// Numbas version: finer_feedback_settings
{"showQuestionGroupNames": false, "percentPass": 0, "name": "Maths refresher self diagnostic test 2", "metadata": {"description": "", "licence": "None specified"}, "question_groups": [{"pickQuestions": 1, "name": "Group", "pickingStrategy": "all-ordered", "questions": [{"name": "Temperature arithmetic", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}], "functions": {}, "ungrouped_variables": ["stockholm", "rise"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"displayColumns": 0, "prompt": "<p>The temperature in Stockholm is $\\var{stockholm}^\\circ\\mbox{C}$. In Plymouth, it is $\\var{rise}^\\circ\\mbox{C}$ warmer. 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{"description": "<p>This question tests ability to calculate differences using negative numbers in context.</p>", "licence": "None specified"}, "type": "question"}, {"name": "Rounding to a whole number", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}], "functions": {}, "ungrouped_variables": ["round_me", "rounded_number"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>Round $\\var{round_me}$ to the nearest whole number.</p>\n<p>Answer: [[0]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "rounded_number", "minValue": 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{"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}], "functions": {}, "ungrouped_variables": ["base_1", "base_2"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"maxAnswers": 0, "displayColumns": 0, "prompt": "<p>Work out $\\var{base_1}^2+\\var{base_2}^2$.</p>", "matrix": [0, 0, 0, "1"], "shuffleChoices": false, "variableReplacements": [], "minAnswers": 0, "variableReplacementStrategy": "originalfirst", "maxMarks": 0, "distractors": ["", "", "", ""], "showCorrectAnswer": true, "scripts": {}, "warningType": "none", "marks": 0, "choices": ["<p>$\\simplify{{base_1}^2}$</p>", "<p>$\\simplify{{base_1}^2+{base_2}}$</p>", "<p>$\\simplify{{base_1}+{base_2}^2}$</p>", "<p>$\\simplify{{base_1}^2+{base_2}^2}$</p>"], "type": "m_n_2", "displayType": "checkbox", "minMarks": 0}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"base_1": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "base_1", "description": ""}, "base_2": {"definition": "random(2..9 except base_1)", "templateType": "anything", "group": "Ungrouped variables", "name": "base_2", "description": ""}}, "metadata": {"description": "", "licence": "None specified"}, "type": "question"}, {"name": "Linear equation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}], "functions": {}, "ungrouped_variables": ["const_1", "const_2"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>If $\\var{const_2}-x=\\var{const_1}$, what is the value of $x$?</p>\n<p>Answer: [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "const_2-const_1", "minValue": "const_2-const_1", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"const_2": {"definition": "random((1+const_1)..(15+const_1))", "templateType": "anything", "group": "Ungrouped variables", "name": "const_2", "description": ""}, "const_1": {"definition": "random(15..29 except 20)", "templateType": "anything", "group": "Ungrouped variables", "name": "const_1", "description": ""}}, "metadata": {"description": "", "licence": "None 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What is the volume of the cube?</p>\n<p><img src=\"resources/question-resources/Cuboid_simple.svg.png\" height=\"220\" width=\"354\"/></p>\n<p>Answer: [[0]] $\\mbox{cm}^3$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "width*height*depth", "minValue": "width*height*depth", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"width": {"definition": "random(7..11 except 10)", "templateType": "anything", "group": "Ungrouped variables", "name": "width", "description": ""}, "depth": {"definition": "random(3..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "depth", "description": ""}, "height": {"definition": "random(4..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "height", "description": ""}}, "metadata": {"description": "", "licence": "None specified"}, "type": "question"}, {"name": "Highest common factor and least common multiple", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}], "functions": {}, "ungrouped_variables": ["power_1", "power_2", "base", "const_1", "const_2", "const_3", "hint"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "<p>What is the highest common factor of $\\var{const_1}$ and $\\var{const_2}$?</p>\n<p>Answer: [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>You need to find the largest whole number that goes into both of the original numbers exactly. For example, $\\var{const_1}$ and&nbsp;$\\var{const_2}$ have a common factor of $\\var{hint}$, but this is not the highest common factor.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "gcd(const_1,const_2)", "minValue": "gcd(const_1,const_2)", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": false, "scripts": {}, "marks": "2", "type": "numberentry", "correctAnswerStyle": "plain"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>What is the least common multiple of $\\var{const_2}$ and $\\var{const_3}$?</p>\n<p>Answer: [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>You need to find the smallest whole number that is a multiple of both $\\var{const_2}$ and $\\var{const_3}$. For example, $\\var{const_2}\\times\\var{const_3}=\\simplify{{const_2}*{const_3}}$ is a common multiple of $\\var{const_2}$ and $\\var{const_3}$, but it is not the least common multiple.