// Numbas version: exam_results_page_options
{"metadata": {"description": "", "licence": "None specified"}, "showstudentname": true, "navigation": {"showresultspage": "oncompletion", "showfrontpage": true, "browse": true, "preventleave": true, "onleave": {"message": "", "action": "none"}, "allowregen": true, "reverse": true}, "percentPass": "80", "question_groups": [{"pickQuestions": 1, "pickingStrategy": "all-ordered", "name": "Group", "questions": [{"name": "BODMAS: Basic", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Hayley Moore", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/495/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "m", "n", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>To answer questions&nbsp;these types of questions you need to remember the order of BODMAS.</p>\n<p></p>\n<p><strong>For the questions of the type $7 \\times 5 + 9$.</strong></p>\n<p></p>\n<p>We first calculate the multiplication</p>\n<p></p>\n<p>$7 \\times 5 + 9 = 35 + 9$</p>\n<p></p>\n<p>and then the addition since the M comes before A in BODMAS</p>\n<p></p>\n<p>$<span>35 + 9&nbsp;</span>= 44$</p>\n<p></p>\n<p><strong>Similarly for questions of the form $85 \\div 5 - (-3)$.</strong></p>\n<p></p>\n<p>We start by doing the division</p>\n<p></p>\n<p>$17 - (-3)$</p>\n<p></p>\n<p>and then the subtraction. Remember that $-$(-ve number)$ = +$</p>\n<p></p>\n<p>$17 - (-3) = 20.$</p>\n<p></p>\n<p></p>\n<p>For mor information on this see&nbsp;<a href=\"http://mathsupport.mas.ncl.ac.uk/wiki/Order_of_Operations:_BODMAS\" target=\"_blank\">BODMAS</a></p>\n<p></p>", "rulesets": {}, "parts": [{"integerPartialCredit": 0, "prompt": "<p>$\\var{a} \\times&nbsp;\\simplify[!collectNumbers, basic]{{b} + {c}}$</p>", "integerAnswer": true, "allowFractions": false, "marks": 1, "maxValue": "(a*b)+c", "minValue": "(a*b)+c", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "prompt": "<p>$\\var{d} - \\var{f} \\times \\var{g}$</p>", "integerAnswer": true, "allowFractions": false, "marks": 1, "maxValue": "d-(f*g)", "minValue": "d-(f*g)", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$\\var{h} \\div \\var{j} - \\var{k}$&nbsp;</p>\n<p>$\\simplify[!basic]{ {h} / {j} - {k} }$</p>", "allowFractions": false, "marks": 1, "maxValue": "(h/j) - k", "minValue": "(h/j) - k", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$\\var{r} + \\var{s} \\div \\var{t}$&nbsp;</p>", "allowFractions": false, "marks": 1, "maxValue": "r + (s/t)", "minValue": "r + (s/t)", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$\\var{l} + \\var{m} \\times \\var{n} - \\var{p} \\div \\var{q}$</p>", "allowFractions": false, "marks": 1, "maxValue": "l+(m*n)-(p/q)", "minValue": "l+(m*n)-(p/q)", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>Calculate the following using BODMAS:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(-15..15 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(1..15)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(-10..10 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random(1..10)*j", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(-15..15 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random(1..15)", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "n": {"definition": "random(1..15)", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "q": {"definition": "random(0..10 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "p": {"definition": "random(1..10)*q", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "s": {"definition": "random(-10..10 except 0)*t", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "r": {"definition": "random(1..15)", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "u": {"definition": "random(1..10)*v", "templateType": "anything", "group": "Ungrouped variables", "name": "u", "description": ""}, "t": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}, "w": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "w", "description": ""}, "v": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "v", "description": ""}, "y": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "y", "description": ""}, "x": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "x", "description": ""}, "z": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "z", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "BODMAS: Decimals", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Hayley Moore", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/495/"}], "functions": {}, "ungrouped_variables": ["smallest", "nd_smallest", "middle", "nd_largest", "largest", "p_value", "a", "b", "c", "d", "f", "sum_of_marks", "sum_marks"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"maxAnswers": 0, "prompt": "<p>Order the following decimals from smallest to largest.