// Numbas version: exam_results_page_options
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"answersimplification": "basic", "scripts": {}, "answer": "{x1^n}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "prompt": "\n\t\t\t<p>Evaluate</p>\n\t\t\t      <p>$ (\\simplify{ &nbsp; {x2}/{x3} &nbsp; })^\\var{n3} $</p>\n\t\t\t      <p>&nbsp;</p>\n\t\t\t", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{x2/x3}^{n3}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"prompt": "\n\t\t\t<p>Express each of the following in the form &nbsp;$ &nbsp;\\var{x4}^n &nbsp;$.</p>\n\t\t\t      <p>For negative values of \"n\" enclose your answer in brackets &nbsp;&nbsp;</p>\n\t\t\t      <p>i) &nbsp; $\\var{x4}^{\\var{n1}} \\times &nbsp;\\var{x4}^{\\var{n2}} $ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [[0]]</p>\n\t\t\t      <p>ii) &nbsp; $\\var{x4}^{\\var{n4}} \\div &nbsp;\\var{x4}^{\\var{n5}} $ &nbsp; &nbsp; &nbsp; [[1]]</p>\n\t\t\t      <p>iii) &nbsp;&nbsp;$ (\\var{x4}^{\\var{n6}})^\\var{n7} &nbsp;$ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [[2]]&nbsp;</p>\n\t\t\t      <p>&nbsp;</p>\n\t\t\t", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "basic", "scripts": {}, "answer": "{x4}^{n1+n2}", "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": "{x4}^{n4-n5}", "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": "{x4}^{n6*n7}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "\n\t\t\t<p>Evaluate the following.</p>\n\t\t\t      <p>Please leave <em><strong>non-integer</strong></em> answers as <strong><em>fractions</em></strong> in each case.</p>\n\t\t\t      <p>i) $ (\\var{x5}) ^{\\var{n8}} &nbsp;$ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[0]]</p>\n\t\t\t      <p>ii) $ (\\var{x6}) ^{\\tfrac{\\var{n9}}{2}} &nbsp;$ &nbsp; &nbsp; &nbsp;[[1]]</p>\n\t\t\t      <p>iii) $ (\\var{x7}) ^{\\tfrac{\\var{n10}}{3}}&nbsp;&nbsp;$ &nbsp; &nbsp; [[2]]</p>\n\t\t\t      <p>iv) $ (\\simplify{ {{x8}}/{{x9}} })^{\\var{n11}} $ &nbsp; &nbsp; [[3]]</p>\n\t\t\t      <p>v) $ (\\simplify{ {{x10}}/{{x11}} })^{\\var{n12}} $ &nbsp; &nbsp; &nbsp; [[4]]</p>\n\t\t\t      <p>&nbsp;</p>\n\t\t\t      <p>&nbsp;</p>\n\t\t\t      <p>&nbsp;</p>\n\t\t\t      <p>&nbsp;</p>\n\t\t\t      <p>&nbsp;</p>\n\t\t\t      <p>&nbsp;</p>\n\t\t\t", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{x5^n8}", "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": "{x6}^{n9/2}", "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": "{x73}^{n10}", "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": "{x8/x9}^{n11}", "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": "{x10/x11}^{n12}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"n12": {"definition": "random(-3..-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "n12", "description": ""}, "n10": {"definition": "random(1,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "n10", "description": ""}, "n11": {"definition": "random(0,2,3)", "templateType": "anything", "group": "Ungrouped variables", "name": "n11", "description": ""}, "x8": {"definition": "random(1,3,5,7,11)", "templateType": "anything", "group": "Ungrouped variables", "name": "x8", "description": ""}, "x9": {"definition": "random(2,4,6,9,10,12)", "templateType": "anything", "group": "Ungrouped variables", "name": "x9", "description": ""}, "n1": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "n1", "description": ""}, "x2": {"definition": "random(-8..8 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "x2", "description": ""}, "x3": {"definition": "random(-8..8 except[0,x2])", "templateType": "anything", "group": "Ungrouped variables", "name": "x3", "description": ""}, "x1": {"definition": "random(2..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "x1", "description": ""}, "x6": {"definition": "(random(2..10))^2", "templateType": "anything", "group": "Ungrouped variables", "name": "x6", "description": ""}, "x7": {"definition": "x73^3", "templateType": "anything", "group": "Ungrouped variables", "name": "x7", "description": ""}, "x4": {"definition": "random(2..