Originally put together for EG4140/50 group UEL, 2015.
\n", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "allQuestions": true, "shuffleQuestions": false, "percentPass": 0, "timing": {"allowPause": false, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "warn", "message": "You have 5 minutes left to complete this test.
"}}, "pickQuestions": 0, "navigation": {"onleave": {"action": "none", "message": ""}, "reverse": true, "allowregen": true, "showresultspage": "oncompletion", "preventleave": true, "browse": true, "showfrontpage": true}, "feedback": {"intro": "", "showtotalmark": true, "advicethreshold": 0, "allowrevealanswer": true, "feedbackmessages": [], "showanswerstate": true, "showactualmark": true}, "type": "exam", "questions": [], "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": [{"name": "Arithmetic with Negative Numbers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}], "functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "f"], "tags": ["Arithmetic", "arithmetic", "negative numbers", "Negative Numbers"], "preamble": {"css": "", "js": ""}, "advice": "Recall that, for instance, adding $-3$ is the same as subtracting $3$ and that $-3 \\times -4 = 12$
\nSee the following pages for further examples and some explanations of why this makes sense.
\nhttp://www.mathsisfun.com/positive-negative-integers.html
\nhttp://www.mathsisfun.com/multiplying-negatives.html
\n", "rulesets": {}, "parts": [{"prompt": "$(\\var{a}) + (\\var{b})$
\n[[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{a}+{b}", "minValue": "{a}+{b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "$\\var{d} \\times (\\var{c})$
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", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{d}*{c}", "minValue": "{d}*{c}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "$(\\var{b}) \\times (\\var{c})$
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", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{b}*{c}", "minValue": "{b}*{c}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "$ \\var{f} \\div 5$
\n(Give your answer as a decimal.)
\n[[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{f}/5", "minValue": "{f}/5", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "$\\dfrac{\\var{c}}{-5}$.
\n(Give your answer as a decimal.)
\n[[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{c}/(-5)", "minValue": "{c}/(-5)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "Find the value of the following:
", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(-8..-2)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(-9..-2 except[a,b])", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random( -9..-3 except a)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "f": {"definition": "random(-10..-1#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "f", "description": ""}}, "metadata": {"description": "Testing addition, multiplication and division involving negative numbers.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Equivalent Expressions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}], "functions": {}, "ungrouped_variables": ["a", "asq", "b", "c", "g", "h", "j", "d", "f"], "tags": ["algebra", "equivalent expressions"], "preamble": {"css": "", "js": ""}, "advice": "This interactive Algebra Refresher Booklet provides help and practice with algebra.
", "rulesets": {}, "parts": [{"distractors": ["It might help to think of this as multiplying out two brackets.", ""], "prompt": "${(\\simplify {t + {a}})^2}$ and $ t^2 + \\var{asq}$
", "matrix": [0, "1"], "shuffleChoices": false, "variableReplacements": [], "choices": ["Yes, the expressions are equivalent.
", "No, the expressions will not always take the same value.
"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "marks": 0, "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"distractors": ["Remember that you need to multiply all the terms in the bracket by the number outside.", ""], "prompt": "$ \\var{b}(\\simplify{t + {c}})$ and $\\var{b}t +\\var{c}$
", "matrix": [0, "1"], "shuffleChoices": false, "variableReplacements": [], "choices": ["Yes, the expressions are equivalent.
", "No, the expressions will not always have the same value.
"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "marks": 0, "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"distractors": ["", ""], "prompt": "$ \\dfrac { \\var{d}t - \\var{f}}{\\var{g}}$ and $ \\var{h}t - \\var{j}$
", "matrix": ["1", 0], "shuffleChoices": false, "variableReplacements": [], "choices": ["Yes, the expressions are equivalent.
", "No, the expressions will not always take the same value.
"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "marks": 0, "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}], "statement": "Two algebraic expressions are equivalent if they take the same value whatever the value of the variable (in this case $t$).
