// Numbas version: exam_results_page_options
{"name": "Arithmetic: adjustments in multiplication and division", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"ungrouped_variables": [], "tags": [], "name": "Arithmetic: adjustments in multiplication and division", "statement": "", "preamble": {"css": "", "js": ""}, "functions": {}, "advice": "<p>There is nothing directly like this in lectures or workshops. It involves having an intuition for multiplication and division.</p>\n<p>If you are struggling with part (c), try describing a real-life situation for these calculations, like in part (b).</p>\n<p>If you are still struggling, remember you are welcome to ask us for help.</p>", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Questions about how the answer to a multiplication or a division is affected if you adjust the numbers involved. E.g. if you double the denominator, what happens to the answer.</p>"}, "variables": {"max_mark": {"templateType": "anything", "name": "max_mark", "group": "change these", "definition": "3", "description": ""}, "marks": {"templateType": "anything", "name": "marks", "group": "do not change these", "definition": "matrix(\n  [\n    if(rand[0]=1,[max_mark/n,-max_mark],[-max_mark,max_mark/n]),\n    if(rand[1]=1,[max_mark/n,-max_mark],[-max_mark,max_mark/n]),\n    if(rand[2]=1,[max_mark/n,-max_mark],[-max_mark,max_mark/n]),\n    if(rand[3]=1,[max_mark/n,-max_mark],[-max_mark,max_mark/n]),\n    if(rand[4]=1,[max_mark/n,-max_mark],[-max_mark,max_mark/n]),\n    if(rand[5]=1,[max_mark/n,-max_mark],[-max_mark,max_mark/n]),\n    if(rand[6]=1,[max_mark/n,-max_mark],[-max_mark,max_mark/n])\n    ]\n  )\n", "description": ""}, "n": {"templateType": "anything", "name": "n", "group": "do not change these", "definition": "length(statements)", "description": ""}, "statements_false": {"templateType": "anything", "name": "statements_false", "group": "change these", "definition": "[\"$\\\\var{c*10} \\\\div \\\\var{a}$ is ten times smaller than $\\\\var{c} \\\\div \\\\var{a}$\",\n  \"$\\\\var{c} \\\\div \\\\var{a*10}$ is ten times bigger than $\\\\var{c} \\\\div \\\\var{a}$\",\n  \"If I replace $\\\\var{a}$ with $\\\\var{a/2}$, the answer would be halved\",\n  \"If I replace $\\\\var{a}$ with $\\\\var{a/3}$, the answer would be three times smaller\",\n  \"If I make $\\\\var{a}$ four times smaller, the answer would become four times smaller\",\n  \"If I make $\\\\var{c}$ a hundred times smaller, the answer would become hundred times bigger\",\n  \"$\\\\var{c} \\\\div \\\\var{a*2}$ is twice as big as $\\\\var{c} \\\\div \\\\var{a}$\"]\n ", "description": "<p></p>\n<p></p>"}, "b": {"templateType": "anything", "name": "b", "group": "change these", "definition": "random(11..18)", "description": ""}, "statements_true": {"templateType": "anything", "name": "statements_true", "group": "change these", "definition": "[\"$\\\\var{c*10} \\\\div \\\\var{a}$ is ten times bigger than $\\\\var{c} \\\\div \\\\var{a}$\",\n  \"$\\\\var{c} \\\\div \\\\var{a*10}$ is ten times smaller than $\\\\var{c} \\\\div \\\\var{a}$\",\n  \"If I replace $\\\\var{a}$ with $\\\\var{a/2}$, the answer would double\",\n  \"If I replace $\\\\var{a}$ with $\\\\var{a/3}$, the answer would triple\",\n  \"If I make $\\\\var{a}$ four times smaller, the answer would become four times bigger\",\n  \"If I make $\\\\var{c}$ a hundred times smaller, the answer would become hundred times smaller\",\n  \"$\\\\var{c} \\\\div \\\\var{a*2}$ is a half of $\\\\var{c} \\\\div \\\\var{a}$\"]\n ", "description": ""}, "c": {"templateType": "anything", "name": "c", "group": "change these", "definition": "a*b", "description": ""}, "rand": {"templateType": "anything", "name": "rand", "group": "do not change these", "definition": "vector(shuffle([digits[n_true],\n  digits[n_true+1],\n  digits[n_true+2],\n  digits[n_true+3],\n  digits[n_true+4],\n  digits[n_true+5],\n  digits[n_true+6]]))", "description": ""}, "statements": {"templateType": "anything", "name": "statements", "group": "do not change these", "definition": "[if(rand[0]=1,\n    