</p>\n<p></p>\n<p></p>", "matrix": [["1", 0, 0, 0, 0], [0, "1", 0, 0, 0], [0, 0, "1", 0, 0], [0, 0, 0, "1", 0], [0, 0, 0, 0, "1"]], "shuffleAnswers": false, "minAnswers": 0, "scripts": {}, "answers": ["Smallest", "2nd Smallest", "Middle", "2nd Largest", "Largest"], "choices": ["$\\var{smallest}$", "$\\var{nd_smallest}$", "$\\var{middle}$", "$\\var{nd_largest}$", "$\\var{largest}$"], "marks": 0, "displayType": "radiogroup", "maxMarks": 0, "warningType": "none", "showCorrectAnswer": true, "type": "m_n_x", "shuffleChoices": true, "minMarks": 0, "layout": {"expression": "", "type": "all"}}, {"distractors": ["", "", "", "", ""], "prompt": "<p>Choose&nbsp;the samllest value for which the following statement is true.</p>\n<p></p>\n<p>The value $p = \\var{p_value}$ is less than</p>", "matrix": ["{a}", "{b}", "{c}", "{d}", "{f}"], "shuffleChoices": false, "scripts": {}, "choices": ["<p>$0.1$</p>", "<p>$0.05$</p>", "<p>$0.01$</p>", "<p>$0.001$</p>", "<p>Non of these</p>"], "displayType": "radiogroup", "maxMarks": "1", "marks": 0, "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}], "statement": "<p>Answer the following questions regarding decimals.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "largest > nd_largest"}, "variables": {"a": {"definition": "(sign(0.1 - p_value) + 1)/2 - max(max(b,c),d)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "p_value": {"definition": "random(1..1500)/10000", "templateType": "anything", "group": "Ungrouped variables", "name": "p_value", "description": ""}, "c": {"definition": "(sign(0.01 - p_value) + 1)/2 - d", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "(sign(0.05 - p_value) + 1)/2 - max(c,d)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "nd_largest": {"definition": "largest - random(1..9)/1000", "templateType": "anything", "group": "Ungrouped variables", "name": "nd_largest", "description": ""}, "f": {"definition": "if(sum_of_marks,1,0)", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "middle": {"definition": "smallest + random(1..59)/100", "templateType": "anything", "group": "Ungrouped variables", "name": "middle", "description": ""}, "smallest": {"definition": "random(1..99)/1000", "templateType": "anything", "group": "Ungrouped variables", "name": "smallest", "description": ""}, "largest": {"definition": "random(middle*1000..999)/1000", "templateType": "anything", "group": "Ungrouped variables", "name": "largest", "description": ""}, "sum_of_marks": {"definition": "a+b+c+d = 0", "templateType": "anything", "group": "Ungrouped variables", "name": "sum_of_marks", "description": ""}, "nd_smallest": {"definition": "smallest+ random(1..9)/10000", "templateType": "anything", "group": "Ungrouped variables", "name": "nd_smallest", "description": ""}, "sum_marks": {"definition": "a+b+c+d+f", "templateType": "anything", "group": "Ungrouped variables", "name": "sum_marks", "description": ""}, "d": {"definition": "(sign(0.001 - p_value) + 1)/2", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "BODMAS: Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Hayley Moore", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/495/"}], "functions": {}, "ungrouped_variables": [], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p><strong>Questions of the form $\\dfrac{\\var{ac}}{\\var{bc}}$</strong></p>\n<p>First identify the greatest common&nbsp;factor the numberator and denominator have in common. In this case the factor in common is $\\var{gcd_ac_bc}$. We can the divide both through by this number</p>\n<p>$\\dfrac{\\var{ac}}{\\var{bc}} = \\dfrac{\\var{a} \\times \\var{gcd_ac_bc}}{\\var{b} \\times \\var{gcd_ac_bc}} = \\dfrac{\\var{a}}{\\var{b}}$.</p>\n<p><span></span></p>\n<p><strong>Questions of the form $\\dfrac{\\var{d}}{\\var{f}} + \\dfrac{\\var{g}}{\\var{h}}$</strong></p>\n<p><span>In order to add these two fractions we firstly need to make sure the denominators are the same. </span></p>\n<p><span>In this example we would multiply the top and bottom of the first fraction by $\\var{h}$ and the second fraction by $\\var{f}$. The causes both fractions to have a denominator of $\\simplify{{f}*{h}}$.</span></p>\n<p>Therefore the question becomes</p>\n<p>$\\dfrac{\\var{d}}{\\var{f}}+ \\dfrac{\\var{g}}{\\var{h}} = \\dfrac{\\simplify{({d}*{h})}}{\\simplify{({f}*{h})}} + \\dfrac{\\simplify{{g}*{f}}}{\\simplify{{f}*{h}}}$</p>\n<p>We can now add the fractions together</p>\n<p>$\\dfrac{\\simplify{({d}*{h})}}{\\simplify{({f}*{h})}}+ \\dfrac{\\simplify{({g}*{f})}}{\\simplify{({f}*{h})}}= \\dfrac{\\simplify{{d}*{h}} + \\simplify{{g}*{f}}}{\\simplify{{f}*{h}}} = \\dfrac{\\simplify{{d}*{h}+{g}*{f}}}{\\simplify{{f}*{h}}}$</p>\n<p>And then simplify (if necessary)</p>\n<p>$= \\dfrac{\\var{b_num}}{\\var{b_den}}$.