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "extension"}], "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "lcm(const_2,const_3)", "minValue": "lcm(const_2,const_3)", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "2", "type": "numberentry", "correctAnswerStyle": "plain"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"const_3": {"definition": "random([3,5,7])*base", "templateType": "anything", "group": "Ungrouped variables", "name": "const_3", "description": ""}, "const_2": {"definition": "2^power_2*base^2", "templateType": "anything", "group": "Ungrouped variables", "name": "const_2", "description": ""}, "const_1": {"definition": "2^power_1*base*5", "templateType": "anything", "group": "Ungrouped variables", "name": "const_1", "description": ""}, "hint": {"definition": "gcd(const_1,const_2)/base", "templateType": "anything", "group": "Ungrouped variables", "name": "hint", "description": ""}, "base": {"definition": "random(2,3)", "templateType": "anything", "group": "Ungrouped variables", "name": "base", "description": ""}, "power_1": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "power_1", "description": ""}, "power_2": {"definition": "random(1..3 except power_1)", "templateType": "anything", "group": "Ungrouped variables", "name": "power_2", "description": ""}}, "metadata": {"description": "<p>Understanding the concept of the highest common factor and least common multiple of two positive integers.</p>", "licence": "None specified"}, "type": "question"}, {"name": "Perimeter", "extensions": [], "custom_part_types": [], "resources": [["question-resources/trapezium_y9AhE2q.png", "/srv/numbas/media/question-resources/trapezium_y9AhE2q.png"], ["question-resources/trapezium_ySmDvow.png", "/srv/numbas/media/question-resources/trapezium_ySmDvow.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}], "functions": {}, "ungrouped_variables": ["seed_side", "side_2", "side_3"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "<p>The following shape has two sides of lengths $\\var{seed_side}$ cm and $\\var{side_3}$ cm. The other two sides both have length $\\var{side_2}$ cm. Work out the perimeter of the shape.</p>\n<p><img src=\"resources/question-resources/trapezium_ySmDvow.png\" height=\"209\" width=\"465\"/></p>\n<p>Answer: [[0]] cm</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>The perimeter of the shape is the total length of all its sides added together $\\var{seed_side}+\\var{side_2}+\\var{side_2}+\\var{side_3}$.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "seed_side+side_3+2*side_2", "minValue": "seed_side+side_3+2*side_2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "2", "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"side_2": {"definition": "seed_side+random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "side_2", "description": ""}, "side_3": {"definition": "seed_side+random(6..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "side_3", "description": ""}, "seed_side": {"definition": "random(9..15)", "templateType": "anything", "group": "Ungrouped variables", "name": "seed_side", "description": ""}}, "metadata": {"description": "<p>Tests basic arithmetic and the concept of perimeter.</p>", "licence": "None specified"}, "type": "question"}, {"name": "Time calculations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}], "functions": {}, "ungrouped_variables": ["wake_hour", "wake_minutes", "sleep_hour", "sleep_minutes", "calc_minutes", "remainder_minutes", "hour_carry"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "<p>Gabriel wakes up at $\\var{wake_hour}:\\var{wake_minutes}$ am and goes to sleep at $\\var{sleep_hour}:\\var{sleep_minutes}$ pm. How long is Gabriel awake?</p>\n<p>Answer: [[0]] hours [[1]] minutes</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>It is $\\simplify{12-({wake_hour}+1)}$ hours and $\\simplify{60-{wake_minutes}}$ minutes from when Gabriel wakes up until 12 noon. Add this time in hours and minutes to the time Gabriel goes to sleep. If the sum of the minutes is more than sixty, then the total number of hours increases by 1 and the total number of minutes decreases by 60.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "12-(wake_hour+1)+sleep_hour+hour_carry", "minValue": "12-(wake_hour+1)+sleep_hour+hour_carry", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "correctAnswerStyle": "plain"}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "remainder_minutes", "minValue": "remainder_minutes", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "correctAnswerStyle": "plain"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"wake_hour": {"definition": "random(5..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "wake_hour", "description": ""}, "remainder_minutes": {"definition": "mod(calc_minutes,60)", "templateType": "anything", "group": "Ungrouped variables", "name": "remainder_minutes", "description": ""}, "wake_minutes": {"definition": "random(2..11)*5", "templateType": "anything", "group": "Ungrouped variables", "name": "wake_minutes", "description": ""}, "hour_carry": {"definition": "(calc_minutes-remainder_minutes)/60", "templateType": "anything", "group": "Ungrouped variables", "name": "hour_carry", "description": ""}, "sleep_hour": {"definition": "random(9..11)", "templateType": "anything", "group": "Ungrouped variables", "name": "sleep_hour", "description": ""}, "sleep_minutes": {"definition": "random(2..11 except (wake_minutes)/5)*5", "templateType": "anything", "group": "Ungrouped variables", "name": "sleep_minutes", "description": ""}, "calc_minutes": {"definition": "(60-wake_minutes)+sleep_minutes", "templateType": "anything", "group": "Ungrouped variables", "name": "calc_minutes", "description": ""}}, "metadata": {"description": "<p>Test ability to calculate the difference between two times.