// Numbas version: exam_results_page_options
{"name": "NUMBAS Test", "feedback": {"showtotalmark": true, "advicethreshold": 0, "showanswerstate": true, "showactualmark": true, "allowrevealanswer": true}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "allQuestions": true, "shuffleQuestions": false, "percentPass": 0, "duration": 0, "pickQuestions": 0, "navigation": {"onleave": {"action": "none", "message": ""}, "reverse": true, "allowregen": true, "showresultspage": "oncompletion", "preventleave": true, "browse": true, "showfrontpage": true}, "metadata": {"notes": "", "description": "<p>New version of 30 questions.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "exam", "questions": [], "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": [{"name": "Percentages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a", "Discount", "b", "Price"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>Price $=\\$\\;$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "100*{a}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>A shop gives a {Discount}$\\%$ &nbsp;discount on an item. If the selling price of the item is $\\$\\var{Price}$, what was it's original price?&nbsp;</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(5..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "Discount": {"definition": "random(10,20,30,40,50,60)", "templateType": "anything", "group": "Ungrouped variables", "name": "Discount", "description": ""}, "Price": {"definition": "{a}*{b}", "templateType": "anything", "group": "Ungrouped variables", "name": "Price", "description": ""}, "b": {"definition": "100 - Discount", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"notes": "<p>Percentages</p>", "description": "<p>Percentage calculations</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Differentiation: advanced (chain rule)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a", "b", "t1", "t2", "m", "n"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>$\\simplify[all]{f(x)=cos({a}x+{b})}$</p>\n<p>$\\displaystyle \\frac{df}{dx}=\\;$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "-{a}*sin({a}*x+{b})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Find the derivative of the following function:</p>\n<p></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "b": {"definition": "t1*random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "t2": {"definition": "random(-1,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "t2", "description": ""}, "m": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "n": {"definition": "t2*random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "t1": {"definition": "random(-1,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "t1", "description": ""}}, "metadata": {"notes": "<p>Product rule</p>", "description": "<p>Differentiation</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Functions: domain", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "-{{a}+0.000001}", "minValue": "-infinity", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Give an example of a value of $x$ &nbsp;where the function $f(x)=\\sqrt{\\simplify{x+{a}}}$ is not defined.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(-20..20)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}}, "metadata": {"notes": "<p>Problems on functions.</p>", "description": "<p>Find the domain of a function.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Logarithms: rules", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "showQuestionGroupNames": false, "statement": "<p>Write the following as a single logarithm in the form $\\log (x)$.</p>\n<p>\\[\\var{p} \\log (a^2b)+\\log(b^4)-\\var{q}\\log(ab)\\]</p>", "advice": "", "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"css": "", "js": ""}, "ungrouped_variables": ["p", "q"], "type": "question", "question_groups": [{"pickingStrategy": "all-ordered", "pickQuestions": 0, "name": "", "questions": []}], "tags": [], "variables": {"q": {"description": "", "group": "Ungrouped variables", "name": "q", "templateType": "anything", "definition": "random(2..5)"}, "p": {"description": "", "group": "Ungrouped variables", "name": "p", "templateType": "anything", "definition": "random(6..10)"}}, "metadata": {"notes": "<p>Rules on logarithms.</p>", "description": "<p>Simplify logarithmic expressions using rules on logarithms.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"prompt": "<p>[[0]]</p>", "showCorrectAnswer": true, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "scripts": {}, "gaps": [{"checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "answer": "log({a}^(2{p}-{q}) * b^({p}-{q}+4))", "variableReplacements": [], "checkingaccuracy": 0.001, "type": "jme", "scripts": {}, "showCorrectAnswer": true, "expectedvariablenames": [], "answersimplification": "all", "vsetrangepoints": 5, "marks": 1, "vsetrange": [0, 1], "showpreview": true, "checkingtype": "absdiff"}]}], "variable_groups": [], "rulesets": {}, "functions": {}}, {"name": "Differentiation: simple", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "p", "q"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>$f'(x)=\\;$ [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{a}*{p}*x^({p}-1)+{b}*{q}*x^({q}-1)+{c}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Find $f'(x),$ the derivate of $f(x),$ if $\\simplify{f(x)={a}x^{p}+{b}x^{q}+{c}x+{d}}.$</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(-10..10 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(-100..100 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(-10..10 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(-100..100 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "q": {"definition": "random(-10..10 except 0 except 1 except p)", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "p": {"definition": "random(-10..10 except 0 except 1)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}}, "metadata": {"notes": "", "description": "<p>Finding the derivative &nbsp;of a simple polynomial function.