// Numbas version: finer_feedback_settings {"name": "INTO Foundation Diagnostic Test (2024)", "metadata": {"description": "

A practice test to get used to the NUMBAS environment.

", "licence": "None specified"}, "duration": 3600, "percentPass": "0", "showQuestionGroupNames": true, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Number", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], []], "questions": [{"name": "Simple arithmetic", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Evaluate the following.

", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"c": {"name": "c", "group": "Ungrouped variables", "definition": "random(50..120)", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(20..50)", "description": "", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "q": {"name": "q", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(3..20)", "description": "", "templateType": "anything", "can_override": false}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "n*q", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(11..50 except a)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(11..50)", "description": "", "templateType": "anything", "can_override": false}, "j": {"name": "j", "group": "Ungrouped variables", "definition": "random(-0.9..0.9#0.1 except 0)", "description": "", "templateType": "anything", "can_override": false}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(-0.9..0.9#0.1 except 0 except j)", "description": "", "templateType": "anything", "can_override": false}, "n1": {"name": "n1", "group": "Ungrouped variables", "definition": "random(6..12)", "description": "", "templateType": "anything", "can_override": false}, "n2": {"name": "n2", "group": "Ungrouped variables", "definition": "random(-4,-3,-2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "c-d>10", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "n", "q", "p", "j", "k", "n1", "n2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "prompt": "

$\\var{a}+\\var{b}$

", "minValue": "a+b", "maxValue": "a+b", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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, "prompt": "

$\\var{c}-\\var{d}$

", "minValue": "c-d", "maxValue": "c-d", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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, "prompt": "

$\\var{f}\\times\\var{g}$

", "minValue": "f*g", "maxValue": "f*g", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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, "prompt": "

$\\var{p}\\div\\var{q}$

", "minValue": "{n}", "maxValue": "{n}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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, "prompt": "

$\\var{j}\\times\\var{k}$

", "minValue": "j*k", "maxValue": "j*k", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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, "prompt": "

$\\sqrt{\\var{n1^2}}$

", "minValue": "n1", "maxValue": "n1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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, "prompt": "

$\\sqrt[3]{\\var{n2^3}}$

", "minValue": "n2", "maxValue": "n2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Rounding values", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "advice": "", "parts": [{"correctAnswerFraction": false, "type": "numberentry", "allowFractions": false, "minValue": "{a1}", "correctAnswerStyle": "plain", "scripts": {}, "marks": 1, "showCorrectAnswer": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{a1}", "mustBeReduced": false, "showFeedbackIcon": true, "prompt": "

Round $\\var{d1}$ to $\\var{n1}$ decimal places.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst"}, {"correctAnswerFraction": false, "type": "numberentry", "allowFractions": false, "minValue": "{a2}", "correctAnswerStyle": "plain", "scripts": {}, "marks": 1, "showCorrectAnswer": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{a2}", "mustBeReduced": false, "showFeedbackIcon": true, "prompt": "

Round $\\var{d2}$ to $\\var{n2}$ decimal places.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst"}, {"correctAnswerFraction": false, "type": "numberentry", "allowFractions": false, "minValue": "{a3}", "correctAnswerStyle": "plain", "scripts": {}, "marks": 1, "showCorrectAnswer": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{a3}", "mustBeReduced": false, "showFeedbackIcon": true, "prompt": "

Round $\\var{d3}$ to $\\var{n3}$ decimal places.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst"}], "statement": "

Round the following numbers to the specified number of decimal places.

