// Numbas version: finer_feedback_settings
{"name": "Numbas Test", "duration": 0, "metadata": {"description": "<p>This is a test of the Numbas math question examiner</p>", "licence": "All rights reserved"}, "allQuestions": true, "shuffleQuestions": true, "percentPass": 0, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "pickQuestions": 0, "navigation": {"onleave": {"action": "none", "message": ""}, "reverse": true, "allowregen": true, "showresultspage": "oncompletion", "preventleave": true, "browse": true, "showfrontpage": true}, "feedback": {"showtotalmark": true, "advicethreshold": 0, "showanswerstate": true, "showactualmark": true, "allowrevealanswer": true, "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "never"}, "type": "exam", "questions": [], "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-shuffled", "pickQuestions": 0, "questions": [{"name": "Adding Decimals", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Rob Cade", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/70/"}], "functions": {}, "ungrouped_variables": ["num1", "num2", "ans1", "num3", "num4", "ans2", "num5", "num6", "ans3", "num7", "num8", "ans4"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>THere is no advice for this question.</p>", "rulesets": {}, "parts": [{"prompt": "<p>What's&nbsp; $\\var{num1} + \\var{num2} $?&nbsp;</p>\n<p>Please give your answer with exactly 1 decimal place.</p>\n<p>Answer: $\\var{num1} + \\var{num2} =$ [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "1", "maxValue": "ans1", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "ans1", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>What's&nbsp; $\\var{num3} + \\var{num4} $?&nbsp;</p>\n<p>Please give your answer with exactly 2 decimal places.</p>\n<p>Answer: $\\var{num3} + \\var{num4} =$ [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "ans2", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "ans2", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>What's&nbsp; $\\var{num7} + \\var{num8} $?&nbsp;</p>\n<p>Please give your answer with exactly 3 decimal places.</p>\n<p>Answer: $\\var{num7} + \\var{num8} =$ [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "ans4", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "ans4", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>What's&nbsp; $\\var{num5} + \\var{num6} $?&nbsp;</p>\n<p>Please give your answer with exactly 3 decimal places.</p>\n<p>Answer: $\\var{num5} + \\var{num6} =$ [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "ans3", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "ans3", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Try these without using a calculator.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"num4": {"definition": "random(1..5)+random(1..5)/10 +random(1..5)/100", "templateType": "anything", "group": "Ungrouped variables", "name": "num4", "description": ""}, "num5": {"definition": "random(1..5)+random(1..5)/100 +random(1..5)/1000", "templateType": "anything", "group": "Ungrouped variables", "name": "num5", "description": ""}, "num6": {"definition": "random(1..5)+random(1..5)/100 +random(1..5)/1000", "templateType": "anything", "group": "Ungrouped variables", "name": "num6", "description": ""}, "num7": {"definition": " random(1..5)+random(1..5)/10 +random(1..5)/100", "templateType": "anything", "group": "Ungrouped variables", "name": "num7", "description": ""}, "num1": {"definition": "random(1..5)+random(1..5)/10", "templateType": "anything", "group": "Ungrouped variables", "name": "num1", "description": ""}, "num2": {"definition": "random(1..5)+random(1..5)/10", "templateType": "anything", "group": "Ungrouped variables", "name": "num2", "description": ""}, "num3": {"definition": "random(1..5)+random(1..5)/10 +random(1..5)/100", "templateType": "anything", "group": "Ungrouped variables", "name": "num3", "description": ""}, "ans1": {"definition": "num1+num2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "num3+num4", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "num5+num6", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "num8": {"definition": "random(1..5)+random(1..5)/10 +random(1..5)/100+random(1..5)/1000", "templateType": "anything", "group": "Ungrouped variables", "name": "num8", "description": ""}, "ans4": {"definition": "num7+num8", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "description": ""}}, "metadata": {"description": "<p>Four questions, of increasing complexity, involving addition of decimals.