</p>\n<p><span></span></p>\n<p><strong>Questions of the form $\\dfrac{\\var{j}}{\\var{k}} - \\dfrac{\\var{l}}{\\var{m}}$</strong></p>\n<p><span>In order to subtract one&nbsp;fraction from the other we need to make sure the denominators are the same as we did above.</span></p>\n<p><span>In this example we would multiply the top and bottom of the first fraction by $\\var{m}$ and the second fraction by $\\var{k}$. The causes both fractions to have a denominator of $\\simplify{{k}*{m}}$.</span></p>\n<p>Therefore the question becomes</p>\n<p>$\\dfrac{\\var{j}}{\\var{k}} - \\dfrac{\\var{l}}{\\var{m}} = \\dfrac{\\simplify{{j}*{m}}}{\\simplify{{k}*{m}}} - \\dfrac{\\simplify{{l}*{k}}}{\\simplify{{k}*{m}}}$.</p>\n<p>We can now subtract one fraction from the other</p>\n<p>$\\dfrac{\\var{j}}{\\var{k}} - \\dfrac{\\var{l}}{\\var{m}} = \\dfrac{\\simplify{{j}*{m}}}{\\simplify{{k}*{m}}} - \\dfrac{\\simplify{{l}*{k}}}{\\simplify{{k}*{m}}} = \\dfrac{\\simplify{{j}*{m}} - \\simplify{{l}*{k}}}{\\simplify{{k}*{m}}} = \\dfrac{\\simplify{{j}*{m} - {l}*{k}}}{\\simplify{{k}*{m}}}$</p>\n<p>and simplify (if necessary)</p>\n<p>$=\\dfrac{\\var{c_num}}{\\var{c_den}}.$</p>\n<p></p>\n<p><strong>Questions of the form $\\dfrac{\\var{n}}{\\var{p}} \\times \\dfrac{\\var{q}}{\\var{r}}$</strong></p>\n<p><span>In this example we would multiply the top&nbsp;of each fraction together and the bottom of each fraction together.</span></p>\n<p>Therefore the question becomes&nbsp;</p>\n<p>$\\dfrac{\\var{n}}{\\var{p}} \\times \\dfrac{\\var{q}}{\\var{r}} =&nbsp;\\dfrac{\\var{n} \\times \\var{q}}{\\var{p} \\times \\var{r}} = \\dfrac{\\simplify{{n}*{q}}}{\\simplify{{p}*{r}}}$.</p>\n<p>and simplify (if necessary)</p>\n<p>$=\\dfrac{\\var{d_num}}{\\var{d_den}}$</p>\n<p></p>\n<p><strong>Questions of the form $\\dfrac{\\var{s}}{\\var{t}} \\div \\dfrac{\\var{u}}{\\var{v}}$</strong></p>\n<p>To divide one fraction by another we start by flipping the second fraction</p>\n<p>$\\dfrac{\\var{u}}{\\var{v}} \\rightarrow \\dfrac{\\var{v}}{\\var{u}}$</p>\n<p>and then multiplying by the new fraction.</p>\n<p>Therefore the question becomes&nbsp;</p>\n<p>$\\dfrac{\\var{s}}{\\var{t}} \\times \\dfrac{\\var{v}}{\\var{u}} = \\dfrac{\\simplify{{s}*{v}}}{\\simplify{{t}*{u}}}$.</p>\n<p>This can then be simplified (if necessary)</p>\n<p>$=\\dfrac{\\var{e_num}}{\\var{e_den}}$.</p>\n<p></p>\n<p><strong>Questions of the form $\\Bigg(\\dfrac{\\var{w}}{\\var{x}}\\Bigg)^2$</strong></p>\n<p>This is the same as multiplying the fraction by itself</p>\n<p>$\\Bigg(\\dfrac{\\var{w}}{\\var{x}}\\Bigg)^2 = \\dfrac{\\var{w}}{\\var{x}} \\times \\dfrac{\\var{w}}{\\var{x}}$.</p>\n<p>This can be solved in the same way as in part d). We multiply numerators together and denominators together</p>\n<p>$\\Bigg(\\dfrac{\\var{w}}{\\var{x}}\\Bigg)^2 = \\dfrac{\\var{w}}{\\var{x}} \\times \\dfrac{\\var{w}}{\\var{x}} = \\dfrac{\\var{w}^2}{\\var{x}^2} = \\dfrac{\\simplify{{w}^2}}{\\simplify{{x}^2}}$.</p>\n<p>This is simplified to (if necessary)</p>\n<p>$=\\dfrac{\\var{f_num}}{\\var{f_den}}$.</p>", "rulesets": {}, "parts": [{"prompt": "<p>$\\dfrac{\\var{ac}}{\\var{bc}}$</p>\n<p>Input your answer here: [[0]]/[[1]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{a}", "minValue": "{a}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{b}", "minValue": "{b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\dfrac{\\var{d}}{\\var{f}}+ \\dfrac{\\var{g}}{\\var{h}}$</p>\n<p>Input your answer here: [[0]]/[[1]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{b_num}", "minValue": "{b_num}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{b_den}", "minValue": "{b_den}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\dfrac{\\var{j}}{\\var{k}} - \\dfrac{\\var{l}}{\\var{m}}$</p>\n<p>Input your answer here: [[0]]/[[1]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{c_num}", "minValue": "{c_num}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{c_den}", "minValue": "{c_den}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\dfrac{\\var{n}}{\\var{p}} \\times \\dfrac{\\var{q}}{\\var{r}}$</p>\n<p>Input your answer here: [[0]]/[[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{d_num}", "minValue": "{d_num}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{d_den}", "minValue": "{d_den}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\dfrac{\\var{s}}{\\var{t}} \\div \\dfrac{\\var{u}}{\\var{v}}$</p>\n<p>Input your answer here: [[0]]/[[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{e_num}", "minValue": "{e_num}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "e_den}", "minValue": "{e_den}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\Bigg(\\dfrac{\\var{w}}{\\var{x}}\\Bigg)^2$</p>\n<p>Input your answer here: [[0]]/[[1]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{f_num}", "minValue": "{f_num}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{f_den}", "minValue": "{f_den}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Simplify the following fractions,&nbsp;the answers should be in simplest or lowest form i.e. no further cancellations possible.