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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:

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• Algebra
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• Numbers
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• Shape, space and geometry
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You should be able to do this test in less than 45 minutes and without a calculator.

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This test does not count towards your final module mark.  You can take the test as many times as you want.

A practice test to get used to the NUMBAS environment.

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

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

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

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

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Answer the following questions (without a calculator!)

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Carry out the following calculations.

$\\var{a} \\times\\var{b}$

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$\\var{c} \\times\\var{d}$

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

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

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

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

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

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Calculate  10% of {a}.

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Calculate  5% of {a}.

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Calculate  15% of {a}.

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den1

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"random(1..m-1) //random numerator less than denominator", "description": "", "name": "l"}, "j": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "j"}, "r": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "r"}, "ss": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..tt-1) //random numerator less than denominator", "description": "", "name": "ss"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..b-1) //random numerator less than denominator", "description": "", "name": "a"}, "answer1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "simplenum1+\"/\"+simpleden1", "description": "", "name": "answer1"}, "pp": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "pp"}, "f": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "f"}, "gg": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..hh-1) //random numerator less than denominator", "description": "", "name": "gg"}, "answer3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "simplenum3+\"/\"+simpleden3", "description": "", "name": "answer3"}, "multiple": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(3,4,5,6,7,8,9)", "description": "", "name": "multiple"}, "simplenum1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "num1/gcd(num1,den1)", "description": "", "name": "simplenum1"}, "d": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..f-1) //random numerator less than denominator", "description": "", "name": "d"}, "dd": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "dd"}, "num2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "{d}", "description": "", "name": "num2"}, "jj": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "jj"}, "nn": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "nn"}, "multiple_d": {"templateType": "anything", "group": "Ungrouped variables", "definition": "{multiple}*{d}", "description": "", "name": "multiple_d"}, "s": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..t-1) //random numerator less than denominator", "description": "", "name": "s"}, "y": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..x-1) //random numerator less than denominator", "description": "", "name": "y"}, "aa": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..bb-1) //random numerator less than denominator", "description": "", "name": "aa"}, "ii": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..jj-1) //random numerator less than denominator", "description": "", "name": "ii"}, "answer2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "simplenum2+\"/\"+simpleden2", "description": "", "name": "answer2"}, "simplenum4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "num4/gcd(num4,den4)", "description": "", "name": "simplenum4"}, "ll": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "ll"}, "kk": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..ll-1) //random numerator less than denominator", "description": "", "name": "kk"}, "simpleden1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "den1/gcd(num1,den1)", "description": "", "name": "simpleden1"}, "v": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "v"}, "c": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..b-a) //random numerator less than denominator", "description": "", "name": "c"}, "g": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..f-d) //random numerator less than denominator", "description": "", "name": "g"}, "simpleden2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "den2/gcd(num2,den2)", "description": "", "name": "simpleden2"}, "num3": {"templateType": "anything", "group": "Ungrouped variables", "definition": 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denominator", "description": "", "name": "bb"}, "rr": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "rr"}, "num1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "{a}{c}", "description": "", "name": "num1"}, "x": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(4..10) //random denominator", "description": "", "name": "x"}, "ee": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..ff-1) //random numerator less than denominator", "description": "", "name": "ee"}, "den2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "multiple_d", "description": "", "name": "den2"}, "simplenum2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "num2/gcd(num2,den2)", "description": "", "name": "simplenum2"}, "mm": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..nn-1) //random numerator less than denominator", "description": "", "name": "mm"}, "k": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..j-h) //random numerator less than denominator", "description": "", "name": "k"}, "q": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..r-1) //random numerator less than denominator", "description": "", "name": "q"}, "simplenum3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "num3/gcd(num3,den3)", "description": "", "name": "simplenum3"}, "tt": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "tt"}, "multiple_m": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(m*3,m*4,m*5,m*6,m*7)", "description": "", "name": "multiple_m"}, "ff": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "ff"}, "w": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..3) ", "description": "", "name": "w"}, "o": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..p-1) //random numerator less than denominator", "description": "", "name": "o"}}, "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"], "functions": {}, "parts": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "gapfill", "showFeedbackIcon": true, "prompt": "

\n

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

\n

[[0]]

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

\n

[[0]]

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

\n

[[0]]

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

\n

[[0]]

", "marks": 0, "gaps": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "matchMode": "regex", "showFeedbackIcon": true, "answer": "{answer4}", "displayAnswer": "{answer4}", "showCorrectAnswer": true, "marks": 1, "type": "patternmatch", "scripts": {}}], "showCorrectAnswer": true, "scripts": {}}], "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "preamble": {"js": "", "css": ""}, "statement": "