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Inequalities: product of two factors", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a", "b"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>&nbsp;[[0]]&nbsp;$\\leq x\\leq$&nbsp;[[1]]&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "-{b}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{a}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Find the value(s) of $x$ which satisfy the following inequality.</p>\n<p></p>\n<p>\\[\\simplify{(x-{a})(x+{b})}\\leq 0\\]</p>\n<p></p>\n<p></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "b": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"notes": "<p>Inequality with product of two linear factors. &nbsp;</p>", "description": "<p>Finding the values which satisfy an inequality containing two linear factors.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Trigonometry: degrees and radians", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["radians", "degrees", "radians1", "radians2"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>An angle of $\\var{degrees}^{\\circ}$ corresponds in radians to [[0]] radians.</p>\n<p>(Note: you should leave your answer as a fraction in terms of $\\pi,$ which can be entered by typing \"pi\" without the quotation marks)</p>\n<p>An angle of $\\frac{\\pi}{\\var{radians}}$ radians corresponds to&nbsp;[[1]]&nbsp;degrees.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "", "showStrings": false, "strings": ["."], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all ", "scripts": {}, "answer": "(pi*{degrees})/180", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": "2", "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all ", "scripts": {}, "answer": "180*{radians2}", "marks": 1, "checkvariablenames": false, "checkingtype": "dp", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Find the value of</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"radians2": {"definition": "radians1/pi", "templateType": "anything", "group": "Ungrouped variables", "name": "radians2", "description": ""}, "degrees": {"definition": "random(1..360)", "templateType": "anything", "group": "Ungrouped variables", "name": "degrees", "description": ""}, "radians": {"definition": "random(2,3,4,5,9,12,15,18,20,30,36,45,60,90)", "templateType": "anything", "group": "Ungrouped variables", "name": "radians", "description": ""}, "radians1": {"definition": "(pi/radians)", "templateType": "anything", "group": "Ungrouped variables", "name": "radians1", "description": ""}}, "metadata": {"notes": "<p>Converting angles.</p>", "description": "<p>Convert degrees to radians and radians to degrees.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Functions: value of a function", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "p"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>$f(\\var{p})=\\;$ [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{p}^3+{a}*{p}^2+{b}*{p}+{c}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Evaluate $f(x)=\\simplify{x^3+{a}*x^2+{b}*x+{c}}$ at $x=\\var{p}.$</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "p": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "c": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"notes": "<p>Evaluating functions.</p>", "description": "<p>Calculate the functional value at a point.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Functions: functional value ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>$f(\\var{a})$ = [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "-{a}+{b}+{c}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Find $f(\\var{a})$ if $f(x)=\\big| \\; |-x+\\var{b}|-\\var{c}\\big|,$ where $|x|$ denote the absolute value of $x.$</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(6..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(11..15)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"notes": "<p>An absolute value function.</p>", "description": "<p>Functional value of a function at a point.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Functions: domain and range", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>$x$ =&nbsp;[[0]]&nbsp;</p>\n<p>$f(x)$=[[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "infinity", "minValue": "{a}+0.00001", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "infinity", "minValue": "0.000001", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Give an example of a value of $x$ where \\[f(x)=\\frac{1}{\\sqrt{x-\\var{a}}}\\] is defined and a possible value for $f(x).$</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}}, "metadata": {"notes": "<p>Another domain question.</p>", "description": "<p>Finding domain and range of a given function.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Transposition of formulae", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": [], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>$p=\\;$ [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "q*r/(s*r+q*t)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Transpose the following formula to make $p$ the subject.</p>\n<p>\\[\\frac{1}{p}=\\frac{s}{q}+\\frac{t}{r}\\]</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {}, "metadata": {"notes": "", "description": "<p>Rearranging a formula</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Functions: composite functions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>$h(f(x))=\\;$ [[0]]&nbsp;</p>\n<p>$f(h(x))=\\;$ [[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "1/(x^2+{a})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "1/(x^2)+{a}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>If $f(x)=\\simplify{x^2+{a}}$ and $h(x)=\\frac{1}{x}$ then find $h(f(x))$ and $f(h(x)).$</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(-5..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}}, "metadata": {"notes": "", "description": "<p>Composite functions.