</p>\n<p></p>\n<p>You may have to use BODMAS.</p>", "variable_groups": [{"variables": ["a", "b", "c", "ac", "bc", "gcd_ac_bc"], "name": "Part a"}, {"variables": ["d", "f", "g", "h", "gcd_b", "b_num", "b_den"], "name": "Part b"}, {"variables": ["j", "k", "l", "m", "gcd_c", "c_num", "c_den"], "name": "Part c"}, {"variables": ["n", "p", "q", "r", "gcd_d", "d_num", "d_den"], "name": "Part d"}, {"variables": ["e_den", "e_num", "gcd_e", "s", "t", "u", "v"], "name": "Part e"}, {"variables": ["w", "x", "gcd_f", "f_num", "f_den"], "name": "Part f"}], "variablesTest": {"maxRuns": 100, "condition": "gcd(a,b)=1\n"}, "variables": {"e_den": {"definition": "t*u/gcd_e", "templateType": "anything", "group": "Part e", "name": "e_den", "description": ""}, "ac": {"definition": " a*c", "templateType": "anything", "group": "Part a", "name": "ac", "description": ""}, "e_num": {"definition": "s*v/gcd_e", "templateType": "anything", "group": "Part e", "name": "e_num", "description": ""}, "b_num": {"definition": "(d*h+g*f)/gcd_b", "templateType": "anything", "group": "Part b", "name": "b_num", "description": ""}, "c_den": {"definition": "k*m/gcd_c", "templateType": "anything", "group": "Part c", "name": "c_den", "description": ""}, "d_num": {"definition": "n*q/gcd_d", "templateType": "anything", "group": "Part d", "name": "d_num", "description": ""}, "c_num": {"definition": "(j*m-l*k)/gcd_c", "templateType": "anything", "group": "Part c", "name": "c_num", "description": ""}, "d_den": {"definition": "p*r/gcd_d", "templateType": "anything", "group": "Part d", "name": "d_den", "description": ""}, "gcd_b": {"definition": "gcd(d*h + g*f,f*h)", "templateType": "anything", "group": "Part b", "name": "gcd_b", "description": ""}, "gcd_c": {"definition": "gcd(j*m-l*k,k*m)", "templateType": "anything", "group": "Part c", "name": "gcd_c", "description": ""}, "gcd_f": {"definition": "gcd(w^2, x^2)", "templateType": "anything", "group": "Part f", "name": "gcd_f", "description": ""}, "gcd_d": {"definition": "gcd(n*q,p*r)", "templateType": "anything", "group": "Part d", "name": "gcd_d", "description": ""}, "gcd_e": {"definition": "gcd(s*v,t*u)", "templateType": "anything", "group": "Part e", "name": "gcd_e", "description": ""}, "b_den": {"definition": "f*h/gcd_b", "templateType": "anything", "group": "Part b", "name": "b_den", "description": ""}, "f_num": {"definition": "w^2/gcd_f", "templateType": "anything", "group": "Part f", "name": "f_num", "description": ""}, "bc": {"definition": "b*c", "templateType": "anything", "group": "Part a", "name": "bc", "description": ""}, "f_den": {"definition": "x^2/gcd_f", "templateType": "anything", "group": "Part f", "name": "f_den", "description": ""}, "gcd_ac_bc": {"definition": "gcd(ac,bc)", "templateType": "anything", "group": "Part a", "name": "gcd_ac_bc", "description": ""}, "a": {"definition": "random(1..50)", "templateType": "anything", "group": "Part a", "name": "a", "description": "<p>part a</p>"}, "c": {"definition": "random(2..10)", "templateType": "anything", "group": "Part a", "name": "c", "description": ""}, "b": {"definition": "random(a+1..50)", "templateType": "anything", "group": "Part a", "name": "b", "description": "<p>part a</p>"}, "d": {"definition": "random(1..15)", "templateType": "anything", "group": "Part b", "name": "d", "description": ""}, "g": {"definition": "random(1..15)", "templateType": "anything", "group": "Part b", "name": "g", "description": ""}, "f": {"definition": "random(2..10 except d)", "templateType": "anything", "group": "Part b", "name": "f", "description": ""}, "h": {"definition": "random(2..10 except f except g)", "templateType": "anything", "group": "Part b", "name": "h", "description": ""}, "k": {"definition": "random(2..10)", "templateType": "anything", "group": "Part c", "name": "k", "description": ""}, "j": {"definition": "random(1..15)", "templateType": "anything", "group": "Part c", "name": "j", "description": ""}, "m": {"definition": "random(2..10 except k)", "templateType": "anything", "group": "Part c", "name": "m", "description": ""}, "l": {"definition": "random(1..15) ", "templateType": "anything", "group": "Part