction(vector(B[0]-A[0],B[1]-A[1])))", "description": "<p>Direction of force B</p>", "templateType": "anything", "group": "Outputs", "name": "beta"}, "FC": {"definition": "random(10..100#5)", "description": "<p>Magnitude of force C</p>", "templateType": "anything", "group": "Inputs", "name": "FC"}, "B": {"definition": "vector( random(1,-1) random(4..10),random(1,-1) random(2..5))", "description": "<p>Position of point B</p>", "templateType": "anything", "group": "Inputs", "name": "B"}, "ForceC": {"definition": "FC *( vector(cos(radians(gamma)),sin(radians(gamma))))", "description": "<p>Force C as a vector</p>", "templateType": "anything", "group": "Outputs", "name": "ForceC"}, "FB": {"definition": "random(10..100#10)", "description": "<p>Magnitude of Force B</p>", "templateType": "anything", "group": "Inputs", "name": "FB"}, "R": {"definition": "sqrt(ForceR[0]^2+forceR[1]^2)", "description": "<p>Magnitude of resultant</p>", "templateType": "anything", "group": "Outputs", "name": "R"}, "debug": {"definition": "false", "description": "", "templateType": "anything", "group": "Inputs", "name": "debug"}, "rho": {"definition": "degrees(direction(ForceR))", "description": "<p style=\"text-align: left;\">direction of resultant</p>", "templateType": "anything", "group": "Outputs", "name": "rho"}}, "advice": "<p>Vector Addition: &nbsp;</p>\n<p>$R_x = \\Sigma F_x = &nbsp;(\\var{siground(ForceA[0],4)}) &nbsp;+ (\\var{siground(ForceB[0],4)}) +(&nbsp;\\var{siground(ForceC[0],4)}) = \\var{siground(ForceR[0],4)}$&nbsp;{units[1]}</p>\n<p>$R_y = \\Sigma F_y = &nbsp;(\\var{siground(ForceA[1],4)}) &nbsp;+ (\\var{siground(ForceB[1],4)}) +(&nbsp;\\var{siground(ForceC[1],4)}) = \\var{siground(ForceR[1],4)}$&nbsp;{units[1]}</p>\n<p></p>\n<p>$ R=\\sqrt{R_x^2 + R_y^2} = \\sqrt{(\\var{siground(ForceR[0],4)})^2 +(\\var{siground(ForceR[0],4)})^2} = \\var{siground(abs(ForceR),4)}$&nbsp;{units[1]}</p>\n<p></p>\n<p>$\\theta = \\tan^{-1}\\left(\\left|\\frac{R_y}{R_x}\\right| \\right) = \\tan^{-1}\\left(\\left|\\frac{\\var{siground(ForceR[1],4)}}{\\var{siground(ForceR[0],4)}}\\right| \\right) &nbsp;= \\var{siground(degrees(arctan(abs(forceR[1])/forceR[0])),4)}&deg; &nbsp;= &nbsp;(\\var{siground(rho,4)}&deg; $ from the positive x-axis.)</p>", "statement": "<p><strong></strong>Three forces act on the bracket at point <em>A</em>: &nbsp; <span style=\"color: green;\"><em>A</em> = {FA} {units[1]}</span>, <span style=\"color: blue;\"><em>B</em>&nbsp;= {FB} {units[1]} </span> and, <span style=\"color: red;\"><em>C&nbsp;</em>= {FC} {units[1]}</span>.</p>\n<p><strong>(The diagram may take a moment or two to load - give it chance)</strong></p>\n<p>Find the magnitude and direction of the resultant force&nbsp;<strong>R </strong>by summing scalar components.</p>\n<p>Enter your magnitude quatities in SI units, eg. 500 N and give 2 d.p.</p>\n<p>{geogebra_applet('dtf3t2dp', [['A',A],['B',B],['C',C],['F_a',FA],['F_b',FB],['F_c',FC],['&alpha;', alpha],['unit','\"'+units[0]+'\"']])}</p>\n<p></p>\n<p><span data-jme-visible=\"debug\">Force A: {fa} at {alpha} = {forceA}&nbsp;</span></p>\n<p><span data-jme-visible=\"debug\">Force B: {fb} at {beta} = {forceB}</span></p>\n<p><span data-jme-visible=\"debug\">Force C: {fc} at {gamma} = {forceC}</span></p>\n<p><span data-jme-visible=\"debug\">Resultant: {R} at {rho} &nbsp;= {forceR}</span></p>", "metadata": {"description": "<p>Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "type": "question"}, {"name": "Josh's copy of Vector addition: tip-to-tail method", "extensions": ["geogebra", "quantities", "weh"], "custom_part_types": [{"source": {"pk": 24, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/24/edit"}, "name": "Angle quantity", "short_name": "angle-quantity-from-reference", "description": "<p>Angle&nbsp;as a quantity in degrees.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['correct_quantity'])", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\ncorrect_scalar:\nscalar(correct_quantity)\n  \n\ncorrect_quantity:\nsettings['correct_quantity']\n\ncorrect_units:\nunits(correct_quantity)\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\njoin(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n\n\ngood_units:\ntry(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)\n\nstudent_quantity:\nswitch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)\n\nangle_in_range:\nif(settings['restrict_angle'], abs(student_scalar) <= 90, true)\n\nright:\nwithinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])\n\nclose:\nwithinTolerance(student_scalar, correct_scalar, settings['close'])", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)"}, {"name": "correct_scalar", "description": "", "definition": "scalar(correct_quantity)\n  "}, {"name": "correct_quantity", "description": "", "definition": "settings['correct_quantity']"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "", "definition": "join(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n"}, {"name": "good_units", "description": "", "definition": "try(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)"}, {"name": "student_quantity", "description": "", "definition": "switch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity)"}, {"name": "angle_in_range", "description": "", "definition": "if(settings['restrict_angle'], abs(student_scalar) <= 90, true)"}, {"name": "right", "description": "<p>Will check for correct sign elswhere.</p>", "definition": "withinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])"}, {"name": "close", "description": "<p>Must have correct sign to be close.</p>", "definition": "withinTolerance(student_scalar, correct_scalar, settings['close'])\n"}], "settings": [{"name": "correct_quantity", "label": "Correct Angle as quantity ", "help_url": "", "hint": "", "input_type": "code", "default_value": "qty(45,'deg')", "evaluate": true}, {"name": "right", "label": "Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.1", "evaluate": true}, {"name": "restrict_angle", "label": "Less than 90\u00b0", "help_url": "", "hint": "When checked, angle must be between -90&deg; and +90&deg;.", "input_type": "checkbox", "default_value": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units.", "input_type": "percent", "default_value": "75"}, {"name": "close", "label": " Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.5", "evaluate": true}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value without units.", "input_type": "percent", "default_value": "25"}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}, {"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}], "tags": [], "metadata": {"description": "<p>Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "parts": [{"variableReplacementStrategy": "originalfirst", "unitTests": [], "prompt": "<ol>\n<li>Move the tips of forces <strong class=\"green\">A</strong>, <strong class=\"blue\">B</strong>, and <strong class=\"red\">C</strong> in this diagram to the&nbsp;correct magnitudes and directions. When this has been done correctly the dotted vector will become solid.</li>\n<li>Pick up&nbsp;vectors <strong class=\"green\">A</strong>, <strong class=\"blue\">B</strong> and <strong class=\"red\">C</strong>&nbsp; by their tails, and move them into a tip to tail arrangement.&nbsp;When this has been correctly done the resultant <strong>R</strong> will appear.</li>\n</ol>\n<p>{geogebra_applet('jwussezq ', [['f_a', forceA],['f_b', forceB],['f_c', forceC]])}</p>\n<p>Based on this diagram, estimate the magnitude <strong>R</strong> &nbsp;and direction of the resultant.</p>\n<p><strong>R</strong> =&nbsp;[[0]]&nbsp;@&nbsp;[[2]]&nbsp;measured from the&nbsp;[[1]].</p>\n<p></p>", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "gaps": [{"variableReplacementStrategy": "originalfirst", "marks": "4", "variableReplacements": [], "type": "engineering-answer", "settings": {"C3": "25", "correctAnswer": "qty(R,units[1])", "close": "4", "right": "2", "C2": "50", "C1": "75"}, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "scripts": {}, "unitTests": [], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "marks": "0", "variableReplacements": [], "type": "drop-down-axis-reference", "settings": {"dummy": "'ignore'"}, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "scripts": {"mark": {"script": "index = Numbas.jme.unwrapValue(this.studentAnswerAsJME());\nangles = Numbas.jme.unwrapValue(Numbas.exam.currentQuestion.scope.getVariable('angle_from_ref'));\nans = angles[index]+' deg';\nthis.parentPart.gaps[2].settings.correct_quantity.value=Qty(ans);\nthis.markingComment(\"For your axis, the direction is \" + ans +'.');", "order": "after"}}, "unitTests": [], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}, {"variableReplacementStrategy": "alwaysreplace", "marks": "4", "variableReplacements": [{"must_go_first": false, "variable": "ref", "part": "p0g1"}], "type": "angle-quantity-from-reference", "settings": {"C3": "25", "restrict_angle": false, "close": "4", "correct_quantity": "qty(angle_from_ref[ref],'deg')", "right": "2", "C2": "50", "C1": "75"}, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "scripts": {}, "unitTests": [], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}], "variableReplacements": [], "type": "gapfill", "customMarkingAlgorithm": "", "scripts": {}, "sortAnswers": false, "extendBaseMarkingAlgorithm": true}], "variable_groups": [{"variables": ["alpha", "gamma", "beta", "FA", "FB", "FC", "units", "debug"], "name": "Inputs"}, {"variables": ["ForceA", "ForceB", "ForceC", "ForceR", "rho", "R", "angle_from_ref", "ref"], "name": "Outputs"}], "ungrouped_variables": [], "functions": {"direction": {"parameters": [["v", "vector"]], "language": "javascript", "type": "number", "definition": "return Math.atan2(v[1],v[0])"}}, "rulesets": {}, "variablesTest": {"maxRuns": 100, "condition": "abs(alpha-beta) >= 15 and abs(beta-gamma) >= 15  and  abs(gamma-alpha) >= 15 and r <=100 and r > 10"}, "type": "question", "variables": {"rho": {"description": "<p>direction of resultant</p>", "name": "rho", "group": "Outputs", "templateType": "anything", "definition": "degrees(direction(ForceR))"}, "ForceB": {"description": "<p>Force B as a vector</p>", "name": "ForceB", "group": "Outputs", "templateType": "anything", "definition": "FB *( vector(cos(radians(beta)),sin(radians(beta))))"}, "FB": {"description": "<p>Magnitude of Force B</p>", "name": "FB", "group": "Inputs", "templateType": "anything", "definition": "random(20..80#5)"}, "ref": {"description": "", "name": "ref", "group": "Outputs", "templateType": "anything", "definition": "0"}, "debug": {"description": "", "name": "debug", "group": "Inputs", "templateType": "anything", "definition": "false"}, "beta": {"description": "<p>Direction of force B</p>", "name": "beta", "group": "Inputs", "templateType": "anything", "definition": "(random(-180..180#15))"}, "gamma": {"description": "<p>Direction of force C in