statements_true[0],\n    statements_false[0]),\n  if(rand[1]=1,\n    statements_true[1],\n    statements_false[1]),\n  if(rand[2]=1,\n    statements_true[2],\n    statements_false[2]),\n  if(rand[3]=1,\n    statements_true[3],\n    statements_false[3]),\n  if(rand[4]=1,\n    statements_true[4],\n    statements_false[4]),\n  if(rand[5]=1,\n    statements_true[5],\n    statements_false[5]),\n  if(rand[6]=1,\n    statements_true[6],\n    statements_false[6])\n]", "description": ""}, "n_true": {"templateType": "anything", "name": "n_true", "group": "do not change these", "definition": "random(1..6)", "description": ""}, "digits": {"templateType": "anything", "name": "digits", "group": "do not change these", "definition": "[0,0,0,0,0,0,0,1,1,1,1,1,1,1]", "description": ""}, "a": {"templateType": "anything", "name": "a", "group": "change these", "definition": "random(1..3)*12", "description": ""}}, "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "parts": [{"maxAnswers": 0, "marks": 0, "warningType": "none", "minAnswers": "3", "variableReplacements": [], "matrix": ["-2", "0.6", "0.7", "0.7"], "displayColumns": "1", "scripts": {}, "choices": ["If Bob worked for 70 hours instead of 60, their income would increase by 10", "If Bob worked twice as long, their income would double", "If Bob works ten times as long,&nbsp;their income would increase by a factor of 10", "If Bob worked 20 hours instead of 60, they would earn one third of the total"], "variableReplacementStrategy": "originalfirst", "type": "m_n_2", "minMarks": 0, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "prompt": "<p>Bob works 60 hours at &pound;7 per hour.&nbsp; Altogether Bob earnt &pound;420.&nbsp;&nbsp;</p>\n<p>Which of the following are true.</p>", "shuffleChoices": true, "distractors": ["", "", "", ""], "showFeedbackIcon": true, "displayType": "checkbox", "unitTests": [], "maxMarks": 0, "customMarkingAlgorithm": ""}, {"maxAnswers": 0, "marks": 0, "warningType": "none", "minAnswers": "2", "variableReplacements": [], "matrix": ["-2", "-2", "1", "-2", "1"], "displayColumns": "1", "scripts": {}, "choices": ["If Chris needed to travel 120 miles instead of 100, the time taken would increase by 20.", "If Chris travelled at 50 miles an hour instead of 40 miles, the time taken would reduce by 10.", "If Chris travelled at 20 miles an hour instead of 40, Chris would take twice as long.", "If Chris travelled at 80 miles an hour instead of 40, Chris would take twice as long.", "If Chris travelled ten times faster, it would take Chris ten times less time."], "variableReplacementStrategy": "originalfirst", "type": "m_n_2", "minMarks": 0, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "prompt": "<p>Chris needs to travel 100 miles. They travel at 40 miles an hour.&nbsp; Therefore, the time taken is $100 \\div 40=2.5$ hours.&nbsp;&nbsp;</p>\n<p>Which of the following are true.</p>", "shuffleChoices": true, "distractors": ["", "", "", "", ""], "showFeedbackIcon": true, "displayType": "checkbox", "unitTests": [], "maxMarks": 0, "customMarkingAlgorithm": ""}, {"maxAnswers": 0, "marks": 0, "shuffleAnswers": false, "minAnswers": "n", "variableReplacements": [], "matrix": "{marks}", "scripts": {}, "choices": "{statements}", "variableReplacementStrategy": "originalfirst", "type": "m_n_x", "answers": ["<p>True</p>", "<p>False</p>"], "layout": {"type": "all", "expression": ""}, "minMarks": 0, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "prompt": "<p>We know that $\\var{a*b} \\div \\var{a} = \\var{b}$.</p>\n<p>Which of the following are true and which are false?</p>", "shuffleChoices": true, "showFeedbackIcon": true, "displayType": "radiogroup", "unitTests": [], "warningType": "none", "maxMarks": "0", "customMarkingAlgorithm": ""}], "variable_groups": [{"variables": ["statements_true", "statements_false", "max_mark", "a", "b", "c"], "name": "change these"}, {"variables": ["n_true", "digits", "rand", "statements", "n", "marks"], "name": "do not change these"}], "extensions": [], "type": "question", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}