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "x4", "description": ""}, "x5": {"definition": "random(2,3,4,10)", "templateType": "anything", "group": "Ungrouped variables", "name": "x5", "description": ""}, "x73": {"definition": "random(-5..6 except[0,1,-1])", "templateType": "anything", "group": "Ungrouped variables", "name": "x73", "description": ""}, "n": {"definition": "random(0..3 except 1)", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "n8": {"definition": "random(-4..-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "n8", "description": ""}, "n9": {"definition": "random(1,3)", "templateType": "anything", "group": "Ungrouped variables", "name": "n9", "description": ""}, "x10": {"definition": "random(1,3,5,7)", "templateType": "anything", "group": "Ungrouped 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{"description": "<p>Indices</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": []}]}, {"name": "Julie's copy of Simple Index Question", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a", "c", "b"], "tags": ["rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"vsetrangepoints": 5, "prompt": "<p>What is $x^\\var{a}.x^\\var{b}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "x^{c}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "statement": "<p>Give the algebraic expression for the following question:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "a+b", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"description": "<p>Just multiply 2 algebraic expressions with indices</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": []}]}, {"name": "Julie's copy of Index Multiplication Mixed Variables", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a", "a1", "c", "b", "q", "p", "r", "b1", "c1"], "tags": ["rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"vsetrangepoints": 5, "prompt": "<p>What is : $x^\\var{a}.y^\\var{b}.z^\\var{c}.x^\\var{a1}.z^\\var{c1}.y^\\var{b1}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [1, 1.1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "x^{p}*y^{q}*z^{r}", "marks": "3", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "statement": "<p>Give the algebraic answer to the following expression:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "q": {"definition": "b+b1", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "c": {"definition": "random(2..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "a1": {"definition": "random(2..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "p": {"definition": "a+a1", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "r": {"definition": "c+c1", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "b1": {"definition": "random(2..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "c1": {"definition": "random(2..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}}, "metadata": {"description": "<p>This question mixes up three variables in multiplication.Note the checking range is between 1 and 1.1 in the Accuracy and String restrictions section of the Part. This is to ensure that incorrect answers are recorded as incorrect! If the checking range is left as between 0 and 1 then large powers will be very small and be less than the accuracy setting.</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": []}]}, {"name": "BCU Headstart Algebra Q5", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Peter Samuels", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/91/"}], "tags": [], "progress": "in-progress", "metadata": {"notes": "", "description": "<p>Substituting a variable into a formula</p>"}, "statement": "<p><span>Find the value of b when a = 2, using the formula b = (6 - a)/2.</span></p>", "advice": "<p>This is a diagnostic test so there is no advice.</p>", "rulesets": {}, "variables": {}, "functions": {}, "parts": [{"type": "jme", "marks": 1.0, "prompt": "<p>Enter the value of b then click on Submit answer.