c", "name": "l", "description": ""}, "n": {"definition": "random(1..15)", "templateType": "anything", "group": "Part d", "name": "n", "description": ""}, "q": {"definition": "random(1..15)", "templateType": "anything", "group": "Part d", "name": "q", "description": ""}, "p": {"definition": "random(2..10 except n)", "templateType": "anything", "group": "Part d", "name": "p", "description": ""}, "s": {"definition": "random(1..15)", "templateType": "anything", "group": "Part e", "name": "s", "description": ""}, "r": {"definition": "random(2..10 except q)", "templateType": "anything", "group": "Part d", "name": "r", "description": ""}, "u": {"definition": "random(1..15)", "templateType": "anything", "group": "Part e", "name": "u", "description": ""}, "t": {"definition": "random(2..10 except s)", "templateType": "anything", "group": "Part e", "name": "t", "description": ""}, "w": {"definition": "random(1..10)", "templateType": "anything", "group": "Part f", "name": "w", "description": ""}, "v": {"definition": "random(2..10 except u)", "templateType": "anything", "group": "Part e", "name": "v", "description": ""}, "x": {"definition": "random(2..10 except w)", "templateType": "anything", "group": "Part f", "name": "x", "description": ""}}, "metadata": {"notes": "", "description": "<p>Simplifing and combining fractions</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "BODMAS: Orders", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Hayley Moore", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/495/"}], "functions": {}, "ungrouped_variables": ["negative_number", "a", "b", "length_side", "c", "d"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p><b>For questions of the type \"$2 + (4)^2$\"</b></p>\n<p>In this question we have both squaring and addition. Using BODMAS we see that <strong>O</strong>rders comes before <strong>A</strong>ddition so we calculate the square before the addition. The squaring gives</p>\n<p>$2+ (4)^2 = 2 + 16$</p>\n<p>and then calculating the addition gives</p>\n<p>$2+16 = 18$</p>\n<p></p>\n<p><strong>For questions of the type \"$(7-4)^2$\"</strong></p>\n<p>Using BODMAS we see that <strong>B</strong>rackets come before <b>O</b>rder. So simplifying the brakets gives</p>\n<p>$(7-4)^2 = 3^2$.</p>\n<p>Then we have a number squared. So the answer is</p>\n<p>$3^2 = 9$.</p>\n<p><strong></strong></p>\n<p><strong>For questions of the type \"What is $-3$ squared?\"</strong></p>\n<p>It is first good to write down the question in mathematical notation</p>\n<p>$(-3)^2$</p>\n<p>and then calculate</p>\n<p>$(-3)^2 = 9$.</p>\n<p></p>\n<p><strong>For questions of the type \"A square has length $8$. What is its area?\"</strong></p>\n<p>We know that the area of a square is the length of its sides squared. Hence&nbsp;</p>\n<p>Area$= 8^2$</p>\n<p>So the area is $64$</p>\n<p></p>\n<p></p>", "rulesets": {}, "parts": [{"prompt": "<p>$\\var{a} + (\\var{b})^2$</p>", "allowFractions": false, "marks": 1, "maxValue": "a + b^2", "minValue": "a + b^2", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$(\\var{c}-\\var{d})^2$</p>", "allowFractions": false, "marks": 1, "maxValue": "(c-d)^2", "minValue": "(c-d)^2", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\var{negative_number}$ squared?</p>", "allowFractions": false, "marks": 1, "maxValue": "negative_number^2", "minValue": "negative_number^2", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The area of a square is defined to be the length of &nbsp;its sides squared.</p>\n<p>If a square has sides of length $\\var{length_side}$, what is its area?</p>", "allowFractions": false, "marks": 1, "maxValue": "length_side^2", "minValue": "length_side^2", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>Using BODMAS answer the follwing questions</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(-10..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(-10..10 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(-5..5 except c)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "negative_number": {"definition": "random(-10..-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "negative_number", "description": ""}, "length_side": {"definition": "random(1..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "length_side", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "BODMAS: Percentages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Hayley Moore", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/495/"}], "functions": {}, "ungrouped_variables": ["a", "b", "mint", "chocolate", "sweets", "num", "den", "n", "d", "per", "marks", "increase", "new_mark", "decimal", "gcd_per100", "numerator", "denominator", "marks_increased", "p", "dec"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p><strong>Questions of the form \"find $\\var{a}\\%$ of $\\var{b}$\".