", "rulesets": {}, "variablesTest": {"condition": "n2<>n1 and n3<>n1 and n2<>n3 and isint(a1)<>true and isint(a2)<>true and isint(a3)<>true", "maxRuns": "200"}, "variables": {"d1": {"description": "", "definition": "random(0..1#0.00001)*random(0..1#0.0001)*10^(random(-2..5))", "name": "d1", "templateType": "anything", "group": "Ungrouped variables"}, "n2": {"description": "", "definition": "random(1,2,3)", "name": "n2", "templateType": "anything", "group": "Ungrouped variables"}, "a1": {"description": "", "definition": "precround(d1,n1)", "name": "a1", "templateType": "anything", "group": "Ungrouped variables"}, "d2": {"description": "", "definition": "random(0..1#0.0001)*random(0..1#0.0001)*10^(random(-2..5))", "name": "d2", "templateType": "anything", "group": "Ungrouped variables"}, "a2": {"description": "", "definition": "precround(d2,n2)", "name": "a2", "templateType": "anything", "group": "Ungrouped variables"}, "d3": {"description": "", "definition": "random(0..1#0.0001)*random(0..1#0.0001)*10^(random(-2..5))", "name": "d3", "templateType": "anything", "group": "Ungrouped variables"}, "n3": {"description": "", "definition": "random(1,2,3)", "name": "n3", "templateType": "anything", "group": "Ungrouped variables"}, "n1": {"description": "", "definition": "random(1,2,3)", "name": "n1", "templateType": "anything", "group": "Ungrouped variables"}, "a3": {"description": "", "definition": "precround(d3,n3)", "name": "a3", "templateType": "anything", "group": "Ungrouped variables"}}, "ungrouped_variables": ["d1", "d2", "d3", "n1", "n2", "n3", "a1", "a2", "a3"], "metadata": {"licence": "None specified", "description": ""}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "functions": {}, "tags": [], "type": "question"}, {"name": "Simple ratio", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Two people decide to split some money between them.

They have £$\\var{(a+b)*n}$ and decide to divide the cash in the ratio $\\var{a}:\\var{b}$.

", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(a+1..a+2)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(3..9)", "description": "", "templateType": "anything", "can_override": false}, "v1": {"name": "v1", "group": "Ungrouped variables", "definition": "a*n", "description": "", "templateType": "anything", "can_override": false}, "v2": {"name": "v2", "group": "Ungrouped variables", "definition": "b*n", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "n", "v1", "v2"], "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": "

How much does each person get?

£ [[0]]

£ [[1]]

(Input amounts in any order).

", "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": "{v1}", "maxValue": "{v1}", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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": "{v2}", "maxValue": "{v2}", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": true}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Simple percentages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "metadata": {"description": "", "licence": "None specified"}, "variable_groups": [], "tags": [], "functions": {}, "advice": "", "rulesets": {}, "variables": {"a": {"description": "", "name": "a", "definition": "random(41..99#1)", "templateType": "randrange", "group": "Ungrouped variables"}}, "statement": "

Calculate the following percentages and give the exact answer in decimal form.

", "preamble": {"css": "", "js": ""}, "ungrouped_variables": ["a"], "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"vsetrangepoints": 5, "showpreview": true, "showFeedbackIcon": true, "checkvariablenames": false, "variableReplacements": [], "scripts": {}, "expectedvariablenames": [], "variableReplacementStrategy": "originalfirst", "prompt": "

Calculate 10% of {a}.

", "marks": 1, "type": "jme", "answer": "0.1{a}", "checkingtype": "absdiff", "showCorrectAnswer": true, "checkingaccuracy": 0.001, "vsetrange": [0, 1]}, {"vsetrangepoints": 5, "showpreview": true, "showFeedbackIcon": true, "checkvariablenames": false, "variableReplacements": [], "scripts": {}, "expectedvariablenames": [], "variableReplacementStrategy": "originalfirst", "prompt": "

Calculate 5% of {a}.

", "marks": 1, "type": "jme", "answer": "0.05{a}", "checkingtype": "absdiff", "showCorrectAnswer": true, "checkingaccuracy": 0.001, "vsetrange": [0, 1]}, {"vsetrangepoints": 5, "showpreview": true, "showFeedbackIcon": true, "checkvariablenames": false, "variableReplacements": [], "scripts": {}, "expectedvariablenames": [], "variableReplacementStrategy": "originalfirst", "prompt": "

Calculate 15% of {a}.