</p>", "licence": "None specified"}, "type": "question"}, {"name": "Percentages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}], "functions": {}, "ungrouped_variables": ["percentage", "amount"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "<p>What is $\\var{percentage}$% of &pound;$\\var{amount}$?</p>\n<p>Answer: &pound;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>As a first step, use the fact that $10$% of &pound;$\\var{amount}$ is $\\var{amount}\\div 10 = \\mbox{&pound;}\\simplify{{amount}/10}$.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "percentage*amount/100", "minValue": "percentage*amount/100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "2", "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"percentage": {"definition": "random(2..9 except 5)*10", "templateType": "anything", "group": "Ungrouped variables", "name": "percentage", "description": ""}, "amount": {"definition": "random(5..12 except 10)*10", "templateType": "anything", "group": "Ungrouped variables", "name": "amount", "description": ""}}, "metadata": {"description": "<p>Find a given percentage of a sum of money.</p>", "licence": "None specified"}, "type": "question"}, {"name": "Addition of fractions with hints", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}], "functions": {}, "ungrouped_variables": ["num1", "num2", "denominator", "common_denominator"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "<p>Calculate the following and give your answer as a fraction (<em>enter your answer in the form $a/b$ using the slash symbol</em>).</p>\n<p>$\\frac{{\\var{num1}}}{{\\var{denominator}}}+\\frac{{\\var{num2}}}{\\simplify{{denominator}+1}}=$ [[0]] </p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>To add the fractions, you need to find a common denominator. This is a whole number which is a multiple of both $\\var{denominator}$ and $\\simplify{{denominator}+1}$. The easiest choice is $\\var{common_denominator}$. Then rewrite the calcuation as</p>\n<p>$\\dfrac{\\Box}{\\var{common_denominator}}+\\dfrac{\\Box}{\\var{common_denominator}}$</p>\n<p>where you need to work out the new numerators to fill in the boxes. For example, $\\dfrac{\\var{num1}}{\\var{denominator}}=\\dfrac{\\simplify{{num1}*({denominator}+1)}}{\\var{common_denominator}}$ and this tells you what to enter in the first box.&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "(num1/denominator)+(num2/(denominator+1))", "minValue": "(num1/denominator)+(num2/(denominator+1))", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "2", "type": "numberentry", "correctAnswerStyle": "plain"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"denominator": {"definition": "random(2..8 except num1)", "templateType": "anything", "group": "Ungrouped variables", "name": "denominator", "description": ""}, "common_denominator": {"definition": "denominator*(denominator+1)", "templateType": "anything", "group": "Ungrouped variables", "name": "common_denominator", "description": ""}, "num1": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "num1", "description": ""}, "num2": {"definition": "random(2..9 except denominator+1)", "templateType": "anything", "group": "Ungrouped variables", "name": "num2", "description": ""}}, "metadata": {"description": "<p>Tests the addition rule for fractions.</p>", "licence": "None specified"}, "type": "question"}, {"name": "Comparing cost per item", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}], "functions": {}, "ungrouped_variables": ["num1", "num2", "cost1", "cost1_string", "cost2", "cost2_string", "cheapest_cost_per_apple"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "<p>What is the cost per apple at the cheapest supermarket (answer in pence)?</p>\n<p>Answer: [[0]] pence</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>First work out the cost per apple in supermarket A in pence, that is, $\\simplify{{cost1}*100}\\div\\var{num1}$. Then you will need to do a similar calculation for supermarket B. Compare your answers to find the cheapest cost per apple.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "cheapest_cost_per_apple", "minValue": "cheapest_cost_per_apple", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": false, "scripts": {}, "marks": "3", "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Supermarket A has an offer for $\\var{num1}$ gala apples for &pound;$\\var{cost1_string}$. Supermarket B has an offer for $\\var{num2}$ gala apples for &pound;$\\var{cost2_string}$.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"cost1_string": {"definition": "dpformat(cost1,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "cost1_string", "description": ""}, "num1": {"definition": "random(4..