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Logarithms", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>$x$ = [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{c}/{b}-{a}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Find $x$ if $\\log(x+\\var{a})+\\log(\\var{b})=\\log(\\var{c})$</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(1..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(10..20)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"notes": "", "description": "<p>Solve a logarithmic expression for an unknown $x$</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Equation of a straight line ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["m", "b", "c"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>$y=$ [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{m}*x+ {c}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Write the equation of the straight parallel to \\[\\simplify {y={m}x+{b}}\\] and passes through the point $(0,\\var{c}).$</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"c": {"definition": "random(-10..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(-5..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "m": {"definition": "random(-5..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}}, "metadata": {"notes": "<p>Equation of a straight line.</p>", "description": "<p>Find the equation of a straight line parrarell to a given straight line passes through a given point.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Trigonometry: application", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{a}/sqrt(3)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>A building has a $\\var{a}$ meter shadow. The line between the top of the buiding and the end of the shadow makes an angle of &nbsp;$\\frac{\\pi}{6}$ radians. Find the height of the building without using any calculators.</p>\n<p>Note: Type sqrt(3) to denote $\\sqrt3$ in your answer.</p>\n<p>(Hint: $sin(\\frac{\\pi}{6})=\\frac{1}{2}$ and $cos(\\frac{\\pi}{6})=\\frac{\\sqrt3}{2}$).</p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}}, "metadata": {"notes": "", "description": "<p>Applying trigonometry to find heughts and lengths.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Inequalities: simple", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "P"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>$x\\geq$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all ", "scripts": {}, "answer": "({c}-{b}-{a})/{P}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Find the value(s) of $x$ which satisfy the following inequality.</p>\n<p>\\[ \\var{b}+(\\var{a}+\\var{P} x)\\geq \\var{c}\\]</p>\n<p></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(-25..25)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "P": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "P", "description": ""}, "c": {"definition": "random(-25..25)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(-25..25)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"notes": "<p>Solving simple inequalities.</p>", "description": "<p>Finding values which satisfy an inequality.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Adding rational functions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "(2x^2+({a}+{b}+1)x+{a}*{b}+{b}-{a}^2)/((x^2-{a}^2)(x+{b}))", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Turn the following expression into a single fraction whose denominator is in the simplest form possible.</p>\n<p>\\[\\frac {1}{x-\\var{a}}+\\frac{1}{x^2-\\var{c}}+\\frac{1}{x+\\var{b}}\\]</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "{a}*{a}", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(6..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"notes": "<p>Needs to find the LCM of the denominators.</p>", "description": "<p>Adding several rational functions.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Simple Trigonometry", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": [], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>$cos(\\theta) =$ [[0]]&nbsp;and $tan(\\theta) =$ [[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "sqrt(b^2-a^2)/b", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "a/sqrt(b^2-a^2)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>If $sin(\\theta)=\\frac{a}{b}$ then find $cos(\\theta)$ and $tan(\\theta)$ in terms of $a$ and $b.$</p>\n<p></p>\n<p>Note: For any number, $x$ type sqrt(x) to denote $\\sqrt{x}.$&nbsp;</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {}, "metadata": {"notes": "<p>Simple trigonometry.</p>", "description": "<p>Finding Cosine and Tangent values for an angle if Sine value is given.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Equation of a straight line: using 2 points on the line", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "m", "b1"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>$y=\\;$ &nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>answer should contain fractions.</p>", "showStrings": true, "strings": ["."], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({b}-{d})/({a}-{c})*x+ ({a}*{d}-{b}*{c})/({a}-{c})", "marks": 1, "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Find the equation of the straight line that passes through the ponts, $(\\var{a}, \\var{b})$ and $(\\var{c}, \\var{d})$ in the form $y=mx+b$</p>", "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 except a)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(1..5 except b)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "m": {"definition": "({b}-{d})/({a}-{c})", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "b1": {"definition": "({a}*{d}-{b}*{c})/({a}-{c})", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}}, "metadata": {"notes": "<p>Equation of a straight line.</p>", "description": "<p>Obtain the equation of a straight line that passes through 2 points.