degrees</p>", "name": "gamma", "group": "Inputs", "templateType": "anything", "definition": "(random(-180..180#15))"}, "ForceC": {"description": "<p>Force C as a vector</p>", "name": "ForceC", "group": "Outputs", "templateType": "anything", "definition": "FC *( vector(cos(radians(gamma)),sin(radians(gamma))))"}, "angle_from_ref": {"description": "", "name": "angle_from_ref", "group": "Outputs", "templateType": "anything", "definition": "[if(rho>180,rho-360,rho),\nif(rho>270,rho-450,rho-90),\nrho-180,\nif(rho>90,rho-270,90+rho)]\n\n"}, "ForceA": {"description": "<p>force A&nbsp;as a vector</p>", "name": "ForceA", "group": "Outputs", "templateType": "anything", "definition": "FA *( vector(cos(radians(alpha)),sin(radians(alpha))))"}, "ForceR": {"description": "<p>Resultant as a vector</p>", "name": "ForceR", "group": "Outputs", "templateType": "anything", "definition": "ForceA+ForceB+ForceC"}, "R": {"description": "<p>Magnitude of resultant</p>", "name": "R", "group": "Outputs", "templateType": "anything", "definition": "abs(ForceR)"}, "FC": {"description": "<p>Magnitude of force C</p>", "name": "FC", "group": "Inputs", "templateType": "anything", "definition": "random(20..80#5)"}, "units": {"description": "", "name": "units", "group": "Inputs", "templateType": "anything", "definition": "random(['ft','lb'],['in','lb'],['cm','N'])"}, "alpha": {"description": "<p>direction of force A</p>", "name": "alpha", "group": "Inputs", "templateType": "anything", "definition": "(random(-180..180#15))\n"}, "FA": {"description": "<p>Magnitude of force A</p>", "name": "FA", "group": "Inputs", "templateType": "anything", "definition": "random(20..80#5)"}}, "advice": "<p>Vector Addition: &nbsp;</p>\n<p>$\\Sigma F_x = &nbsp;R_x&nbsp;\\qquad &nbsp;R=\\sqrt{R_x^2 + R_y^2}\\\\\\\\&nbsp;\\Sigma F_y = &nbsp;R_y &nbsp;\\qquad \\theta = \\tan^{-1}\\left(\\left|\\frac{R_y}{R_x}\\right| \\right)$</p>", "statement": "<p><strong></strong>Three forces act on &nbsp;point <em>A</em>: &nbsp; <span style=\"color: green;\"><em>A</em> = {FA} {units[1]} at {alpha}&deg;</span>, <span style=\"color: blue;\"><em>B</em>&nbsp;= {FB} {units[1]} at {beta}&deg;&nbsp;</span> and, <span style=\"color: red;\"><em>C&nbsp;</em>= {FC} {units[1]} at {gamma}&deg;</span>.</p>\n<p>Estimate the magnitude and direction of the resultant force&nbsp;<strong>R</strong>&nbsp;using the&nbsp;tip-to-tail method.</p>\n<p><span data-jme-visible=\"debug\">Force A: {fa} {units[1]}&nbsp;at {alpha} = {forceA}&nbsp;</span></p>\n<p><span data-jme-visible=\"debug\">Force B: {fb} {units[1]}&nbsp;at {beta} = {forceB}</span></p>\n<p><span data-jme-visible=\"debug\">Force C: {fc}{units[1]} at {gamma} = {forceC}</span></p>\n<p><span data-jme-visible=\"debug\">Resultant: {R}{units[1]} &nbsp;at {rho} &nbsp;= {forceR}</span></p>", "preamble": {"js": "", "css": ".red{color:red;}\n.blue{color:blue;}\n.green{color:green;}"}}, {"name": "Josh's copy of Carnot cycle efficiency", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Tom Stallard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/841/"}, {"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}], "ungrouped_variables": ["v1", "v2", "v3", "v4", "th", "tc", "n", "r", "p1", "p2", "p3", "p4", "hcr", "n3", "efficiency", "w_12", "w_34", "w_23", "w_41", "work", "q_h"], "variable_groups": [], "statement": "<p>{draw_block()}</p>\n<p>A Carnot engine is in action. The temperature of its hot reservoir is {th} K, and the temperature of its cold reservoir is {tc} K</p>", "type": "question", "tags": [], "advice": "<p><strong>a)</strong></p>\n<p>$Efficiency = (1-\\frac{T_c}{T_h})$ = 1-({tc}/{th}) = {siground(efficiency/100,3)}</p>\n<p>So the efficiency of the carnot cycle is {siground(efficiency,3)} %.</p>\n<p><strong>b)</strong></p>\n<p>$Efficiency = \\frac{useful\\,energy}{total\\,energy} = \\frac{work}{heat\\,from\\,hot\\,reservoir}$</p>\n<p>$Q_h = \\frac{W}{eff} =$ {work} / {siground(efficiency/100,3)}</p>\n<p>So the heat extracted from the hot reservoir is {siground(q_h,3)} J.</p>", "rulesets": {}, "parts": [{"showFeedbackIcon": true, "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "prompt": "<p>Calculate the efficiency of the carnot engine, in percent to three significant figures.</p>", "allowFractions": false, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "showCorrectAnswer": true, "marks": "2", "correctAnswerFraction": false, "maxValue": "siground(efficiency,3)+siground(abs(efficiency/100),3)", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "minValue": "siground(efficiency,3)-siground(abs(efficiency/100),3)"}, {"showFeedbackIcon": true, "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "prompt": "<p>The work done by the Carnot cycle was {work} J. Calculate the amount of heat added to the system from the hot reservoir, to three significant figures.</p>", "allowFractions": false, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "showCorrectAnswer": true, "marks": "2", "correctAnswerFraction": false, "maxValue": "siground(q_h,3)+siground(abs(q_h/100),3)", "variableReplacements": [{"must_go_first": true, "variable": "efficiency", "part": "p0"}], "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "minValue": "siground(q_h,3)-siground(abs(q_h/100),3)"}], "functions": {"draw_block": {"type": "html", "definition": "\n//Set values\np1 = Numbas.jme.unwrapValue(scope.variables.p1);\np2 = Numbas.jme.unwrapValue(scope.variables.p2);\np3 = Numbas.jme.unwrapValue(scope.variables.p3);\np4 = Numbas.jme.unwrapValue(scope.variables.p4);\n\nv1 = Numbas.jme.unwrapValue(scope.variables.v1);\nv2 = Numbas.jme.unwrapValue(scope.variables.v2);\nv3 = Numbas.jme.unwrapValue(scope.variables.v3);\nv4 = Numbas.jme.unwrapValue(scope.variables.v4);\nth = Numbas.jme.unwrapValue(scope.variables.th);\ntc = Numbas.jme.unwrapValue(scope.variables.tc);\n\nr = Numbas.jme.unwrapValue(scope.variables.r);\nn = Numbas.jme.unwrapValue(scope.variables.n);\nhcr = Numbas.jme.unwrapValue(scope.variables.hcr);\n\nvstep12=(v2-v1)/20.0\nvstep23=(v3-v2)/20.0\nvstep43=(v3-v4)/20.0\nvstep14=(v4-v1)/20.0\n\n\nmaxp=Math.max(p1,p2,p3,p4)*1.1;\nminp=Math.min(p1,p2,p3,p4)-0.5;\n\nmaxv=Math.max(v1,v2,v3,v4)*1.1;\nminv=Math.min(v1,v2,v3,v4)-0.5;\n\n\npticks=parseInt(maxp/16)*2\nvticks=parseInt(maxv/10)\n\n// The function provided by the JSXGraph extension wraps the board up in\n// a div tag so that it's easier to embed in the page.\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','360px',\n  {boundingBox: [-0.5,maxp,maxv,-0.5],\n     axis: false,\n     showNavigation: false,\n     grid: false\n    });\n\n// div.board is the object created by JSXGraph, which you use to\n// manipulate elements\nvar board = div.board;\n\n\n\n// create the x-axis.\nvar xaxis = board.create('line',[[0,0],[maxv,0]], {strokeColor: 'black', fixed: false});\nvar xticks = board.create('ticks',[xaxis,vticks],{\n  drawLabels: true,\n  minorTicks: 1,\n  label: {offset: [-3, 20]}\n});\n\n// create the y-axis\n\nvar yaxis = board.create('line',[[0,0],[0,maxp]], {strokeColor: 'black', fixed: false});\nvar yticks = board.create('ticks',[yaxis,pticks],{\n  drawLabels: true,\n  minorTicks: 1,\n  label: {offset: [20, -3]}\n});\n\n\n// each line needs four coordinates start x,y and end x,y - these can then all be rotated\n\n\n//\n//slope 1\n\n\nvar X12 = []\nvar Y12 = []\n\nfor (i = 0; i < 21; i++) {\n X12.push(v1+(vstep12*i));\n Y12.push(p1*v1/(v1+(vstep12*i)));\n}\n\nvar X23 = []\nvar Y23 = []\n\nfor (i = 0.0; i < 21.0; i++) {\n X23.push(v2+(vstep23*i));\n Y23.push(p2*Math.pow(v2, hcr)/Math.pow((v2+(vstep23*i)), hcr));\n}\n\nvar X43 = []\nvar Y43 = []\n\nfor (i = 0; i < 21; i++) {\n X43.push(v4+(vstep43*i));\n Y43.push(p4*v4/(v4+(vstep43*i)));\n}\n\nvar X14 = []\nvar Y14 = []\n\nfor (i = 0.0; i < 21.0; i++) {\n X14.push(v1+(vstep14*i));\n Y14.push(p1*Math.pow(v1, hcr)/Math.pow((v1+(vstep14*i)), hcr));\n}\n\n\n\n\n\n\nvar step12 = board.create('curve', [X12,Y12],{strokeColor:'red',strokeWidth:3});\nvar step23 = board.create('curve', [X23,Y23],{strokeColor:'black',strokeWidth:3, dash:2});\nvar step43 = board.create('curve', [X43,Y43],{strokeColor:'blue',strokeWidth:3});\nvar step14 = board.create('curve', [X14,Y14],{strokeColor:'black',strokeWidth:3, dash:2});\n\n//var dash43 = board.create('line',[[v1,p1],[v2,p2]], {dash:1, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n//var dash43 = board.create('line',[[v1,p1],[v4,p4]], {dash:2, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n\nboard.create('text',[v1,p1,'1'],{fontSize:20,anchorX:'middle',anchorY:'middle'});\nboard.create('text',[v2,p2,'2'],{fontSize:20,anchorX:'middle',anchorY:'middle'});\nboard.create('text',[v3,p3,'3'],{fontSize:20,anchorX:'middle',anchorY:'middle'});\nboard.create('text',[v4,p4,'4'],{fontSize:20,anchorX:'middle',anchorY:'middle'});\n\n\nboard.create('text',[maxv/2,-0.2,'Volume'],{fontSize:20,anchorX:'middle',anchorY:'middle'});\nboard.create('text',[-0.2,maxp/2,'Pressure'],{display:'internal',fontSize:20,anchorX:'middle',anchorY:'middle',rotate:90});\n\n// and return the container div\nreturn div;", "language": "javascript", "parameters": []}}, "preamble": {"js": "", "css": ""}, "metadata": {"description": "<p>Calculate the efficiency and heat from the hot reservoir in a Carnot Cycle (with carnot diagram)</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"w_12": {"description": "", "definition": "n*R*Th*ln(v2/v1)", "name": "w_12", "templateType": "anything", "group": "Ungrouped variables"}, "p4": {"description": "", "definition": "n*r*tc/v4", "name": "p4", "templateType": "anything", "group": "Ungrouped variables"}, "th": {"description": "<p>random(600..950)</p>", "definition": "random(1300..1950)", "name": "th", "templateType": "anything", "group": "Ungrouped variables"}, "p2": {"description": "", "definition": "n*r*th/v2", "name": "p2", "templateType": "anything", "group": "Ungrouped variables"}, "v2": {"description": "<p>v1+random(0.5..4#0.1)</p>", "definition": "v1+random(4.5..8#0.1)", "name": "v2", "templateType": "anything", "group": "Ungrouped variables"}, "w_34": {"description": "", "definition": "n*R*Tc*ln(v4/v3)", "name": "w_34", "templateType": "anything", "group": "Ungrouped variables"}, "p1": {"description": "", "definition": "n*r*th/v1", "name": "p1", "templateType": "anything", "group": "Ungrouped variables"}, "q_h": {"description": "", "definition": "work/(efficiency/100)", "name": "q_h", "templateType": "anything", "group": "Ungrouped variables"}, "tc": {"description": "<p>th-random(50..300)</p>", "definition": "th-random(400..600)", "name": "tc", "templateType": "anything", "group": "Ungrouped variables"}, "efficiency": {"description": "", "definition": "(1-(tc/th))*100", "name": "efficiency", "templateType": "anything", "group": "Ungrouped variables"}, "p3": {"description": "<p>P2V2<sup>hcr</sup> = P3V<sup>3hcr</sup><sub><br /></sub></p>", "definition": "p2*v2^(hcr)/v3^(hcr)", "name": "p3", "templateType": "anything", "group": "Ungrouped