&nbsp; These should all be solvable without using a calculator.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Adding fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Rob Cade", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/70/"}], "functions": {}, "ungrouped_variables": ["denom1", "num1", "denom2", "num2", "lcm", "num1b", "num2b", "num3", "denom3", "num1simp", "denom1simp", "num2simp", "denom2simp", "prompts", "prompt"], "tags": [], "advice": "<p>See step for part b.</p>", "rulesets": {"std": ["all"]}, "parts": [{"prompt": "<p>We want to find:</p>\n<div class=\"fractiontable\">\n<table>\n<tbody>\n<tr>\n<td class=\"tdnum\">{num1simp}</td>\n<td class=\"tdeq\">+</td>\n<td class=\"tdnum\">{num2simp}</td>\n</tr>\n<tr>\n<td class=\"tddenom\">{denom1simp}</td>\n<td></td>\n<td class=\"tddenom\">{denom2simp}</td>\n</tr>\n</tbody>\n</table>\n</div>\n<p>We need to write the fractions with the same \"denominator\" (the number on the bottom).</p>\n<p>What's the smallest number that divides by {denom1simp} and {denom2simp}&nbsp; (the \"lowest common multiple\")?&nbsp;</p>\n<p>Answer: the lowest common multiple of&nbsp; {denom1simp} and {denom2simp} = [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "lcm", "minValue": "lcm", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>So we can write both fractions as something over the lowest comon multiple.</p>\n<p>Then we can add the numerators (the numbers on the top).</p>\n<p>$\\var{prompt} $</p>\n<div class=\"fractiontable\">\n<table>\n<tbody>\n<tr>\n<td class=\"tdnum\">{num1simp}</td>\n<td class=\"tdeq\">+</td>\n<td class=\"tdnum\">{num2simp}</td>\n<td class=\"tdeq\">=</td>\n<td class=\"tdnum\">[[0]]</td>\n<td class=\"tdeq\">+</td>\n<td class=\"tdnum\">[[1]]</td>\n<td class=\"tdeq\">=</td>\n<td class=\"tdnum\">[[4]]</td>\n</tr>\n<tr>\n<td class=\"tddenom\">{denom1simp}</td>\n<td></td>\n<td class=\"tddenom\">{denom2simp}</td>\n<td></td>\n<td class=\"tddenom\">[[2]]</td>\n<td></td>\n<td class=\"tddenom\">[[3]]</td>\n<td></td>\n<td class=\"tddenom\">[[5]]</td>\n</tr>\n</tbody>\n</table>\n</div>\n<pre></pre>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "num1b", "minValue": "num1b", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "num2b", "minValue": "num2b", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "lcm", "minValue": "lcm", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "lcm", "minValue": "lcm", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "num3", "minValue": "num3", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "denom3", "minValue": "denom3", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>The lowest common multiple of $\\var{denom1simp}$&nbsp; and $\\var{denom2simp}$&nbsp; is&nbsp; $\\var{lcm}$</p>\n<p>So you need to write $\\frac {\\var{num1simp}} {\\var{denom1simp}}$ as $\\frac {something} {\\var{lcm}}$ = $\\frac {?} {\\var{lcm}}$&nbsp;</p>\n<p>and write $\\frac {\\var{num2simp}} {\\var{denom2simp}}$ as $\\frac {something} {\\var{lcm}}$ = $\\frac {?} {\\var{lcm}}$&nbsp;</p>\n<p>Then you can add the numerators .</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}], "statement": "<p>Adding 2 fractions with different denominators.</p>", "variable_groups": [], "variablesTest": {"maxRuns": "100", "condition": "((num1simp/denom1simp)+ (num2simp/denom2simp) <1)"}, "preamble": {"css": ".fractiontable table {\n  width: 10%; \n  padding: 0px; \n  border-width: 0px; \n  layout: fixed;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  width: 15%; \n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n.fractiontable .tdeq \n{\n  width: 5%; \n  border-bottom: 0px;\n  font-size:x-large;\n}\n\n\n.fractiontable th {\n    background-color:#aaa;\n}\n/*Fix the height of all cells EXCEPT table-headers to 40px*/\n.fractiontable td {\n    height:40px;\n}\n", "js": ""}, "variables": {"denom1": {"definition": "random(2..12)\n", "templateType": "anything", "group": "Ungrouped variables", "name": "denom1", "description": ""}, "num2b": {"definition": "num2simp*lcm/denom2simp", "templateType": "anything", "group": "Ungrouped variables", "name": "num2b", "description": ""}, "denom3": {"definition": "lcm/gcd(num1b+num2b, lcm)", "templateType": "anything", "group": "Ungrouped