", "marks": 1, "type": "jme", "answer": "0.15{a}", "checkingtype": "absdiff", "showCorrectAnswer": true, "checkingaccuracy": 0.001, "vsetrange": [0, 1]}], "type": "question"}, {"name": "Fraction Arithmetic with answers in simplest form", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}, {"name": "Amy Barker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4520/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Give your answer as a fraction in its simplest form. (Type a/b to enter a fraction. For example, 1/2 becomes $\\frac{1}{2}$.)

", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"simpleden4": {"name": "simpleden4", "group": "Ungrouped variables", "definition": "den4/gcd(num4,den4)", "description": "", "templateType": "anything", "can_override": false}, "answer4": {"name": "answer4", "group": "Ungrouped variables", "definition": "simplenum4+\"/\"+simpleden4", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(2..10) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "z": {"name": "z", "group": "Ungrouped variables", "definition": "random(2..10) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(1..m-l) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "qq": {"name": "qq", "group": "Ungrouped variables", "definition": "random(1..rr-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "den3": {"name": "den3", "group": "Ungrouped variables", "definition": "{m}*{multiple_m}", "description": "", "templateType": "anything", "can_override": false}, "den1": {"name": "den1", "group": "Ungrouped variables", "definition": "2*{b}{b}", "description": "

den1

", "templateType": "anything", "can_override": false}, "hh": {"name": "hh", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2..12) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "num4": {"name": "num4", "group": "Ungrouped variables", "definition": "{w}*{z}+{y}*{x}", "description": "", "templateType": "anything", "can_override": false}, "simpleden3": {"name": "simpleden3", "group": "Ungrouped variables", "definition": "den3/gcd(num3,den3)", "description": "", "templateType": "anything", "can_override": false}, "t": {"name": "t", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "l": {"name": "l", "group": "Ungrouped variables", "definition": "random(1..m-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "j": {"name": "j", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "r": {"name": "r", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "ss": {"name": "ss", "group": "Ungrouped variables", "definition": "random(1..tt-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..b-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "answer1": {"name": "answer1", "group": "Ungrouped variables", "definition": "simplenum1+\"/\"+simpleden1", "description": "", "templateType": "anything", "can_override": false}, "pp": {"name": "pp", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "gg": {"name": "gg", "group": "Ungrouped variables", "definition": "random(1..hh-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "answer3": {"name": "answer3", "group": "Ungrouped variables", "definition": "simplenum3+\"/\"+simpleden3", "description": "", "templateType": "anything", "can_override": false}, "multiple": {"name": "multiple", "group": "Ungrouped variables", "definition": "random(3,4,5,6,7,8,9)", "description": "", "templateType": "anything", "can_override": false}, "simplenum1": {"name": "simplenum1", "group": "Ungrouped variables", "definition": "num1/gcd(num1,den1)", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(1..f-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "dd": {"name": "dd", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "num2": {"name": "num2", "group": "Ungrouped variables", "definition": "{d}", "description": "", "templateType": "anything", "can_override": false}, "jj": {"name": "jj", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "nn": {"name": "nn", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "multiple_d": {"name": "multiple_d", "group": "Ungrouped variables", "definition": "{multiple}*{d}", "description": "", "templateType": "anything", "can_override": false}, "s": {"name": "s", "group": "Ungrouped variables", "definition": "random(1..t-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(1..x-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "aa": {"name": "aa", "group": "Ungrouped variables", "definition": "random(1..bb-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "ii": {"name": "ii", "group": "Ungrouped variables", "definition": "random(1..jj-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "answer2": {"name": "answer2", "group": "Ungrouped