variables"}, "v4": {"description": "", "definition": "(th*(v1^(hcr-1))/tc)^(1/(hcr-1))", "name": "v4", "templateType": "anything", "group": "Ungrouped variables"}, "r": {"description": "", "definition": "0.082", "name": "r", "templateType": "anything", "group": "Ungrouped variables"}, "hcr": {"description": "", "definition": "1.6", "name": "hcr", "templateType": "anything", "group": "Ungrouped variables"}, "v3": {"description": "<p>(Th V2<sup>(&gamma; - 1)</sup>/Tc )<sup>1/(&gamma; - 1)</sup>= V3</p>", "definition": "(th*(v2^(hcr-1))/tc)^(1/(hcr-1))", "name": "v3", "templateType": "anything", "group": "Ungrouped variables"}, "work": {"description": "", "definition": "siground(w_12+w_23+w_34+w_41,3)", "name": "work", "templateType": "anything", "group": "Ungrouped variables"}, "n3": {"description": "<p>test - should match n</p>", "definition": "p3*v3/(r*tc)", "name": "n3", "templateType": "anything", "group": "Ungrouped variables"}, "w_41": {"description": "", "definition": "((p1*v1)-(p4*v4))/(1-hcr)", "name": "w_41", "templateType": "anything", "group": "Ungrouped variables"}, "w_23": {"description": "", "definition": "((p3*v3)-(p2*v2))/(1-hcr)", "name": "w_23", "templateType": "anything", "group": "Ungrouped variables"}, "n": {"description": "", "definition": "random(0.1..5.0#0.1)", "name": "n", "templateType": "anything", "group": "Ungrouped variables"}, "v1": {"description": "", "definition": "random(8.5..15.0#0.1)", "name": "v1", "templateType": "anything", "group": "Ungrouped variables"}}}]}, {"name": "Data analysis", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questions": [{"name": "Josh's copy of Use data uploaded by the student", "extensions": ["stats"], "custom_part_types": [], "resources": [["question-resources/Data.csv", "/srv/numbas/media/question-resources/Data.csv"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}], "tags": [], "metadata": {"description": "<p>Get the student to upload their experimental data in a CSV file, then ask them to compute statistics on it.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p><strong>This question will only work in browsers that support the HTML5 File API! For Internet Explorer users, that means version 10 onwards.</strong></p>\n<p>How does the length of a spring change when you suspend different masses from it? Make measurements of your spring's length when hanging various different weights from it.</p>\n<p>Download <a href=\"resources/question-resources/Data.csv\">the data spreadsheet</a> and open it in a program such as <em>Microsoft Excel</em>. Enter your data, save the file, and then upload it using the button below.</p>", "advice": "", "rulesets": {}, "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "// read a csv file\nfunction readCSV(text) {\n  var lines = text.split('\\n');\n  return lines.map(function(line){return line.split(',')});\n}\n\n// wait until the question has been generated\nquestion.signals.on('HTMLAttached',function(e) {\n  var display = question.display;\n\n  // set up an observable for the data array\n  var _data = display.data = ko.observableArray([]);\n  \n  // has the student uploaded data?\n  display.gotData = ko.computed(function() {\n    return _data().length>0;\n  });\n  \n  // an observable object containing various computed statistics about the data - updates automatically when the data changes\n  var stats = question.stats = ko.computed(function() {\n    var data = _data();\n    \n    // weights are in the first column\n    var weights = data.map(function(r){return r[0]});\n    // lengths in the second column\n    var lengths = data.map(function(r){return r[1]});\n    \n    // how many samples?\n    var n = data.length;\n    \n    // components of the linear regression calculation\n    var sx = jStat.sum(weights);\n    var sy = jStat.sum(lengths);\n    var sxx = jStat.sum(weights.map(function(x){return x*x}));\n    var syy = jStat.sum(lengths.map(function(x){return x*x}));\n    var sxy = jStat.sum(data.map(function(r){ return r[0]*r[1]}));\n    \n    // coefficients of the linear regression model\n    var beta = (sxy - (sx*sy)/n)/(sxx-(sx*sx)/n);\n    var alpha = (sy-beta*sx)/n;\n    \n    var stats = {\n      sx: sx,\n      sy: sy,\n      sxx: sxx,\n      syy: syy,\n      sxy: sxy,\n      alpha: alpha,\n      beta: beta,\n      n: data.length\n    };\n    \n    return stats;\n  });\n  \n  // format a number to 3 d.p.\n  function niceNumber(n) {\n    return 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{"script": "var stats = this.question.stats();\nthis.settings.minvalue = stats.sxy;\nthis.settings.maxvalue = stats.sxy;", "order": "before"}}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "type": "question"}, {"name": "Josh's copy of Loading JSON data: Cooper Hewitt collection", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Josh 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\\\"1979\\\", \\\"participants\\\": [{\\\"person_name\\\": \\\"Victorian Collectibles\\\", \\\"role_name\\\": \\\"Donor\\\", \\\"role_url\\\": \\\"https://collection.cooperhewitt.org/roles/35351535/\\\", \\\"person_id\\\": \\\"18064161\\\", \\\"role_display_name\\\": \\\"Donated by\\\", \\\"person_date\\\": \\\"\\\", \\\"person_url\\\": \\\"https://collection.cooperhewitt.org/people/18064161/\\\", \\\"role_id\\\": \\\"35351535\\\"}, {\\\"person_name\\\": \\\"Maxwell & Co., S.A.\\\", \\\"role_name\\\": \\\"Distributor\\\", \\\"role_url\\\": \\\"https://collection.cooperhewitt.org/roles/35236659/\\\", \\\"person_id\\\": \\\"18046361\\\", \\\"role_display_name\\\": \\\"Distributed by\\\", \\\"person_date\\\": \\\"Chicago, Illinois, USA\\\", \\\"person_url\\\": \\\"https://collection.cooperhewitt.org/people/18046361/\\\", \\\"role_id\\\": \\\"35236659\\\"}], \\\"title\\\": \\\"Frieze (USA), 1890\\\\u20131910\\\", \\\"medium\\\": \\\"machine-printed\\\", \\\"description\\\": \\\"Series of 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Joined to the back with bobbin lace. Pillow covered in green silk.\\\", \\\"decade\\\": null},\\n{\\\"colors\\\": [], \\\"images\\\": [], \\\"url\\\": \\\"https://collection.cooperhewitt.org/objects/18572247/\\\", \\\"year_acquired\\\": \\\"1944\\\", \\\"participants\\\": [{\\\"person_name\\\": \\\"John Kenneth Tilton\\\", \\\"role_name\\\": \\\"Cataloguer\\\", \\\"role_url\\\": \\\"https://collection.cooperhewitt.org/roles/35352245/\\\", \\\"person_id\\\": \\\"18047817\\\", \\\"role_display_name\\\": \\\"Catalogued by\\\", \\\"person_date\\\": \\\"\\\", \\\"person_url\\\": \\\"https://collection.cooperhewitt.org/people/18047817/\\\", \\\"role_id\\\": \\\"35352245\\\"}, {\\\"person_name\\\": \\\"M.H. Birge & Sons Co.\\\", \\\"role_name\\\": \\\"Manufacturer\\\", \\\"role_url\\\": \\\"https://collection.cooperhewitt.org/roles/35236657/\\\", \\\"person_id\\\": \\\"18046415\\\", \\\"role_display_name\\\": \\\"Manufactured by\\\", \\\"person_date\\\": \\\"1834\\\", \\\"person_url\\\": \\\"https://collection.cooperhewitt.org/people/18046415/\\\", \\\"role_id\\\": \\\"35236657\\\"}], \\\"title\\\": \\\"Imitation Leather (USA), 1920\\\", \\\"medium\\\": \\\"block-printed, embossed\\\", \\\"description\\\": \\\"A geometric design on a large scale of interlacing circular bands. The bands in turn are covered with small designs as though studded with nail heads. All of design is embossed and finished in brass-colored gilt. Field is plain ivory. Entire surface is antiqued by hand. Printed from wood blocks in oil paints. On reverse side is printed: \\\\\\\"No 8066 2\\\\\\\". 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The scenic miniatures are enclosed in a black portfolio with a large gold Diament label.\\\", \\\"decade\\\": \\\"1970\\\"}\\n]\"))", "group": "Ungrouped variables", "templateType": "json", "description": "<p>From <a href=\"https://github.com/cooperhewitt/collection\">https://github.com/cooperhewitt/collection</a></p>"}, "img": {"name": "img", "definition": "image(items[0]['images'][0]['n']['url'])", "group": "Ungrouped variables", "templateType": "anything", "description": "<p>An image representing one of the items - see how it's displayed in the editor's preview column.</p>"}}, "advice": "", "tags": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Load data on some items held in the Cooper Hewitt collection, and show a table of 5 randomly picked items.</p>"}, "variable_groups": [], "preamble": {"js": "", "css": ".question td {\n  text-align: left;\n}\ntd.photo {\n  text-align: center;\n}\n.statement {\n  padding-left: 0;\n}\n.statement p {\n  padding-left: 1em;\n}\n.statement p > .full-width {\n  margin-left: -1em;\n}"}, "variablesTest": {"maxRuns": 100, "condition": ""}, "ungrouped_variables": ["data", "eligible_items", "items", "img", "rows", "info"]}]}, {"name": "Custom Feedback", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questions": [{"name": "Josh's copy of Custom marking - answer is a set", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": ""}, "preamble": {"css": "", "js": ""}, "ungrouped_variables": ["f", "ea", "odds", "det", "ec", "eb", "qb", "x0", "x1", "roots"], "rulesets": {}, "statement": "", "variable_groups": [], "tags": [], "functions": {}, "advice": "", "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"prompt": "<p>Give the set of real-valued roots of the equation&nbsp;</p>\n<p>\\[ \\simplify[all,fractionnumbers]{{ea}x^2+{eb}x+{ec}}=0 \\]</p>\n<p>Enter your answer as a list of numbers separated by commas and enclosed by square brackets, e.g. <code>[1,2]</code>.</p>\n<p>If the equation has no roots, enter <code>[]</code></p>", "variableReplacementStrategy": "originalfirst", "type": "jme", "showPreview": true, "showCorrectAnswer": true, "customName": "", "customMarkingAlgorithm": "", "useCustomName": false, "variableReplacements": [], "valuegenerators": [], "checkingType": "absdiff", "unitTests": [], "checkVariableNames": false, "answer": "{roots}", "checkingAccuracy": 0.001, "vsetRange": [0, 1], "failureRate": 1, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "vsetRangePoints": 5, "scripts": {"validate": {"script": "// Use the built-in validation function to catch syntax errors and so on\nif(!Numbas.parts.JMEPart.prototype.validate.apply(this)) {\n  return false;\n}\n// Give a warning if the student's answer is not a list\nif(this.notAList) {\n  this.giveWarning('You must enter a list, i.e. numbers separated by commas and enclosed by square brackets. For example, <code>[1,2]</code>.');\n  return false;\n}\nreturn true;", "order": "instead"}, "mark": {"script": "// evaluate the student's answer\ntry {\n  var list = Numbas.jme.evaluate(this.studentAnswer,this.question.scope);\n}\ncatch(e)\n{\n  this.setCredit(0,R('part.jme.answer invalid',e.message));\n  return;\n}\n\n// check the answer is a list\nthis.notAList = list.type!