\n

In the form a/b

", "rulesets": {}, "variable_groups": [], "type": "question"}, {"name": "Formula for temperature (conversion/substitution)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "advice": "", "rulesets": {}, "preamble": {"css": "", "js": ""}, "parts": [{"prompt": "

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

", "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "allowFractions": true, "mustBeReducedPC": 0, "correctAnswerFraction": false, "marks": 1, "minValue": "1.8*C+32", "scripts": {}, "maxValue": "1.8*C+32", "variableReplacements": [], "correctAnswerStyle": "plain"}, {"prompt": "

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

\n

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

", "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "mustBeReduced": true, "notationStyles": ["plain", "en", "si-en"], "allowFractions": true, "mustBeReducedPC": "50", "correctAnswerFraction": true, "marks": 1, "minValue": "5*(F-32)/9", "scripts": {}, "maxValue": "5*(F-32)/9", "variableReplacements": [], "correctAnswerStyle": "plain"}], "variable_groups": [], "metadata": {"licence": "None specified", "description": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "ungrouped_variables": ["C", "F"], "functions": {}, "variables": {"F": {"templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "random(-100..500 except 0)", "name": "F"}, "C": {"templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "random(-40..300 except 0)", "name": "C"}}, "tags": [], "statement": "

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

\n

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

", "type": "question"}, {"name": "Simple modulus", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "functions": {}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"b1": {"templateType": "randrange", "name": "b1", "group": "Ungrouped variables", "description": "", "definition": "random(21..35#1)"}, "a1": {"templateType": "randrange", "name": "a1", "group": "Ungrouped variables", "description": "", "definition": "random(5..20#1)"}}, "advice": "", "preamble": {"css": "", "js": ""}, "parts": [{"mustBeReduced": false, "type": "numberentry", "scripts": {}, "variableReplacements": [], "correctAnswerStyle": "plain", "maxValue": "abs(a1-b1)", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "minValue": "abs(a1-b1)", "prompt": "

$|\\var{a1}-\\var{b1}|$

", "allowFractions": false, "marks": 1, "mustBeReducedPC": 0, "showFeedbackIcon": true, "correctAnswerFraction": false}], "statement": "

The statement below contains a modulus (absolute value).  Simplify the following expression:

", "metadata": {"licence": "None specified", "description": ""}, "ungrouped_variables": ["a1", "b1"], "tags": [], "rulesets": {}, "type": "question"}]}, {"pickQuestions": 1, "pickingStrategy": "all-ordered", "name": "Algebra", "questions": [{"name": "Expanding brackets", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "advice": "", "metadata": {"description": "", "licence": "None specified"}, "preamble": {"js": "", "css": ""}, "variables": {"b": {"definition": "random(2..10#1)", "name": "b", "group": "Ungrouped variables", "description": "", "templateType": "randrange"}, "c": {"definition": "random(-9..9#1)", "name": "c", "group": "Ungrouped variables", "description": "", "templateType": "randrange"}, "a": {"definition": "random(-10..10#1)", "name": "a", "group": "Ungrouped variables", "description": "", "templateType": "randrange"}}, "functions": {}, "ungrouped_variables": ["a", "b", "c"], "rulesets": {}, "tags": [], "variablesTest": {"condition": "a<>0 and b<>0 and c<>0", "maxRuns": 100}, "statement": "

Multiply out the brackets and select the correct answer.

", "variable_groups": [], "parts": [{"variableReplacementStrategy": "originalfirst", "choices": ["

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

", "

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

", "

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

", "

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

"], "variableReplacements": [], "displayColumns": 0, "marks": 0, "shuffleChoices": true, "showCorrectAnswer": true, "matrix": ["1", 0, 0, 0], "scripts": {}, "minMarks": 0, "type": "1_n_2", "prompt": "

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

", "showFeedbackIcon": true, "displayType": "radiogroup", "maxMarks": 0, "distractors": ["", "", "", ""]}, {"variableReplacementStrategy": "originalfirst", "choices": ["

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

", "

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

", "

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

", "

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

"], "variableReplacements": [], "displayColumns": 0, "marks": 0, "shuffleChoices": true, "showCorrectAnswer": true, "matrix": ["1", 0, 0, 0], "scripts": {}, "minMarks": 0, "type": "1_n_2", "prompt": "

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

", "showFeedbackIcon": true, "displayType": "radiogroup", "maxMarks": 0, "distractors": ["", "", "", ""]}], "type": "question"}, {"name": "Simple equations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "ungrouped_variables": ["a", "b", "ans", "c", "ans2"], "statement": "