&nbsp;</strong></p>\n<p>In order to answer this you multiply the number, $\\var{b}$, by the percentage over 100, $\\dfrac{\\var{a}}{100}$</p>\n<p>$\\var{b} \\times \\dfrac{\\var{a}}{100} = \\simplify{{a}*{b}/100}$</p>\n<p><strong>Remember:</strong>&nbsp;Give you answer to 2 decimal places.</p>\n<p></p>\n<p></p>\n<p><strong>Questions of the form \"if a mixed bag of $\\var{sweets}$ sweets contains $\\var{mint}$ mints and $\\var{chocolate}$ chocolates. What percentage of the contents&nbsp;is chocolate\"</strong></p>\n<p>To calculate the percentage of chocolate sweets in the bag you must divide the number of chocolates by the total number of sweets and then multiply by $100%$.</p>\n<p>$\\dfrac{\\var{chocolate}}{\\var{sweets}}\\times 100 = \\simplify{100*{chocolate}/{sweets}}.</p>\n<p><strong>Remember:</strong>&nbsp;Give you answer to 2 decimal places.</p>\n<p></p>\n<p></p>\n<p><strong>Questions of the form \"convert $\\dfrac{\\var{num}}{\\var{den}}$ into a percentage\"</strong></p>\n<p>This question is very similar to part b). We already have the number in fractional form if we covert this into a decimal and multiply by $100\\%$ we obtain the percentage</p>\n<p>$\\dfrac{\\var{num}}{\\var{den}} = \\var{deciamal}\\times 100\\% = \\simplify{{decimal}*100}\\%$</p>\n<p><strong>Remember:</strong> Give you answer to 2 decimal places.</p>\n<p></p>\n<p></p>\n<p><strong>Questions of the form \"convert $\\var{per}\\%$ into a fraction\"</strong></p>\n<p>To do this you simply divide by $100$.</p>\n<p>$\\var{per}\\% = \\dfrac{\\var{per}}{100} = \\dfrac{\\var{numerator}}{\\var{denominator}}$&nbsp;</p>\n<p></p>\n<p></p>\n<p><strong>Questions of the form \"Last year the average mark in an exam was $\\var{marks}$. They have now increased by $\\var{increase}$ percent. What is the current average mark?\"</strong></p>\n<p>We start by finding $\\var{increase}$ % of $\\var{marks}$.</p>\n<p>$\\var{marks}\\times\\dfrac{\\var{increase}}{100} = \\var{marks_increased}$</p>\n<p>We then add this onto last years average marks to find this years</p>\n<p>$\\var{marks} + \\var{marks_increased} = \\var{new_mark}$</p>", "rulesets": {}, "parts": [{"prompt": "<p>Find $\\var{a}\\%$ of $\\var{b}$</p>\n<p>Answer: &nbsp; [[0]] &nbsp;(2.d.p)</p>", "marks": 0, "gaps": [{"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct number of decimal places.</p>", "allowFractions": false, "marks": 1, "precision": "2", "maxValue": "(a/100)*b", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "minValue": "(a/100)*b", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "<p>If a mixed bag of $\\var{sweets}$ sweets contains $\\var{mint}$ mints and $\\var{chocolate}$ chocolates. What percentage of the contents&nbsp;is chocolate?</p>\n<p></p>\n<p>Answer: &nbsp;[[0]] %(2.dp)</p>", "marks": 0, "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "marks": 1, "precision": "2", "maxValue": "(chocolate/sweets)*100", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "minValue": "(chocolate/sweets)*100", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "<p>Convert $\\dfrac{\\var{num}}{\\var{den}}$ into a percentage.</p>\n<p>Answer: [[0]] % (2dp)</p>", "marks": 0, "gaps": [{"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct number of decimal places.</p>", "allowFractions": false, "marks": 1, "precision": "2", "maxValue": "(num/den)*100", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "minValue": "(num/den)*100", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "<p>Convert $\\var{per}\\%$ into a fraction. Fraction must be in it's simplest form.</p>\n<p>Answer: [[0]]&nbsp;/[[1]]</p>", "marks": 0, "gaps": [{"allowFractions": false, "marks": 1, "maxValue": "numerator", "minValue": "numerator", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "denominator", "minValue": "denominator", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "<p>Last year the average mark in an exam was $\\var{marks}$. They have now increased by $\\var{increase}$ percent. What is the current average mark?</p>\n<p>Answer: [[0]]</p>", "marks": 0, "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "marks": 1, "precision": "2", "maxValue": "new_mark", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "minValue": "new_mark", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "<p>Write $\\var{p}$ as a decimal?</p>\n<p>Answer: &nbsp;[[0]] (2 d.p.)</p>", "marks": 0, "gaps": [{"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision. Please give your answer to 2 decimal places.