='list';\nif(this.notAList) {\n  this.setCredit(0,'Your answer is not a list of numbers.');\n  return;\n}\n\nvar variables = this.question.scope.variables;\nvar unwrap = Numbas.jme.unwrapValue;\n\n// get the roots of the equation\nvar roots = unwrap(variables.roots);\n\n// unwrap the student's list to a Javascript array of numbers\nvar list = unwrap(list);\n\n// get the coefficients of the equation\nvar ea = unwrap(variables.ea);\nvar eb = unwrap(variables.eb);\nvar ec = unwrap(variables.ec);\n\n// check each root the student gave, keeping track of how many they got right\nvar got = 0;\nvar wrong = [];\nfor(var i=0;i<list.length;i++) {\n  var n = list[i];\n  if(roots.contains(n)) {\n     got += 1;\n  } else {\n    var total = ea*n*n+eb*n+ec; // evaluate polynomial using chosen root\n    this.markingComment('$\\\\simplify[fractionnumbers]{'+n+'}$ is not a root of the equation. On substituting $x = \\\\simplify[fractionnumbers]{'+n+'}$ into the equation, you should get $0$. \\\\[ \\\\simplify[fractionnumbers]{{ea}*('+n+'^2)+{eb}*('+n+')+{ec} = '+total+'} \\\\]');\n  }\n}\n\n// check if the student missed any roots\nvar notgot = 0;\nlist.sort();\nroots.sort();\nfor(var i=0;i<roots.length;i++) {\n  var n = roots[i];\n  if(!list.contains(n)) {\n    got -= 1;\n    this.markingComment(\"You did not give the root $\\\\simplify[fractionnumbers]{\"+n+\"}$.\");\n  }\n}\n\n// Give feedback\nif(list.length>roots.length) {\n  this.setCredit(0,\"This equation does not have \"+(list.length)+\" real-valued \"+Numbas.util.pluralise(list.length,'root','roots')+\".\");\n} else if(got<roots.length) {\n  this.setCredit(got/roots.length, \"You did not give every real-valued root of the equation.\");\n} else {\n  var message;\n  switch(roots.length) {\n    case 0:\n      message = \"Correct: this equation does not have any real-valued roots.\";\n      break;\n    case 1:\n      message = \"Correct: this equation has a repeated root.\";\n      break;\n    case 2:\n      message = \"You gave both roots of this equation.\";\n  }\n  this.setCredit(1,message);\n}", "order": "instead"}}, "answerSimplification": "fractionNumbers", "marks": 2}], "variables": {"det": {"templateType": "anything", "description": "", "definition": "random(0..3)*random(1,i)", "group": "Ungrouped variables", "name": "det"}, "x1": {"templateType": "anything", "description": "", "definition": "(-qb-det)/2", "group": "Ungrouped variables", "name": "x1"}, "f": {"templateType": "anything", "description": "", "definition": "if(odds=0,1,4)", "group": "Ungrouped variables", "name": "f"}, "eb": {"templateType": "anything", "description": "", "definition": "-f*(x0+x1)", "group": "Ungrouped variables", "name": "eb"}, "qb": {"templateType": "anything", "description": "", "definition": "random(-3..3)", "group": "Ungrouped variables", "name": "qb"}, "odds": {"templateType": "anything", "description": "", "definition": "mod(im(qb+det),2)+mod(re(qb+det),2)", "group": "Ungrouped variables", "name": "odds"}, "x0": {"templateType": "anything", "description": "", "definition": "(-qb+det)/2", "group": "Ungrouped variables", "name": "x0"}, "roots": {"templateType": "anything", "description": "", "definition": "if(im(det)<>0,[],if(det=0,[x0],[x0,x1]))", "group": "Ungrouped variables", "name": "roots"}, "ec": {"templateType": "anything", "description": "", "definition": "x0*x1*f", "group": "Ungrouped variables", "name": "ec"}, "ea": {"templateType": "anything", "description": "", "definition": "f", "group": "Ungrouped variables", "name": "ea"}}, "type": "question"}, {"name": "Josh's copy of Julie's copy of Pupil Teacher Ratio randomised", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Deirdre Casey", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/681/"}, {"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}], "metadata": {"description": "<p>Simple ratio question with custom marking and partial credit possible</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>The ratio of teachers to pupils in a school is 1:{studentrat}</p>", "variable_groups": [], "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "ungrouped_variables": ["studentrat", "percent"], "variables": {"percent": {"templateType": "anything", "description": "", "name": "percent", "definition": "(1/(studentrat+1))*100", "group": "Ungrouped variables"}, "studentrat": {"templateType": "anything", "description": "", "name": "studentrat", "definition": "Random(17..22)", "group": "Ungrouped variables"}}, "parts": [{"allowFractions": false, "type": "numberentry", "precision": "2", "strictPrecision": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "showPrecisionHint": true, "customMarkingAlgorithm": "\nmark:\n   apply(validNumber);\n    if(isFraction,\n        apply(cancelled)\n    ,\n        apply(correctPrecision)\n    );\n    switch(\n    studentNumber=precround(100/(1+studentrat),studentPrecision),set_credit(1,\"Correct Answer, Well Done!\"),\n    studentNumber=precround(100/studentrat,studentPrecision),set_credit(0.5,\"Some good work done but not quite there yet. Have a think about your denominator\"),\n    studentNumber=precround(1/(1+studentrat),studentPrecision),set_credit(0.7,\"Is your answer a percentage?\"),\n    studentNumber=precround((1+studentrat)/100.0,studentPrecision),set_credit(0.3,\"Something worthwhile here but you need to think further\"),\n    set_credit(0,\"Incorrect\") \n    )", "marks": "10", "unitTests": [], "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "precisionType": "dp", "minValue": "percent", "scripts": {}, "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReduced": false, "variableReplacements": [], "precisionPartialCredit": 0, "prompt": "<p>What percentage of the school population are teachers?</p>", "maxValue": "percent", "mustBeReducedPC": 0, "correctAnswerFraction": false}], "tags": [], "advice": "<p>The fraction of the school population that are teachers is&nbsp;$\\frac{1}{1+\\var{studentrat}}$</p>\n<p>Convert this to a decimal by multiplying by 100.</p>\n<p>$\\frac{1}{\\simplify{1+{studentrat}}}*100=\\var{percent}$</p>\n<p></p>", "type": "question", "functions": {}, "rulesets": {}}, {"name": "Josh's copy of Catch malrules", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Identify when the student gives an expected incorrect answer, and give appropriate feedback as well as partial marks.</p>"}, "preamble": {"css": "", "js": ""}, "ungrouped_variables": ["test"], "rulesets": {}, "statement": "<p>This question catches some expected incorrect answers and gives appropriate feedback, along with partial marks.</p>", "variable_groups": [], "tags": [], "functions": {}, "advice": "", "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"prompt": "<p>Differentiate $f(x) = \\cos(2x)$</p>\n<p>$\\var{test}$</p>", "variableReplacementStrategy": "originalfirst", "type": "jme", "showPreview": true, "showCorrectAnswer": true, "customName": "", "customMarkingAlgorithm": "malrules:\n  [\n    [\"2sin(2x)\", \"Did you forget a minus sign?\"],\n    [\"-sin(2x)\", \"You might have forgotten to apply the chain rule.\"],\n    [\"2cos(2x)\", \"It looks like you forgot to differentiate $\\\\cos$.\"],\n    [\"1/2sin(2x)\", \"It looks like you integrated instead of differentiating.\"]\n  ]\n\n\nparsed_malrules: \n    map(\n        [\"expr\":parse(x[0]),\"feedback\":x[1]],\n        x,\n        malrules\n    )\n\nagree_malrules (Do the student's answer and the expected answer agree on each of the sets of variable values?):\n    map(\n        len(filter(not x ,x,map(\n            try(\n                resultsEqual(unset(question_definitions,eval(studentexpr,vars)),unset(question_definitions,eval(malrule[\"expr\"],vars)),settings[\"checkingType\"],settings[\"checkingAccuracy\"]),\n                message,\n                false\n            ),\n            vars,\n            vset\n        )))<settings[\"failureRate\"],\n        malrule,\n        parsed_malrules\n    )\n\nmatched_malrules:\n  filter(x[0],x,zip(agree_malrules,parsed_malrules))\n  \nmalrule_feedback:\n    assert(numericallyCorrect,\n        assert(len(matched_malrules)=0,\n            set_credit(0.5,matched_malrules[0][1][\"feedback\"])\n        )\n    )\n\nmark:\n    apply(studentExpr);\n    apply(unexpectedVariables);\n    apply(sameVars);\n    apply(numericallyCorrect);\n    apply(malrule_feedback);\n    apply(failMinLength);\n    apply(failMaxLength);\n    apply(forbiddenStringsPenalty);\n    apply(requiredStringsPenalty)", "useCustomName": false, "variableReplacements": [], "valuegenerators": [{"value": "", "name": "x"}], "checkingType": "absdiff", "unitTests": [], "checkVariableNames": false, "answer": "-2sin(2x)", "checkingAccuracy": 0.001, "vsetRange": [0, 1], "failureRate": 1, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "vsetRangePoints": 5, "scripts": {}, "marks": 1}], "variables": {"test": {"templateType": "anything", "description": "", "definition": "5", "group": "Ungrouped variables", "name": "test"}}, "type": "question"}]}, {"name": "Randomisation", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questions": [{"name": "Josh's copy of Find stationary point of a curve and determine its nature", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"variableReplacementStrategy": "originalfirst", "unitTests": [], "useCustomName": false, "prompt": "<p>Let $y = \\simplify{{a1}x^2 + {b1}x + {c1}}$.</p>\n<p>$\\dfrac{\\mathrm{d}y}{\\mathrm{d}x} = $ [[0]]</p>\n<p>Enter the coordinates of the stationary point of $y$: $\\big($ [[1]] $, $ [[2]] $\\big)$</p>\n<p>$\\dfrac{\\mathrm{d}^2y}{\\mathrm{d}x^2} = $ [[3]]</p>\n<p>What is the nature of the stationary point of $y$?