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Simultaneous equations", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a", "b", "d", "c", "P", "Q"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>$x=\\;$ [[0]] and $y=\\;$ [[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({P}*{d}-{Q}*{b})/({a}*{d}-{b}*{c})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({a}*{Q}-{P}*{c})/({a}*{d}-{b}*{c})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Find the values of $x, y$ if</p>\n<p>\\[\\simplify{{a}x+ {b}y= {P}}\\]</p>\n<p>\\[\\simplify{{c}x+ {d}y={Q}}\\]</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "a*d-b*c<>0"}, "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(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "Q": {"definition": "random(6..10 except P)", "templateType": "anything", "group": "Ungrouped variables", "name": "Q", "description": ""}, "P": {"definition": "random(6..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "P", "description": ""}}, "metadata": {"notes": "<p>Simple simultaneous equations.</p>", "description": "<p>Solve two simultaneous equations.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Expanding a linear factor", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": [], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>[[0]] &nbsp; &nbsp;</p>\n<p></p>\n<p></p>\n<p>Note: When you have an xt or tx term, type it as t*x. &nbsp;To denote powers such as $t^3,$ type t^3.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "x^3- 3 x^2*t+ 3 x *t^2- t^3", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Expand $\\displaystyle (x-t)^3$</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {}, "metadata": {"notes": "<p>Expanding linear factors</p>", "description": "<p>Expanding linear factors</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Indices : advanced", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["P", "a", "b", "c", "d", "f", "g", "q", "r"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "({P}^{c}) x^{q}*y^{r}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Simplify $\\displaystyle (\\var{P}x^\\var{a} y^\\var{b})^\\var{c}(x^\\var{d}y^\\var{f})^\\var{g}$</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(-9..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(-9..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(-9..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(-9..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "q": {"definition": "a*c+d*g", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "P": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "P", "description": ""}, "r": {"definition": "b*c+f*g", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}}, "metadata": {"notes": "", "description": "<p>Simplifying algebraic expressions</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Indices : simple", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>$\\displaystyle \\var{c}^{1/2}+\\var{d}^{1/2}$</p>\n<p></p>\n<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{a}+{b}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Simplify the following:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "{a}*{a}", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "{b}*{b}", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"notes": "<p>Simple indices</p>", "description": "<p>Simple problem on indices</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Scientific Notation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["n1", "p1", "q1"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>Write {q1} in scientific notation.</p>\n<p>{q1}$=\\;$ [[0]] $\\times$ 10<sup>[[1]]</sup></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{n1}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": "0.00000000000001", "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{p1}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Represent {a} in scientific notation.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"q1": {"definition": "n1*(10^p1)", "templateType": "anything", "group": "Ungrouped variables", "name": "q1", "description": ""}, "n1": {"definition": "random(1000..9999)/1000", "templateType": "anything", "group": "Ungrouped variables", "name": "n1", "description": ""}, "p1": {"definition": "random(-5..8 except 0..1)", "templateType": "anything", "group": "Ungrouped variables", "name": "p1", "description": ""}}, "metadata": {"notes": "<p>Number Representation</p>", "description": "<p>Scientific Notation</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Factoring quadratics", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p></p>\n<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "", "showStrings": true, "strings": ["^"], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "musthave": {"message": "", "showStrings": true, "strings": ["("], "partialCredit": 0}, "scripts": {}, "answer": "(x+{a})(x+{b})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Factorize the following quadratic equation:</p>\n<p>$\\simplify {x^2+ {c}x+{d}}$</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(-9..9 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "{a}+{b}", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(-9..9 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "{a}*{b}", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"notes": "<p>Factoring</p>", "description": "<p>Factoring a quadratic equation</p>\n<p></p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Adding and subtracting fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "m", "n", "g", "f", "nm", "cd", "gf"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>$ \\frac{\\var{n}}{\\var{m}}+\\frac{\\var{c}}{\\var{d}} - \\frac{\\var{g}}{\\var{f}}$</p>\n<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>You entered an invalid answer. The answer must be a fraction not a decimal number.