variables", "definition": "simplenum2+\"/\"+simpleden2", "description": "", "templateType": "anything", "can_override": false}, "simplenum4": {"name": "simplenum4", "group": "Ungrouped variables", "definition": "num4/gcd(num4,den4)", "description": "", "templateType": "anything", "can_override": false}, "ll": {"name": "ll", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "kk": {"name": "kk", "group": "Ungrouped variables", "definition": "random(1..ll-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "simpleden1": {"name": "simpleden1", "group": "Ungrouped variables", "definition": "den1/gcd(num1,den1)", "description": "", "templateType": "anything", "can_override": false}, "v": {"name": "v", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(1..b-a) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "random(1..f-d) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "simpleden2": {"name": "simpleden2", "group": "Ungrouped variables", "definition": "den2/gcd(num2,den2)", "description": "", "templateType": "anything", "can_override": false}, "num3": {"name": "num3", "group": "Ungrouped variables", "definition": "{l}*multiple_m}-{n}*{m}", "description": "", "templateType": "anything", "can_override": false}, "oo": {"name": "oo", "group": "Ungrouped variables", "definition": "random(1..pp-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "u": {"name": "u", "group": "Ungrouped variables", "definition": "random(1..v-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "random(1..j-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "cc": {"name": "cc", "group": "Ungrouped variables", "definition": "random(1..dd-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "den4": {"name": "den4", "group": "Ungrouped variables", "definition": "{x}*{z}", "description": "", "templateType": "anything", "can_override": false}, "bb": {"name": "bb", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "rr": {"name": "rr", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "num1": {"name": "num1", "group": "Ungrouped variables", "definition": "{a}{c}", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "random(4..10) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "ee": {"name": "ee", "group": "Ungrouped variables", "definition": "random(1..ff-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "den2": {"name": "den2", "group": "Ungrouped variables", "definition": "multiple_d", "description": "", "templateType": "anything", "can_override": false}, "simplenum2": {"name": "simplenum2", "group": "Ungrouped variables", "definition": "num2/gcd(num2,den2)", "description": "", "templateType": "anything", "can_override": false}, "mm": {"name": "mm", "group": "Ungrouped variables", "definition": "random(1..nn-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(1..j-h) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "q": {"name": "q", "group": "Ungrouped variables", "definition": "random(1..r-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}, "simplenum3": {"name": "simplenum3", "group": "Ungrouped variables", "definition": "num3/gcd(num3,den3)", "description": "", "templateType": "anything", "can_override": false}, "tt": {"name": "tt", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "multiple_m": {"name": "multiple_m", "group": "Ungrouped variables", "definition": "random(m*3,m*4,m*5,m*6,m*7)", "description": "", "templateType": "anything", "can_override": false}, "ff": {"name": "ff", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "templateType": "anything", "can_override": false}, "w": {"name": "w", "group": "Ungrouped variables", "definition": "random(1..3) ", "description": "", "templateType": "anything", "can_override": false}, "o": {"name": "o", "group": "Ungrouped variables", "definition": "random(1..p-1) //random numerator less than denominator", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "j", "m", "p", "r", "t", "v", "x", "z", "bb", "dd", "ff", "hh", "jj", "ll", "nn", "pp", "rr", "tt", "h", "k", "l", "n", "o", "q", "s", "u", "w", "y", "aa", "cc", "ee", "gg", "ii", "kk", "mm", "oo", "qq", "ss", "num1", "den1", "simplenum1", "simpleden1", "answer1", "num2", "den2", "simplenum2", "simpleden2", "answer2", "multiple", "multiple_d", "multiple_m", "num3", "den3", "simplenum3", "simpleden3", "answer3", "num4", "den4", "simplenum4", "simpleden4", "answer4"], "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": "

$\\frac{\\var{a}}{\\var{b}} \\times \\frac{\\var{c}}{\\var{2*b}}$

[[0]]

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$\\frac{\\var{d}}{\\var{f}} \\div \\frac{\\var{multiple_d}}{\\var{f}}$

