// Numbas version: finer_feedback_settings
{"navigation": {"onleave": {"action": "none", "message": ""}, "preventleave": true, "allowregen": true, "browse": true, "reverse": true, "showfrontpage": true, "showresultspage": "oncompletion"}, "timing": {"timedwarning": {"action": "none", "message": ""}, "timeout": {"action": "none", "message": ""}, "allowPause": true}, "question_groups": [{"pickQuestions": 1, "pickingStrategy": "all-ordered", "name": "Group", "questions": [{"name": "Midpoint", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "rulesets": {}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "<p>Calculate the&nbsp;midpoint of two points.</p>"}, "variables": {"xa1": {"definition": "l[0]", "name": "xa1", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "ya": {"definition": "(ya1+ya2)/2", "name": "ya", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "xa": {"definition": "(xa1+xa2)/2", "name": "xa", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "ya2": {"definition": "l[3]", "name": "ya2", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "xa2": {"definition": "l[1]", "name": "xa2", "templateType": "anything", "description": "<p>xa</p>", "group": "Ungrouped variables"}, "l": {"definition": "shuffle(-12..12)[0..4]", "name": "l", "templateType": "anything", "description": "<p>l</p>", "group": "Ungrouped variables"}, "ya1": {"definition": "l[2]", "name": "ya1", "templateType": "anything", "description": "", "group": "Ungrouped variables"}}, "functions": {"line_and_2points": {"definition": "\nvar div = Numbas.extensions.jsxgraph.makeBoard('600px','600px',{boundingBox:[-13,13,13,-13],grid:true,axis:false});\nvar board = div.board;\n\n// create the x-axis.\nvar xaxis = board.create('line',[[0,0],[1,0]], { strokeColor: 'black', fixed: true});\nvar xticks = board.create('ticks',[xaxis,2],{\n  drawLabels: true,\n  label: {offset: [-4, -10]},\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,2],{\ndrawLabels: true,\nlabel: {offset: [-20, 0]},\nminorTicks: 0\n});\n\n\nx0 = Numbas.jme.unwrapValue(scope.variables.xa1);\ny0 = Numbas.jme.unwrapValue(scope.variables.ya1);\nx1 = Numbas.jme.unwrapValue(scope.variables.xa2);\ny1 = Numbas.jme.unwrapValue(scope.variables.ya2);\n\nboard.create('point',[x0,y0],{fixed:true,withLabel:false});\nboard.create('point',[x1,y1],{fixed:true,withLabel:false});\nboard.create('point',[(x0+x1)/2,(y0+y1)/2],{fixed:true,withLabel:false});\n\n\nboard.create('text',[(x0+x1)/2+0.5,(y0+y1)/2,'The midpoint']);\n\n\nreturn div;", "parameters": [], "language": "javascript", "type": "html"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"js": "", "css": ""}, "advice": "<p>{line_and_2points()}</p>\n<p></p>\n<p>The midpoint of two points is simply the point whose&nbsp;$x$ coordinate is&nbsp;the average of the other $x$&nbsp;coordinates, and whose $y$ coordinate is&nbsp;the average of the other $y$&nbsp;coordinates. That is, the midpoint of $(\\var{xa1},\\var{ya1})$ and $(\\var{xa2},\\var{ya2})$ is the point $\\left(\\simplify[basic]{({xa1}+{xa2})/2},\\simplify[basic]{({ya1}+{ya2})/2}\\right)=\\left(\\simplify{({xa1}+{xa2})/2},\\simplify{({ya1}+{ya2})/2}\\right)=\\left(\\simplify{{(xa1+xa2)/2}},\\simplify{{(ya1+ya2)/2}}\\right)$.</p>\n<p></p>\n<p></p>", "ungrouped_variables": ["l", "xa1", "xa2", "ya1", "ya2", "xa", "ya"], "statement": "<p>Fill in the blanks.</p>", "parts": [{"prompt": "<p>The midpoint of $(\\var{xa1},\\var{ya1})$ and $(\\var{xa2},\\var{ya2})$ is $\\large($[[0]], [[1]]$\\large)$.