// Numbas version: finer_feedback_settings
{"name": "Using formulas", "metadata": {"description": "<p>A quick practice set of problems for education students to take in preparation for their numeracy test.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", ""], "variable_overrides": [[], [], [], []], "questions": [{"name": "Given a formula for something use it (drip rate)", "extensions": [], "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/"}], "variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "statement": "<p>Write the following question down on paper and evaluate&nbsp;it without using a calculator.</p>\n<p>If you are unsure of how to do&nbsp;a question, click on&nbsp;<em>Show steps</em>&nbsp;to see the full working. Then, once you understand how to do the question, click on&nbsp;<em>Try another question like this one</em>&nbsp;to start again.</p>", "variable_groups": [], "ungrouped_variables": ["v", "f", "h", "drip", "driprounded", "cfvh", "v'", "h'", "cfvs", "v''", "s'", "cffh'", "f'", "h''", "cffs'", "f''", "s''", "vf", "hs", "vf''", "hs''"], "parts": [{"prompt": "<p>You are told that&nbsp;&nbsp;</p>\n<p>$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\text{volume (mL)} \\times \\text{drop factor (drops/mL)}}{\\text{time (hr)}\\times \\text{60 (min/hr)}}$</p>\n<p>If the volume is $\\var{v}$ mL,&nbsp;the duration is $\\var{h}$ hours and&nbsp;there are&nbsp;$\\var{f}$ drops/mL, then the drip rate is</p>\n<p>[[0]] (drops/min) to the nearest whole number</p>", "sortAnswers": false, "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "useCustomName": false, "steps": [{"prompt": "<p>We take the formula</p>\n<p>$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\text{volume (mL)} \\times \\text{drop factor (drops/mL)}}{\\text{time (hr)}\\times \\text{60 (min/hr)}}$</p>\n<p>and substitute the following</p>\n<p>$\\text{volume}=\\var{v}$,</p>\n<p>$\\text{drop factor}= \\var{f}$,</p>\n<p>$\\text{time}= \\var{h}$</p>\n<p>so that we have&nbsp;</p>\n<p>$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\var{v} \\times \\var{f}}{\\var{h}\\times 60}$</p>\n<p>Using a <strong>calculator</strong>&nbsp;we would find</p>\n<p>$\\begin{align}\\text{drip rate (dpm)}&amp;\\approx\\var{drip} \\text{ dpm}\\\\&amp;=\\var{driprounded}\\text{ dpm (to the nearest whole number)}\\end{align}$</p>\n<p></p>\n<p><strong>Without a calculator</strong>, you&nbsp;<strong>could</strong> do this calculation by&nbsp;</p>\n<ul>\n<li>first determining $\\var{v} \\times \\var{f}=\\var{vf}$,</li>\n<li>then $\\var{h}&nbsp;\\times 60=\\var{hs}$,</li>\n<li>and&nbsp;then using long division for&nbsp;&nbsp;$\\displaystyle \\frac{\\var{vf}}{\\var{hs}}&nbsp;=\\var{driprounded}$ <span data-jme-visible=\"drip&lt;&gt;driprounded\">(nearest whole number).</span></li>\n</ul>\n<p>However, it is often best to look for <strong>common factors and cancel</strong> them before the multiplication and division. That is, given:</p>\n<p>$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\var{v} \\times \\var{f}}{\\var{h}\\times 60}$</p>\n<p>I would look for a common factor between $\\var{v}$ and $\\var{h}$.&nbsp;<span data-jme-visible=\"cfvh=1\"> But, alas, there isn't one.</span>&nbsp;<span data-jme-visible=\"cfvh&gt;1\">There is a common factor of&nbsp;$\\var{cfvh}$, so&nbsp;I'd remove this from the top and bottom and be left with</span></p>\n<p><span data-jme-visible=\"cfvh&gt;1\">$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\var{v'} \\times \\var{f}}{\\var{h'}\\times 60}$</span></p>\n<p>Then I'd look for a common factor between $\\var{v'}$ and $\\var{60}$. <span data-jme-visible=\"cfvs=1\"> But, alas, there isn't one.</span> <span data-jme-visible=\"cfvs&gt;1\">There is a common factor of $\\var{cfvs}$, so I'd remove that from the top and bottom and be left with</span></p>\n<p><span data-jme-visible=\"cfvs&gt;1\">$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\var{v''} \\times \\var{f}}{\\var{h'}\\times \\var{s'}}$</span></p>\n<p><span data-jme-visible=\"h'&gt;1\">Then I'd look for a common factor between $\\var{f}$ and $\\var{h'}$.</span> <span data-jme-visible=\"h'&gt;1 and cffh'=1\"> But, alas, there isn't one.