\nAre the following pairs of expressions equivalent?
", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(-5..9 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "asq": {"definition": "a^2", "templateType": "anything", "group": "Ungrouped variables", "name": "asq", "description": ""}, "b": {"definition": "random(-8..-3)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "g*h", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(2..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "g*j", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random(1..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "j": {"definition": "random(1..7 except h)", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "c": {"definition": "random(2..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}}, "metadata": {"description": "True/false questions on multiplying brackets and dividing an expression by a number.
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Linear Inequality : direct input (Bill)", "extensions": ["difference"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}], "functions": {}, "ungrouped_variables": ["inequal", "ansinequal", "sum", "q", "p", "diff"], "tags": ["inequality", "linear inequality", "simple inequality", "solving inequalities"], "advice": "\nFor $\\var{p}-t \\ \\var{inequal} \\ \\var{q}$, the easiest way to start is to add $t$ to both sides of the inequality.
\nThis will give you $ \\var{p} \\ \\var{inequal} \\ t \\ + \\ \\var{q} $.
\nNow subtracting $ \\var{q} $ from both sides gives $ t \\ \\var{ansinequal} \\var{diff} $
\n\nThese online resources might help you revise this topic.
\nhttp://www.mathsisfun.com/algebra/inequality-solving.html
\n\n\nhttp://www.sosmath.com/algebra/inequalities/ineq01/ineq01.html
", "rulesets": {}, "parts": [{"prompt": "$\\var{p}-t \\ \\var{inequal} \\ \\var{q}$
\nInput the appropriate inequality sign, either < or >, in the first box and the correct range in the second.
\n$t\\;\\;$ [[0]]$\\;\\;$ [[1]]
\n\n", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "displayAnswer": "{ansinequal}", "scripts": {}, "answer": "{ansinequal}", "marks": "1", "type": "patternmatch"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "diff", "minValue": "diff", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "Find the range of values of $t$ which satisfy the following inequality.
", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"inequal": {"definition": "random ('$>$', '$<$')", "templateType": "anything", "group": "Ungrouped variables", "name": "inequal", "description": ""}, "ansinequal": {"definition": "switch( inequal = '$>$', '<', '>' )", "templateType": "anything", "group": "Ungrouped variables", "name": "ansinequal", "description": ""}, "sum": {"definition": "p + q", "templateType": "anything", "group": "Ungrouped variables", "name": "sum", "description": ""}, "q": {"definition": "random(16..25)", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "p": {"definition": "random(8..15)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "diff": {"definition": "p-q", "templateType": "anything", "group": "Ungrouped variables", "name": "diff", "description": ""}}, "metadata": {"description": "Solve $p - t < \\text{or}> q$
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Lois's copy of Simultaneous linear equations (variables)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}], "functions": {}, "ungrouped_variables": ["a", "c", "b", "a1", "b1", "c1"], "tags": ["Defining variables", "Except", "linear equations", "Linear equations", "simultaneous equations", "Simultaneous equations", "solving equations", "Solving equations"], "preamble": {"css": "", "js": ""}, "advice": "A general method is to make the coefficients of either $x$ or $y$ equal by multiplying one or both equations by a constant.
\nYou can then add or subtract the resulting equations to get an equation in just $x$ or $y$, which you can solve.
\nThe value of the other variable can be found by substitution into one of the original equations.
\nSee the following link for more explanation and some worked examples:
\nhttp://www.mathcentre.ac.uk/resources/uploaded/mc-bus-simult-2009-1.pdf.
\n\n", "rulesets": {"std": ["All", "fractionnumbers"]}, "parts": [{"prompt": "$x=$ [[0]]
\n$y=$ [[1]]
\nInput your answers as fractions (use the '/' key) and not as decimals.