</p>", "allowFractions": false, "marks": 1, "precision": "2", "maxValue": "dec", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "minValue": "dec", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}], "statement": "<p>Answer the following questions on percentages.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..20)*5", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "b": {"definition": "random(1..30)*10", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(n+1..20)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "p": {"definition": "random(1..99)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "marks_increased": {"definition": "marks*increase/100", "templateType": "anything", "group": "Ungrouped variables", "name": "marks_increased", "description": ""}, "new_mark": {"definition": "marks*(1+(increase/100))", "templateType": "anything", "group": "Ungrouped variables", "name": "new_mark", "description": ""}, "denominator": {"definition": "100/gcd_per100", "templateType": "anything", "group": "Ungrouped variables", "name": "denominator", "description": ""}, "numerator": {"definition": "per/gcd_per100", "templateType": "anything", "group": "Ungrouped variables", "name": "numerator", "description": ""}, "per": {"definition": "precround(100*n/d,0)", "templateType": "anything", "group": "Ungrouped variables", "name": "per", "description": ""}, "chocolate": {"definition": "sweets - mint", "templateType": "anything", "group": "Ungrouped variables", "name": "chocolate", "description": ""}, "increase": {"definition": "random(1..40)", "templateType": "anything", "group": "Ungrouped variables", "name": "increase", "description": ""}, "sweets": {"definition": "random(1..4)*10", "templateType": "anything", "group": "Ungrouped variables", "name": "sweets", "description": ""}, "num": {"definition": "random(1..90)", "templateType": "anything", "group": "Ungrouped variables", "name": "num", "description": ""}, "gcd_per100": {"definition": "gcd(per,100)", "templateType": "anything", "group": "Ungrouped variables", "name": "gcd_per100", "description": ""}, "den": {"definition": "random(num..99 except num)", "templateType": "anything", "group": "Ungrouped variables", "name": "den", "description": ""}, "marks": {"definition": "random(40..100)", "templateType": "anything", "group": "Ungrouped variables", "name": "marks", "description": ""}, "n": {"definition": "random(1..18)", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "dec": {"definition": "p/100", "templateType": "anything", "group": "Ungrouped variables", "name": "dec", "description": ""}, "mint": {"definition": "random(1..sweets)", "templateType": "anything", "group": "Ungrouped variables", "name": "mint", "description": ""}, "decimal": {"definition": "num/den", "templateType": "anything", "group": "Ungrouped variables", "name": "decimal", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "BODMAS: Rounding", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Hayley Moore", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/495/"}], "functions": {}, "ungrouped_variables": ["a", "sig_a", "b", "prec_b", "c", "sig_c"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"precisionType": "sigfig", "prompt": "<p>$\\var{a}$ to 3 significant figures</p>", "precisionMessage": "<p>You have not given your answer to the correct precision. You need to round to 3 significant figures.</p>", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "sig_a", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "sig_a", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$\\var{b}$ to 2 decimal places</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "prec_b", "minValue": "prec_b", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "sigfig", "prompt": "<p>$\\var{c}$ to 3 significant figures</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "sig_c", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "sig_c", "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>Round the following number to the appropriate number of significant figures or decimal places</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "c > 10"}, "variables": {"a": {"definition": "random(7..69 except 14 except 21 except 28 except 35 except 42 except 49 except 56 except 63)/7", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(1..69 except 7 except 14 except 21 except 28 except 35 except 42 except 49 except 56 except 63)*10/7", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(1..69 except 7 except 14 except 21 except 28 except 35 except 42 except 49 except 56 except 63)*10/7", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "prec_b": {"definition": "precround(b, 2)", "templateType": "anything", "group": "Ungrouped