</p>", "showStrings": false, "strings": [".", "-", "+"], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{n*d*f+m*c*f- g*m*d}/{m*d*f}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Simplify the following to a single fraction:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "n*d*f+m*c*f>g*m*d"}, "variables": {"a": {"definition": "{n}*{c}", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "cd[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "{m}*{d}", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "cd[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "gf[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "gf[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "m": {"definition": "nm[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "n": {"definition": "nm[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "gf": {"definition": "satisfy (\n  // variables to be defined using gf\n  [g,f],\n  // definition of variable,\n  [random (2..9), random (2..9)],\n  // condition on the variables, g and f force \n  [gcd(g,f)=1]\n  )", "templateType": "anything", "group": "Ungrouped variables", "name": "gf", "description": ""}, "cd": {"definition": "satisfy (\n  // variables to be defined using cd\n  [c,d],\n  // definition of variable,\n  [random (2..9), random (2..9)],\n  // condition on the variables, c and d force \n  [gcd(c,d)=1]\n  )", "templateType": "anything", "group": "Ungrouped variables", "name": "cd", "description": ""}, "nm": {"definition": "satisfy (\n  // variables to be defined using nm\n  [n,m],\n  // definition of variable,\n  [random (3..5), random (2..5)],\n  // condition on the variables, m and n force \n  [gcd(m,n)=1]\n  )", "templateType": "anything", "group": "Ungrouped variables", "name": "nm", "description": ""}}, "metadata": {"notes": "<p>Fractions</p>", "description": "<p>Adding and Subtracting Fractions</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "BODMAS Rule: simple", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>[[0]]</p>\n<p></p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>You entered an invalid answer.</p>", "showStrings": false, "strings": ["*"], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{g}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Find the value of following:</p>\n<p></p>\n<p>$\\var{a}-\\var{b}\\times \\var{c}+\\var{d}\\div \\var{f}$</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "({a}*{f}-{b}*{c}*{f}+{d})/{f}", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}}, "metadata": {"notes": "<p>BODMAS rule</p>", "description": "<p>Order of operations</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "s"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>You have to give your answer as a fraction.</p>", "showStrings": true, "strings": [".", "-"], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "({a}*{b}-{a}-{b})/({a}*{b})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>John spent a $\\frac{1}{\\var{a}}$ of his salary on food, a $\\frac{1}{\\var{b}}$ on clothes and saved the rest. What fraction of his salary did he save?&nbsp;</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "a*b>a+b"}, "variables": {"a": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "1/a", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..9 except a)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "1/b", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "a*b", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "a+b", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "f/g", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "s": {"definition": "1-h", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}}, "metadata": {"notes": "<p>Adding and subtractinf fractions.</p>", "description": "<p>Word problem on fractions.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Quadratic Formula: roots", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "p", "q"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>&nbsp;$x_{1}=$&nbsp;[[0]]&nbsp;</p>\n<p>&nbsp;$x_{2}=$&nbsp;[[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all ", "scripts": {}, "answer": "(-{b}-sqrt({b}^2-4*{a}*{c}))/(2*{a})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "(-{b}+ sqrt({b}^2-4*{a}*{c}))/(2*{a})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Find the roots $x_{1}, x_{2}$ of the quadratic equation $\\simplify{{a} x^2 +{b} x + {c} =0}.$&nbsp;</p>\n<p>(Note: Here $x_{1}&lt;x_{2}.$ Your answers should have square roots and for any number $p,$ type sqrt(p) to denote $\\sqrt{p}$)</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "b^2-4*a*c>0 "}, "variables": {"a": {"definition": "random(1,3,5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "q": {"definition": "(-b+(b^2-4*a*c)^(1/2))/(2*a)", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "c": {"definition": "random(1,3,5)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(3,5,7,11)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "p": {"definition": "(-b-(b^2-4*a*c)^(1/2))/(2*a)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}}, "metadata": {"notes": "<p>Quadratic formula</p>", "description": "<p>Solving quadratic equations using the formula</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Simplifying an algebraic expression", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all ", "scripts": {}, "answer": "({a}-{d})x^2+{a}*({c}-{b})x-{a}*{b}*{c}+{d}*{f}-{g}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Simplify the following expression:</p>\n<p>\\[\\simplify{{a}(x-{b})(x+{c})-[{d}(x^2-{f})+{g}]}\\]</p>", "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(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}}, "metadata": {"notes": "<p>Algebraic expression manupulation.</p>", "description": "<p>Expanding and simplifying an expression.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}], "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}], "extensions": ["jsxgraph"], "custom_part_types": [], "resources": []}