variables", "name": "denom3", "description": ""}, "denom2": {"definition": "random(2..12 except denom1)", "templateType": "anything", "group": "Ungrouped variables", "name": "denom2", "description": ""}, "num1b": {"definition": "num1simp*lcm/denom1simp", "templateType": "anything", "group": "Ungrouped variables", "name": "num1b", "description": ""}, "num1": {"definition": "denom1-random(1..denom1-1) //make sure the numerator's bigger than denom\n", "templateType": "anything", "group": "Ungrouped variables", "name": "num1", "description": ""}, "num2": {"definition": "denom2-random(1..denom2-1) //make sure the numerator's bigger than denom", "templateType": "anything", "group": "Ungrouped variables", "name": "num2", "description": ""}, "num3": {"definition": "(num1b+num2b)/gcd(num1b+num2b, lcm)", "templateType": "anything", "group": "Ungrouped variables", "name": "num3", "description": ""}, "num1simp": {"definition": "num1/gcd(num1, denom1)", "templateType": "anything", "group": "Ungrouped variables", "name": "num1simp", "description": ""}, "prompts": {"definition": "[ \"Make sure you show the result in its simplest form:  you\\'ll have to cancel ...\", \" \" ]", "templateType": "list of strings", "group": "Ungrouped variables", "name": "prompts", "description": ""}, "denom1simp": {"definition": "denom1/gcd(num1,denom1)", "templateType": "anything", "group": "Ungrouped variables", "name": "denom1simp", "description": ""}, "denom2simp": {"definition": "denom2/gcd(num2,denom2)", "templateType": "anything", "group": "Ungrouped variables", "name": "denom2simp", "description": ""}, "num2simp": {"definition": "num2/gcd(num2, denom2)", "templateType": "anything", "group": "Ungrouped variables", "name": "num2simp", "description": ""}, "prompt": {"definition": "switch(gcd(num1b+num2b,lcm)>1, prompts[0], prompts[1])", "templateType": "anything", "group": "Ungrouped variables", "name": "prompt", "description": ""}, "lcm": {"definition": "lcm(denom1simp,denom2simp)\n", "templateType": "anything", "group": "Ungrouped variables", "name": "lcm", "description": ""}}, "metadata": {"description": "<p>Practice of adding fractions.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Decimal to Percentage", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Rob Cade", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/70/"}], "functions": {}, "ungrouped_variables": ["a1", "p2", "p1", "a2"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p><span style=\"text-decoration: underline;\"><strong>To convert a decimal to a percentage</strong></span></p>\n  <ol>\n  <li>Move the decimal point 2 places to the right.</li>\n  </ol>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>What is $\\var{a1}$ expressed as a percentage?&nbsp; [[0]]%</p>\n      <p>&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{p1}", "minValue": "{p1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>To&nbsp; convert $\\var{a1}$&nbsp; to&nbsp; a&nbsp; percentage,&nbsp; move&nbsp; the&nbsp; decimal&nbsp; point&nbsp; 2&nbsp; places&nbsp; to&nbsp; the&nbsp; right.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"prompt": "<p>What is $\\var{a2}$ expressed as a percentage?&nbsp; [[0]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{p2}", "minValue": "{p2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Converting Decimals to Percentages.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a1": {"definition": "random(0..1)+random(0..99)/100", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "p2": {"definition": "100*a2", "templateType": "anything", "group": "Ungrouped variables", "name": "p2", "description": ""}, "p1": {"definition": "100*a1", "templateType": "anything", "group": "Ungrouped variables", "name": "p1", "description": ""}, "a2": {"definition": "random(0..1)+random(0..999)/1000", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}}, "metadata": {"description": "<p>Converting decimals to percentages.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Dividing by a decimal", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Rob Cade", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/70/"}], "functions": {}, "ungrouped_variables": ["basedividend", "divisor", "poweroften", "dividendredux", "numdp1", "basedivisor", "answer", "dividend"], "tags": ["decimals"], "advice": "<p>See step.