// Numbas version: exam_results_page_options
{"name": "Q4 & 5 Arithmetic", "extensions": [], "custom_part_types": [], "resources": [["question-resources/bodmas.png", "/srv/numbas/media/question-resources/bodmas.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"Neg": {"definition": "random(-2..-9)", "type": "number", "language": "jme", "parameters": []}, "Pos": {"definition": "random(3..12)", "type": "number", "language": "jme", "parameters": []}, "poslow": {"definition": "random(1..{Pos})", "type": "number", "language": "jme", "parameters": []}}, "ungrouped_variables": ["A1", "a2", "Ans1a", "b1", "B2", "Ans2b", "C1", "C2", "Ans3b", "D1", "D2", "Ans4b", "E1", "E2", "Ans5", "a3", "a4", "b3", "b4", "b5", "c3", "c4", "c5", "d3", "e3", "a5", "a6", "b6", "b7", "b8", "b9", "c6", "c7", "c8", "c9", "d4", "d5", "d6", "d7", "d8", "d9", "e4", "e5", "e6", "e7", "e8", "e9", "e10", "e11", "e12", "f1", "f2", "f4", "f5", "f3", "f6", "ans1b", "ans6", "ans2a", "ans3a", "ans4a", "ans4c", "ans4d", "ans3c", "ans3d", "ans5a", "ans5b", "ans5c", "ans5d", "ans5e", "ans6a", "ans1", "ans11", "ans2", "ans22", "ans3", "ans33", "ans4", "ans44", "ans555", "ans55", "ans666", "ans66"], "name": "Q4 & 5 Arithmetic", "tags": ["rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "<p>When adding and/or subtracting fractions, do the following;</p>\n<p>First make sure the number is a fraction, including an improper fraction i.e. $1\\frac{2}{3} = \\frac{5}{3}$</p>\n<p>Find the lowest common multiply of the denominator i.e. $\\frac{5}{3} + \\frac{1}{2} = \\frac{}{6}$</p>\n<p>Next, transform each number into the form of the LCM i.e. $\\frac{5}{3} + \\frac{1}{2} = \\frac{10}{6} + \\frac{3}{6}$</p>\n<p>Add/subtract the numbers above the denominator i.e. $\\frac{10}{6} + \\frac{3}{6} = \\frac{10 + 3}{6} = \\frac{13}{6} = 2\\frac{1}{6}$</p>\n<p></p>\n<p>When multipling fractions, multipy the numbers above the line by each other and then the numbers below the line by each other i.e.</p>\n<p>$\\frac{5}{3}&nbsp;\\times \\frac{1}{4} = \\frac{5}{12}$</p>\n<p>If possible simplify the answer i.e.</p>\n<p>$\\frac{5}{3}&nbsp;\\times \\frac{1}{5} = \\frac{5}{15} = \\frac{1}{3}$</p>\n<p>If no than 2 fractions follow the same rules:</p>\n<p>i.e. $\\frac{5}{3}&nbsp;\\times \\frac{1}{4} \\times \\frac{2}{5} \\times \\frac{3}{2} = \\frac{30}{120} = \\frac{1}{4}$</p>\n<p></p>\n<p>When dividing fractions, invert the divisor and then follow the rules for multiplying fractions (multipy the numbers above the line by each other and then the numbers below the line by each other) i.e.</p>\n<p>$\\frac{5}{3}&nbsp;\\div \\frac{3}{4} = \\frac{5}{3}&nbsp;\\times \\frac{4}{3} = \\frac{20}{9}$</p>\n<p>If possible simplify the answer i.e.</p>\n<p>$\\frac{5}{3}&nbsp;\\div \\frac{4}{21} = \\frac{5}{3}&nbsp;\\times \\frac{21}{4} = \\frac{105}{12} = \\frac{35}{4} = 8\\frac{3}{4}$</p>\n<p>If no than 2 fractions follow the same rules:</p>\n<p>i.e. $\\frac{5}{3}&nbsp;\\div \\frac{1}{4} \\div \\frac{2}{5} \\div \\frac{3}{2} = \\frac{5}{3}&nbsp;\\times \\frac{4}{1} \\times \\frac{5}{2} \\times \\frac{2}{3} = \\frac{200}{18} = \\frac{100}{9} = 11\\frac{1}{9}$</p>\n<p>Or</p>\n<p>$\\frac{5}{3}&nbsp;\\div \\frac{1}{4} \\times \\frac{2}{7} = \\frac{5}{3}&nbsp;\\times \\frac{4}{1} \\times \\frac{2}{7}&nbsp;= \\frac{40}{21} = 1\\frac{19}{20}$</p>\n<p></p>\n<p></p>", "rulesets": {}, "parts": [{"prompt": "<p>$\\simplify{{a2}/{a1}}&nbsp;+ \\simplify{{a4}/{a3}} -&nbsp;\\simplify{{a6}/{a5}}$</p>\n<p>[[0]][[1]]</p>\n<p></p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{ans1}", "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": true, "variableReplacements": [], "maxValue": "{ans11}/{ans1b}", "minValue": "{ans11}/{ans1b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{b1}\\simplify{{b3}/{b2}} + \\var{b4}\\simplify{{b6}/{b5}} &nbsp;- \\var{b7}\\simplify{{b9}/{b8}} $</p>\n<p>[[0]][[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{ans2}", "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "{ans22}/{ans2b}", "minValue": "{ans22}/{ans2b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{c1}\\simplify{{c3}/{c2}}&nbsp;\\times \\var{c4}\\simplify{{c6}/{c5}} - \\var{c7}\\simplify{{c9}/{c8}} $</p>\n<p>[[0]][[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{ans3}", "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "{ans33}/{ans3c}", "minValue": "{ans33}/{ans3c}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{d1}\\simplify{{d3}/{d2}}&nbsp;\\div (\\var{d4}\\simplify{{d6}/{d5}}&nbsp;\\times \\var{d7}\\simplify{{d9}/{d8}}) $</p>\n<p>[[0]][[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{ans4}", "minValue": "{ans4}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "{ans44}/{ans4d}", "minValue": "{ans44}/{ans4d}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{\\var{e1}\\simplify{{e3}/{e2}}&nbsp;\\times \\var{e4}\\simplify{{e6}/{e5}}}{\\var{e7}\\simplify{{e9}/{e8}} \\times \\var{e10}\\simplify{{e12}/{e11}}}$</p>\n<p>[[0]][[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{ans555}", "minValue": "{ans555}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "{ans55}/{ans5e}", "minValue": "{ans55}/{ans5e}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{f1}\\simplify{{f3}/{f2}}&nbsp;\\div \\var{f4}\\simplify{{f6}/{f5}}$&nbsp;</p>\n<p>[[0]][[1]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{ans666}", "minValue": "{ans666}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "{ans66}/{ans6a}", "minValue": "{ans66}/{ans6a}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Evaluate the following without using a calculator:</p>\n<p>Answer in whole number and/or fraction!!