</p>", "answer": 2.0, "checkingtype": "absdiff", "checkingaccuracy": 0.001, "vsetrangepoints": 5.0, "vsetrange": [0.0, 1.0], "notallowed": {"strings": ["4/8"], "showstrings": false, "partialcredit": 0.0, "message": ""}}], "type": "question", "variable_groups": [], "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Transposition Q1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a", "c", "b", "atimesc"], "tags": ["rebel", "REBEL", "rebelmaths", "transposition"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>Transpose the formula $y=x+\\var{a}$ to make $x$ the subject</p>\n<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": "y-{a}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Write $x$ in terms of $y$ if&nbsp;</p>\n<p>$y =\\dfrac{x}{\\var{b}}$.</p>\n<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": "{b}y", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Make $c$ the subject of the formula $y=\\var{c}x+c$.</p>\n<p>$c= $[[0]]&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "y-{c}x", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p><span style=\"color: #222222; font-family: sans-serif; font-size: 16px; line-height: 20.8020801544189px;\">Make</span><span style=\"color: #222222; font-family: sans-serif; font-size: 16px; line-height: 20.8020801544189px;\">&nbsp;$x$</span><span style=\"color: #222222; font-family: sans-serif; font-size: 16px; line-height: 20.8020801544189px;\">&nbsp;the subject of the formula $y=\\var{a}x+\\var{b}$.</span></p>\n<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": "(y-{b})/{a}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Find $x$ in terms of $y$ if</p>\n<p>$\\var{c}y &nbsp;= &nbsp;\\var{c}x+\\var{a}$</p>\n<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}y-{a})/{c}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Find $y$ in terms of $x$ if&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>\n<p>$\\var{a}y=\\var{c}x+\\var{a}$</p>\n<p>$y= $[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({c}x+{a})/{a}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Note: to input the answer \"$x=y+2$\" the \"$x=$\" is already given and you just need to input \"$y+2$\".</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(2..9 except[a,b])", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..9 except a)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "atimesc": {"definition": "{a}*{c}", "templateType": "anything", "group": "Ungrouped variables", "name": "atimesc", "description": ""}}, "metadata": {"description": "<p>Transposition</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "transposing formula 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a", "c", "b", "d"], "tags": ["REBEL", "rebel", "Rebel", "rebelmaths", "transpose"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "parts": [{"stepsPenalty": 1, "prompt": "<p>$\\simplify[std]{{a}y + {b}x = {c} + {d}xy}\\;$</p>\n<p>$y =$ [[0]].</p>\n<p>You can click on \"Show steps\" for more information, but you will lose one mark if you do so.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>To re-arrange $ay + bx = c + dxy$ we should first collect all of the terms involving $y$ to the one side</p>\n          <p>$ay - dxy = c - bx$</p>\n          <p>we should then factorize out $y$ to find</p>\n          <p>$y(a-dx) = c - bx$</p>\n          <p>and then divide by $a-dx$ to get $y$ on its own</p>\n          <p>$y = \\frac{c - bx}{a - dx}$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "({c} - {b}x)/({a} - {d}x)", "marks": "5", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Rearrange the following equation to make $y$ the subject.&nbsp;</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(-10..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(-10..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(-10..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"description": "<p>Another transposition question.</p>\n<p>rebalmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Julie's copy of Algebra: Expansion of two brackets (one linear)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "a1", "b1", "c1"], "tags": ["algebra", "Algebra", "algebraic manipulation", "expansion of brackets", "expansion of the product of two linear terms", "rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "\n  <p>1. Using the method given by Show steps we have:</p>\n  <p>\\[\\simplify[std]{ {a}x*({c}x+{d})}=\\simplify[std]{{a*c}x^2+{a*d}x}\\]</p>\n  <p>2.