</p>\n<p>[[4]]</p>", "marks": 0, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "gaps": [{"failureRate": 1, "variableReplacementStrategy": "originalfirst", "unitTests": [], "vsetRangePoints": 5, "useCustomName": false, "checkVariableNames": false, "answer": "2*{a1}*x+{b1}", "valuegenerators": [{"value": "", "name": "x"}], "marks": 1, "showCorrectAnswer": true, "showPreview": true, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "checkingType": "absdiff", "customName": "", "type": "jme", "vsetRange": [0, 1], "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true}, {"failureRate": 1, "marks": 1, "showPreview": false, "checkingType": "absdiff", "customName": "", "showFeedbackIcon": true, "type": "jme", "vsetRange": [0, 1], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "useCustomName": false, "vsetRangePoints": 5, "answerSimplification": "fractionnumbers", "answer": "{sx1}", "valuegenerators": [], "showCorrectAnswer": true, "checkVariableNames": false, "checkingAccuracy": 0.001, "variableReplacements": [], "scripts": {}}, {"failureRate": 1, "marks": 1, "showPreview": false, "checkingType": "absdiff", "customName": "", "showFeedbackIcon": true, "type": "jme", "vsetRange": [0, 1], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "useCustomName": false, "vsetRangePoints": 5, "answerSimplification": "fractionnumbers", "answer": "{sy1}", "valuegenerators": [], "showCorrectAnswer": true, "checkVariableNames": false, "checkingAccuracy": 0.001, "variableReplacements": [], "scripts": {}}, {"failureRate": 1, "variableReplacementStrategy": "originalfirst", "unitTests": [], "vsetRangePoints": 5, "useCustomName": false, "checkVariableNames": false, "answer": "{2a1}", "valuegenerators": [], "marks": 1, "showCorrectAnswer": true, "showPreview": true, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "checkingType": "absdiff", "customName": "", "type": "jme", "vsetRange": [0, 1], "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "unitTests": [], "choices": ["<p>Maximum</p>", "<p>Minimum</p>", "<p>Point of inflection</p>"], "useCustomName": false, "displayType": "radiogroup", "shuffleChoices": false, "showCellAnswerState": true, "marks": 0, "showCorrectAnswer": true, "maxMarks": 0, "extendBaseMarkingAlgorithm": true, "distractors": ["", "", ""], "customName": "", "type": "1_n_2", "matrix": [0, 1, 0], "minMarks": 0, "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "displayColumns": 0, "showFeedbackIcon": true}], "customName": "", "type": "gapfill", "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "sortAnswers": false, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "unitTests": [], "useCustomName": false, "prompt": "<p>Let $z = \\simplify{{a2}x^2+{b2}x+{c2}}$.</p>\n<p>$\\dfrac{\\mathrm{d}z}{\\mathrm{d}x} = $ [[0]]</p>\n<p>Enter the coordinates of the stationary point of $z$: $\\big($ [[1]] $, $ [[2]] $\\big)$</p>\n<p>$\\dfrac{\\mathrm{d}^2z}{\\mathrm{d}x^2} = $ [[3]]</p>\n<p>What is the nature of the stationary point of $z$?</p>\n<p>[[4]]</p>", "marks": 0, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "gaps": [{"failureRate": 1, "variableReplacementStrategy": "originalfirst", "unitTests": [], "vsetRangePoints": 5, "useCustomName": false, "checkVariableNames": false, "answer": "2*{a2}x+{b2}", "valuegenerators": [{"value": "", "name": "x"}], "marks": 1, "showCorrectAnswer": true, "showPreview": true, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "checkingType": "absdiff", "customName": "", "type": "jme", "vsetRange": [0, 1], "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true}, {"failureRate": 1, "marks": 1, "showPreview": false, "checkingType": "absdiff", "customName": "", "showFeedbackIcon": true, "type": "jme", "vsetRange": [0, 1], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "useCustomName": false, "vsetRangePoints": 5, "answerSimplification": "fractionnumbers", "answer": "{sx2}", "valuegenerators": [], "showCorrectAnswer": true, "checkVariableNames": false, "checkingAccuracy": 0.001, "variableReplacements": [], "scripts": {}}, {"failureRate": 1, "marks": 1, "showPreview": false, "checkingType": "absdiff", "customName": "", "showFeedbackIcon": true, "type": "jme", "vsetRange": [0, 1], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "useCustomName": false, "vsetRangePoints": 5, "answerSimplification": "fractionnumbers", "answer": "{sy2}", "valuegenerators": [], "showCorrectAnswer": true, "checkVariableNames": false, "checkingAccuracy": 0.001, "variableReplacements": [], "scripts": {}}, {"failureRate": 1, "variableReplacementStrategy": "originalfirst", "unitTests": [], "vsetRangePoints": 5, "useCustomName": false, "checkVariableNames": false, "answer": "2{a2}", "valuegenerators": [], "marks": 1, "showCorrectAnswer": true, "showPreview": true, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "checkingType": "absdiff", "customName": "", "type": "jme", "vsetRange": [0, 1], "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "unitTests": [], "choices": ["<p>Maximum</p>", "<p>Minimum</p>", "<p>Point of inflection</p>"], "useCustomName": false, "displayType": "radiogroup", "shuffleChoices": false, "showCellAnswerState": true, "marks": 0, "showCorrectAnswer": true, "maxMarks": 0, "extendBaseMarkingAlgorithm": true, "distractors": ["", "", ""], "customName": "", "type": "1_n_2", "matrix": [1, 0, 0], "minMarks": 0, "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "displayColumns": 0, "showFeedbackIcon": true}], "customName": "", "type": "gapfill", "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "sortAnswers": false, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "unitTests": [], "useCustomName": false, "prompt": "<p>Let $t = \\var{m}x^3+\\var{q}$.</p>\n<p>$\\dfrac{\\mathrm{d}t}{\\mathrm{d}x} = $ [[0]]</p>\n<p>Enter the coordinates of the stationary point of $t$: $\\big($ [[1]] $, $ [[2]] $\\big)$</p>\n<p>$\\dfrac{\\mathrm{d}^2t}{\\mathrm{d}x^2} = $ [[3]]</p>\n<p>What is the nature of the stationary point of $t$?</p>\n<p>[[4]]</p>", "marks": 0, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "gaps": [{"failureRate": 1, "variableReplacementStrategy": "originalfirst", "unitTests": [], "vsetRangePoints": 5, "useCustomName": false, "checkVariableNames": false, "answer": "3*{m}*x^2", "valuegenerators": [{"value": "", "name": "x"}], "marks": 1, "showCorrectAnswer": true, "showPreview": true, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "checkingType": "absdiff", "customName": "", "type": "jme", "vsetRange": [0, 1], "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true}, {"failureRate": 1, "marks": 1, "showPreview": false, "checkingType": "absdiff", "customName": "", "showFeedbackIcon": true, "type": "jme", "vsetRange": [0, 1], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "useCustomName": false, "vsetRangePoints": 5, "answerSimplification": "fractionnumbers", "answer": "0", "valuegenerators": [], "showCorrectAnswer": true, "checkVariableNames": false, "checkingAccuracy": 0.001, "variableReplacements": [], "scripts": {}}, {"failureRate": 1, "marks": 1, "showPreview": false, "checkingType": "absdiff", "customName": "", "showFeedbackIcon": true, "type": "jme", "vsetRange": [0, 1], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "useCustomName": false, "vsetRangePoints": 5, "answerSimplification": "fractionnumbers", "answer": "{q}", "valuegenerators": [], "showCorrectAnswer": true, "checkVariableNames": false, "checkingAccuracy": 0.001, "variableReplacements": [], "scripts": {}}, {"failureRate": 1, "variableReplacementStrategy": "originalfirst", "unitTests": [], "vsetRangePoints": 5, "useCustomName": false, "checkVariableNames": false, "answer": "6*{m}*x", "valuegenerators": [{"value": "", "name": "x"}], "marks": 1, "showCorrectAnswer": true, "showPreview": true, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "checkingType": "absdiff", "customName": "", "type": "jme", "vsetRange": [0, 1], "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true}, {"variableReplacementStrategy": "originalfirst", "unitTests": [], "choices": ["<p>Maximum</p>", "<p>Minimum</p>", "<p>Point of inflection</p>"], "useCustomName": false, "displayType": "radiogroup", "shuffleChoices": false, "showCellAnswerState": true, "marks": 0, "showCorrectAnswer": true, "maxMarks": 0, "extendBaseMarkingAlgorithm": true, "distractors": ["", "", ""], "customName": "", "type": "1_n_2", "matrix": [0, 0, 1], "minMarks": 0, "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "displayColumns": 0, "showFeedbackIcon": true}], "customName": "", "type": "gapfill", "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "sortAnswers": false, "showFeedbackIcon": true}], "variable_groups": [], "ungrouped_variables": ["a1", "sx1", "m", "sy1", "q", "sy2", "sx2", "a2", "b1", "b2", "c2", "c1"], "functions": {}, "rulesets": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"sx1": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "sx1", "definition": "-b1/(2*a1)"}, "a2": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "definition": "random(-5..-2)"}, "b2": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "definition": "random(-6..6 except (-1..1))"}, "sx2": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "sx2", "definition": "-b2/(2*a2)"}, "m": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "definition": "random(2,3,4)"}, "c1": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "definition": "random(-10..10 except (-1..1))"}, "b1": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "definition": "random(-6..6 except (-1..1))"}, "c2": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "c2", "definition": "random(-10..10 except (-1..1))"}, "sy2": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "sy2", "definition": "a2*(sx2^2)+b2*sx2+c2"}, "a1": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "definition": "random(2..5)"}, "sy1": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "sy1", "definition": "a1*(sx1^2)+b1*sx1+c1"}, "q": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "definition": "random(-10..10 except 0)"}}, "advice": "<h4>a)</h4>\n<p>$\\dfrac{\\mathrm{d}y}{\\mathrm{d}x} = \\simplify{{2a1}x+{b1}}$.</p>\n<p>To find the $x$-coordinate of the stationary point, solve $\\frac{\\mathrm{d}y}{\\mathrm{d}x} = 0$ for $x$:</p>\n<p>\\[ \\begin{align} \\frac{\\mathrm{d}y}{\\mathrm{d}x} = \\simplify{{2a1}x + {b1}} &amp;= 0&nbsp;\\\\ x &amp;= \\simplify[all,fractionNumbers]{{sx1}}&nbsp;\\end{align} \\]</p>\n<p>Find the $y$-coordinate by substituting this value of $x$ into the definition of $y(x)$:</p>\n<p>\\[\\begin{align} \\simplify[fractionnumbers]{y({sx1})} &amp;= \\simplify[basic,fractionnumbers]{{a1}{sx1}^2+{b1}{sx1}+{c1}} \\\\ &amp;= \\simplify[fractionnumbers]{{sy1}} \\end{align}\\]</p>\n<p>Finally, to determine the nature of the stationary point, look at $\\frac{\\mathrm{d}^2y}{\\mathrm{d}x^2}$ at $x = \\simplify[fractionnumbers]{{sx1}}$.</p>\n<p>\\[ \\frac{\\mathrm{d}^2y}{\\mathrm{d}x^2} = \\simplify{{2*a1}} \\]</p>\n<p>This is&nbsp;<strong>positive</strong>, so the stationary point is a&nbsp;<strong>minimum</strong>.</p>\n<h4>b)</h4>\n<p>$\\dfrac{\\mathrm{d}z}{\\mathrm{d}x} = \\simplify{{2a2}x+{b2}}$.</p>\n<p>To find the $x$-coordinate of the stationary point, solve $\\frac{\\mathrm{d}z}{\\mathrm{d}x} = 0$ for $x$:</p>\n<p>\\[ \\begin{align} \\frac{\\mathrm{d}z}{\\mathrm{d}x} = \\simplify{{2a2}x + {b2}} &amp;= 0&nbsp;\\\\ x &amp;= \\simplify[all,fractionNumbers]{{sx2}}&nbsp;\\end{align} \\]</p>\n<p>Find the $y$-coordinate by substituting this value of $x$ into the definition of $z(x)$:</p>\n<p>\\[\\begin{align} \\simplify[fractionnumbers]{z({sx1})} &amp;= \\simplify[basic,fractionnumbers]{{a2}{sx2}^2+{b2}{sx2}+{c2}} \\\\ &amp;= \\simplify[fractionnumbers]{{sy2}} \\end{align}\\]</p>\n<p>Finally, to determine the nature of the stationary point, look at $\\frac{\\mathrm{d}^2z}{\\mathrm{d}x^2}$ at $x = \\simplify[fractionnumbers]{{sx2}}$.</p>\n<p>\\[ \\frac{\\mathrm{d}^2z}{\\mathrm{d}x^2} = \\simplify{{2*a2}} \\]</p>\n<p>This is&nbsp;<strong>negative</strong>, so the stationary point is a&nbsp;<strong>maximum</strong>.</p>\n<h4>c)</h4>\n<p>$\\dfrac{\\mathrm{d}t}{\\mathrm{d}x} = \\simplify{{3m}x^2}$.