// Numbas version: exam_results_page_options
{"name": "Engineering Mathematics Diagnostic Test", "feedback": {"showtotalmark": false, "advicethreshold": 0, "showanswerstate": false, "showactualmark": false, "allowrevealanswer": false}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "allQuestions": true, "shuffleQuestions": false, "percentPass": 0, "duration": 0, "pickQuestions": 0, "navigation": {"onleave": {"action": "warnifunattempted", "message": "<p>You haven't submitted an answer to this question. Are you sure you want to move to a different question?</p>"}, "reverse": true, "allowregen": false, "showresultspage": "oncompletion", "preventleave": true, "browse": true, "showfrontpage": false}, "metadata": {"description": "<p>Version 1.0 (July 2016)</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "exam", "questions": [], "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": [{"name": "Demographic Question", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ant Edwards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/49/"}], "functions": {}, "ungrouped_variables": [], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [], "statement": "<p>Do&nbsp;you consent to us accessing your data when we conduct the evaluation of this diagnostic test?</p>\n<p>This will involve us looking at the responses you give on the diagnostic test, your class test and exam results, and also whether you have used the University&rsquo;s MASH Centre. You will not have to provide this data to us, and we will only use data for students who have consented to the project. Once we have matched your grade to your responses, we will remove your name and any other identifiable information.</p>\n<p>Your answer to this question does not form part of the diagnostic test</p>\n<p></p>", "variable_groups": [], "variablesTest": {"maxRuns": "1", "condition": ""}, "variables": {}, "metadata": {"description": "", "licence": "None specified"}, "type": "question", "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": "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": "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: 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": "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": "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": "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": "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": "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": "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": "Ant Edwards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/49/"}], "extensions": ["jsxgraph"], "custom_part_types": [], "resources": []}