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "num1", "description": ""}, "num2": {"definition": "num1+2", "templateType": "anything", "group": "Ungrouped variables", "name": "num2", "description": ""}, "cheapest_cost_per_apple": {"definition": "min(cost1*100/num1,cost2*100/num2)", "templateType": "anything", "group": "Ungrouped variables", "name": "cheapest_cost_per_apple", "description": ""}, "cost1": {"definition": "num1*(random(25..45 except[30,40])/100)", "templateType": "anything", "group": "Ungrouped variables", "name": "cost1", "description": ""}, "cost2": {"definition": "num2*(random(25..45 except[30,40,cost1*100/num1])/100)", "templateType": "anything", "group": "Ungrouped variables", "name": "cost2", "description": ""}, "cost2_string": {"definition": "dpformat(cost2,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "cost2_string", "description": ""}}, "metadata": {"description": "<p>This application of arithmetic tests division as a method to compare cost per item, in order to determine value for money.</p>", "licence": "None specified"}, "type": "question"}, {"name": "Bar charts and percentages (fixed)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Untitled_2.png", "/srv/numbas/media/question-resources/Untitled_2.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}], "functions": {}, "preamble": {"css": "", "js": ""}, "tags": [], "rulesets": {}, "metadata": {"licence": "None specified", "description": ""}, "parts": [{"scripts": {}, "showCorrectAnswer": true, "type": "gapfill", "variableReplacements": [], "gaps": [{"mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "variableReplacements": [], "maxValue": "freq1", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true, "allowFractions": false, "correctAnswerFraction": false, "minValue": "freq1", "correctAnswerStyle": "plain"}], "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>How many people voted for {film1}?</p>\n<p>Answer: [[0]]</p>"}, {"scripts": {}, "showCorrectAnswer": true, "type": "gapfill", "variableReplacements": [], "gaps": [{"mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "variableReplacements": [], "maxValue": "freq1+freq2", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true, "allowFractions": false, "correctAnswerFraction": false, "minValue": "freq1+freq2", "correctAnswerStyle": "plain"}], "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>How many people voted for either {film1} or {film2}?</p>\n<p>Answer: [[0]]</p>"}, {"steps": [{"scripts": {}, "showCorrectAnswer": true, "type": "information", "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>To find an exact percentage, if&nbsp;\\<span class=\"p\">[</span><span class=\"MathJax\" id=\"MathJax-Element-1-Frame\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;\" role=\"presentation\" style=\"box-sizing: border-box; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\" tabindex=\"0\"><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>n\\]</mi></math></span></span>&nbsp;is the number of votes for {film2}, then you need to calculate</p>\n<p><span class=\"MathJax\" id=\"MathJax-Element-2-Frame\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mn&gt;100&lt;/mn&gt;&lt;/mrow&gt;&lt;mstyle displaystyle=&quot;false&quot; scriptlevel=&quot;0&quot;&gt;&lt;mtext&gt;total number of votes&lt;/mtext&gt;&lt;/mstyle&gt;&lt;/mfrac&gt;&lt;/math&gt;\" role=\"presentation\" style=\"box-sizing: border-box; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-4\"><span class=\"mrow\" id=\"MathJax-Span-5\"><span class=\"mfrac\" id=\"MathJax-Span-6\"><span class=\"mrow\" id=\"MathJax-Span-7\"><span class=\"mi\" id=\"MathJax-Span-8\">\\<span class=\"p\">[frac{</span>n</span><span class=\"mo\" id=\"MathJax-Span-9\">&times;</span><span class=\"mn\" id=\"MathJax-Span-10\">100}{</span></span></span></span></span></nobr><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mtext>total number of votes}<meta charset=\"utf-8\"/>\\]</mtext></mstyle></mfrac></math></span></span></p>\n<p>Since there are 50 votes in total, you will be able to simplify this and give your answer as a whole number.</p>"}], "scripts": {}, "showCorrectAnswer": true, "type": "gapfill", "variableReplacements": [], "gaps": [{"mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "variableReplacements": [], "maxValue": "percentage", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true, "allowFractions": false, "correctAnswerFraction": false, "minValue": "percentage", "correctAnswerStyle": "plain"}], "stepsPenalty": 0, "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>What percentage of people surveyed voted for {film2}?</p>\n<p>Answer: [[0]]</p>"}], "ungrouped_variables": ["film1", "film2", "freq1", "freq2", "percentage"], "variable_groups": [], "variables": {"film2": {"group": "Ungrouped variables", "definition": "random([\"The Third Man\",\"Brief Encounter\", \"Lawrence of Arabia\", \"The 39 Steps\", \"Great Expectations\",\"Kes\"] except film1)", "name": "film2", "description": "", "templateType": "anything"}, "freq2": {"group": "Ungrouped variables", "definition": "switch(film2=\"The Third Man\",15,film2=\"Brief Encounter\",4,film2=\"Lawrence of Arabia\",13,film2=\"The 39 Steps\",8,film2=\"Great Expectations\",3,film2=\"Kes\",7,0)", "name": "freq2", "description": "", "templateType": "anything"}, "film1": {"group": "Ungrouped variables", "definition": "random([\"The Third Man\",\"Brief Encounter\", \"Lawrence of Arabia\", \"The 39 Steps\", \"Great Expectations\",\"Kes\"])", "name": "film1", "description": "", "templateType": "anything"}, "freq1": {"group": "Ungrouped variables", "definition": "switch(film1=\"The Third Man\",15,film1=\"Brief Encounter\",4,film1=\"Lawrence of Arabia\",13,film1=\"The 39 Steps\",8,film1=\"Great Expectations\",3,film1=\"Kes\",7,0)", "name": "freq1", "description": "", "templateType": "anything"}, "percentage": {"group": "Ungrouped variables", "definition": "precround((freq2/49)*100,0)", "name": "percentage", "description": "", "templateType": "anything"}}, "advice": "", "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "<p>A group of people were asked to vote for their favourite British film of all time from a selection of six taken from the the BFI top 100. The following bar chart shows the results of the survey.