Solve these equations to find the value of $x$

", "advice": "", "metadata": {"description": "", "licence": "None specified"}, "variable_groups": [], "parts": [{"gaps": [{"notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "scripts": {}, "correctAnswerStyle": "plain", "allowFractions": true, "minValue": "{ans}", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "mustBeReduced": false, "showFeedbackIcon": true, "maxValue": "{ans}", "variableReplacements": [], "marks": 1, "mustBeReducedPC": 0}], "showFeedbackIcon": true, "scripts": {}, "prompt": "

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

\n

$x =$ [[0]]

", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "type": "gapfill", "marks": 0}, {"gaps": [{"notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "scripts": {}, "correctAnswerStyle": "plain", "allowFractions": true, "minValue": "{ans2}", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "mustBeReduced": false, "showFeedbackIcon": true, "maxValue": "{ans2}", "variableReplacements": [], "marks": 1, "mustBeReducedPC": 0}], "showFeedbackIcon": true, "scripts": {}, "prompt": "

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

\n

$x =$ [[0]]

", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "type": "gapfill", "marks": 0}], "functions": {}, "rulesets": {}, "variables": {"a": {"group": "Ungrouped variables", "description": "", "name": "a", "definition": "random(2..20)", "templateType": "anything"}, "ans2": {"group": "Ungrouped variables", "description": "", "name": "ans2", "definition": "c^2", "templateType": "anything"}, "b": {"group": "Ungrouped variables", "description": "", "name": "b", "definition": "random(-50..50)", "templateType": "anything"}, "ans": {"group": "Ungrouped variables", "description": "", "name": "ans", "definition": "a/b", "templateType": "anything"}, "c": {"group": "Ungrouped variables", "description": "", "name": "c", "definition": "random(3..15)", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "preamble": {"js": "", "css": ""}, "type": "question"}, {"name": "Solve a linear equation $ax+b = cx+d$", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "ungrouped_variables": ["d", "f", "g", "h", "x", "gcd_hfdg", "hf_coprime", "dg_coprime", "finalb"], "parts": [{"variableReplacements": [], "prompt": "

What is the value of $x$?

\n

$x =$ [[0]]

", "variableReplacementStrategy": "originalfirst", "scripts": {}, "gaps": [{"maxValue": "finalb", "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "correctAnswerFraction": false, "marks": "2", "mustBeReduced": false, "minValue": "finalb", "scripts": {}, "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacements": [], "allowFractions": false, "type": "numberentry"}], "showFeedbackIcon": true, "marks": 0, "type": "gapfill", "showCorrectAnswer": true}], "rulesets": {}, "variables": {"finalb": {"definition": "hf_coprime/dg_coprime", "group": "Ungrouped variables", "templateType": "anything", "name": "finalb", "description": ""}, "f": {"definition": "random(2..6)", "group": "Ungrouped variables", "templateType": "anything", "name": "f", "description": ""}, "gcd_hfdg": {"definition": "gcd((h+f),(d-g))", "group": "Ungrouped variables", "templateType": "anything", "name": "gcd_hfdg", "description": ""}, "d": {"definition": "random(g+2..8)", "group": "Ungrouped variables", "templateType": "anything", "name": "d", "description": ""}, "h": {"definition": "(x*(d-g))-f", "group": "Ungrouped variables", "templateType": "anything", "name": "h", "description": ""}, "dg_coprime": {"definition": "(d-g)/gcd_hfdg", "group": "Ungrouped variables", "templateType": "anything", "name": "dg_coprime", "description": ""}, "x": {"definition": "random(2..6)", "group": "Ungrouped variables", "templateType": "anything", "name": "x", "description": ""}, "hf_coprime": {"definition": "(h+f)/gcd_hfdg", "group": "Ungrouped variables", "templateType": "anything", "name": "hf_coprime", "description": ""}, "g": {"definition": "random(2..5)", "group": "Ungrouped variables", "templateType": "anything", "name": "g", "description": ""}}, "statement": "