</p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>What's $\\var{dividend}$ divided by $\\var{divisor}$?</p>\n        <p>Answer: $\\var{dividend}$ divided by $\\var{divisor}$ = [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{answer}", "minValue": "{answer}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>We want to find $\\frac {\\var{dividend}} {\\var{divisor}}$</p>\n          <p>$\\var{divisor} $ has $\\var{numdp1}$ number(s) after the decimal point.</p>\n          <p>So we need to move the decimal point $\\var{numdp1}$ place(s) to the right to turn it into a whole number.</p>\n          <p>So we have to multiply $\\var{divisor} $ by $\\var{powerOfTen}$</p>\n          <p>If we multiply the bottom of the fraction by $\\var{powerOfTen}$, we'll have to multiply the top by $\\var{powerOfTen}$, too.</p>\n          <p>That will give us $\\frac {\\var{dividendredux}} {\\var{basedivisor}}$ = ?</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}], "statement": "<p>Try this without using a calculator.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"basedividend": {"definition": "random(0..3)*10 + random(0..3)+ random(0..5 except 0) * 0.1", "templateType": "anything", "group": "Ungrouped variables", "name": "basedividend", "description": ""}, "divisor": {"definition": "baseDivisor*10^(-numdp1)", "templateType": "anything", "group": "Ungrouped variables", "name": "divisor", "description": ""}, "poweroften": {"definition": "10^numdp1", "templateType": "anything", "group": "Ungrouped variables", "name": "poweroften", "description": ""}, "dividendredux": {"definition": "dividend*10^numdp1", "templateType": "anything", "group": "Ungrouped variables", "name": "dividendredux", "description": ""}, "numdp1": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "numdp1", "description": ""}, "basedivisor": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "basedivisor", "description": ""}, "answer": {"definition": "dividend / divisor", "templateType": "anything", "group": "Ungrouped variables", "name": "answer", "description": ""}, "dividend": {"definition": "baseDividend * baseDivisor", "templateType": "anything", "group": "Ungrouped variables", "name": "dividend", "description": ""}}, "metadata": {"description": "<p>Practice of dividing by a decimal.&nbsp; This should be solvable without using a calculator.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Dividing by a fraction", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Rob Cade", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/70/"}], "functions": {}, "ungrouped_variables": ["denom1", "num1", "denom2", "num2", "num3", "denom3", "num1simp", "denom1simp", "num2simp", "denom2simp", "prompts", "prompt"], "tags": [], "preamble": {"css": ".fractiontable table {\n  width: 10%; \n  padding: 0px; \n  border-width: 0px; \n  layout: fixed;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  width: 15%; \n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n.fractiontable .tdeq \n{\n  width: 5%; \n  border-bottom: 0px;\n  font-size: x-large;\n}\n\n\n.fractiontable th {\n    background-color:#aaa;\n}\n/*Fix the height of all cells EXCEPT table-headers to 40px*/\n.fractiontable td {\n    height:40px;\n}\n", "js": ""}, "advice": "<p>See steps.</p>", "rulesets": {"std": ["all"]}, "parts": [{"stepsPenalty": 0, "prompt": "<p>We want to find:</p>\n<div class=\"fractiontable\">\n<table>\n<tbody>\n<tr>\n<td class=\"tdnum\">{num1simp}</td>\n<td class=\"tdeq\">&divide;</td>\n<td class=\"tdnum\">{num2simp}</td>\n</tr>\n<tr>\n<td class=\"tddenom\">{denom1simp}</td>\n<td></td>\n<td class=\"tddenom\">{denom2simp}</td>\n</tr>\n</tbody>\n</table>\n</div>\n<p>To divide by a fraction, turn it upsidedown and then multiply by the result.