</p>\n<p><img src=\"resources/question-resources/Untitled_2.png\"/></p>\n<p></p>", "type": "question"}, {"name": "Scatter plot", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}], "functions": {"drawgraph": {"definition": "      var miny = Numbas.jme.unwrapValue(scope.variables.miny);\n      var maxy = Numbas.jme.unwrapValue(scope.variables.maxy);\n      var minx = Numbas.jme.unwrapValue(scope.variables.minx);\n      var maxx = Numbas.jme.unwrapValue(scope.variables.maxx);\n      var regy1 = Numbas.jme.unwrapValue(scope.variables.regy1);\n      var regy2 = Numbas.jme.unwrapValue(scope.variables.regy2);\n\n      var p1x = Numbas.jme.unwrapValue(scope.variables.p1x);\n      var p1y = Numbas.jme.unwrapValue(scope.variables.p1y);\n      var p2x = Numbas.jme.unwrapValue(scope.variables.p2x);\n      var p2y= Numbas.jme.unwrapValue(scope.variables.p2y);\n      var p3x = Numbas.jme.unwrapValue(scope.variables.p3x);\n      var p3y= Numbas.jme.unwrapValue(scope.variables.p3y);\n      var p4x = Numbas.jme.unwrapValue(scope.variables.p4x);\n      var p4y= Numbas.jme.unwrapValue(scope.variables.p4y);\n      var p5x = Numbas.jme.unwrapValue(scope.variables.p5x);\n      var p5y= Numbas.jme.unwrapValue(scope.variables.p5y);\n      var p6x = Numbas.jme.unwrapValue(scope.variables.p6x);\n      var p6y= Numbas.jme.unwrapValue(scope.variables.p6y);\n      \n      var div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',\n      {boundingBox:[minx,maxy,maxx,miny],\n       axis:false,\n       showNavigation:false,\n       grid:true});\n        var brd = div.board;          \n        var xaxis=brd.createElement('axis', [[minx,0],[maxx,0]]);\n        var yaxis=brd.createElement('axis', [[minx+5,miny],[minx+5,maxy]]);\n        var li1=brd.create('line',[[minx,regy1],[maxx,regy2]],{fixed:true,withLabel:false});\n        var pt1=brd.create('point',[p1x,p1y],{visible:true,withLabel:false}); \n        var pt2=brd.create('point',[p2x,p2y],{visible:true,withLabel:false}); \n        var pt3=brd.create('point',[p3x,p3y],{visible:true,withLabel:false}); \n        var pt4=brd.create('point',[p4x,p4y],{visible:true,withLabel:false}); \n        var pt5=brd.create('point',[p5x,p5y],{visible:true,withLabel:false}); \n        var pt6=brd.create('point',[p6x,p6y],{visible:true,withLabel:false}); \nreturn div;\n      ", "type": "html", "language": "javascript", "parameters": []}}, "ungrouped_variables": [], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>What is the height of the tallest person in the sample?</p>\n<p>Answer: [[0]] cm</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "tallest", "minValue": "tallest", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "correctAnswerStyle": "plain"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>What is the maximum difference in time taken to walk to work for people in the sample?</p>\n<p>Answer: [[0]] minutes</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "timediff+1", "minValue": "timediff-1", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "correctAnswerStyle": "plain"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"displayColumns": 0, "prompt": "<p>Mark the statement that best describes what this scatter plot shows.</p>", "matrix": ["0", "1", 0, "1", 0, 0], "shuffleChoices": false, "variableReplacements": [], "choices": ["<p>In general, there is a positive correlation between a person's height and how long it takes them to walk to work.</p>", "<p>There is a positive correlation between the variables for the sample.</p>", "<p>In general, there is a negative correlation between a person's height and how long it takes them to walk to work.</p>", "<p>There is a negative correlation between the variables for the sample.</p>", "<p>In general, there is a no correlation between a person's height and how long it takes them to walk to work.</p>", "<p>There is a no correlation between the variables for the sample.</p>"], "variableReplacementStrategy": "originalfirst", "maxMarks": 0, "distractors": ["", "", "", "", "", ""], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "1_n_2", "displayType": "radiogroup", "minMarks": 0}], "statement": "<p><span style=\"font-weight: 400;\">The scatter plot below shows the relationship between an employee&rsquo;s height in centimetres and how long it takes them to walk to work in minutes.