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

We are asked to solve the equation

\n

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

\n

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

\n

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

\n

\\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} ", "variablesTest": {"condition": "", "maxRuns": 100}, "functions": {}, "tags": [], "preamble": {"js": "", "css": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": " Solve a simple linear equation algebraically. The unknown appears on both sides of the equation. "}, "variable_groups": [], "type": "question"}, {"name": "Simultaneous equations (harder)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "metadata": {"licence": "None specified", "description": " Solve a pair of simultaneous equations. "}, "variables": {"x": {"name": "x", "group": "Ungrouped variables", "templateType": "randrange", "description": "", "definition": "random(-10..10#1)"}, "c": {"name": "c", "group": "Coefficients", "templateType": "randrange", "description": "", "definition": "random(-10..10#1)"}, "d": {"name": "d", "group": "Coefficients", "templateType": "randrange", "description": "", "definition": "random(-10..10#1)"}, "b1": {"name": "b1", "group": "RHS", "templateType": "anything", "description": "", "definition": "a*x+b*y"}, "a": {"name": "a", "group": "Coefficients", "templateType": "randrange", "description": "", "definition": "random(-10..10#1)"}, "b": {"name": "b", "group": "Coefficients", "templateType": "randrange", "description": "", "definition": "random(-10..10#1)"}, "y": {"name": "y", "group": "Ungrouped variables", "templateType": "randrange", "description": "", "definition": "random(-10..10#1)"}, "b2": {"name": "b2", "group": "RHS", "templateType": "anything", "description": "", "definition": "c*x+d*y"}, "det": {"name": "det", "group": "RHS", "templateType": "anything", "description": "", "definition": "a*d-b*c"}}, "ungrouped_variables": ["x", "y"], "variable_groups": [{"variables": ["a", "b", "c", "d"], "name": "Coefficients"}, {"variables": ["b1", "b2", "det"], "name": "RHS"}], "tags": [], "variablesTest": {"condition": "abs(a)>1 and abs(b)>1 and abs(c)>1 and abs(d)>1 and det<>0", "maxRuns": "250"}, "preamble": {"css": "", "js": ""}, "parts": [{"showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill", "gaps": [{"maxValue": "x", "mustBeReducedPC": 0, "variableReplacements": [], "type": "numberentry", "minValue": "x", "marks": "1.5", "mustBeReduced": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "correctAnswerFraction": false}, {"maxValue": "y", "mustBeReducedPC": 0, "variableReplacements": [], "type": "numberentry", "minValue": "y", "marks": "1.5", "mustBeReduced": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "correctAnswerFraction": false}], "marks": 0, "prompt": " Solve the equations \n \\simplify{ {a}x + {b}y = {b1} }\\\\ \\simplify{{c}x + {d}y = {b2} } \n Solutions x =  [[0]] , y =  [[1]] "}], "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. \n 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 $x$.

\n

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} } \$

\n

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

\n

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} } \$

\n

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

", "statement": "

Simultaneous equations have two equations with two unknowns.

", "rulesets": {}, "functions": {}, "type": "question"}, {"name": "Factorise a quadratic expression", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "rulesets": {}, "preamble": {"js": "", "css": ""}, "advice": "", "variable_groups": [], "statement": "

", "tags": [], "variablesTest": {"maxRuns": "300", "condition": "a<>0 and b<>0 and c<>0 and d<>0 and p<>0 and q<>0 and a*c>1 and p+q<>0 and p*q<>0"}, "parts": [{"checkingtype": "absdiff", "marks": "2", "scripts": {}, "variableReplacements": [], "expectedvariablenames": [], "prompt": "

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

", "type": "jme", "answer": "(x + {p})(x + {q})", "checkvariablenames": false, "answersimplification": "all", "vsetrange": [0, 1], "showpreview": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "showCorrectAnswer": true, "checkingaccuracy": 0.001, "vsetrangepoints": 5}, {"checkingtype": "absdiff", "marks": "3", "scripts": {}, "variableReplacements": [], "expectedvariablenames": [], "prompt": "

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

", "type": "jme", "answer": "({a} x + {b})({c} x + {d})", "checkvariablenames": false, "vsetrange": [0, 1], "showpreview": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "showCorrectAnswer": true, "checkingaccuracy": 0.001, "vsetrangepoints": 5}], "variables": {"p": {"templateType": "randrange", "name": "p", "description": "", "definition": "random(-10..10#1)", "group": "Ungrouped variables"}, "a": {"templateType": "randrange", "name": "a", "description": "", "definition": "random(-3..3#1)", "group": "Ungrouped variables"}, "c": {"templateType": "randrange", "name": "c", "description": "", "definition": "random(-3..3#1)", "group": "Ungrouped variables"}, "b": {"templateType": "randrange", "name": "b", "description": "", "definition": "random(-5..5#1)", "group": "Ungrouped variables"}, "q": {"templateType": "randrange", "name": "q", "description": "", "definition": "random(-10..10#1)", "group": "Ungrouped variables"}, "d": {"templateType": "randrange", "name": "d", "description": "", "definition": "random(-5..5#1)", "group": "Ungrouped variables"}}, "ungrouped_variables": ["a", "b", "c", "d", "p", "q"], "metadata": {"description": "

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

", "licence": "None specified"}, "functions": {}, "type": "question"}]}, {"pickQuestions": 1, "pickingStrategy": "all-ordered", "name": "Shape, space and trigonometry", "questions": [{"name": "Drag points to given Cartesian coordinates", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "statement": "

Move the points to the required coordinates on the graph.