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", "showStrings": false, "strings": ["."], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "Std", "scripts": {}, "answer": "{-c*a1+c1*a}/{a*b1-a1*b}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "Solve:
\n\\[\\begin{eqnarray*} \\simplify{{a}x+{b}y}&=&\\var{c}\\\\\\\\\\simplify{{a1}x+{b1}y}&=&\\var{c1}\\end{eqnarray*}\\]
", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(-5..5 except [0,1,-1, a])", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "a1": {"definition": "random(1..5 except a)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "b1": {"definition": "random(2..6 except[round(a1*b/a), -b, b])", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "c1": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}}, "metadata": {"description": "Shows how to define variables to stop degenerate examples.
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Simple linear equation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}], "functions": {}, "ungrouped_variables": ["a", "c", "b", "s", "fromto", "op"], "tags": ["algebra", "equation", "linear"], "preamble": {"css": "", "js": ""}, "advice": "Remember that you need to treat both sides of the equation in exactly the same way.
\nGiven $ \\simplify {n/{a} + {s}*{b} = {c} } $,
\nyour first step could be to $ \\var{op} \\ \\ \\var{b}$ $ \\ \\ \\var{fromto}$ both sides, giving you $ \\simplify { n/{a} = {c} - {s}*{b}}$.
\nThen multiplying both sides by $ \\var{a}$ will give $ \\simplify{ n= {a}*({c}-{s}*{b})}$.
\nIf you decide to multiply by $\\var{a}$ first, you need to be careful to multiply all of the terms by $\\var{a}$ giving
\n$ \\simplify{ n +{s}*{b}*{a} = {c}*{a}}$.
\nFor some general advice on solving equations see http://www.mathsisfun.com/algebra/equations-solving.html
", "rulesets": {}, "parts": [{"prompt": "If $ \\simplify{{n}/{a} + {s}* {b} = {c}} $, enter the value of $n$ in the space below.
\n$n= $ [[0]]
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", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..6#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(8..12#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "c", "description": "Chosen so that c>b to avoid negative answers.
"}, "b": {"definition": "random(3..6#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b", "description": ""}, "s": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "fromto": {"definition": "if( op= 'add','to','from')", "templateType": "anything", "group": "Ungrouped variables", "name": "fromto", "description": ""}, "op": {"definition": "if(s=-1, 'add', 'subtract')", "templateType": "anything", "group": "Ungrouped variables", "name": "op", "description": ""}}, "metadata": {"description": "Simple Linear Equation.
\n$ \\dfrac{n}{a} \\pm b = c$
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Using your Calculator Effectively", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}], "functions": {}, "ungrouped_variables": ["a", "c", "b"], "tags": ["BODMAS", "bodmas", "order of operations", "using a calculator"], "preamble": {"css": "", "js": ""}, "advice": "You need to check in which order your calculator carries out the operations.
\nIf, when you input $2+3 \\times 4$ you get the answer $14$, then your calculator is scientific and will perform multiplication and division before addition and subtraction. If you get the answer $20$ then your calculator is performing operations in the order written.
\nBe careful with negative numbers. Remember that squaring a negative number gives a positive number. For instance if you are using your calculator to find the square of $-6$ you need to input $(-6)^2$, not $-6^2$.
", "rulesets": {}, "parts": [{"prompt": "$a + b c$
\n[[0]]
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\n[[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{b}^2 - sqrt{c}+0.1", "minValue": "{b}^2 - sqrt{c}-0.1", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "$ \\dfrac{c^3 -a}{b+ a}$
\n[[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "0.1+({c}^3 -a})/({b}+{a})", "minValue": "(({c}^3 -a})/({b}+{a}))-0.1", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "If $a = \\var{a}, \\ b= \\var{b}$ and $c= \\var{c}$, use your calculator to work out the value of the following expressions. Round your answer to 2 d. p. where necessary.
", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(-5..9#0.1 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(4..24#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(-15..-8#0.1 except -a)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"description": "Understanding order of operations on a calculator and using power and root keys.
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}], "contributors": [{"name": "Francis Duah", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/339/"}], "extensions": ["difference"], "custom_part_types": [], "resources": []}