</p>\n  <p>\\[\\simplify[std]{ ({a1}x+{b1})*({c1}x)}=\\simplify[std]{{a1*c1}x^2+{b1*c1}x}\\]</p>\n  <p>&nbsp;</p>\n  <p>&nbsp;</p>\n  ", "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "parts": [{"stepsPenalty": 1, "prompt": "\n      <p>$\\simplify[std]{({a}x)({c}x+{d})}=\\;$[[0]].</p>\n      <p>$\\simplify[std]{({a1}x+{b1})({c1}x)}=\\;$[[1]].</p>\n      <p>Your answers should be quadratics in $x$ and should not include any brackets.</p>\n      <p>You can click on Show steps to get more information, but you will lose one mark if you do so.</p>\n      ", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>\\[ax(cx+d)=acx^2+adx\\]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"notallowed": {"message": "<p>Do not include brackets in your answer. Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.</p>", "showStrings": false, "strings": ["("], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{a*c}x^2+{a*d}x", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme", "maxlength": {"length": 13, "message": "<p>Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.</p>", "partialCredit": 0}}, {"notallowed": {"message": "<p>Do not include brackets in your answer. Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.</p>", "showStrings": false, "strings": ["("], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{a1*c1}*x^2+{b1*c1}*x", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme", "maxlength": {"length": 13, "message": "<p>Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.</p>", "partialCredit": 0}}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Expand the following to give quadratics in $x$.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "0", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(-9..9 except [0,c])", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "a1": {"definition": "random(-5..5 except [0,a])", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "b1": {"definition": "random(-9..9 except [0,c])", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "c1": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}}, "metadata": {"description": "<p>Expansion of two brackets</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": []}]}, {"name": "Expansion of two brackets: Linear 2 positive coefficients", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a", "c", "b", "d"], "tags": ["algebra", "algebraic manipulation", "expansion of brackets", "expansion of the product of two linear terms", "Rebel", "REBEL", "rebel", "rebelmaths"], "advice": "\n  <p>Using the method given by Show steps we have:</p>\n  <p>\\[\\begin{eqnarray*}\\simplify[std]{ ({a}x+{b})({c}x+{d})}&amp;=&amp;\\simplify[std]{{a}x*({c}x+{d})+{b}({c}x+{d})}\\\\&amp;=&amp;\\simplify[std]{{a*c}x^2+{a*d}x+{b*c}x+{b*d}}\\\\&amp;=&amp;\\simplify[std]{{a*c}x^2+{(a*d+b*c)}x+{b*d}}\\end{eqnarray*}\\]</p>\n  <p>&nbsp;</p>\n  ", "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "parts": [{"stepsPenalty": 1, "prompt": "\n      <p>$\\simplify[std]{({a}x+{b})({c}x+{d})}=\\;$[[0]].</p>\n        <p>Your answer should be a quadratic in $x$ and should not include any brackets.</p>\n        <p>You can click on Show steps for more information, but you will lose one mark if you do so.</p>\n      ", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>Do not include brackets in your answer. Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.</p>", "showStrings": false, "strings": ["("], "partialCredit": 0}, "variableReplacements": [], "expectedvariablenames": [], "maxlength": {"length": 17, "message": "<p>Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.</p>", "partialCredit": 0}, "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "musthave": {"message": "<p>Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.</p>", "showStrings": false, "strings": ["x^2"], "partialCredit": 0}, "scripts": {}, "answer": "{a*c}x^2+{b*c+a*d}x+{b*d}", "marks": 2, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1], "answersimplification": "std"}], "steps": [{"prompt": "\n          <p>There are many ways to expand an expression such as $(ax+b)(cx+d)$.