</p>\n<p>To find the $x$-coordinate of the stationary point, solve $\\frac{\\mathrm{d}t}{\\mathrm{d}x} = 0$ for $x$:</p>\n<p>\\[ \\begin{align} \\frac{\\mathrm{d}t}{\\mathrm{d}x} = \\simplify{{3m}x^2} &amp;= 0&nbsp;\\\\ x &amp;= 0 \\end{align} \\]</p>\n<p>Find the $y$-coordinate by substituting this value of $x$ into the definition of $t(x)$:</p>\n<p>\\[\\begin{align} z(0) &amp;= \\simplify[basic,fractionnumbers]{{m}*0^3 + {q}} \\\\ &amp;= \\var{q} \\end{align}\\]</p>\n<p>Finally, to determine the nature of the stationary point, look at $\\frac{\\mathrm{d}^2t}{\\mathrm{d}x^2}$ at $x = 0$.</p>\n<p>\\[ \\frac{\\mathrm{d}^2t}{\\mathrm{d}x^2} = \\simplify{{6m}x} \\]</p>\n<p>\\[ \\left.\\frac{\\mathrm{d}^2t}{\\mathrm{d}x^2} \\right\\rvert_{x=0} = \\var{6m} \\times 0 = 0 \\]</p>\n<p>This is&nbsp;<strong>zero</strong>, so the stationary point is a&nbsp;<strong>point of inflection</strong>.</p>", "statement": "<p>For the following, find the stationary point and determine its nature. For your answers, where appropriate, write your solutions as fractions, NOT decimals, and cancel down where possible.</p>", "preamble": {"js": "", "css": ""}, "type": "question"}, {"name": "Josh's copy of Solid phase change, radiation, entropy", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Tom Stallard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/841/"}, {"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}], "metadata": {"description": "<p>A random heating question, that randomly picks a material, and then heats it through either one or two phase changes, provides an example graph of the heating with scaled temperature ranges (though not with scaled latent and specific heats), and a table with the suitable constants.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "advice": "<p><strong>a) </strong></p>\n<p>$Q = m L_H$</p>\n<p>$Q = \\var{mass} \\times \\var{phase1_latentheat} = \\var{fusionheat}$</p>\n<p></p>\n<p>So the energy needed to melt the cube is {sigformat(fh_kj,3)} kJ.</p>\n<p><strong></strong></p>\n<p><strong>b) </strong></p>\n<p>$P_{net} = e \\sigma A \\Delta T^4$</p>\n<p>$P_{net} = e \\sigma A (T_1^4 - T_2^4)$</p>\n<p>where A is the surface area of the cube: $A = 6x^2 = 6 \\times (\\var{xx}^2) = 6*\\var{xx^2} = \\var{area}$</p>\n<p>$P_{net} = \\var{emissivity} \\times \\var{ksb2}\\times10^{-8} \\times \\var{area} \\times (\\var{phase1_temp}^4 - \\var{oven_temp}^4) = \\var{-power}$</p>\n<p></p>\n<p>So the net power emitted by the cube is&nbsp;{sigformat(-p_kw,3)} W , and the net power <strong>absorbed</strong> by the block is {sigformat(p_kw,3)} W.</p>\n<p><strong></strong></p>\n<p><strong>c) </strong></p>\n<p>$t = \\frac{E}{P}$</p>\n<p>$t = \\frac{\\var{fusionheat}}{\\var{sigformat(power,5)}} = \\var{time} $</p>\n<p></p>\n<p>So the time the cube takes to melt is {sigformat(time,3)} seconds.</p>\n<p></p>\n<p><strong>d) </strong></p>\n<p>$\\lambda_{max} = \\frac{K_W}{T}$</p>\n<p>$\\lambda_{max} = \\frac{\\var{kw}}{\\var{phase1_temp}} = \\var{wave}$</p>\n<p></p>\n<p>So the wavelength at which the cube's radiation is at a maximum is {sigformat(wave,3)} microns.</p>", "variable_groups": [{"name": "switcharoo values", "variables": []}, {"name": "kg or g", "variables": ["mass_string"]}, {"name": "Material values", "variables": ["mat_string", "container_string", "phase1_temp", "phase1_latentheat", "emissivity", "density"]}, {"name": "Energy", "variables": ["fusionheat", "fh_kj", "p_kw", "time", "power", "tt", "pp", "x", "xx", "xxx", "area", "ksb", "ksb2", "kw", "wave"]}, {"name": "Lists of values", "variables": ["material_list", "fusion_lh_list", "fusion_temp_list", "material_emissivity", "material_density"]}, {"name": "Random variables", "variables": ["wat_mat", "start_temp", "oven_start_temp", 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"phase1_latentheat", "group": "Material values"}, "question_string": {"templateType": "anything", "description": "", "definition": "if(switcharoo=0,' for {time} hours, calculate the power of the heater in W, to three significant figures',' with a power of {power} W, calculate how long the {mat_string} took to melt in hours, to three significant figures')", "name": "question_string", "group": "Ungrouped variables"}, "mass_string": {"templateType": "anything", "description": "", "definition": "if(mass<1,dpformat(mass*1000,0)+' g',dpformat(mass,2)+' kg')", "name": "mass_string", "group": "kg or g"}, "tt": {"templateType": "anything", "description": "", "definition": "fh_kj*1000/(power*60*60)", "name": "tt", "group": "Energy"}, "answer": {"templateType": "anything", "description": "", "definition": "if(switcharoo=0,pp,tt)", "name": "answer", "group": "Ungrouped variables"}, "kw": {"templateType": "anything", "description": "", "definition": "2898", "name": "kw", "group": "Energy"}, 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"description": "", "definition": "(emissivity*ksb*area*oven_temp^4)-(emissivity*ksb*area*phase1_temp^4)", "name": "power", "group": "Energy"}, "start_temp": {"templateType": "anything", "description": "", "definition": "phase1_temp-273.15", "name": "start_temp", "group": "Random variables"}, "material_density": {"templateType": "anything", "description": "<p>g/cm3</p>", "definition": "[8.91,21.1,8.97,19.32,7.87,10.49,2.70]", "name": "material_density", "group": "Lists of values"}, "ksb2": {"templateType": "anything", "description": "", "definition": "ksb*10^8", "name": "ksb2", "group": "Energy"}}, "functions": {"twostep": {"definition": "// Takes variables\n\n// showing K or C?\nk_c = Numbas.jme.unwrapValue(scope.variables.k_c_switch);\n\nif (k_c = 0) {\n    var k_c_corr =0;\n    var k_c_str=\"K\";\n} else {\n     var k_c_corr =-273;\n    var k_c_str=\"\u00b0C\";\n}\n\n//Set values\nst = Numbas.jme.unwrapValue(scope.variables.start_temp)+k_c_corr;\net = Numbas.jme.unwrapValue(scope.variables.end_temp)+k_c_corr;\npt1 = Numbas.jme.unwrapValue(scope.variables.phase1_temp)+k_c_corr;\npt2 = Numbas.jme.unwrapValue(scope.variables.phase2_temp)+k_c_corr;\n\n\n// The function provided by the JSXGraph extension wraps the board up in\n// a div tag so that it's easier to embed in the page.\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','300px',\n    {boundingBox: [-5,et+(et-st)/10.,28,st-(et-st)/10.],\n     axis: false,\n     showNavigation: false,\n     grid: false\n    });\n\n// div.board is the object created by JSXGraph, which you use to\n// manipulate elements\nvar board = div.board;\n\n\n\n// create the x-axis.\n//var xaxis = board.create('line',[[0,0],[1,0]], {strokeColor: 'black', fixed: true});\n//var xticks = board.create('ticks',[xaxis,20],{\n//  drawLabels: true,\n//  minorTicks: 0\n//});\n\n// create the y-axis\n\nvar yaxis = board.create('line',[[0,0],[0,1]], { strokeColor: 'black', fixed: true });\nvar yticks = 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return the container div\nreturn div;", "type": "html", "parameters": [], "language": "javascript"}, "onestep": {"definition": "// Takes variables\n\n// showing K or C?\nk_c = Numbas.jme.unwrapValue(scope.variables.k_c_switch);\n\nif (k_c = 0) {\n    var k_c_corr =0;\n    var k_c_str=\"K\";\n} else {\n     var k_c_corr =-273;\n    var k_c_str=\"\u00b0C\";\n}\n\n//Set values\nst = Numbas.jme.unwrapValue(scope.variables.start_temp)+k_c_corr;\net = Numbas.jme.unwrapValue(scope.variables.end_temp)+k_c_corr;\npt = Numbas.jme.unwrapValue(scope.variables.phase_temp)+k_c_corr;\n\n\n// The function provided by the JSXGraph extension wraps the board up in\n// a div tag so that it's easier to embed in the page.\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','300px',\n    {boundingBox: [-4,et+10,20,st-10],\n     axis: false,\n     showNavigation: false,\n     grid: false\n    });\n\n// div.board is the object created by JSXGraph, which you use to\n// manipulate elements\nvar board = div.board;\n\n\n\n// create the x-axis.\n//var xaxis = board.create('line',[[0,0],[1,0]], {strokeColor: 'black', fixed: true});\n//var xticks = board.create('ticks',[xaxis,20],{\n//  drawLabels: true,\n//  minorTicks: 0\n//});\n\n// create the y-axis\nvar yaxis = board.create('line',[[0,0],[0,1]], { strokeColor: 'black', fixed: true });\nvar yticks = board.create('ticks',[yaxis,parseInt((et-st)/50.)*10],{\ndrawZero:true,\ndrawLabels: true,\nlabel: {offset: [20, 0]},\nminorTicks: 0\n});\n\n//\n//slope 1\nvar slope1 = board.create('line',[[4,st],[((pt-st)/((pt-st)+(et-pt))*8)+4,pt]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar slope2 = board.create('line',[[((pt-st)/((pt-st)+(et-pt))*8)+4,pt],[16-((et-pt)/((pt-st)+(et-pt))*8),pt]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar slope3 = board.create('line',[[16-((et-pt)/((pt-st)+(et-pt))*8),pt],[16,et]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n\nvar dash1 = board.create('line',[[((pt-st)/((pt-st)+(et-pt))*8)+4,st-5],[((pt-st)/((pt-st)+(et-pt))*8)+4,et+5]], {dash:2, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar dash2 = board.create('line',[[16-((et-pt)/((pt-st)+(et-pt))*8),st-5],[16-((et-pt)/((pt-st)+(et-pt))*8),et+5]], {dash:2, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n\n\n//label the y-axis\n  var label = board.create('text',[-2,(et+st)/2,k_c_str]);\n\n\n// and return the container div\nreturn div;", "type": "html", "parameters": [], "language": "javascript"}}, "tags": [], "parts": [{"notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "type": "numberentry", "mustBeReduced": false, "mustBeReducedPC": 0, "variableReplacements": [], "correctAnswerFraction": false, "showFeedbackIcon": true, "maxValue": "siground(fh_kj,3)+siground(abs(fh_kj/100),3)", "correctAnswerStyle": "plain", "marks": "1", "showCorrectAnswer": true, "minValue": "siground(fh_kj,3)-siground(abs(fh_kj/100),3)", "scripts": {}, "prompt": "<p>Calculate the total heat absorbed by the {Mat_string} as it melts in kJ, to three significant figures.</p>", "variableReplacementStrategy": "originalfirst"}, {"notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "type": "numberentry", "mustBeReduced": false, "mustBeReducedPC": 0, "variableReplacements": [], "correctAnswerFraction": false, "showFeedbackIcon": true, "maxValue": "siground(p_kw,3)+siground(abs(p_kw/100),3)", "correctAnswerStyle": "plain", "marks": "1", "showCorrectAnswer": true, "minValue": "siground(p_kw,3)-siground(abs(p_kw/100),3)", "scripts": {}, "prompt": "<p>Calculate the net power absorbed by the {mat_string}&nbsp;from radiation in kW, to three significant figures. </p>", "variableReplacementStrategy": "originalfirst"}, {"notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "type": "numberentry", "mustBeReduced": false, "mustBeReducedPC": 0, "variableReplacements": [{"must_go_first": true, "part": "p0", "variable": "fh_kj"}, {"must_go_first": true, "part": "p1", "variable": "p_kw"}], "correctAnswerFraction": false, "showFeedbackIcon": true, "maxValue": "siground(time,3)+siground(abs(time/100),3)", "correctAnswerStyle": "plain", "marks": 1, "showCorrectAnswer": true, "minValue": "siground(time,3)-siground(abs(time/100),3)", "scripts": {}, "prompt": "<p>Using the values from part a) and b), calculate how long the block took to melt in seconds, to three significant figures</p>", "variableReplacementStrategy": "originalfirst"}, {"notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "type": "numberentry", "mustBeReduced": false, "mustBeReducedPC": 0, "variableReplacements": [], "correctAnswerFraction": false, "showFeedbackIcon": true, "maxValue": "siground(wave,3)+siground(abs(wave/100),3)", "correctAnswerStyle": "plain", "marks": 1, "showCorrectAnswer": true, "minValue": "siground(wave,3)-siground(abs(wave/100),3)", "scripts": {}, "prompt": "<p>At what wavelength does the cube shine most brightly as it melts, in microns, to three significant figures?