</p>", "showFeedbackIcon": true, "marks": 0, "variableReplacements": [], "type": "gapfill", "showCorrectAnswer": true, "gaps": [{"correctAnswerStyle": "plain", "marks": 1, "correctAnswerFraction": true, "mustBeReduced": false, "allowFractions": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "minValue": "xa", "maxValue": "xa", "scripts": {}, "showFeedbackIcon": true, "type": "numberentry", "variableReplacements": [], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}, {"correctAnswerStyle": "plain", "marks": 1, "correctAnswerFraction": true, "mustBeReduced": false, "allowFractions": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "minValue": "ya", "maxValue": "ya", "scripts": {}, "showFeedbackIcon": true, "type": "numberentry", "variableReplacements": [], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}], "scripts": {}, "variableReplacementStrategy": "originalfirst"}], "variable_groups": [], "tags": [], "type": "question"}, {"name": "Addition and subtraction of numbers in standard form", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}], "variable_groups": [], "functions": {}, "rulesets": {}, "ungrouped_variables": ["B"], "metadata": {"description": "<p>Add two numbers in standard form, then subtract two numbers in standard form.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "advice": "<p>The easiest way to do this is to convert these numbers in standard form&nbsp;into decimals,&nbsp;do the calculation with decimal forms,&nbsp;then change them back into standard form.</p>\n<h4>a)</h4>\n<p style=\"padding-left: 30px;\">\\[\\begin{align} \\var{B[0]} \\times 10^3 + \\var{B[1]} \\times 10^4 &amp;= \\var{B[0]*10^3}&nbsp;+ \\var{B[1]*10^4} \\\\&amp;= \\var{B[0]*10^3 + B[1]*10^4} \\\\&amp;= \\var{(B[0]*10^3 + B[1]*10^4)/10^4} \\times 10^4\\end{align}\\]</p>\n<p style=\"padding-left: 30px;\">&nbsp;</p>\n<h4>b)</h4>\n<p style=\"padding-left: 30px;\">\\[\\begin{align} \\var{B[2]} \\times 10^3&nbsp;- \\var{B[2] - 1.70} \\times 10^2 &amp;= \\var{B[2]*10^3}&nbsp;- \\var{(B[2] - 1.70)*10^2} \\\\&amp;= \\var{(B[2]*10^3)&nbsp;- ((B[2] - 1.70)*10^2)} \\\\&amp;= \\var{(B[2]*10^3 - (B[2] - 1.70)*10^2)/10^3} \\times 10^3\\end{align}\\]</p>", "statement": "<p>Calculate the following and&nbsp;write the result in standard index form (for example, for&nbsp;$2.01\\times 10^5$ we would write <code>2.01*10^5</code> in the gap).</p>", "preamble": {"css": "", "js": ""}, "variables": {"B": {"templateType": "anything", "description": "", "name": "B", "group": "Ungrouped variables", "definition": "repeat(random(3..9 #0.01), 3)"}}, "parts": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p style=\"padding-left: 30px;\">$\\var{B[0]} \\times 10^3 + \\var{B[1]} \\times 10^4 =$&nbsp; [[0]]</p>\n<p></p>\n<p></p>", "gaps": [{"variableReplacementStrategy": "originalfirst", "answer": "{(B[0]*10^3 + B[1]*10^4)/10^4}*10^4", "answersimplification": "!collectnumbers", "vsetrangepoints": 5, "notallowed": {"message": "", "showStrings": false, "partialCredit": 0, "strings": ["10^-4", "10^(-4)", "+", "-"]}, "checkingtype": "absdiff", "type": "jme", "showpreview": true, "checkvariablenames": false, "checkingaccuracy": 0.001, "vsetrange": [0, 1], "variableReplacements": [], "expectedvariablenames": [], "showFeedbackIcon": true, "musthave": {"message": "", "showStrings": false, "partialCredit": 0, "strings": ["*10^4"]}, "marks": 