[[0]]

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$\\frac{\\var{l}}{\\var{m}} - \\frac{\\var{n}}{\\var{multiple_m}}$

[[0]]

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$\\frac{\\var{w}}{\\var{x}} + \\frac{\\var{y}}{\\var{z}}$

[[0]]

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The formula for converting a temperature in Celsius (C) to Fahrenheit (F) is given by:

$F = \\frac{9}{5}C+32$

", "advice": "

a) Plug $\\var{C}^{\\circ}$ in for $C$ in the formula: $F = \\frac{9}{5}\\left(\\var{C}\\right)+32=\\simplify{1.8*{C}+32}^{\\circ}$

b) First, rearrange the formula to make C the subject: $F = \\frac{9}{5}C+32$ becomes $C=\\frac{5}{9}\\left(F-32\\right)$

Next, plug $\\var{F}^{\\circ}$ in for $F$: $C=\\frac{5}{9}\\left(\\var{F}-32\\right)=\\simplify{ 5*({F}-32)/9}^{\\circ}$

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Convert $\\var{C}^{\\circ}\\textrm{C}$ to Fahrenheit.

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Convert $\\var{F}^{\\circ}\\textrm{F}$ to Celsius.

(Don't input decimals unless it is exact; use fractions if necessary)

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Multiply out the brackets and select the correct answer.

", "advice": "

(a) To expand the brackets $\\simplify{(x+{a})^2}$ - there are different ways to do this! You could write it out like this

\\[ \\simplify{(x+{a})^2} \\equiv \\simplify[!cancelTerms]{(x+{a})(x+{a})} \\equiv \\simplify[basic,collectNumbers]{x^2 + {a}x+{a}x+{a}^2} \\equiv \\simplify{x^2+{2*a}x +{a^2} } \\]

(b) Same process for this part:

\\[ \\simplify{({b}x+{c})^2} \\equiv \\simplify[collectNumbers,!cancelTerms]{({b}x+{c})({b}x+{c})} \\equiv \\simplify[basic,collectNumbers]{{b^2}x^2 + {b*c}x+{b*c}x+{c}^2} \\equiv \\simplify{{b^2}x^2 + {2*b*c}x+{c^2}} \\]

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$\\simplify{(x+{a})^2}$

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$\\simplify{x^2 + 2{a}x+{a^2}}$

", "

$\\simplify{x^2 +{a^2}}$

", "

$\\simplify{x^2 +3{a}x+{a}}$

", "

$\\simplify{x^2 -{a^2}}$

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$\\simplify{({b}x+{c})^2}$

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["

$\\simplify{{b^2}x^2 + 2{b}{c}x+{c^2}}$

", "

$\\simplify{{b^2}x^2 +{c^2}}$

", "

$\\simplify{{b}x^2 + 3{a}{b}x+{c^2}}$

", "

$\\simplify{{b}x^2 - 3{a}x-{c^3}}$

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Factorise the following expression.

$\\simplify{{a*b}x+{a*c}x^2+{a}x^3} \\equiv $ [[0]]

(Use the ^ key to enter powers. For example, x^3 gives $x^3$.)

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Solve these equations to find the value of $x$

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$\\dfrac{\\var{a}}{x}=\\var{b}$

$x = $ [[0]]

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$\\sqrt{x}=\\var{c}$

$x = $ [[0]]

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What is the value of $x$?

$x = $ [[0]]

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Consider the equation \\[ \\var{d}x-\\var{f}=\\var{g}x+\\var{h} \\]

", "advice": "

We are asked to solve the equation

\\[ \\var{d}x-\\var{f}=\\var{g}x+\\var{h} \\]

In this equation, there are $x$ terms and constant terms on both sides of the equals sign.

To solve this equation, we must rearrange it to get $x$ on its own.