</p>", "variableReplacementStrategy": "originalfirst"}], "statement": "<p></p>\n<p>A {mass_string} cube of solid {Mat_string} measures {x} cm along each side. It has a temperature of {phase1_temp} K, the fusion temperature of {mat_string}.&nbsp; The cube sits in an oven with a temperature of {oven_temp} K and is heated only by radiation (no conduction or convection) until it entirely melts.</p>\n<p>Assume Stefan's constant $\\sigma&nbsp; = \\var{ksb2}\\times10^{-8}$&nbsp; $W m^{-2}K^{-4}$ and Wien's displacement constant $k_W = \\var{kw}$ $\\mu mK$.</p>\n<table style=\"width: 541.833px;\" border=\"1\">\n<tbody>\n<tr>\n<td style=\"width: 92px;\"></td>\n<td style=\"width: 294px;\">Latent Heat of fusion</td>\n<td style=\"width: 105.833px;\">emissivity</td>\n</tr>\n<tr>\n<td style=\"width: 92px;\">{Mat_string}</td>\n<td style=\"width: 294px;\">{phase1_latentheat} Jkg&lt;sup&gt;-1&lt;/sup&gt;</td>\n<td style=\"width: 105.833px;\">{emissivity}</td>\n</tr>\n</tbody>\n</table>", "type": "question", "ungrouped_variables": ["switcharoo", "answer", "question_string"], "rulesets": {}}, {"name": "Josh's copy of Decide if variable is binomial or Poisson, from description,", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}], "parts": [{"type": "m_n_x", "choices": ["{ch1}", "{ch2}", "{ch3}"], "maxAnswers": 0, "minAnswers": 0, "maxMarks": 0, "showCorrectAnswer": true, "marks": 0, "matrix": "mm", "layout": {"type": "all", "expression": ""}, "displayType": "radiogroup", "shuffleAnswers": false, "scripts": {}, "shuffleChoices": true, "answers": ["Binomial Distribution", "Poisson Distribution"], "warningType": "none", "minMarks": 0}], "variable_groups": [], "statement": "\n  <p>Which of the following random variables could be modelled with a binomial distribution and which could be modelled with a Poisson distribution?</p>\n<p>You will lose 1 mark for every incorrect answer. The minimum mark is 0.</p>\n  ", "type": "question", "showQuestionGroupNames": false, "tags": ["ACC1012", "checked2015", "MAS1403"], "rulesets": {}, "metadata": {"notes": "<p><strong>06/12/2013</strong></p>\n<p>Replaced a Poisson scenario that wasn't strictly Poisson. (AJY)</p>\n<p><strong>31/12/2012:</strong></p>\n<p><strong><br /></strong>Checked choices, OK. Added tag sc as examples can be easily added to via the arrays b and pd.</p>", "description": "<p>Given descriptions of &nbsp;3 random variables, decide whether or not each is from a Poisson or Binomial distribution.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "ungrouped_variables": ["p2", "p3", "b", "mm", "ch3", "ch1", "ch2", "p1", "t", "pd"], "functions": {}, "preamble": {"js": "", "css": ""}, "advice": "<p>No solution given.</p>", "variables": {"t": {"description": "", "definition": "random(0,1)", "name": "t", "templateType": "anything", "group": "Ungrouped variables"}, "p3": {"description": "", "definition": "random(0..abs(pd)-1)", "name": "p3", "templateType": "anything", "group": "Ungrouped variables"}, "mm": {"description": "", "definition": "[[1,-1],[1-2*t,2*t-1],[-1,1]]", "name": "mm", "templateType": "anything", "group": "Ungrouped variables"}, "p1": {"description": "", "definition": "random(0..abs(b)-1)", "name": "p1", "templateType": "anything", "group": "Ungrouped variables"}, "ch2": {"description": "", "definition": "switch(t=0,b[p2],pd[p2])", "name": "ch2", "templateType": "anything", "group": "Ungrouped variables"}, "b": {"description": "", "definition": "\n[\"20% of eggs from a family-run farm are bad. X is the number of bad eggs in a box of a dozen.\",\n  \"A salesperson has a 50% chance of making a sale on a customer visit and she arranges 10 visits in a day. Let X be the number of sales that day.\",\n  \"30% of items off a factory production line have been shown to have defects. Let A be the number of defectives in a box of 20 such items.\",\n  \"One in ten new small businesses in the north-east goes bust within a year. Let X be the number of small businesses that fail in the next year out of thirty that have been set up.\",\n  \"The probability that an office photocopier will fail on any given day is 0.15. The human resources office at Newcastle University has ten such photocopiers; Let Y be the number of photocopiers that fail today.\",\n  \"Callers to the Vodaphone call centre will get through to an operator immediately with probability 0.25. X is the number of callers that speak to an operator immediately out of thirty such callers.\",\n  \"Experience has shown that two in every ten components produced by a circuitboard company will be defective. A random sample of 100 components is inspected for defects, and D is the number of defectives in this sample.\"]\n", "name": "b", "templateType": "anything", "group": "Ungrouped variables"}, "pd": {"description": "", "definition": "\n[\"Y is the number of flights sold per hour by an online travel agency. This travel agency usually sells 10 flights per hour.\",\n  \"X is the number of cars sold by a local garage in a month. This garage usually sells about 10 cars per month.\",\n  \"The number of calls, Y, received at the British Passport Office in Durham occurs at the rate of 10 a minute.\",\n  \"We are interested in X, the number of machine breakdowns in a day. Such breakdowns at a particular IT company occur at a rate of eight per week.\",\n  \"X is the number of e-mails arriving in your inbox in a one hour period.  On average you receive 3 e-mails per hour.\",\n  \"On average, three patients arrive at a local Accident and Emergency department every hour. We count the number, X, of patients in an hour period.\",\n  \"About five customers arrive at a fish shop queue every ten minutes during the lunch time rush. We count X, the number of customers arriving during the lunch time rush.\"]\n", "name": "pd", "templateType": "anything", "group": "Ungrouped variables"}, "ch3": {"description": "", "definition": "pd[p3]", "name": "ch3", "templateType": "anything", "group": "Ungrouped variables"}, "ch1": {"description": "", "definition": "b[p1]", "name": "ch1", "templateType": "anything", "group": "Ungrouped variables"}, "p2": {"description": "", "definition": "switch(t=0,random(0..abs(b)-1 except p1),random(0..abs(pd)-1 except p3))", "name": "p2", "templateType": "anything", "group": "Ungrouped variables"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "question_groups": [{"pickQuestions": 0, "pickingStrategy": "all-ordered", "name": "", "questions": []}]}]}, {"name": "More Simple Examples", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questions": [{"name": "Factorise a quadratic", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}], "tags": [], "metadata": {"description": "Demonstrate how string restrictions work", "licence": "None specified"}, "parts": [{"failureRate": 1, "marks": 1, "showPreview": true, "musthave": {"strings": ["(", ")"], "partialCredit": 0, "message": "", "showStrings": false}, "checkingType": "absdiff", "customName": "", "showFeedbackIcon": true, "type": "jme", "vsetRange": [0, 1], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "useCustomName": false, "vsetRangePoints": 5, "prompt": "<p>Factorise $\\simplify{ x^2 + {x0+x1}*x + {x0*x1} }$</p>", "valuegenerators": [{"value": "", "name": "x"}], "showCorrectAnswer": true, "checkVariableNames": false, "checkingAccuracy": 0.001, "answer": "(x+{x0})(x+{x1})", "notallowed": {"strings": ["^"], "partialCredit": 0, "message": "There should be no $x^2$ powers if you've factorised this correctly", "showStrings": true}, "variableReplacements": [], "scripts": {}}], "variable_groups": [], "ungrouped_variables": ["x0", "x1"], "functions": {}, "rulesets": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"x0": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "x0", "definition": "random(-9..9)"}, "x1": {"description": "<p>except x0 to avoid repeated roots</p>", "templateType": "anything", "group": "Ungrouped variables", "name": "x1", "definition": "random(-9..9 except x0)"}}, "advice": "", "statement": "", "preamble": {"js": "", "css": ""}, "type": "question"}, {"name": "Josh's copy of Indefinite Integrals", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME UCC", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/351/"}, {"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}], "metadata": {"description": "<p>Indefinite Integrals</p>\n<p>rebel</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Solve the following indefinite integrals, using $C$ to represent an unknown constant.</p>", "variable_groups": [], "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"b": {"templateType": "anything", "description": "", "name": "b", "definition": "random(2..9 except a)", "group": "Ungrouped variables"}, "c": {"templateType": "anything", "description": "", "name": "c", "definition": "random(1..9 except a except b)", "group": "Ungrouped variables"}, "a": {"templateType": "anything", "description": "", "name": "a", "definition": "random(2..9)", "group": "Ungrouped variables"}, "f": {"templateType": "anything", "description": "", "name": "f", "definition": "random(1..8 except d)", "group": "Ungrouped variables"}, "d": {"templateType": "anything", "description": "", "name": "d", "definition": "random(1..8)", "group": "Ungrouped variables"}}, "ungrouped_variables": ["a", "c", "b", "d", "f"], "tags": [], "parts": [{"showPreview": true, "type": "jme", "vsetRange": [0, 1], "showFeedbackIcon": true, "useCustomName": false, "customMarkingAlgorithm": "", "marks": 1, "unitTests": [], "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "scripts": {}, "vsetRangePoints": 5, "variableReplacementStrategy": "originalfirst", "answer": "x^5/5-{a}x^4/4+{b}x^2/2-{c}x+C", "variableReplacements": [], "checkVariableNames": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}], "prompt": "<p>$\\int(x^4-\\var{a}x^3+\\var{b}x-\\var{c})\\mathrm{dx}$</p>", "failureRate": 1, "checkingType": "absdiff", "customName": "", "musthave": {"partialCredit": 0, "message": "Did you forget the constant of integration?", "showStrings": false, "strings": ["C"]}}, {"showPreview": true, "type": "jme", "vsetRange": [0, 1], "showFeedbackIcon": true, "useCustomName": false, "customMarkingAlgorithm": "", "marks": 1, "unitTests": [], "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "scripts": {}, "vsetRangePoints": 5, "variableReplacementStrategy": "originalfirst", "answer": "2u^3/3+u^2({f}+2{d})/2+{d}{f}u+C", "variableReplacements": [], "checkVariableNames": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "u", "value": ""}], "prompt": "<p>$\\int(u+\\var{d})(2u+\\var{f})\\mathrm{du}$</p>", "failureRate": 1, "checkingType": "absdiff", "customName": ""}, {"showPreview": true, "type": "jme", "vsetRange": [0, 1], "showFeedbackIcon": true, "useCustomName": false, "customMarkingAlgorithm": "", "marks": 1, "unitTests": [], "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "scripts": {}, "vsetRangePoints": 5, "variableReplacementStrategy": "originalfirst", "answer": "2sin(x) + C", "variableReplacements": [], "checkVariableNames": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}], "prompt": "<p>$\\int\\frac{\\sin(2x)}{\\sin(x)}\\mathrm{dx}$.