</p>\n<p>Remember the BODMAS rule</p>\n<p><img width=\"237\" height=\"190\" src=\"resources/question-resources/bodmas.png\"/></p>\n<p>N.B.&nbsp;</p>\n<p>First box is for whole number and second box is for fraction.</p>\n<p>If no whole number place 0 in the first box.</p>\n<p>E.g. $\\frac{3}{2} =&gt; $first box $ =1 $ second box$ =\\frac{1}{2}$</p>\n<p>E.g. $\\frac{1}{2} =&gt; $first box $ =0 $ second box$ &nbsp;=\\frac{1}{2}$</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans1b": {"definition": "lcm([a1,a3,a5])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1b", "description": ""}, "f1": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "f1", "description": ""}, "f2": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "f2", "description": ""}, "f3": {"definition": "random(1..{f2}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "f3", "description": ""}, "f4": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "f4", "description": ""}, "f5": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "f5", "description": ""}, "f6": {"definition": "random(1..{f5}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "f6", "description": ""}, "ans3a": {"definition": "((c2*c1)+c3)*((c4*c5)+c6)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3a", "description": ""}, "ans2": {"definition": "trunc(ans2a/ans2b)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "d9": {"definition": "random(1..{d8}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "d9", "description": ""}, "ans3d": {"definition": "((ans3c/ans3b)*(ans3a))-((ans3c/c8)*((c7*c8)+c9))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3d", "description": ""}, "ans6": {"definition": "((f1*f2)+f3)*f5", "templateType": "anything", "group": "Ungrouped variables", "name": "ans6", "description": ""}, "ans66": {"definition": "abs(ans6)-(ans6a*abs(ans666))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans66", "description": ""}, "b4": {"definition": "random(2..5)+b7", "templateType": "anything", "group": "Ungrouped variables", "name": "b4", "description": ""}, "b5": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "b5", "description": ""}, "b6": {"definition": "random(1..{b5}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b6", "description": ""}, "b7": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "b7", "description": ""}, "b1": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "d8": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "d8", "description": ""}, "b3": {"definition": "random(1..{b2}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "description": ""}, "d6": {"definition": "random(1..{d5}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "d6", "description": ""}, "d7": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "d7", "description": ""}, "d4": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "d4", "description": ""}, "d5": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "d5", "description": ""}, "b8": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "b8", "description": ""}, "d3": {"definition": "random(1..{d2}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "d3", "description": ""}, "ans4a": {"definition": "((d4*d5)+d6)*((d7*d8)+d9)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4a", "description": ""}, "e6": {"definition": "random(1..{e5}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "e6", "description": ""}, "e11": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "e11", "description": ""}, "e10": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "e10", "description": ""}, "c8": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "c8", "description": ""}, "e12": {"definition": "random(1..{e11}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "e12", "description": ""}, "e5": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "e5", "description": ""}, "Ans2b": {"definition": "lcm([b2,b5,b8])", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans2b", "description": ""}, "b9": {"definition": "random(1..{b8}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b9", "description": ""}, "A1": {"definition": "(pos())", "templateType": "anything", "group": "Ungrouped variables", "name": "A1", "description": ""}, "e3": {"definition": "random(1..