\\begin{align}
\\var{d}x-\\var{f} &= \\var{g}x+\\var{h} \\\\[0.5em]
\\var{d}x-\\var{g}x &= \\var{h}+\\var{f} & \\text{Move } x \\text{ terms to the left, and constant terms to the right.}\\\\[0.5em]
\\simplify{{d-g}*x} &= {\\var{h+f}} & \\text{Collect like terms together.}\\\\[0.5em]
x &=\\frac{\\var{h+f}}{\\var{d-g}} & \\text{Divide both sides by } \\var{d-g} \\text{.} \\\\[0.5em]
x &= \\simplify{{h+f}/{d-g}}
\\end{align}

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Solve a simple linear equation algebraically. The unknown appears on both sides of the equation.

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Which of the following equations has no solutions?

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Solve a pair of simultaneous equations.

", "licence": "None specified"}, "statement": "

Simultaneous equations have two equations with two unknowns.

", "advice": "

We can't immediately eliminate $x$ or $y$ from each equation so there are couple of ways to approach this. One possibility is to multiply each equation by a constant so that we can do elimination.

For example: multiply the first equation by $\\var{c}$ and the second equation by $\\simplify{-{a}}$: \\[ \\simplify{ {c}{a}x+{c}{b}y = {c}{b1}} \\\\ \\simplify{ {-a}{c}x+{-a}{d}y = {-a}{b2}} \\] Now we have two equations with the same coefficient on $x$.

We can do elimination (of $x$) by adding the equations. \\[ \\simplify{{c}{b}y + {-a}{d}y} = \\simplify{{c}{b1}} + \\simplify{{-a}{b2} } \\\\ \\simplify{({c}{b}+{-a}{d})y ={c}{b1}+{-a}{b2} } \\]

Therefore $y=\\var{y}$.

Substitute this value into one of the original equations. For example, using the first: \\[ \\simplify{ {a}x+{b}{y} = {b1}} \\\\ \\simplify{ {a}x = {b1} - {b}{y} } \\]

Therefore $x=\\var{x}$.

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Solve the equations \\[ \\begin{eqnarray} \\simplify[!noLeadingMinus]{ {a}x + {b}y } & = & \\var{b1} \\\\ \\simplify[noLeadingMinus]{{c}x + {d}y} &=& \\var{b2} \\end{eqnarray} \\]

Solutions $x = $ [[0]] , $y = $ [[1]]

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This question will generate a quadratic expression which can be expressed in terms of rational factors.

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Factorise the following quadratic expressions:

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$\\simplify{ x^2 + {p+q}x + {p*q}}$.

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$\\simplify{{a*c} x^2 + {b*c+a*d}x + {b*d}}$.

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Drag points on a graph to the given Cartesian coordinates. There are points in each of the four quadrants and on each axis.

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Move the points to the required coordinates on the graph.

", "advice": "

Coordinates are given as $(x\\text{-coordinate},y\\text{-coordinate})$. So, for example $(2,5)$ has $x$-coordinate $= 2$ and $y$-coordinate$= 5$.

Plot the first coordinate ($x$-coordinate) against the horizontal axis and then plot the second coordinate ($y$-coordinate) against the vertical axis.