</span> <span data-jme-visible=\"h'&gt;1 and cffh'&gt;1\">There is a common factor of $\\var{cffh'}$, so I'd remove that from the top and bottom and be left with</span></p>\n<p><span data-jme-visible=\"h'&gt;1 and cffh'&gt;1\">$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\var{v''} \\times \\var{f'}}{\\var{h''}\\times \\var{s'}}$</span></p>\n<p><span data-jme-visible=\"s'&gt;1\">Then I'd look for a common factor between $\\var{f'}$ and $\\var{s'}$.</span> <span data-jme-visible=\"s'&gt;1 and cffs'=1\"> But, alas, there isn't one.</span> <span data-jme-visible=\"s'&gt;1 and cffs'&gt;1\">There is a common factor of $\\var{cffs'}$, so I'd remove that from the top and the bottom and be left with&nbsp;</span></p>\n<p><span data-jme-visible=\"s'&gt;1 and cffs'&gt;1\">$\\displaystyle \\text{drip rate (dpm)}=\\frac{\\var{v''} \\times \\var{f''}}{\\var{h''}\\times \\var{s''}}$</span></p>\n<p></p>\n<p>So, after all that, I only need to do</p>\n<ul>\n<li>$\\var{v''} \\times \\var{f''}=\\var{vf''}$,</li>\n<li>then $\\var{h''}&nbsp;\\times \\var{s''}=\\var{hs''}$,</li>\n<li>and then perform the&nbsp;division $\\displaystyle \\frac{\\var{v''*f''}}{\\var{s''*h''}}=\\var{driprounded}$ <span data-jme-visible=\"drip&lt;&gt;driprounded\">(nearest whole number)</span></li>\n</ul>", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "useCustomName": false, "customName": "", "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "type": "information", "marks": 0, "scripts": {}, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": []}], "customName": "", "customMarkingAlgorithm": "", "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "marks": 0, "scripts": {}, "showCorrectAnswer": true, "unitTests": [], "gaps": [{"minValue": "drip", "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to&nbsp;the nearest whole number.", "useCustomName": false, "variableReplacements": [], "customName": "", "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "marks": 1, "scripts": {}, "unitTests": [], "correctAnswerFraction": false, "allowFractions": false, "showFeedbackIcon": true, "precisionType": "dp", "strictPrecision": false, "precisionPartialCredit": 0, "type": "numberentry", "maxValue": "drip", "precision": 0, "showPrecisionHint": false, "showCorrectAnswer": true}], "variableReplacements": []}], "variables": {"v": {"definition": "random(random(500,1000),random(100..1000#100))", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "v"}, "s'": {"definition": "60/cfvs", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "s'"}, "cffh'": {"definition": "gcd(f,h')", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "cffh'"}, "vf''": {"definition": "v''*f''", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "vf''"}, "driprounded": {"definition": "precround(drip,0)", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "driprounded"}, "h": {"definition": "random(2..6)", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "h"}, "cffs'": {"definition": "gcd(f',s')", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "cffs'"}, "hs": {"definition": "h*60", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "hs"}, "h'": {"definition": "h/cfvh", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "h'"}, "f'": {"definition": "f/cffh'", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "f'"}, "f''": {"definition": "f'/cffs'", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "f''"}, "v'": {"definition": "v/cfvh", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "v'"}, "v''": {"definition": "v'/cfvs", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "v''"}, "vf": {"definition": "v*f", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "vf"}, "cfvh": {"definition": "gcd(v,h)", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "cfvh"}, "hs''": {"definition": "h''*s''", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "hs''"}, "cfvs": {"definition": "gcd(v',60)", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "cfvs"}, "drip": {"definition": "(v*f)/(h*60)", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "drip"}, "h''": {"definition": "h'/cffh'", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "h''"}, "s''": {"definition": "s'/cffs'", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "s''"}, "f": {"definition": "random(20,60)", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "f"}}, "preamble": {"css": "", "js": ""}, "functions": {}, "metadata": {"description": "Checking if a student can substitute into an equation. This is a nursing calculation question. Solution is given for with a calculator and without a calculator, however the point of this question is really substitution.