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

"}, "parts": [{"variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "gapfill", "gaps": [{"variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{a1}", "marks": "0.5", "scripts": {}, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "showCorrectAnswer": true, "allowFractions": false, "correctAnswerFraction": false, "minValue": "{a1}"}, {"variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{a2}", "marks": "0.5", "scripts": {}, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "showCorrectAnswer": true, "allowFractions": false, "correctAnswerFraction": false, "minValue": "{a2}"}], "showFeedbackIcon": true, "showCorrectAnswer": true, "prompt": "

{dragpoints()}

\n

Move the points as follows:

\n

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

", "scripts": {"mark": {"script": "console.log(this.question.points);\nthis.question.points.a.setAttribute({fillColor: this.credit==1 ? 'green' : 'red'});\n", "order": "after"}}, "marks": 0}, {"variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "gapfill", "gaps": [{"variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{b1}", "marks": "0.5", "scripts": {}, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "showCorrectAnswer": true, "allowFractions": false, "correctAnswerFraction": false, "minValue": "{b1}"}, {"variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{b2}", "marks": "0.5", "scripts": {}, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "showCorrectAnswer": true, "allowFractions": false, "correctAnswerFraction": false, "minValue": "{b2}"}], "showFeedbackIcon": true, "showCorrectAnswer": true, "prompt": "

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

\n

", "scripts": {"mark": {"script": "console.log(this.question.points);\nthis.question.points.b.setAttribute({fillColor: this.credit==1 ? 'green' : 'red'});\n", "order": "after"}}, "marks": 0}, {"variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "gapfill", "gaps": [{"variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{c1}", "marks": "0.5", "scripts": {}, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "showCorrectAnswer": true, "allowFractions": false, "correctAnswerFraction": false, "minValue": "{c1}"}, {"variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{c2}", "marks": "0.5", "scripts": {}, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "showCorrectAnswer": true, "allowFractions": false, "correctAnswerFraction": false, "minValue": "{c2}"}], "showFeedbackIcon": true, "showCorrectAnswer": true, "prompt": "

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

\n

", "scripts": {"mark": {"script": "console.log(this.question.points);\nthis.question.points.c.setAttribute({fillColor: this.credit==1 ? 'green' : 'red'});\n", "order": "after"}}, "marks": 0}, {"variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "gapfill", "gaps": [{"variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{d1}", "marks": "0.5", "scripts": {}, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "showCorrectAnswer": true, "allowFractions": false, "correctAnswerFraction": false, "minValue": "{d1}"}, {"variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{d2}", "marks": "0.5", "scripts": {}, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "showCorrectAnswer": true, "allowFractions": false, "correctAnswerFraction": false, "minValue": "{d2}"}], "showFeedbackIcon": true, "showCorrectAnswer": true, "prompt": "

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

\n

", "scripts": {"mark": {"script": "console.log(this.question.points);\nthis.question.points.d.setAttribute({fillColor: this.credit==1 ? 'green' : 'red'});\n", "order": "after"}}, "marks": 0}, {"variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "gapfill", "gaps": [{"variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{e1}", "marks": "0.5", "scripts": {}, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "showCorrectAnswer": true, "allowFractions": false, "correctAnswerFraction": false, "minValue": "{e1}"}, {"variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{e2}", "marks": "0.5", "scripts": {}, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "showCorrectAnswer": true, "allowFractions": false, "correctAnswerFraction": false, "minValue": "{e2}"}], "showFeedbackIcon": true, "showCorrectAnswer": true, "prompt": "

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

", "scripts": {"mark": {"script": "console.log(this.question.points);\nthis.question.points.e.setAttribute({fillColor: this.credit==1 ? 'green' : 'red'});", "order": "after"}}, "marks": 0}, {"variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "gapfill", "gaps": [{"variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{f1}", "marks": "0.5", "scripts": {}, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "showCorrectAnswer": true, "allowFractions": false, "correctAnswerFraction": false, "minValue": "{f1}"}, {"variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{f2}", "marks": "0.5", "scripts": {}, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "mustBeReduced": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "showCorrectAnswer": true, "allowFractions": false, "correctAnswerFraction": false, "minValue": "{f2}"}], "showFeedbackIcon": true, "showCorrectAnswer": true, "prompt": "