</p>\n<p>Take care to include the brackets in the trigonometric expressions, i.e. write sin(x) rather than sinx.</p>", "failureRate": 1, "checkingType": "absdiff", "customName": ""}], "advice": "<p>Indefinite Integrals</p>", "functions": {}, "rulesets": {}, "type": "question"}, {"name": "Matrix arithmetic", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}], "functions": {}, "ungrouped_variables": ["A", "C1", "C2", "UNIT"], "statement": "<p>Given the matrix</p>\n<p>$\\mathbf{A} = \\var{A}$</p>\n<p></p>", "tags": [], "variables": {"C1": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(2..5)", "name": "C1"}, "UNIT": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "id(2)", "name": "UNIT"}, "A": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "matrix(repeat(random(-3..3),2),repeat(random(-3..3),2))", "name": "A"}, "C2": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(2..5)", "name": "C2"}}, "advice": "<p>$\\mathbf{A} = \\var{A}$</p>\n<p>$\\mathbf{A}^2 = \\var{A}\\var{A} = \\var{A*A}$</p>\n<p>$\\var{C1}\\mathbf{A} = \\var{C1}\\var{A} = \\var{C1*A}$</p>\n<p>Putting it all together:</p>\n<p>$(\\mathbf{A}^2+\\var{C1}\\mathbf{A}+\\var{C2}\\mathbf{I})^T$</p>\n<p>$=\\left[\\var{A*A}+\\var{C1*A}+\\var{C2*UNIT}\\right]^T$</p>\n<p>$=\\var{A*A+C1*A+C2*UNIT}^T$</p>\n<p>$\\var{transpose(A*A+C1*A+C2*UNIT)}$</p>", "variable_groups": [], "preamble": {"js": "", "css": ""}, "metadata": {"description": "", "licence": "None specified"}, "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"variableReplacementStrategy": "originalfirst", "marks": 1, "prompt": "<p>Calculate</p>\n<p>$(\\mathbf{A}^2+\\var{C1}\\mathbf{A}+\\var{C2}\\mathbf{I})^T$</p>", "customMarkingAlgorithm": "", "correctAnswer": "transpose(A*A+C1*A+C2*UNIT)", "allowResize": false, "scripts": {}, "variableReplacements": [], "unitTests": [], "showCorrectAnswer": true, "type": "matrix", "tolerance": 0, "useCustomName": false, "allowFractions": false, "customName": "", "numColumns": "2", "correctAnswerFractions": false, "numRows": "2", "markPerCell": true, "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true}, {"variableReplacementStrategy": "originalfirst", "showFractionHint": true, "marks": 1, "prompt": "<p>Calculate $\\det \\left[ A \\right]$</p>", "customMarkingAlgorithm": "", "mustBeReduced": false, "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "scripts": {}, "mustBeReducedPC": 0, "variableReplacements": [], "unitTests": [], "showCorrectAnswer": true, "minValue": "det(A)", "type": "numberentry", "useCustomName": false, "customName": "", "adaptiveMarkingPenalty": 0, "maxValue": "det(A)", "showFeedbackIcon": true, "correctAnswerFraction": false, "extendBaseMarkingAlgorithm": true}, {"variableReplacementStrategy": "originalfirst", "marks": 1, "prompt": "<p>Calculate&nbsp;$\\mathbf{A}^T$</p>", "customMarkingAlgorithm": "", "correctAnswer": "transpose(A)", "allowResize": true, "scripts": {}, "variableReplacements": [], "unitTests": [], "showCorrectAnswer": true, "type": "matrix", "tolerance": 0, "useCustomName": false, "allowFractions": false, "customName": "", "numColumns": 1, "correctAnswerFractions": false, "numRows": 1, "markPerCell": false, "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true}], "rulesets": {}, "type": "question"}, {"name": "Simple Matrix Multiplication", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"customMarkingAlgorithm": "", "allowFractions": false, "unitTests": [], "steps": [{"customMarkingAlgorithm": "", "prompt": "<p><img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Matrix_multiplication_diagram_2.svg/313px-Matrix_multiplication_diagram_2.svg.png\"/></p>", "type": "information", "scripts": {}, "customName": "", "useCustomName": false, "unitTests": [], "marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "showFeedbackIcon": true}, {"customMarkingAlgorithm": "", "prompt": "<p><a href=\"https://en.wikipedia.org/wiki/Matrix_multiplication#Definition\">https://en.wikipedia.org/wiki/Matrix_multiplication#Definition</a></p>", "type": "information", "scripts": {}, "customName": "", "useCustomName": false, "unitTests": [], "marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "showFeedbackIcon": true}], "type": "matrix", "scripts": {}, "correctAnswerFractions": false, "markPerCell": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "numRows": 1, "showFeedbackIcon": true, "prompt": "<p>$\\mathbf{C} = \\mathbf{AB}$</p>\n<p>$\\mathbf{C} =$</p>\n<p></p>", "numColumns": 1, "customName": "", "useCustomName": false, "correctAnswer": "A*B", "marks": 1, "allowResize": true, "tolerance": 0, "stepsPenalty": 0, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true}, {"customMarkingAlgorithm": "", "prompt": "<p>$\\mathbf{D} = \\mathbf{BA}$</p>\n<p>$\\mathbf{D} =$</p>", "correctAnswerFractions": false, "correctAnswer": "B*A", "type": "matrix", "scripts": {}, "customName": "", "useCustomName": false, "unitTests": [], "marks": 1, "markPerCell": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "allowFractions": false, "allowResize": true, "numColumns": 1, "tolerance": 0, "numRows": 1, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "showFeedbackIcon": true}], "statement": "<p>Do the following matrix problems :<br/>Let</p>\n<p>$\\mathbf{A}= \\var{A}$ and $\\mathbf{B}=\\var{B}$<br/>Calculate the following products of these matrices:</p>", "rulesets": {}, "variable_groups": [], "tags": [], "advice": "<p>See&nbsp;<a href=\"https://en.wikipedia.org/wiki/Matrix_multiplication#Definition\">https://en.wikipedia.org/wiki/Matrix_multiplication#Definition</a></p>", "metadata": {"description": "Multiply a 2x3 and a 3x2 matrix together", "licence": "None specified"}, "functions": {}, "variables": {"amax": {"description": "", "templateType": "number", "group": "Ungrouped variables", "definition": "3", "name": "amax"}, "A": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "matrix([random(-amax..amax),random(-amax..amax),random(-amax..amax)],[random(-amax..amax),random(-amax..amax),random(-amax..amax)])", "name": "A"}, "B": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "matrix(repeat(random(1..4),2),repeat(random(1..4),2),repeat(random(1..4),2))", "name": "B"}, "bmax": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-4..4)", "name": "bmax"}, "BA": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "B*A", "name": "BA"}}, "preamble": {"css": "", "js": ""}, "ungrouped_variables": ["A", "amax", "B", "bmax", "BA"], "type": "question"}]}], "percentPass": 0, "name": "Interesting NUMBAS examples", "type": "exam", "contributors": [{"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}], "extensions": ["geogebra", "jsxgraph", "quantities", "stats", "weh"], "custom_part_types": [{"source": {"pk": 24, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/24/edit"}, "name": "Angle quantity", "short_name": "angle-quantity-from-reference", "description": "<p>Angle&nbsp;as a quantity in degrees.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['correct_quantity'])", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\ncorrect_scalar:\nscalar(correct_quantity)\n  \n\ncorrect_quantity:\nsettings['correct_quantity']\n\ncorrect_units:\nunits(correct_quantity)\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\njoin(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n\n\ngood_units:\ntry(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)\n\nstudent_quantity:\nswitch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)\n\nangle_in_range:\nif(settings['restrict_angle'], abs(student_scalar) <= 90, true)\n\nright:\nwithinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])\n\nclose:\nwithinTolerance(student_scalar, correct_scalar, settings['close'])", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)"}, {"name": "correct_scalar", "description": "", "definition": "scalar(correct_quantity)\n  "}, {"name": "correct_quantity", "description": "", "definition": "settings['correct_quantity']"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "", "definition": "join(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n"}, {"name": "good_units", "description": "", "definition": "try(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)"}, {"name": "student_quantity", "description": "", "definition": "switch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity)"}, {"name": "angle_in_range", "description": "", "definition": "if(settings['restrict_angle'], abs(student_scalar) <= 90, true)"}, {"name": "right", "description": "<p>Will check for correct sign elswhere.</p>", "definition": "withinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])"}, {"name": "close", "description": "<p>Must have correct sign to be close.</p>", "definition": "withinTolerance(student_scalar, correct_scalar, settings['close'])\n"}], "settings": [{"name": "correct_quantity", "label": "Correct Angle as quantity ", "help_url": "", "hint": "", "input_type": "code", "default_value": "qty(45,'deg')", "evaluate": true}, {"name": "right", "label": "Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.1", "evaluate": true}, {"name": "restrict_angle", "label": "Less than 90\u00b0", "help_url": "", "hint": "When checked, angle must be between -90&deg; and +90&deg;.", "input_type": "checkbox", "default_value": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units.", "input_type": "percent", "default_value": "75"}, {"name": "close", "label": " Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.5", "evaluate": true}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value without units.", "input_type": "percent", "default_value": "25"}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [["question-resources/Data.csv", "/srv/numbas/media/question-resources/Data.csv"]]}