1, "showCorrectAnswer": true, "scripts": {}}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "showCorrectAnswer": true}, {"variableReplacementStrategy": "originalfirst", "prompt": "<p style=\"padding-left: 30px;\">$\\var{B[2]} \\times 10^3&nbsp;- \\var{B[2] - 1.70} \\times 10^2 =$&nbsp; [[0]]</p>\n<p></p>\n<p></p>\n<p></p>", "gaps": [{"variableReplacementStrategy": "originalfirst", "answer": "{(B[2]*10^3 - (B[2] - 1.70)*10^2)/10^3}*10^3", "answersimplification": "!collectnumbers", "vsetrangepoints": 5, "notallowed": {"message": "<p>+</p>\n<p></p>", "showStrings": false, "partialCredit": 0, "strings": ["*10^-3", "*10^(-3)", "+", "-"]}, "checkingtype": "absdiff", "type": "jme", "showpreview": true, "checkvariablenames": false, "checkingaccuracy": 0.001, "vsetrange": [0, 1], "variableReplacements": [], "expectedvariablenames": [], "showFeedbackIcon": true, "musthave": {"message": "", "showStrings": false, "partialCredit": 0, "strings": ["*10^3"]}, "marks": 1, "showCorrectAnswer": true, "scripts": {}}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "showCorrectAnswer": true}], "tags": ["addition", "Addition", "conversion", "converting", "standard form", "standard index form", "subtraction", "taxonomy"], "variablesTest": {"maxRuns": 100, "condition": ""}}, {"name": "Exact values for sin, cos, tan (0 to 330, degrees)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/exact_values.svg", "/srv/numbas/media/question-resources/exact_values.svg"], ["question-resources/unit_circle_working.svg", "/srv/numbas/media/question-resources/unit_circle_working.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "tags": ["trig", "trigonometry", "Trigonometry"], "metadata": {"description": "<p>multiple choice testing sin, cos, tan of &nbsp;random(0,90,120,135,150,180,210,225,240,270,300,315,330) degrees</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Often we prefer to work with&nbsp;exact values rather than approximations from a calculator. In this question we require you input your answer without decimals and without entering the words sin, cos or tan. For example to input the exact value of $\\sin(60^\\circ)$, which is $\\dfrac{\\sqrt{3}}{2}$, you would input&nbsp;<strong>sqrt(3)/2</strong></p>", "advice": "<p>By drawing the following triangles we can determine the <strong>exact values</strong> of $\\sin$, $\\cos$ and $\\tan$ (and their reciprocals $\\csc$, $\\sec$, $\\cot$) for the angles $30^\\circ$, $45^\\circ$ and $60^\\circ$.</p>\n<p><br/><img src=\"resources/question-resources/exact_values.svg\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>Alternatively, one can memorise the following table:&nbsp;</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">$30^\\circ$</td>\n<td style=\"text-align: center;\">$45^\\circ$</td>\n<td style=\"text-align: center;\">$60^\\circ$</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\sin$</td>\n<td style=\"text-align: center;\">$\\dfrac{1}{2}$</td>\n<td style=\"text-align: center;\">$\\dfrac{1}{\\sqrt{2}}$</td>\n<td style=\"text-align: center;\">$\\dfrac{\\sqrt{3}}{2}$</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\cos$</td>\n<td style=\"text-align: center;\">$\\dfrac{\\sqrt{3}}{2}$</td>\n<td style=\"text-align: center;\">$\\dfrac{1}{\\sqrt{2}}$</td>\n<td style=\"text-align: center;\">$\\dfrac{1}{2}$</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\tan$</td>\n<td style=\"text-align: center;\">$\\dfrac{1}{\\sqrt{3}}$</td>\n<td