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

\n

", "scripts": {"mark": {"script": "console.log(this.question.points);\nthis.question.points.f.setAttribute({fillColor: this.credit==1 ? 'green' : 'red'});", "order": "after"}}, "marks": 0}], "advice": "

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

\n

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

\n

{correctPoints()}

", "rulesets": {}, "preamble": {"css": "", "js": ""}, "variable_groups": [], "functions": {"correctPoints": {"definition": "var div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',{boundingBox:[-11,11,11,-11],grid: true});\nvar board = div.board;\nquestion.board = board;\n\nvar a1 = Numbas.jme.unwrapValue(scope.variables.a1);\nvar a2 = Numbas.jme.unwrapValue(scope.variables.a2);\nvar 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/*\n$('body').on('question-html-attached',function(e,question,qd) {\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;", "parameters": [], "language": "javascript", "type": "html"}, "dragpoints": {"definition": "var div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',{boundingBox:[-11,11,11,-11],grid: true});\nvar board = div.board;\nquestion.board = board;\n\n//var x = Numbas.jme.unwrapValue(scope.variables.x);\n//var y = Numbas.jme.unwrapValue(scope.variables.y);\n\nvar a = board.create('point',[10,10],{name: 'A', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: false});\nvar b = board.create('point',[10,9],{name: 'B', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow',snapToGrid: true, showInfobox: false});\nvar c = 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/*\n$('body').on('question-html-attached',function(e,question,qd) {\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", "parameters": [], "language": "javascript", "type": "html"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "variables": {"b2": {"definition": "random(1..10)", "name": "b2", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "c2": {"definition": "random(-10..-1)", "name": "c2", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "d1": {"definition": "random(-10..-1)", "name": "d1", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "f2": {"definition": "random(-10..10 except 0)", "name": "f2", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "e2": {"definition": "0", "name": "e2", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "y": {"definition": "2", "name": "y", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "x": {"definition": "1", "name": "x", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "a2": {"definition": "random(-10..-1)", "name": "a2", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "f1": {"definition": "0", "name": "f1", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "e3": {"definition": "random(-10..10 except 0)", "name": "e3", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "b1": {"definition": "random(1..9)", "name": "b1", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "a1": {"definition": "random(-10..-1)", "name": "a1", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "e1": {"definition": "random(-10..10 except 0)", "name": "e1", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "d2": {"definition": "random(1..10)", "name": "d2", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "c1": {"definition": "random(1..10)", "name": "c1", "group": "Ungrouped variables", "templateType": "anything", "description": ""}}, "ungrouped_variables": ["x", "y", "a1", "a2", "b1", "b2", "c1", "c2", "d1", "d2", "e1", "e2", "e3", "f1", "f2"], "type": "question"}, {"name": "Straight line graph", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "variables": {"c": {"description": "", "group": "Ungrouped variables", "definition": "random(-3..3)", "name": "c", "templateType": "anything"}, "defs": {"description": "", "group": "Ungrouped variables", "definition": "[\n ['m',m],\n ['c',c]\n]", "name": "defs", "templateType": "anything"}, "m": {"description": "", "group": "Ungrouped variables", "definition": "(random(random(0..3),random(1/2,2/3,1/4,3/4,1/3)))*random(-1,1)", "name": "m", "templateType": "anything"}}, "statement": "

The graph shows a straight line on a graph.

\n

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

\n

", "parts": [{"showCorrectAnswer": true, "type": "gapfill", "marks": 0, "gaps": [{"vsetrangepoints": 5, "type": "jme", "vsetrange": [0, 1], "scripts": {}, "variableReplacementStrategy": "originalfirst", "checkingaccuracy": 0.001, "answer": "{m}x+{c}", "showCorrectAnswer": true, "showFeedbackIcon": true, "marks": "2", "expectedvariablenames": [], "answersimplification": "zeroFactor,fractionNumbers,unitFactor", "checkvariablenames": false, "showpreview": true, "checkingtype": "absdiff", "variableReplacements": []}], "scripts": {}, "prompt": "

What is the equation of this line?