{e2}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "e3", "description": ""}, "ans1": {"definition": "floor(ans1a/ans1b)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "c7": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "c7", "description": ""}, "C2": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "C2", "description": ""}, "C1": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "C1", "description": ""}, "ans5e": {"definition": "ans5a * ans5b", "templateType": "anything", "group": "Ungrouped variables", "name": "ans5e", "description": ""}, "ans5b": {"definition": "((e7*e8)+e9) * ((e10*e11)+e12)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans5b", "description": ""}, "ans5c": {"definition": "e8 * e11", "templateType": "anything", "group": "Ungrouped variables", "name": "ans5c", "description": ""}, "E2": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "E2", "description": ""}, "ans4d": {"definition": "ans4a*d2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4d", "description": ""}, "ans3c": {"definition": "lcm([ans3b,c8])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3c", "description": ""}, "ans666": {"definition": "floor(ans6/ans6a)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans666", "description": ""}, "ans4": {"definition": "floor(ans4c/ans4d)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "description": ""}, "ans3": {"definition": "floor(ans3d/ans3c)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "ans2a": {"definition": "((ans2b/b2)*((b2*b1)+b3))+((ans2b/b5)*((b4*b5)+b6))-((ans2b/b8)*((b7*b8)+b9))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2a", "description": ""}, "a3": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "ans11": {"definition": "ans1a-(ans1b*ans1)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "e9": {"definition": "random(1..{e8}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "e9", "description": ""}, "e8": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "e8", "description": ""}, "a6": {"definition": "random(1..{a5}-3)", "templateType": "anything", "group": "Ungrouped variables", "name": "a6", "description": ""}, "c3": {"definition": "random(1..{c2}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "c3", "description": ""}, "e4": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "e4", "description": ""}, "e7": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "e7", "description": ""}, "ans33": {"definition": "abs(ans3d)-(ans3c*abs(ans3))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans33", "description": ""}, "ans22": {"definition": "abs(ans2a)-(ans2b*abs(ans2))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "c6": {"definition": "random(1..{c5}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "c6", "description": ""}, "c5": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "c5", "description": ""}, "c4": {"definition": "random(2..5)+c7", "templateType": "anything", "group": "Ungrouped variables", "name": "c4", "description": ""}, "a4": {"definition": "random(2..{a3}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}, "Ans4b": {"definition": "d5*d8", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans4b", "description": ""}, "Ans1a": {"definition": "((ans1b/a1)*a2)+((ans1b/a3)*a4)-((ans1b/a5)*a6)", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans1a", "description": ""}, "ans5d": {"definition": "ans5 * ans5c", "templateType": "anything", "group": "Ungrouped variables", "name": "ans5d", "description": ""}, "E1": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "E1", "description": ""}, "Ans3b": {"definition": "c2*c5", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans3b", "description": ""}, "ans55": {"definition": "abs(ans5d)-(ans5e*abs(ans555))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans55", "description": ""}, "c9": {"definition": "random(1..{c8}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "c9", "description": ""}, "Ans5": {"definition": "((e1*e2)+e3) * ((e4*e5)+e6)", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans5", "description": ""}, "a5": {"definition": "random(2..5)+a1", "templateType": "anything", "group": "Ungrouped variables", "name": "a5", "description": ""}, "a2": {"definition": "random(2..{a1}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "B2": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "B2", "description": ""}, "ans44": {"definition": "abs(ans4c)-(ans4d*abs(ans4))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans44", "description": ""}, "ans555": {"definition": "floor(ans5d/ans5e)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans555", "description": ""}, "ans6a": {"definition": "((f4*f5)+f6)*f2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans6a", "description": ""}, "ans5a": {"definition": "e2 * e5", "templateType": "anything", "group": "Ungrouped variables", "name": "ans5a", "description": ""}, "D2": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "D2", "description": ""}, "ans4c": {"definition": "(((d2*d1)+d3))* ans4b", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4c", "description": ""}, "D1": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "D1", "description": ""}}, "metadata": {"description": "<p>Arithmetic</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}