</p>\n          <p>One way:</p>\n          <p>\\[\\begin{eqnarray*} (ax+b)(cx+d)&amp;=&amp;ax(cx+d)+b(cx+d)\\\\&amp;=&amp;acx^2+adx+bcx+bd\\\\&amp;=&amp;acx^2+(ad+bc)x+bd\\end{eqnarray*}\\]</p>\n          ", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}], "statement": "<p>Expand the following to give a quadratic in $x$.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(2..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(1..9 except a)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(2..9 except [0,c])", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"description": "<p>Expand $(ax+b)(cx+d)$.</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": []}]}, {"name": "Simplify Algebraic Expressions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}], "functions": {}, "tags": ["algebra", "algebraic manipulation", "expanding brackets", "simplification", "simplifying an expression"], "advice": "\n  <p>Expanding the brackets we have:</p>\n  <p>\\[\\begin{eqnarray*}\\simplify[std]{({a}x+{b})({c}x+{d})-({a}x+{d})({c}x+{b})}&amp;=&amp;(\\simplify[std]{{a*c}x^2+{b*c+a*d}x+{b*d}})-(\\simplify[std]{{a*c}x^2+{b*a+c*d}x+{b*d}})\\\\&amp;=&amp;\\simplify[std]{{b*c+a*d}x-{b*a+c*d}x}\\\\&amp;=&amp;\\var{(a-c)*(d-b)}x\\end{eqnarray*}\\]</p>\n  ", "rulesets": {"std": ["all", "!collectNumbers", "!noLeadingMinus"]}, "parts": [{"prompt": "\n      <p>Simplify:</p>\n      <p>$\\simplify[std]{({a}x+{b})({c}x+{d})-({a}x+{d})({c}x+{b})}=\\;$[[0]]</p>\n      <p>Do not include brackets in your answer.</p>\n      ", "gaps": [{"notallowed": {"message": "<p>Do not include brackets in your answer.</p>", "showstrings": false, "strings": ["("], "partialcredit": 0.0}, "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 2.0, "answer": "{(a-c)*(d-b)}*x", "type": "jme", "maxlength": {"length": 6.0, "message": "<p>You can simplify the expression further.</p>", "partialcredit": 0.0}}], "type": "gapfill", "marks": 0.0}], "statement": "<p>Simplify the following expression.</p>", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(-6..6 except 0)", "name": "a"}, "c": {"definition": "random(-6..6 except [0,a])", "name": "c"}, "b": {"definition": "random(1..9 except a)", "name": "b"}, "d": {"definition": "random(1..9 except c)", "name": "d"}}, "metadata": {"notes": "\n    \t\t<p><strong>18/08/2012:</strong></p>\n    \t\t        <p>Added tags.</p>\n    \t\t        <p>Added description.</p>\n    \t\t", "description": "<p>Simplify $(ax+b)(cx+d)-(ax+d)(cx+b)$. Answer is a multiple of $x$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Simplify Algebraic Expressions: 2 unknowns", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}], "functions": {}, "tags": ["algebra", "algebraic manipulation", "expanding brackets", "simplification", "simplifying an expression"], "advice": "\n  <p>Expanding the brackets we have:</p>\n    <p>\\[\\begin{eqnarray*}\\simplify[std]{({a}x+{b}y)({c}x+{d}y)-({a}x+{d}y)({c}x+{b}y)}&amp;=&amp;(\\simplify[std]{{a*c}x^2+{b*c+a*d}x*y+{b*d}y^2})-(\\simplify[std]{{a*c}x^2+{b*a+c*d}x*y+{b*d}y^2})\\\\&amp;=&amp;\\simplify[std]{{b*c+a*d}x*y-{b*a+c*d}x*y}\\\\&amp;=&amp;\\var{(a-c)*(d-b)}xy\\end{eqnarray*}\\]</p>\n  ", "rulesets": {"std": ["all", "!collectNumbers", "!noLeadingMinus"]}, "parts": [{"prompt": "\n      <p>Simplify:</p>\n        <p>$\\simplify[std]{({a}x+{b}y)({c}x+{d}y)-({a}x+{d}y)({c}x+{b}y)}=\\;$[[0]]</p>\n        <p>Do not include brackets in your answer.</p>\n        <p>Input $xy$ as $x*y$.</p>\n      ", "gaps": [{"notallowed": {"message": "<p>Do not include brackets in your answer.</p>", "showstrings": false, "strings": ["("], "partialcredit": 0.0}, "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 2.0, "answer": "{(a-c)*(d-b)}*x*y", "type": "jme", "maxlength": {"length": 7.0, "message": "<p>You can simplify the expression further.</p>", "partialcredit": 0.0}}], "type": "gapfill", "marks": 0.0}], "statement": "<p>Simplify the following expression.</p>", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(-6..6 except 0)", "name": "a"}, "c": {"definition": "random(-6..6 except [0,a])", "name": "c"}, "b": {"definition": "random(1..9 except a)", "name": "b"}, "d": {"definition": "random(1..9 except [c,b])", "name": "d"}}, "metadata": {"notes": "\n    \t\t    \t\t<p><strong>18/08/2012:</strong></p>\n    \t\t    \t\t        <p>Added tags.