\n

$y =$ [[0]]

", "showFeedbackIcon": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": []}], "variable_groups": [], "ungrouped_variables": ["defs", "m", "c"], "preamble": {"js": "", "css": ""}, "variablesTest": {"condition": "", "maxRuns": "200"}, "metadata": {"description": "

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

", "licence": "Creative Commons Attribution 4.0 International"}, "advice": "", "tags": [], "rulesets": {}, "functions": {"graph": {"parameters": [], "definition": "", "language": "jme", "type": "html"}}, "type": "question"}, {"name": "Angle facts", "extensions": [], "custom_part_types": [], "resources": [["question-resources/angle_line.JPG", "/srv/numbas/media/question-resources/angle_line.JPG"], ["question-resources/angle_circle.JPG", "/srv/numbas/media/question-resources/angle_circle.JPG"], ["question-resources/triangle_angles.JPG", "/srv/numbas/media/question-resources/triangle_angles.JPG"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "preamble": {"js": "", "css": ""}, "statement": "

Calculate the missing angles in the diagrams below.

", "metadata": {"licence": "None specified", "description": ""}, "tags": [], "advice": "", "ungrouped_variables": ["x1", "a", "b", "c", "p", "q"], "variablesTest": {"maxRuns": 100, "condition": ""}, "variable_groups": [], "functions": {}, "parts": [{"showCorrectAnswer": true, "mustBeReducedPC": 0, "showFeedbackIcon": true, "maxValue": "180-x1", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "mustBeReduced": false, "scripts": {}, "variableReplacements": [], "correctAnswerStyle": "plain", "minValue": "180-x1", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "prompt": "

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

\n

\n

Given that $x = \\var{x1}^{\\circ}$, calculate $y$.

", "correctAnswerFraction": false, "marks": 1}, {"showCorrectAnswer": true, "mustBeReducedPC": 0, "showFeedbackIcon": true, "maxValue": "360-(a+b+c)", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "mustBeReduced": false, "scripts": {}, "variableReplacements": [], "correctAnswerStyle": "plain", "minValue": "360-(a+b+c)", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "prompt": "

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

\n

\n

Given that $a = \\var{a}^{\\circ}$, $b = \\var{b}^{\\circ}$ and $c = \\var{c}^{\\circ}$

\n

Calculate the angle $d$.

", "correctAnswerFraction": false, "marks": 1}, {"showCorrectAnswer": true, "mustBeReducedPC": 0, "showFeedbackIcon": true, "maxValue": "180-(p+q)", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "mustBeReduced": false, "scripts": {}, "variableReplacements": [], "correctAnswerStyle": "plain", "minValue": "180-(p+q)", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "prompt": "

Angles in triangle.  This picture is not drawn accurately!

\n

\n

Given that $p = \\var{p}^{\\circ}$ and $q = \\var{q}^{\\circ}$

\n

Calculate the angle $x$.

", "correctAnswerFraction": false, "marks": 1}], "rulesets": {}, "variables": {"a": {"group": "Ungrouped variables", "name": "a", "templateType": "randrange", "definition": "random(15..45#1)", "description": ""}, "c": {"group": "Ungrouped variables", "name": "c", "templateType": "randrange", "definition": "random(95..130#1)", "description": ""}, "q": {"group": "Ungrouped variables", "name": "q", "templateType": "randrange", "definition": "random(95..129#1)", "description": ""}, "p": {"group": "Ungrouped variables", "name": "p", "templateType": "randrange", "definition": "random(11..29#1)", "description": ""}, "x1": {"group": "Ungrouped variables", "name": "x1", "templateType": "randrange", "definition": "random(18..44#1)", "description": ""}, "b": {"group": "Ungrouped variables", "name": "b", "templateType": "randrange", "definition": "random(35..50#1)", "description": ""}}, "type": "question"}, {"name": "Sphere and cuboid", "extensions": [], "custom_part_types": [], "resources": [["question-resources/sphere.JPG", "/srv/numbas/media/question-resources/sphere.JPG"], ["question-resources/cuboid.JPG", "/srv/numbas/media/question-resources/cuboid.JPG"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "ungrouped_variables": ["w", "l", "h"], "advice": "", "functions": {}, "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "", "licence": "None specified"}, "tags": [], "variables": {"h": {"name": "h", "templateType": "randrange", "definition": "random(20..30#1)", "description": "", "group": "Ungrouped variables"}, "l": {"name": "l", "templateType": "randrange", "definition": "random(20..50#1)", "description": "", "group": "Ungrouped variables"}, "w": {"name": "w", "templateType": "randrange", "definition": "random(5..30#1)", "description": "", "group": "Ungrouped variables"}}, "parts": [{"variableReplacementStrategy": "originalfirst", "marks": 0, "scripts": {}, "prompt": "