&nbsp;&nbsp;", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "advice": "", "rulesets": {}, "type": "question"}, {"name": "Using a formula to convert between Celsius and Fahrenheit", "extensions": [], "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/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Two common formulas used to convert between the units of temperature Celsius (C) and Fahrenheit (F) are:</p>\n<p>$F=\\frac{9}{5}C+32\\quad$ and $\\quad C=\\frac{5}{9}(F-32)$</p>\n<p>(These are actually equivalent equations, each can be rearranged into the other)</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"seed": {"name": "seed", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}, "to": {"name": "to", "group": "Ungrouped variables", "definition": "if(seed=1,latex('\\\\rm C'),latex('\\\\rm F'))", "description": "", "templateType": "anything", "can_override": false}, "from": {"name": "from", "group": "Ungrouped variables", "definition": "if(seed=0,latex('\\\\rm C'),latex('\\\\rm F'))", "description": "", "templateType": "anything", "can_override": false}, "from_temp": {"name": "from_temp", "group": "Ungrouped variables", "definition": "random(-30..300)", "description": "", "templateType": "anything", "can_override": false}, "to_temp": {"name": "to_temp", "group": "Ungrouped variables", "definition": "if(seed=0,9/5*from_temp+32,5*(from_temp-32)/9)", "description": "", "templateType": "anything", "can_override": false}, "to_temp_approx": {"name": "to_temp_approx", "group": "Ungrouped variables", "definition": "precround(to_temp,0)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["seed", "from", "to", "from_temp", "to_temp", "to_temp_approx"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Using one of the above formulas, determine the following</p>\n<p>$\\var{from_temp} ^\\circ\\var{from}=$[[0]] $^\\circ\\var{to}$ (to the nearest whole $^\\circ\\var{to}$)</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><span data-jme-visible=\"seed=0\">Since we know the temperature in Celsius but want it in Fahrenheit the easiest formula to use would be</span></p>\n<p><span data-jme-visible=\"seed=0\">$F=\\frac{9}{5}C+32$.</span></p>\n<p><span data-jme-visible=\"seed=0\">Recall $\\frac{9}{5}C$ means $\\frac{9}{5}\\times C$ or $\\frac{9}{5}$ of $C$.</span></p>\n<p><span data-jme-visible=\"seed=0\">Substituting (replacing) $C$ with what it is worth ($\\var{from_temp}$) gives</span></p>\n<p><span data-jme-visible=\"seed=0\">$F=\\frac{9}{5}\\times\\var{from_temp}+32$.</span></p>\n<p><span data-jme-visible=\"seed=0\">Following the order of operations we find:</span></p>\n<p><span data-jme-visible=\"seed=0\">$\\begin{align*}F&amp;=\\frac{9}{5}\\times\\var{from_temp}+32\\\\&amp;=\\var{9/5*from_temp}+32\\\\&amp;=\\var{to_temp}\\end{align*}$.</span></p>\n<p><span data-jme-visible=\"seed=0\">We round to the nearest whole number (if necessary) to get&nbsp;</span></p>\n<p><span data-jme-visible=\"seed=0\">$\\var{to_temp_approx}^\\circ\\var{to}$.</span></p>\n<p><span data-jme-visible=\"seed=1\">Since we know the temperature in Fahrenheit but want it in Celsius the easiest formula to use would be</span></p>\n<p><span data-jme-visible=\"seed=1\">$C=\\frac{5}{9}(F-32)$.</span></p>\n<p><span data-jme-visible=\"seed=1\">Recall $\\frac{5}{9}$ in front of the bracket means $\\frac{5}{9}$ times the result of the bracket or $\\frac{5}{9}$ of the result of the bracket.</span></p>\n<p><span data-jme-visible=\"seed=1\">Substituting (replacing) $F$ with what it is worth ($\\var{from_temp}$) gives</span></p>\n<p><span data-jme-visible=\"seed=1\">$C=\\frac{5}{9}(\\var{from_temp}-32)$.</span></p>\n<p><span data-jme-visible=\"seed=1\">Following the order of operations we find:</span></p>\n<p><span data-jme-visible=\"seed=1\">$\\begin{align*}C&amp;=\\frac{5}{9}\\times(\\var{from_temp}-32)\\\\&amp;=\\frac{5}{9}\\times \\var{from_temp-32}\\\\&amp;=\\var[fractionNumbers]{to_temp}\\end{align*}$.</span></p>\n<p><span data-jme-visible=\"seed=1\">We round to the nearest whole number (if necessary) to get&nbsp;</span></p>\n<p><span data-jme-visible=\"seed=1\">$\\var{to_temp_approx}^\\circ\\var{to}$.