</span></p>\n<table>\n<tbody>\n<tr>\n<td>time (mins)</td>\n<td>{drawgraph()}</td>\n</tr>\n<tr>\n<td></td>\n<td style=\"text-align: center;\">height (cm)</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p></p>\n<p></p>\n<p></p>", "variable_groups": [{"variables": ["minx", "maxx", "miny", "maxy"], "name": "Graph Limits"}, {"variables": ["p1x", "p1y", "p2x", "p2y", "p3x", "p3y", "p4x", "p4y", "p5x", "p5y", "p6x", "p6y"], "name": "Points"}, {"variables": ["tallest", "timemax", "timemin", "timediff"], "name": "Calculation variables"}, {"variables": ["sumx", "sumy", "sumxy", "sumxx", "slope", "yintercept", "regy1", "regy2", "roundedslope"], "name": "Regression variables"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"slope": {"definition": "(6*sumxy-sumx*sumy)/(6*sumxx-(sumx)^2)", "templateType": "anything", "group": "Regression variables", "name": "slope", "description": "<p>s</p>"}, "timemax": {"definition": "max([p1y,p2y,p3y,p4y,p5y,p6y])", "templateType": "anything", "group": "Calculation variables", "name": "timemax", "description": ""}, "minx": {"definition": "140", "templateType": "anything", "group": "Graph Limits", "name": "minx", "description": ""}, "miny": {"definition": "-10", "templateType": "anything", "group": "Graph Limits", "name": "miny", "description": ""}, "p3x": {"definition": "random(166..175)", "templateType": "anything", "group": "Points", "name": "p3x", "description": ""}, "p3y": {"definition": "random(26..35)", "templateType": "anything", "group": "Points", "name": "p3y", "description": ""}, "p5x": {"definition": "random(146..155 except p1x)", "templateType": "anything", "group": "Points", "name": "p5x", "description": ""}, "p5y": {"definition": "random(6..15)", "templateType": "anything", "group": "Points", "name": "p5y", "description": ""}, "p1x": {"definition": "random(146..155)", "templateType": "anything", "group": "Points", "name": "p1x", "description": ""}, "p1y": {"definition": "random(6..15)", "templateType": "anything", "group": "Points", "name": "p1y", "description": ""}, "timediff": {"definition": "timemax-timemin", "templateType": "anything", "group": "Calculation variables", "name": "timediff", "description": ""}, "maxx": {"definition": "188", "templateType": "anything", "group": "Graph Limits", "name": "maxx", "description": ""}, "maxy": {"definition": "63", "templateType": "anything", "group": "Graph Limits", "name": "maxy", "description": ""}, "roundedslope": {"definition": "precround(slope,2)", "templateType": "anything", "group": "Regression variables", "name": "roundedslope", "description": ""}, "yintercept": {"definition": "(sumy-slope*sumx)/6", "templateType": "anything", "group": "Regression variables", "name": "yintercept", "description": ""}, "timemin": {"definition": "min([p1y,p2y,p3y,p4y,p5y,p6y])", "templateType": "anything", "group": "Calculation variables", "name": "timemin", "description": ""}, "tallest": {"definition": "max([p1x,p2x,p3x,p4x,p5x,p6x])", "templateType": "anything", "group": "Calculation variables", "name": "tallest", "description": ""}, "regy1": {"definition": "slope*minx+yintercept", "templateType": "anything", "group": "Regression variables", "name": "regy1", "description": ""}, "regy2": {"definition": "slope*maxx+yintercept", "templateType": "anything", "group": "Regression variables", "name": "regy2", "description": ""}, "sumy": {"definition": "p1y+p2y+p3y+p4y+p5y+p6y", "templateType": "anything", "group": "Regression variables", "name": "sumy", "description": ""}, "sumx": {"definition": "p1x+p2x+p3x+p4x+p5x+p6x", "templateType": "anything", "group": "Regression variables", "name": "sumx", "description": ""}, "p6y": {"definition": "random(46..55)", "templateType": "anything", "group": "Points", "name": "p6y", "description": "<p>p6y</p>"}, "p6x": {"definition": "random(176..185 except p4x)", "templateType": "anything", "group": "Points", "name": "p6x", "description": ""}, "p4y": {"definition": "random(36..45)", "templateType": "anything", "group": "Points", "name": "p4y", "description": ""}, "p4x": {"definition": "random(176..185)", "templateType": "anything", "group": "Points", "name": "p4x", "description": ""}, "p2y": {"definition": "random(16..25)", "templateType": "anything", "group": "Points", "name": "p2y", "description": ""}, "p2x": {"definition": "random(156..165)", "templateType": "anything", "group": "Points", "name": "p2x", "description": ""}, "sumxx": {"definition": "p1x^2+p2x^2+p3x^2+p4x^2+p5x^2+p6x^2", "templateType": "anything", "group": "Regression variables", "name": "sumxx", "description": ""}, "sumxy": {"definition": "p1x*p1y+p2x*p2y+p3x*p3y+p4x*p4y+p5x*p5y+p6x*p6y", "templateType": "anything", "group": "Regression variables", "name": "sumxy", "description": ""}}, "metadata": {"description": "<p>Tests understanding of scatter plots and related concepts.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question"}, {"name": "Mean, mode and median", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}], "functions": {}, "ungrouped_variables": ["median", "mode", "x1", "x2", "x3", "x4", "statname", "total", "mean", "tip", "median_or_mode"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "<p>What is the mean height of the group of children in centimetres?</p>\n<p>Answer: [[0]] cm</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>To find the mean of the set of numbers, first add all the numbers together ($\\var{total}$) and then divide by how many numbers there are. So, you need to calculate $\\var{total}\\div 7$.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "mean", "strictPrecision": false, "minValue": "mean", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": "2", "notationStyles": ["plain", "en", "si-en"], "showPrecisionHint": true, "type": "numberentry", "correctAnswerStyle": "plain"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>What is the {statname} for this sample of measurements?