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

\n

\n

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

\n

Volume = [[0]]

\n

Surface area = [[1]]

", "gaps": [{"scripts": {}, "minValue": "w*l*h", "type": "numberentry", "correctAnswerFraction": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "marks": "2", "maxValue": "w*l*h", "allowFractions": false, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacements": []}, {"scripts": {}, "minValue": "2*(w*l+l*h+w*h)", "type": "numberentry", "correctAnswerFraction": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "marks": "2", "maxValue": "2*(w*l+l*h+w*h)", "allowFractions": false, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacements": []}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true}, {"scripts": {}, "prompt": "

The picture shows a sphere of radius $r$.

\n

\n

Write down the expression for finding the exact volume of the sphere.  Give your answer in terms of $\\pi$.

", "checkingtype": "absdiff", "type": "jme", "answer": "4pi*r^3/3", "showpreview": true, "variableReplacementStrategy": "originalfirst", "marks": "2", "showFeedbackIcon": true, "vsetrange": [0, 1], "vsetrangepoints": 5, "showCorrectAnswer": true, "checkvariablenames": false, "expectedvariablenames": ["pi"], "checkingaccuracy": 0.001, "variableReplacements": []}], "statement": "

", "variable_groups": [], "rulesets": {}, "type": "question"}, {"name": "Right-angle triangle", "extensions": [], "custom_part_types": [], "resources": [["question-resources/triangle_abc.JPG", "/srv/numbas/media/question-resources/triangle_abc.JPG"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "advice": "", "parts": [{"variableReplacements": [], "variableReplacementStrategy": "originalfirst", "prompt": "

In the case where side $c=\\var{c1}$ and angle $\\theta = \\var{theta1}^{\\circ}$

\n

$a =$ [[0]]

\n

$b =$ [[1]]

\n

Consider the right angle triangle shown below.

\n

\n

(This picture is not drawn accurately!)

$\\sin x = \\var{s}$  , $0\\le x <360^{\\circ}$

\n

$x =$[[0]]

\n

$x =$[[1]]

\n

\n

\n

$\\cos x = \\var{c}$  , $0^{\\circ} \\le x <360^{\\circ}$

\n

$x =$[[0]]

\n

$x =$[[1]]

\n

\n

\n

$\\tan x = \\var{t}$  , $0^{\\circ} \\le x <360^{\\circ}$

\n

$x =$[[0]]

\n

$x =$[[1]]

\n

\n

\n

"}], "preamble": {"js": "", "css": ""}, "functions": {}, "advice": "", "variables": {"t": {"group": "Ungrouped variables", "description": "", "templateType": "randrange", "definition": "random(-20 .. 20#0.1)", "name": "t"}, "pv": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "(180/pi)*arcsin(s)", "name": "pv"}, "SV": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "180-PV", "name": "SV"}, "c": {"group": "Ungrouped variables", "description": "", "templateType": "randrange", "definition": "random(-0.99 .. 0.99#0.01)", "name": "c"}, "s": {"group": "Ungrouped variables", "description": "", "templateType": "randrange", "definition": "random(0.01 .. 0.99#0.01)", "name": "s"}, "pv3": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "(180/pi)*arctan(t)", "name": "pv3"}, "pv2": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "(180/pi)*arccos(c)", "name": "pv2"}}, "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "s<>0 and c<>0 and t<>0"}, "statement": "

Solve the following trig equations.  Give the two solutions in the specified interval.  You can input your values in any order.

", "tags": []}]}], "duration": 2700, "name": "INTO Diagnostic Test", "timing": {"timedwarning": {"action": "warn", "message": "

You have 5 minutes remaining!

"}, "allowPause": false, "timeout": {"action": "none", "message": ""}}, "type": "exam", "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "extensions": ["geogebra", "jsxgraph"], "custom_part_types": [], "resources": [["question-resources/angle_line.JPG", "/srv/numbas/media/question-resources/angle_line.JPG"], ["question-resources/angle_circle.JPG", "/srv/numbas/media/question-resources/angle_circle.JPG"], ["question-resources/triangle_angles.JPG", "/srv/numbas/media/question-resources/triangle_angles.JPG"], ["question-resources/sphere.JPG", "/srv/numbas/media/question-resources/sphere.JPG"], ["question-resources/cuboid.JPG", "/srv/numbas/media/question-resources/cuboid.JPG"], ["question-resources/triangle_abc.JPG", "/srv/numbas/media/question-resources/triangle_abc.JPG"]]}