</p>\n<p>$\\var{prompt} $</p>\n<div class=\"fractiontable\">\n<table>\n<tbody>\n<tr>\n<td class=\"tdnum\">{num1simp}</td>\n<td class=\"tdeq\">&divide;</td>\n<td class=\"tdnum\">{num2simp}</td>\n<td class=\"tdeq\">=</td>\n<td class=\"tdnum\">{num1simp}</td>\n<td class=\"tdeq\">&times;</td>\n<td class=\"tdnum\">[[0]]</td>\n<td class=\"tdeq\">=</td>\n<td class=\"tdnum\">[[1]]</td>\n</tr>\n<tr>\n<td class=\"tddenom\">{denom1simp}</td>\n<td></td>\n<td class=\"tddenom\">{denom2simp}</td>\n<td></td>\n<td class=\"tddenom\">{denom1simp}</td>\n<td></td>\n<td class=\"tddenom\">[[2]]</td>\n<td></td>\n<td class=\"tddenom\">[[3]]</td>\n</tr>\n</tbody>\n</table>\n</div>\n<pre></pre>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "denom2simp", "minValue": "denom2simp", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "(num1simp*denom2simp)/gcd(num1simp*denom2simp,num2simp*denom1simp)", "minValue": "(num1simp*denom2simp)/gcd(num1simp*denom2simp,num2simp*denom1simp)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "num2simp", "minValue": "num2simp", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "(num2simp*denom1simp)/gcd(num1simp*denom2simp,num2simp*denom1simp)", "minValue": "(num2simp*denom1simp)/gcd(num1simp*denom2simp,num2simp*denom1simp)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>Turn the second fraction upsidedown, then multiply by the result.</p>\n<p>So you'll have to do $\\frac {\\var{num1simp }} {\\var{denom1simp}} &times; \\frac {\\var{denom2simp }} {\\var{num2simp}} $</p>\n<p>The top (or numerator) of the product = {num1simp} &times; {denom2simp} = ?</p>\n<p>The bottom (or denominator) of the product = {denom1simp} &times; {num2simp} = ?</p>\n<p>Remember to cancel the result if you can.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}], "statement": "<p>&nbsp;How to divide by a fraction.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "(num1simp*denom2simp)/(num2simp*denom1simp)<1"}, "variables": {"denom1": {"definition": "random(2..5)\n", "templateType": "anything", "group": "Ungrouped variables", "name": "denom1", "description": ""}, "denom3": {"definition": "(denom1simp*denom2simp)/gcd(num1simp*num2simp, denom1simp*denom2simp)", "templateType": "anything", "group": "Ungrouped variables", "name": "denom3", "description": ""}, "denom2": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "denom2", "description": ""}, "prompt": {"definition": "switch(gcd(num1simp*denom2simp,denom1simp*num2simp)>1, prompts[0],prompts[1])", "templateType": "anything", "group": "Ungrouped variables", "name": "prompt", "description": ""}, "num1": {"definition": "denom1-random(1..denom1-1) //make sure the numerator's bigger than denom\n", "templateType": "anything", "group": "Ungrouped variables", "name": "num1", "description": ""}, "num2": {"definition": "denom2-random(1..denom2-1) //make sure the numerator's bigger than denom", "templateType": "anything", "group": "Ungrouped variables", "name": "num2", "description": ""}, "num3": {"definition": "(num1simp*num2simp)/gcd(num1simp*num2simp, denom1simp*denom2simp)", "templateType": "anything", "group": "Ungrouped variables", "name": "num3", "description": ""}, "num1simp": {"definition": "num1/gcd(num1, denom1)", "templateType": "anything", "group": "Ungrouped variables", "name": "num1simp", "description": ""}, "prompts": {"definition": "[ \"Make sure you show the result in its simplest form:  you\\'ll have to cancel ...\", \" \" ]", "templateType": "list of strings", "group": "Ungrouped variables", "name": "prompts", "description": ""}, "denom1simp": {"definition": "denom1/gcd(num1,denom1)", "templateType": "anything", "group": "Ungrouped variables", "name": "denom1simp", "description": ""}, "denom2simp": {"definition": "denom2/gcd(num2,denom2)", "templateType": "anything", "group": "Ungrouped variables", "name": "denom2simp", "description": ""}, "num2simp": {"definition": "num2/gcd(num2, denom2)", "templateType": "anything", "group": "Ungrouped variables", "name": "num2simp", "description": ""}}, "metadata": {"description": "<p>Pratice of dividing by a fraction.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Pythagorean Identity recognition", "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": ["Pythagoras", "pythagoras", "Trigonometry", "trigonometry"], "metadata": {"description": "<p>Using $\\cos^2\\theta+\\sin^2\\theta=1$ to evaluate expressions.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>The following questions require some familiarity with trigonometric identities.&nbsp;</p>\n<p></p>", "advice": "<p>We will use&nbsp;the following Pythagorean identity &nbsp;\\[\\cos^2\\theta+\\sin^2\\theta=1.\\]&nbsp;</p>\n<p>For part a)</p>\n<p><span data-jme-visible=\"qu=1\">Given&nbsp;$\\simplify{(cos^2(x)+sin^2(x))^{m1}+{m2}}$ we can replace $\\cos^2(x)+\\sin^2(x)$ with $1$. So our expression is $\\simplify{1^{m1}+{m2}}$. Therefore our expression simplifies to $\\var{m2+1}$.