style=\"text-align: center;\">$1$</td>\n<td style=\"text-align: center;\">$\\sqrt{3}$</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>That combined with the <strong>unit circle definitions</strong>:</p>\n<ul>\n<li>$\\cos\\theta$ is the $x$ coordinate of the&nbsp;point on the unit circle $\\theta$ degrees anti-clockwise from the positive $x$-axis&nbsp;</li>\n<li>$\\sin\\theta$ is the $y$ coordinate of the&nbsp;point on the unit circle $\\theta$ degrees anti-clockwise from the positive $x$-axis&nbsp;</li>\n<li>$\\tan\\theta$ is the slope of the line through the origin and the point&nbsp;on the unit circle $\\theta$ degrees anti-clockwise from the positive $x$-axis, or equivalently, $\\tan\\theta=\\dfrac{\\sin\\theta}{\\cos\\theta}$</li>\n</ul>\n<p>and some understanding of <strong>congruent triangles</strong>:</p>\n<div style=\"text-align: center;\"><iframe width=\"808px\" height=\"462px\" style=\"border: 0px;\" scrolling=\"no\" src=\"https://www.geogebra.org/material/iframe/id/e4kaj8M3/width/808/height/462/border/888888/rc/false/ai/false/sdz/false/smb/false/stb/false/stbh/true/ld/false/sri/false/at/auto\"> </iframe></div>\n<p></p>\n<p>allows us to work out $\\sin$, $\\cos$ and $\\tan$ for certain angles regardless of what&nbsp;quadrant the point is in. Because&nbsp;whatever angle we are asked about, we can always use the triangle in the first quadrant to determine the side lengths and then consider the signs of the coordinates separately.</p>\n<p></p>\n<p><strong>For example</strong>, to determine $\\sin(210^\\circ)$, $\\cos(210^\\circ)$ and $\\tan(210^\\circ)$ we first draw the following:</p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/unit_circle_working.svg\" width=\"812\" height=\"536\"/></p>\n<p>From this diagram, we can see&nbsp;that $\\cos(210^\\circ)=-\\cos(30^\\circ)$, and&nbsp;$\\sin(210^\\circ)=-\\sin(30^\\circ)$ since the triangles are congruent and we are in the 3rd quadrant where both the $x$ and $y$ values (and hence the $\\cos$ and $\\sin$ values) are negative.&nbsp;</p>\n<p>But given we know these&nbsp;exact values, we can conclude \\[\\cos(210^\\circ)=-\\cos(30^\\circ)=-\\dfrac{\\sqrt{3}}{2},\\]&nbsp;\\[\\sin(210^\\circ)=-\\sin(30^\\circ)=-\\dfrac{1}{2},\\] and finally \\[\\tan(210^\\circ)=\\dfrac{\\sin(210^\\circ)}{\\cos(210^\\circ)}=\\dfrac{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}=\\dfrac{1}{\\sqrt{3}}.\\]</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"theta": {"name": "theta", "group": "Ungrouped variables", "definition": "random(0,90,120,135,150,180,210,225,240,270,300,315,330)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["theta"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The exact value of $\\sin(\\var{theta}^\\circ)$ is&nbsp;[[0]].</p>\n<p>The exact value of $\\cos(\\var{theta}^\\circ)$ is&nbsp;[[1]].</p>\n<p>If $\\tan(\\var{theta}^\\circ)$ is defined, what is its exact value? If it isn't enter <em>infinity</em> (even though it doesn't equal that).&nbsp; [[2]].</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "sin({theta}*pi/180)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": false, "implicitFunctionComposition": false, "caseSensitive": false, "notallowed": {"strings": [".", "sin", "cos", "tan", "cosec", "sec", "cot"], "showStrings": true, "partialCredit": 0, "message": ""}, "valuegenerators": []}, {"type": "jme", 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