{correctPoints()}

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b1 = Numbas.jme.unwrapValue(scope.variables.b1);\nvar b2 = Numbas.jme.unwrapValue(scope.variables.b2);\nvar c1 = Numbas.jme.unwrapValue(scope.variables.c1);\nvar c2 = Numbas.jme.unwrapValue(scope.variables.c2);\nvar d1 = Numbas.jme.unwrapValue(scope.variables.d1);\nvar d2 = Numbas.jme.unwrapValue(scope.variables.d2);\nvar e1 = Numbas.jme.unwrapValue(scope.variables.e1);\nvar e2 = Numbas.jme.unwrapValue(scope.variables.e2);\nvar f1 = Numbas.jme.unwrapValue(scope.variables.f1);\nvar f2 = Numbas.jme.unwrapValue(scope.variables.f2);\n\n\nvar a = board.create('point',[a1,a2],{name: 'A', size: 7, fillColor: 'limegreen' , strokeColor: 'yellow' , highlightFillColor: 'green', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: true});\nvar b = board.create('point',[b1,b2],{name: 'B', size: 7, fillColor: 'limegreen' , strokeColor: 'yellow' , highlightFillColor: 'green', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: true});\nvar c = board.create('point',[c1,c2],{name: 'C', size: 7, fillColor: 'limegreen' , strokeColor: 'yellow' , highlightFillColor: 'green', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: true});\nvar d = board.create('point',[d1,d2],{name: 'D', size: 7, fillColor: 'limegreen' , strokeColor: 'yellow' , highlightFillColor: 'green', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: true});\nvar e = board.create('point',[e1,e2],{name: 'E', size: 7, fillColor: 'limegreen' , strokeColor: 'yellow' , highlightFillColor: 'green', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: true});\nvar f = board.create('point',[f1,f2],{name: 'F', size: 7, fillColor: 'limegreen' , strokeColor: 'yellow' , highlightFillColor: 'green', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: true});\n\n/*\nquestion.signals.on('HTMLAttached',function(e) {\n ko.computed(function(){ \n var x = parseFloat(question.parts[0].gaps[0].display.studentAnswer());\n var y = 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board.create('point',[10,8],{name: 'C', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow',snapToGrid: true, showInfobox: false});\nvar d = board.create('point',[10,7],{name: 'D', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow',snapToGrid: true, showInfobox: false});\nvar e = board.create('point',[10,6],{name: 'E', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow',snapToGrid: true, showInfobox: false});\nvar f = board.create('point',[10,5],{name: 'F', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow',snapToGrid: true, showInfobox: false});\n\nquestion.points = {\n a:a,b:b,c:c,d:d,e:e,f:f\n}\n\na.on('drag',function(){\n Numbas.exam.currentQuestion.parts[0].gaps[0].display.studentAnswer(a.X());\n Numbas.exam.currentQuestion.parts[0].gaps[1].display.studentAnswer(a.Y());\n});\nb.on('drag',function(){\n Numbas.exam.currentQuestion.parts[1].gaps[0].display.studentAnswer(b.X());\n Numbas.exam.currentQuestion.parts[1].gaps[1].display.studentAnswer(b.Y());\n});\nc.on('drag',function(){\n Numbas.exam.currentQuestion.parts[2].gaps[0].display.studentAnswer(c.X());\n Numbas.exam.currentQuestion.parts[2].gaps[1].display.studentAnswer(c.Y());\n});\nd.on('drag',function(){\n Numbas.exam.currentQuestion.parts[3].gaps[0].display.studentAnswer(d.X());\n Numbas.exam.currentQuestion.parts[3].gaps[1].display.studentAnswer(d.Y());\n});\ne.on('drag',function(){\n Numbas.exam.currentQuestion.parts[4].gaps[0].display.studentAnswer(e.X());\n Numbas.exam.currentQuestion.parts[4].gaps[1].display.studentAnswer(e.Y());\n});\nf.on('drag',function(){\n Numbas.exam.currentQuestion.parts[5].gaps[0].display.studentAnswer(f.X());\n Numbas.exam.currentQuestion.parts[5].gaps[1].display.studentAnswer(f.Y());\n});\n\n/*\nquestion.signals.on('HTMLAttached',function(e) {\n ko.computed(function(){ \n var x = parseFloat(question.parts[0].gaps[0].display.studentAnswer());\n var y = parseFloat(question.parts[0].gaps[1].display.studentAnswer());\n if(!(isNaN(x) || isNaN(y)) && board.mode!=board.BOARD_MODE_DRAG) {\n a.moveTo([x,y],100);\n }\n });\n});\n*/\n\nreturn div;\n\n"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {"mark": {"script": "console.log(this.question.points);\nthis.question.points.a.setAttribute({fillColor: this.credit==1 ? 'green' : 'red'});\n", "order": "after"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

{dragpoints()}

Move the points as follows:

A to $(\\var{a1},\\var{a2})$.