</span></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\"><span data-jme-visible=\"qu=2\">$\\simplify{{m1}+{m2}(2-sin^2(y)-cos^2(y))}$</span></td>\n<td style=\"text-align: center;\"><span data-jme-visible=\"qu=2\">$=$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"qu=2\">$\\simplify{{m1}+{m2}(2-(sin^2(y)+cos^2(y)))}$</span></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\"><span data-jme-visible=\"qu=2\">$=$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"qu=2\">$\\simplify[!collectNumbers]{{m1}+{m2}(2-1)}$</span></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\"><span data-jme-visible=\"qu=2\">$=$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"qu=2\">$\\simplify[!collectNumbers]{{m1}+{m2}}$</span></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\"><span data-jme-visible=\"qu=2\">$=$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"qu=2\">$\\var{m1+m2}$</span></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\"><span data-jme-visible=\"qu=3\">$\\simplify{{m1^2}cos^4(z)+{2*m1^2}cos^2(z)sin^2(z)+{m1^2}sin^4(z)}$</span></td>\n<td style=\"text-align: center;\"><span data-jme-visible=\"qu=3\">$=$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"qu=3\">$\\simplify{{m1^2}(cos^4(z)+2cos^2(z)sin^2(z)+sin^4(z))}$</span></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\"><span data-jme-visible=\"qu=3\">$=$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"qu=3\">$\\simplify{{m1^2}(cos^2(z)+sin^2(z))^2}$</span></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\"><span data-jme-visible=\"qu=3\">$=$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"qu=3\">$\\var{m1^2}\\times 1^2$</span></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\"><span data-jme-visible=\"qu=3\">$=$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"qu=3\">$\\var{m1^2}$</span></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>For part b)</p>\n<p><span data-jme-visible=\"sw=1 or sw=2\">Rearranging the&nbsp;Pythagorean identity $\\cos^2\\theta+\\sin^2\\theta=1$ for $\\sin\\theta$ gives the equation \\[\\sin\\theta=\\pm\\sqrt{1-\\cos^2\\theta}\\]</span></p>\n<p><span data-jme-visible=\"sw=1 or sw=2\">Recall that $\\sin\\theta$ is the $y$ value of a point on the unit circle, whether $\\sin\\theta$ is taken as the postive square root or as the negative square root depends on the whether the&nbsp;point on the circle is on the top semicircle (positive $y$ value) or the bottom semicircle (negative $y$ value).</span></p>\n<p><span data-jme-visible=\"sw=1\">Since we are told $\\theta$ is in the first or second quadrant, the $y$ value must be postive, that is $\\sin\\theta=\\sqrt{1-\\cos^2\\theta}$. Therefore our expresson simplifies as follows</span></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\"><span data-jme-visible=\"sw=1\">$\\simplify{{n}sin(theta)-{n}sqrt(1-cos^2(theta))}$</span></td>\n<td><span data-jme-visible=\"sw=1\">$=$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"sw=1\">$\\simplify{{n}sin(theta)-{n}sin(theta)}$</span></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td><span data-jme-visible=\"sw=1\">$=$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"sw=1\">$0$</span></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p><span data-jme-visible=\"sw=2\">Since we are told $\\theta$ is in the third or fourth&nbsp;quadrant, the $y$ value must be negative, that is $\\sin\\theta=-\\sqrt{1-\\cos^2\\theta}$ or equivalently $-\\sin\\theta=\\sqrt{1-\\cos^2\\theta}$. Therefore our expresson simplifies as follows</span></p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\"><span data-jme-visible=\"sw=2\">$\\simplify{{n}sin(theta)-{n}sqrt(1-cos^2(theta))}$</span></td>\n<td><span data-jme-visible=\"sw=2\">$=$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"sw=2\">$\\simplify{{n}sin(theta)-{n}sin(theta)}$</span></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td><span data-jme-visible=\"sw=2\">$=$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"sw=2\">$0$</span></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p><span data-jme-visible=\"sw=3 or sw=4\">Rearranging the&nbsp;Pythagorean identity $\\cos^2\\theta+\\sin^2\\theta=1$ for $\\cos\\theta$ gives the equation \\[\\cos\\theta=\\pm\\sqrt{1-\\sin^2\\theta}\\]</span></p>\n<p><span data-jme-visible=\"sw=3 or sw=4\">Recall that $\\cos\\theta$ is the $x$ value of a point on the unit circle, whether $\\cos\\theta$ is taken as the postive square root or as the negative square root depends on the whether the&nbsp;point on the circle is on the right&nbsp;semicircle (positive $x$ value) or the left&nbsp;semicircle (negative $x$ value).