</p>\n<p>Answer: [[0]] cm</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>{tip}</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "extension"}], "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "median_or_mode", "minValue": "median_or_mode", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "2", "type": "numberentry", "correctAnswerStyle": "plain"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Seven children's heights in centimetres are recorded as follows:</p>\n<p>$\\var{mode},\\var{median},\\var{mode},\\var{x2},\\var{x3},\\var{x4},\\var{x1}$.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"statname": {"definition": "random(\"median\", \"mode\")", "templateType": "anything", "group": "Ungrouped variables", "name": "statname", "description": ""}, "x4": {"definition": "median+random(11..20)", "templateType": "anything", "group": "Ungrouped variables", "name": "x4", "description": ""}, "tip": {"definition": "switch(statname=\"median\",\"The median is the middle number when all of the numbers are placed in order.\",statname=\"mode\",\"The mode is the most commonly occuring value.\")", "templateType": "anything", "group": "Ungrouped variables", "name": "tip", "description": ""}, "x1": {"definition": "median-random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "x1", "description": ""}, "median": {"definition": "random(91..100)", "templateType": "anything", "group": "Ungrouped variables", "name": "median", "description": ""}, "mode": {"definition": "median+random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "mode", "description": ""}, "x2": {"definition": "median-random(11..20)", "templateType": "anything", "group": "Ungrouped variables", "name": "x2", "description": ""}, "x3": {"definition": "median-random(21..30)", "templateType": "anything", "group": "Ungrouped variables", "name": "x3", "description": ""}, "total": {"definition": "median+2*mode+x1+x2+x3+x4", "templateType": "anything", "group": "Ungrouped variables", "name": "total", "description": ""}, "median_or_mode": {"definition": "switch(statname=\"mode\",mode,statname=\"median\",median)", "templateType": "anything", "group": "Ungrouped variables", "name": "median_or_mode", "description": ""}, "mean": {"definition": "precround(total/7,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "mean", "description": ""}}, "metadata": {"description": "<p>This question tests ability to deal with measures of central tendancy for a small data set. The mode or median is required at random.</p>", "licence": "None specified"}, "type": "question"}, {"name": "Expanding brackets", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}], "functions": {}, "ungrouped_variables": ["const1", "const2"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "vsetrangepoints": 5, "prompt": "<p>Expand and simplify the following algebraic expression:</p>\n<p style=\"text-align: center;\">$(x+\\var{const1})(x+\\var{const2})$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>You need to multiply everything in the first bracket by the second bracket. That is,</p>\n<p>$x (x + \\var{const2}) + \\var{const1} (x + \\var{const2})=x^2+\\var{const2}x+\\var{const1}x+(\\var{const1}\\times\\var{const2})$</p>\n<p>and then simplify your answer. </p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "scripts": {}, "answer": "x^2+({const1}+{const2})*x+({const1}*{const2})", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme", "maxlength": {"length": "14", "message": "<p>You need to simplify your solution as far as possible.</p>", "partialCredit": "50"}}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"const1": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "const1", "description": ""}, "const2": {"definition": "random(2..9 except const1)", "templateType": "anything", "group": "Ungrouped variables", "name": "const2", "description": ""}}, "metadata": {"description": "<p>This question tests the method of expanding a pair of brackets.</p>", "licence": "None specified"}, "type": "question"}, {"name": "Missing side in a right-angled triangle", "extensions": [], "custom_part_types": [], "resources": [["question-resources/triangle_yeq6Xd0.png", "/srv/numbas/media/question-resources/triangle_yeq6Xd0.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}], "functions": {}, "ungrouped_variables": ["short_side", "long_side", "hypotenuse", "sum_of_squares"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "displayColumns": 0, "prompt": "<p>The following triangle has two sides of length $\\var{short_side}$ cm and $\\var{long_side}$ cm.&nbsp;</p>\n<table>\n<tbody>\n<tr>\n<td>$\\var{long_side}$ cm</td>\n<td><img src=\"resources/question-resources/triangle_yeq6Xd0.png\"/></td>\n</tr>\n<tr>\n<td></td>\n<td style=\"text-align: center;\">$\\var{short_side}$ cm</td>\n</tr>\n</tbody>\n</table>\n<p>What is the length of the longest side correct to 1 decimal place?</p>", "matrix": [0, 0, "3", 0], "shuffleChoices": true, "maxMarks": 0, "variableReplacements": [], "choices": ["<p>$\\simplify{{hypotenuse}-0.4}$ cm</p>", "<p>$\\var{sum_of_squares}$ cm</p>", "<p>$\\var{hypotenuse}$ cm</p>", "<p>$\\simplify{{hypotenuse}+0.5}$ cm</p>"], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>If the longest side has length $x$ cm, then $x$ needs to satisfy Pythagoras' theorem:</p>\n<p>$x^2=\\var{short_side}^2+\\var{long_side}^2=\\simplify{{short_side}^2+{long_side}^2}$.</p>\n<p>Depending on the accuracy of $x$, this relationship may only be approximate.