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B to $(\\var{b1},\\var{b2})$.

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C to $(\\var{c1},\\var{c2})$.

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D to $(\\var{d1},\\var{d2})$.

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E to $(\\var{e1},\\var{e2})$.

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F to $(\\var{f1},\\var{f2})$.

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This uses an embedded Geogebra graph of a line $y=mx+c$ with random coefficients set by NUMBAS.

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The graph shows a straight line on a graph.

{geogebra_applet('https://ggbm.at/FTsrJUzg', defs, [])}

What is the equation of this line?

$y = $ [[0]]

Match the graph with the correct function description.

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Which of the following is the graph of $y=x^3$?

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Answer the following questions about these 3D shapes.

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The picture shows a cuboid of of width $w$, length $l$ and height $h$.

Given that $w=\\var{w}$, $l=\\var{l}$ and $h=\\var{h}$. Calculate the value of the following:

Volume = [[0]]

Surface area = [[1]]

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The picture shows a sphere of radius $\\var{r}$.

Write down the expression for finding the exact volume of the sphere. Give your answer in terms of $\\pi$. (Type pi in the answer box where you want $\\pi$ to appear.)

Volume = [[0]]

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Using Pythagoras' Theorem to find a missing side. Illustrated using simple Eukleides diagram

rebelmaths

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Use Pythagoras's Theorem to find the value of $x^2$.

{RightAngledTriangle}

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$x^2 = \\var{lent1}^2 + \\var{lent2}^2$

That means the length is:

$x = \\sqrt(\\var{lent1}^2 + \\var{lent2}^2)$

$x = \\var{ans1}$

(You were not asked to find this in the question!)

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A diagram of a right angled triangle.

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Find the value of $x^2$:

$x^2 = $ [[0]] $\\mathrm{mm^2}$

You were asked for $x^2$, not $x$.

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Calculate the missing angles in the diagrams below.

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These two angles lie on a straight line. This picture is not drawn accurately!

Given that the smaller angle is $\\var{x1}^{\\circ}$, calculate larger angle $y$.

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Angles around a point. This picture is not drawn accurately!

Three angles are given: $\\var{a}^{\\circ}$, $\\var{b}^{\\circ}$ and $\\var{c}^{\\circ}$.

Calculate the missing angle, $y$.

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Angles in triangle. This picture is not drawn accurately!

Two given angles are $\\var{p}^{\\circ}$ and $\\var{q}^{\\circ}$

Calculate the other angle, $x$.

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These questions will assess your prior knowledge of differentiation and integration.

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Given the function \\[ y = \\simplify{{p}x^3 + {q}x+{r}} \\] Find an expression for the first derivative.

$\\displaystyle \\simplify{diff(y,x,1)} = $ [[0]]

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Find the following indefinite integral. Select the correct answer from the list.

\\[ \\simplify{int({a}x^2+{b}x+{c},x)} \\]

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You have 5 minutes remaining!

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This is a practice test to help you get used to the NUMBAS environment. The questions cover a range of topics:

Numbers
Algebra
Shape, space and geometry
Calculus

Some further instructions:

No calculator allowed on this test.
You have been provided with paper for rough work.

Answers will be saved automatically as you move through the test. You can go back and change answers if needed.

If you don't know the answer to a question: just leave it unanswered! Many of the topics will be covered in class this year, so don't worry. This test does not count towards your final module marks. Your result will only be seen by your teachers and they'll use it as a guide to support you in the early weeks of your maths modules.

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Thank you for submitting your answers. You may close the browser and logout of the PC.

https://mas-numbas-lti.ncl.ac.uk/safe_exam_browser/quit

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