</span></p>\n<p></p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "to_temp", "maxValue": "to_temp", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "BMI calculations", "extensions": [], "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/"}], "tags": ["ephlth", "nursing"], "metadata": {"description": "<p>Given the formula&nbsp;for BMI, students are asked to determine a patient's BMI given their height in cm (as people usually do) and their mass in kg.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Calculate the following <strong>with the use</strong> of a calculator.</p>", "advice": "", "rulesets": {}, "variables": {"upordown": {"name": "upordown", "group": "Ungrouped variables", "definition": "if(bmi6dec>bmi,\"down\",if(bmi6dec<bmi,\"up\",\"\"))", "description": "", "templateType": "anything"}, "height": {"name": "height", "group": "Ungrouped variables", "definition": "random(150..190)", "description": "", "templateType": "anything"}, "bmi6dec": {"name": "bmi6dec", "group": "Ungrouped variables", "definition": "precround(10000*mass/(height^2),6)", "description": "", "templateType": "anything"}, "bmi": {"name": "bmi", "group": "Ungrouped variables", "definition": "precround(10000*mass/(height^2),2)", "description": "", "templateType": "anything"}, "mass": {"name": "mass", "group": "Ungrouped variables", "definition": "random(60..130)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["mass", "height", "bmi", "bmi6dec", "upordown"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A patient has a height of $\\var{height}$ cm&nbsp;and weighs $\\var{mass}$ kg.&nbsp;</p>\n<p>The&nbsp;formula for BMI (Body Mass Index) is</p>\n<p>\\[\\text{BMI}=\\frac{\\text{mass (kg)}}{\\text{height (m)}^2}.\\]&nbsp;</p>\n<p>The patient's BMI to two decimal places is&nbsp;[[0]].</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The equation for BMI&nbsp;is</p>\n<p>\\[\\text{BMI}=\\frac{\\text{mass (kg)}}{\\text{height (m)}^2}\\]&nbsp;</p>\n<p>Notice the units in the formula are kilograms and metres. We convert the $\\var{height}$ cm into metres by moving the decimal point twice to the left to get $\\var{height/100}$ m.&nbsp;</p>\n<p>Using a scientific calculator you&nbsp;can type in \\[\\var{mass}\\div \\var{height/100}^2\\] or by using the fraction button you may be able to type in&nbsp;\\[\\frac{\\var{mass}}{\\var{height/100}^2}\\] and it will give you something like $\\var{bmi6dec}$ which you need to round {upordown} to two decimal places and get <span data-jme-visible=\"mod(bmi*10,1)&lt;&gt;0\">$\\var{bmi}$</span>&nbsp;<span data-jme-visible=\"mod(bmi*10,1)=0 and mod(bmi,1)&lt;&gt;0\">$\\var{bmi}0$</span>&nbsp;<span data-jme-visible=\"mod(bmi,1)=0\">$\\var{bmi}.00$</span></p>\n<p></p>\n<p></p>\n<p>A few things to remark:</p>\n<ul>\n<li>Since the height is given in centimetres you would need to know there <g class=\"gr_ gr_67 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar multiReplace\" id=\"67\" data-gr-id=\"67\">are</g> $100$ cm in $1$ m, so for example, $183$ cm would be $1.83$ m.</li>\n<li>If you were using a non-scientific calculator you would need to know that squaring the height must happen&nbsp;before the division, that is you would need to use brackets as so, $\\var{mass}\\div \\left(\\var{height/100}^2\\right)$.</li>\n<li>If you had a pocket calculator you may need to know that $\\text{height}^2=\\text{height}\\times\\text{height}$ and you would have to do a few separate calculations one after the other, or you could do $(\\var{mass}\\div\\var{height/100})\\div\\var{height/100}$.</li>\n</ul>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{bmi}", "maxValue": "{bmi}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Substituting values into algebraic expressions", "extensions": [], "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/"}], "tags": ["algebra", "Algebra", "evaluating", "substituting", "substitution", "Substitution"], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"disans": {"name": "disans", "group": "Discriminant", "definition": "bval^2-4*aval*cval", "description": "", "templateType": "anything", "can_override": false}, "yval": {"name": "yval", "group": "Circle", "definition": "random(-7..7 except [0,cval,xval])", "description": "", "templateType": "anything", "can_override": false}, "aval": {"name": "aval", "group": "Discriminant", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything", "can_override": false}, "cirans": {"name": "cirans", "group": "Circle", "definition": "(xval-aval)^2+(yval-cval)^2", "description": "", "templateType": "anything", "can_override": false}, "xval": {"name": "xval", "group": "Circle", "definition": "random(-7..7 except [0,aval])", "description": "", "templateType": "anything", "can_override": false}, "bval": {"name": "bval", "group": "Discriminant", "definition": "random(-12..12)", "description": "", "templateType": "anything", "can_override": false}, "cval": {"name": "cval", "group": "Discriminant", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "switch(seed=0,cirans,seed=1,disans,seed=2,mans,\"error\")", "description": "", "templateType": "anything", "can_override": false}, "v_sig_figs": {"name": "v_sig_figs", "group": "relativistic mass", "definition": "random(1..2.9#0.01)", "description": "<p>significant figures of velocity</p>", "templateType": "anything", "can_override": false}, "m0": {"name": "m0", "group": "relativistic mass", "definition": "random(1..1000)", "description": "", "templateType": "anything", "can_override": false}, "mans": {"name": "mans", "group": "relativistic mass", "definition": "precround(m0/(sqrt(1-(v_sig_figs/3)^2)),2)", "description": "", "templateType": "anything", "can_override": false}, "seed": {"name": "seed", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": true}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "'x'", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "'y'", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["ans", "seed", "x", "y"], "variable_groups": [{"name": "Circle", "variables": ["xval", "yval", "cirans"]}, {"name": "Discriminant", "variables": ["aval", "bval", "cval", "disans"]}, {"name": "relativistic mass", "variables": ["m0", "mans", "v_sig_figs"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><span data-jme-visible=\"seed=1\">Given $a=\\var{aval}$, $b=\\var{bval}$ and $c=\\var{cval}$, the value of $b^2-4ac$ is&nbsp;</span> <span data-jme-visible=\"seed=0\">If $x=\\var{xval}$ and $y=\\var{yval}$ then $\\simplify{(x-{aval})^2+(y-{cval})^2}$ =&nbsp;</span><span data-jme-visible=\"seed=0\"></span> <span data-jme-visible=\"seed=2\">Suppose $m_0=\\var{m0}$, $v=\\var{v_sig_figs}\\times 10^8$, $c=3\\times 10^8$ and $m=\\dfrac{m_0}{\\sqrt{1-\\frac{v^2}{c^2}}}$. Then we have $m=$</span>&nbsp; [[0]] <span data-jme-visible=\"seed=2\">(rounded to two decimal places)</span></p>\n<p>&nbsp;</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><em>Be mindful of the order of operations and negatives when evaluating expressions.</em></p>\n<p><em></em></p>\n<p><span data-jme-visible=\"seed=1\">Substituting $a=\\var{aval}$, $b=\\var{bval}$ and $c=\\var{cval}$ into $b^2-4ac$ gives</span></p>\n<p><span data-jme-visible=\"seed=1\"><em></em>\\[(\\var{bval})^2-4(\\var{aval})(\\var{cval})=\\simplify[basic]{{bval^2}-4{aval}{cval}}=\\simplify[basic]{{bval^2}+{-4*aval*cval}}=\\var{disans}.\\]</span></p>\n<p><span data-jme-visible=\"seed=0\">Substituting $x=\\var{xval}$ and $y=\\var{yval}$ into $\\simplify{(x-{aval})^2+(y-{cval})^2}$ &nbsp;gives</span></p>\n<p><span data-jme-visible=\"seed=0\">\\[\\simplify[basic]{({xval}-{aval})^2+({yval}-{cval})^2}=(\\var{xval-aval})^2+(\\var{yval-cval})^2=\\var{(xval-aval)^2}+\\var{(yval-cval)^2}=\\var{cirans}.\\]</span></p>\n<p><span data-jme-visible=\"seed=2\">Substituting $m_0=\\var{m0}$, $v=\\var{v_sig_figs}\\times 10^8$ and $c=3\\times 10^8$ into $m=\\dfrac{m_0}{\\sqrt{1-\\frac{v^2}{c^2}}}$ gives</span></p>\n<p><span data-jme-visible=\"seed=2\">\\[m=\\dfrac{\\var{m0}}{\\sqrt{1-\\frac{(\\var{v_sig_figs}\\times 10^8)^2}{(3 \\times 10^8)^2}}}=\\var{mans} \\quad\\text{ (to two decimal places).}\\]</span></p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ans", "maxValue": "ans", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": false, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": "", "allowAttemptDownload": false, "downloadEncryptionKey": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "end_message": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": [], "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "inreview"}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "type": "exam", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "extensions": [], "custom_part_types": [], "resources": []}