</span></p>\n<p><span data-jme-visible=\"sw=3\">Since we are told $\\theta$ is in the first or fourth&nbsp;quadrant, the $x$ value must be postive, that is $\\cos\\theta=\\sqrt{1-\\sin^2\\theta}$. Therefore our expresson simplifies as follows</span></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\"><span data-jme-visible=\"sw=3\">$\\simplify{{n}cos(theta)-{n}sqrt(1-sin^2(theta))}$</span></td>\n<td><span data-jme-visible=\"sw=3\">$=$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"sw=3\">$\\simplify{{n}cos(theta)-{n}cos(theta)}$</span></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td><span data-jme-visible=\"sw=3\">$=$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"sw=3\">$0$</span></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p><span data-jme-visible=\"sw=4\">Since we are told $\\theta$ is in the second or third quadrant, the $x$ value must be negative, that is $\\cos\\theta=-\\sqrt{1-\\sin^2\\theta}$ or equivalently $-\\cos\\theta=\\sqrt{1-\\sin^2\\theta}$. Therefore our expresson simplifies as follows</span></p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\"><span data-jme-visible=\"sw=4\">$\\simplify{{n}cos(theta)-{n}sqrt(1-sin^2(theta))}$</span></td>\n<td><span data-jme-visible=\"sw=4\">$=$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"sw=4\">$\\simplify{{n}cos(theta)-{n}cos(theta)}$</span></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td><span data-jme-visible=\"sw=4\">$=$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"sw=4\">$0$</span></td>\n</tr>\n</tbody>\n</table>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"n": {"name": "n", "group": "Ungrouped variables", "definition": "random(-12..12 except [0,m1,m2])", "description": "", "templateType": "anything", "can_override": false}, "qu": {"name": "qu", "group": "Ungrouped variables", "definition": "random(1..3)", "description": "", "templateType": "anything", "can_override": false}, "m1": {"name": "m1", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "m2": {"name": "m2", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}, "sw": {"name": "sw", "group": "Ungrouped variables", "definition": "random(1..4)", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "if(qu=1,m2+1,if(qu=2,m1+m2,m1^2))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["qu", "m1", "m2", "ans", "sw", "n"], "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>The expression&nbsp;</p>\n<p><span data-jme-visible=\"qu=1\">\\[\\simplify{(cos^2(x)+sin^2(x))^{m1}+{m2}}\\] </span><span data-jme-visible=\"qu=2\">\\[\\simplify{{m1}+{m2}(2-sin^2(y)-cos^2(y))}\\]&nbsp;</span><span data-jme-visible=\"qu=3\">\\[\\simplify{{m1^2}cos^4(z)+{2*m1^2}cos^2(z)sin^2(z)+{m1^2}sin^4(z)}\\]</span></p>\n<p>can be simplified to&nbsp;[[0]].</p>\n<p><strong>Note:</strong> For this question, your answer should be a number.</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}, {"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>The expression</p>\n<p><span data-jme-visible=\"sw=1\">\\[\\simplify{{n}sin(theta)-{n}sqrt(1-cos^2(theta))}\\]</span>&nbsp;<span data-jme-visible=\"sw=2\">\\[\\simplify{{n}sin(theta)+{n}sqrt(1-cos^2(theta))}\\]</span><span data-jme-visible=\"sw=3\">\\[\\simplify{{n}cos(theta)-{n}sqrt(1-sin^2(theta))}\\]</span>&nbsp;<span data-jme-visible=\"sw=4\">\\[\\simplify{{n}cos(theta)+{n}sqrt(1-sin^2(theta))}\\]</span></p>\n<p>can be&nbsp;simplified to&nbsp;[[0]]&nbsp;for $\\theta$ in the <span data-jme-visible=\"sw=1\">first or second quadrant.</span> <span data-jme-visible=\"sw=2\">third or fourth&nbsp;quadrant.&nbsp;</span><span data-jme-visible=\"sw=3\">&nbsp;first or fourth quadrant.</span> <span data-jme-visible=\"sw=4\">second or third quadrant.</span></p>\n<p><strong>Note:</strong> For this question, your answer should be a number.</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": "0", "maxValue": "0", "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", "type": "question"}]}], "contributors": [{"name": "Myles Thies", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/853/"}], "extensions": [], "custom_part_types": [], "resources": []}