variables", "name": "prec_b", "description": ""}, "sig_c": {"definition": "siground(c,3)", "templateType": "anything", "group": "Ungrouped variables", "name": "sig_c", "description": ""}, "sig_a": {"definition": "siground(a,3)", "templateType": "anything", "group": "Ungrouped variables", "name": "sig_a", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "BODMAS: Square Roots", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Hayley Moore", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/495/"}], "functions": {}, "ungrouped_variables": ["a", "a2", "b", "c", "d2", "rand", "d", "b2", "c2", "sq2", "sq", "area", "l"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p><strong>Questions of the type $\\sqrt{9}$</strong></p>\n<p>For this type of question you are asked to give both roots.</p>\n<p>We know that $(-x)^2 = x^2$ and that $(+x)^2 = x^2$.</p>\n<p>So the answer to this question is $\\pm 3$</p>\n<p>Psoitive root: $3$ &nbsp; &nbsp;Negative root: $-3$</p>\n<p></p>\n<p><strong>Questions of the type $\\sqrt{(9+16)}$</strong></p>\n<p>Using BODMAS we know that we fist need to evaluate the brackets</p>\n<p>$\\sqrt{(9+16)} = \\sqrt{25}$.</p>\n<p>We can now take the square root</p>\n<p>$\\sqrt{25} = 5$ and $\\sqrt{25} = -5$</p>\n<p></p>\n<p><strong>Questions of the type \"The area of a square is 81, find the length of its sides\"</strong></p>\n<p>This can be written mathematically as&nbsp;</p>\n<p>$l^2 = 81$</p>\n<p>where $l$ represents the length of the sides.</p>\n<p>Therefore the length of the sides is $9$.</p>\n<p></p>\n<p>NOTE: Lengths <em>cannot</em> be negative, therefore always take the positive square root in this type of question.</p>\n<p></p>", "rulesets": {}, "parts": [{"prompt": "<p>$\\sqrt{\\var{a2}}$</p>\n<p>Positive root:&nbsp;[[0]] &nbsp; &nbsp;Negative root:&nbsp;[[1]]</p>", "marks": 0, "gaps": [{"allowFractions": false, "marks": 1, "maxValue": "a", "minValue": "a", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "-a", "minValue": "-a", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "<p>$\\sqrt{(\\var{b2}+\\var{c2})}$</p>\n<p></p>\n<p>Postitive root: [[0]] &nbsp; &nbsp; Negative root: [[1]]</p>", "marks": 0, "gaps": [{"allowFractions": false, "marks": 1, "maxValue": "d", "minValue": "d", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "-d", "minValue": "-d", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "<p>What is the positive square root of $\\var{sq2}$?</p>", "allowFractions": false, "marks": 1, "maxValue": "sq", "minValue": "sq", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The area of a square is defined to be the square of the length of its side.</p>\n<p>A square has area $\\var{area}$, what is the length of its sides?</p>", "allowFractions": false, "marks": 1, "maxValue": "l", "minValue": "l", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>Answer the following questions using BODMAS</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "rand": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "rand", "description": ""}, "c": {"definition": "4*rand", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "3*rand", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "sqrt(d2)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "area": {"definition": "l^2", "templateType": "anything", "group": "Ungrouped variables", "name": "area", "description": ""}, "sq2": {"definition": "sq^2", "templateType": "anything", "group": "Ungrouped variables", "name": "sq2", "description": ""}, "sq": {"definition": "random(1..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "sq", "description": ""}, "l": {"definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "a2": {"definition": "a^2", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "b2": {"definition": "b^2", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "c2": {"definition": "c^2", "templateType": "anything", "group": "Ungrouped variables", "name": "c2", "description": ""}, "d2": {"definition": "b^2 + c^2", "templateType": "anything", "group": "Ungrouped variables", "name": "d2", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}], "feedback": {"showactualmark": true, "feedbackmessages": [], "showanswerstate": true, "intro": "", "allowrevealanswer": true, "showtotalmark": true, "advicethreshold": 0}, "timing": {"allowPause": true, "timedwarning": {"message": "", "action": "none"}, "timeout": {"message": "", "action": "none"}}, "showQuestionGroupNames": true, "name": "Yoav -  Practice BODMAS", "duration": 0, "type": "exam", "contributors": [{"name": "Yoav Tadmor", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/593/"}], "extensions": [], "custom_part_types": [], "resources": []}