</p>\n    \t\t    \t\t        <p>Added description.</p>\n    \t\t    \n    \t\t", "description": "<p>Simplify $(ax+by)(cx+dy)-(ax+dy)(cx+by)$. Answer is a multiple of $xy$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Expansion of three brackets: (Video)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}], "functions": {}, "tags": ["algebra", "algebraic manipulation", "expansion of brackets", "expansion of the product of three linear terms", "video"], "advice": "\n  <p>Using the method given by Show steps we first multiply out the first two brackets:</p>\n    <p>\\[\\begin{eqnarray*}\\simplify[std]{ ({a}y+{b})({c}y+{d})}&amp;=&amp;\\simplify[std]{{a}y*({c}y+{d})+{b}({c}y+{d})}\\\\&amp;=&amp;\\simplify[std]{{a*c}y^2+{a*d}y+{b*c}y+{b*d}}\\\\&amp;=&amp;\\simplify[std]{{a*c}y^2+{(a*d+b*c)}y+{b*d}}\\end{eqnarray*}\\]</p>\n    <p>And then multiply this by the third bracket:</p>\n    <p>\\[\\begin{eqnarray*}\\simplify[std]{({a}y+{b})({c}y+{d})({p}y+{q})}&amp;=&amp;\\simplify[std]{({a*c}y^2+{(a*d+b*c)}y+{b*d})({p}y+{q})}\\\\&amp;=&amp;\\simplify[std]{{a*c}y^2({p}y+{q})+{(a*d+b*c)}y*({p}y+{q})+{b*d}({p}y+{q})}\\\\&amp;=&amp;\\simplify[std]{{a*c*p}*y^3 +{a*c*q}*y^2+{p*(a*d+b*c)}y^2+{q*(a*d+b*c)}y+{b*d*p}y+{b*d*q}}\\\\&amp;=&amp;\\simplify[std]{{a*c*p}y^3+{a*c*q+a*d*p+p*b*c}y^2+{a*d*q+b*c*q+b*d*p}y+{b*d*q}}\\end{eqnarray*}\\]</p>\n    <p>&nbsp;</p>\n  ", "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "parts": [{"stepspenalty": 1.0, "prompt": "<p>$\\simplify[std]{({a}y+{b})({c}y+{d})({p}y+{q})}=\\;$[[0]].</p>\n        <p>Your answer should be a cubic in $y$ and should not include any brackets.</p>\n        <p>You can click on Show steps for more information, but you will lose one mark if you do so.</p>\n        <p>There is a video in Show steps which expands three brackets, but uses the variable $x$ rather than $y$.</p>", "gaps": [{"notallowed": {"message": "<p>Do not include brackets in your answer. Input your answer as a cubic in $y$, in the form $ay^3+by^2+cy+d$ for appropriate integers $a,\\;b,\\;c,\\;d$.</p>", "showstrings": false, "strings": ["(", "yy", "y*y"], "partialcredit": 0.0}, "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 2.0, "answer": "{a*c*p}y^3+{a*c*q+a*d*p+p*b*c}y^2+{a*d*q+b*c*q+b*d*p}y+{b*d*q}", "type": "jme"}], "steps": [{"prompt": "<p>There are many ways to expand an expression such as $(ay+b)(cy+d)(py+q)$.</p>\n            <p>One way is to expand the first two brackets, and then multiply the resulting quadratic in $y$ by $py+q$.</p>\n            <p>Hence:</p>\n            <p>\\[\\begin{eqnarray*} (ay+b)(cy+d)&amp;=&amp;ay(cy+d)+b(cy+d)\\\\&amp;=&amp;acy^2+ady+bcy+bd\\\\&amp;=&amp;acy^2+(ad+bc)y+bd\\end{eqnarray*}\\]</p>\n            <p>and then work out $(acy^2+(ad+bc)y+bd)(py+q)$.</p>\n            <p>See this video for more help:</p>\n            <p><iframe style=\"display: block; margin-left: auto; margin-right: auto;\" src=\"https://player.vimeo.com/video/8169375\" frameborder=\"0\" width=\"640\" height=\"480\"></iframe></p>", "type": "information", "marks": 0.0}], "marks": 0.0, "type": "gapfill"}], "statement": "<p>Expand the following to give a cubic in $y$.</p>", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(1..5)", "name": "a"}, "c": {"definition": "random(2..5)", "name": "c"}, "b": {"definition": "random(-9..9 except [0,a])", "name": "b"}, "d": {"definition": "random(-9..9 except [0,c])", "name": "d"}, "q": {"definition": "random(-3..3 except [0,b,d])", "name": "q"}, "p": {"definition": "random(1..3 except [a,c])", "name": "p"}}, "metadata": {"notes": "\n                            \t\t<p><strong>16/08/2012:</strong></p>\n                            \t\t        <p>Added tags.</p>\n                            \t\t        <p>Added description.</p>\n                            \t\t", "description": "<p>Expand $(ay+b)(cy+d)(py+q)$.</p>\n                        <p>Includes a video expanding three brackets, however uses the variable $x$ rather than $y$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}], "contributors": [{"name": "Deirdre Casey", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/681/"}], "extensions": [], "custom_part_types": [], "resources": []}