</p>\n<p>You need to check which of the choices best satisfies this relationship.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "distractors": ["", "", "", ""], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "1_n_2", "displayType": "radiogroup", "minMarks": 0}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"sum_of_squares": {"definition": "precround(short_side^2+long_side^2, 1)", "templateType": "anything", "group": "Ungrouped variables", "name": "sum_of_squares", "description": ""}, "long_side": {"definition": "short_side+random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "long_side", "description": ""}, "hypotenuse": {"definition": "precround(sqrt(short_side^2+long_side^2), 1)", "templateType": "anything", "group": "Ungrouped variables", "name": "hypotenuse", "description": ""}, "short_side": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "short_side", "description": ""}}, "metadata": {"description": "<p>This question tests ability to use Pythagoras' theorem.</p>", "licence": "None specified"}, "type": "question"}, {"name": "Interpreting tables", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}], "functions": {}, "ungrouped_variables": ["revenue_forecast", "materials_forecast", "overheads_forecast", "net_profit_forecast", "revenue", "materials", "overheads", "net_profit"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>Calculate the actual net profit.</p>\n<p>Answer: &pound;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "net_profit", "minValue": "net_profit", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "correctAnswerStyle": "plain"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>What&nbsp;would the actual material costs need to be so that the actual net profit is the same as the forecast?</p>\n<p>Answer: &pound;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>From the table, we can see that&nbsp;</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<td>Net profit = Revenue - Materials - Overheads.</td>\n</tr>\n</tbody>\n</table>\n<p>Since the overheads are the same for the forecast and in reality, for the the actual net profit to be equal to that of the forecast, we need</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<td>Forecast Revenue - Forecast Materials = Actual Revenue - Actual Materials</td>\n</tr>\n</tbody>\n</table>\n<p>If the actual materials are considered to be an unknown ($x$), then we can fill in all the other values from the table and rearrange the equation to find $x$.&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "revenue-revenue_forecast+materials_forecast", "minValue": "revenue-revenue_forecast+materials_forecast", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "3", "type": "numberentry", "correctAnswerStyle": "plain"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>The following table shows monthly financial data for a small business.</p>\n<table>\n<tbody>\n<tr>\n<td></td>\n<td>budget forecast (&pound;)</td>\n<td>actual (&pound;)</td>\n<td>actual - forecast (&pound;)</td>\n</tr>\n<tr>\n<td>Revenue</td>\n<td>{revenue_forecast}</td>\n<td>{revenue}</td>\n<td>$\\simplify{{revenue}-{revenue_forecast}}$</td>\n</tr>\n<tr>\n<td>Materials</td>\n<td>{materials_forecast}</td>\n<td>{materials}</td>\n<td>$\\simplify{{materials}-{materials_forecast}}$</td>\n</tr>\n<tr>\n<td>Overheads</td>\n<td>{overheads_forecast}</td>\n<td>{overheads}</td>\n<td>$\\simplify{{overheads}-{overheads_forecast}}$</td>\n</tr>\n<tr>\n<td>Net profit</td>\n<td>{net_profit_forecast}</td>\n<td>?</td>\n<td>$\\simplify{{net_profit}-{net_profit_forecast}}$</td>\n</tr>\n</tbody>\n</table>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"net_profit": {"definition": "revenue-materials-overheads", "templateType": "anything", "group": "Ungrouped variables", "name": "net_profit", "description": ""}, "revenue": {"definition": "revenue_forecast-random(1..10)*10", "templateType": "anything", "group": "Ungrouped variables", "name": "revenue", "description": ""}, "revenue_forecast": {"definition": "1000+random(1..5)*50", "templateType": "anything", "group": "Ungrouped variables", "name": "revenue_forecast", "description": ""}, "materials_forecast": {"definition": "random(30..39)*10", "templateType": "anything", "group": "Ungrouped variables", "name": "materials_forecast", "description": ""}, "overheads": {"definition": "overheads_forecast", "templateType": "anything", "group": "Ungrouped variables", "name": "overheads", "description": ""}, "materials": {"definition": "materials_forecast+random(1..4)*10", "templateType": "anything", "group": "Ungrouped variables", "name": "materials", "description": ""}, "overheads_forecast": {"definition": "random(20..39)*10", "templateType": "anything", "group": "Ungrouped variables", "name": "overheads_forecast", "description": ""}, "net_profit_forecast": {"definition": "revenue_forecast-materials_forecast-overheads_forecast", "templateType": "anything", "group": "Ungrouped variables", "name": "net_profit_forecast", "description": ""}}, "metadata": {"description": "<p>This question tests the ability to read and interpret numerical data summarised in a table and make predictions based on algebraic skills.</p>", "licence": "None specified"}, "type": "question"}]}], "feedback": {"advicethreshold": 0, "showactualmark": true, "feedbackmessages": [], "intro": "", "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": 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