// Numbas version: exam_results_page_options
{"showQuestionGroupNames": false, "duration": 0, "timing": {"timeout": {"message": "", "action": "none"}, "allowPause": true, "timedwarning": {"message": "", "action": "none"}}, "metadata": {"licence": "None specified", "description": ""}, "feedback": {"showactualmark": true, "intro": "", "advicethreshold": 0, "showanswerstate": true, "feedbackmessages": [], "allowrevealanswer": true, "showtotalmark": true}, "percentPass": 0, "navigation": {"onleave": {"message": "", "action": "none"}, "showfrontpage": true, "preventleave": true, "allowregen": true, "browse": true, "showresultspage": "oncompletion", "reverse": true}, "name": "Introductory Maths for analytical chemistry", "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questions": [{"name": "Find the equation of a line through two points - positive gradient", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Bradley Bush", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1521/"}, {"name": "Aiden McCall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1592/"}], "statement": "<p>In this question we will identify&nbsp;the equation of the straight line passing&nbsp;through points &nbsp;$A=(\\var{xa},\\var{ya})$ and &nbsp;$B=(\\var{xb},\\var{yb})$ in the form $y = mx + c$.</p>\n<p>{plotPoints()}</p>", "variables": {"m": {"name": "m", "description": "", "definition": "(ya-yb)/(xa-xb)", "templateType": "anything", "group": "Ungrouped variables"}, "yb": {"name": "yb", "description": "", "definition": "ya+random([2,4])", "templateType": "anything", "group": "Ungrouped variables"}, "xa": {"name": "xa", "description": "", "definition": "random(-4..-1)", "templateType": "anything", "group": "Ungrouped variables"}, "ya": {"name": "ya", "description": "", "definition": "random(-4..2)", "templateType": "anything", "group": "Ungrouped variables"}, "xb": {"name": "xb", "description": "", "definition": "xa+random([2,4] except -xa)", "templateType": "anything", "group": "Ungrouped variables"}, "c": {"name": "c", "description": "", "definition": "ya-m*xa", "templateType": "anything", "group": "Ungrouped variables"}}, "metadata": {"description": "<p>Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.</p>\n<p>The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.</p>\n<p>This particular example has a positive gradient.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "tags": ["gradient", "graphs", "line equation", "Straight Line", "straight line", "taxonomy", "y-intercept"], "variablesTest": {"maxRuns": 100, "condition": "\n"}, "variable_groups": [], "ungrouped_variables": ["xa", "xb", "ya", "yb", "m", "c"], "advice": "<p>We find the equation of a straight line passing through two points by finding the gradient and the $y$-intercept of the line.</p>\n<h4>a)</h4>\n<p>We&nbsp;can find the gradient ($m$) using the points $A = (x_1,y_1)=(\\var{xa},\\var{ya})$ and $B = (x_2,y_2)=(\\var{xb},\\var{yb})$.</p>\n<p>As the definition of gradient is the ratio of vertical change ($y_2-y_1$) to horizontal change ($x_2-x_1$).<br/>The equation for gradient is,</p>\n<p>\\begin{align}<br/>m &amp;= \\frac{y_2-y_1}{x_2-x_1} \\\\[0.5em]<br/>&amp;= \\frac{\\simplify[!collectNumbers]{{yb}-{ya}}}{\\simplify[!collectNumbers]{{xb}-{xa}}} \\\\[0.5em]<br/>&amp;= \\frac{\\simplify[]{{yb}-{ya}}}{\\simplify{{xb}-{xa}}} \\\\[0.5em]<br/>&amp;=&nbsp;\\simplify[simplifyFractions,unitDenominator]{({yb-ya})/({xb-xa})}\\text{.}<br/>\\end{align}</p>\n<h4>b)</h4>\n<p>Rearranging the equation $y=mx+c$ and substituting either of the points gives</p>\n<p>\\[c = y_1-mx_1 \\quad \\mathrm{or} \\quad c = y_2-mx_2 \\,\\text{.} \\]</p>\n<p>We can then also use this equation with the other point's coordinates to check our answer.</p>\n<p>Let's use point $A$ first:</p>\n<p>\\[<br/>\\begin{align}<br/>c &amp;= y_1-mx_1 \\\\<br/>&amp;=&nbsp;\\var{ya}-\\var[fractionnumbers]{m}\\times\\var{xa} \\\\<br/>&amp; =&nbsp;\\simplify[fractionnumbers]{{ya-m*xa}}\\text{.}<br/>\\end{align}<br/>\\]</p>\n<p>We then check this against point $B$:</p>\n<p>\\[<br/>\\begin{align}<br/>y_2 &amp;= mx_2 + c \\\\[0.5em]<br/>&amp;= \\simplify[fractionNumbers]{{m}{xb}+{c}} \\\\[0.5em]<br/>&amp;= \\var[fractionnumbers]{m*xb+c}\\text{.}<br/>\\end{align}<br/>\\]</p>\n<h4>c)</h4>\n<p>We can now substitute these values for $m$ and $c$ into $y=mx+c$ &nbsp;to get:</p>\n<p>\\[y=\\simplify[!noLeadingMinus,fractionNumbers,unitFactor]{{m} x+ {c}}\\text{.}\\]</p>\n<p>The green line drawn on the graph represents the above line equation.</p>\n<p>{correctPoints()}</p>", "preamble": {"css": "", "js": ""}, "parts": [{"showCorrectAnswer": true, "customMarkingAlgorithm": "", "prompt": "<p>Calculate the gradient, $m$, of the straight line between these two points.</p>\n<p>$m=$&nbsp;[[0]]</p>\n<p></p>", "unitTests": [], "scripts": {}, "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "type": "gapfill", "marks": 0, "gaps": [{"correctAnswerFraction": true, "unitTests": [], "scripts": {}, "adaptiveMarkingPenalty": 0, "correctAnswerStyle": "plain", "minValue": "m", "marks": 1, "mustBeReducedPC": 0, "useCustomName": false, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showFractionHint": true, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "allowFractions": true, "mustBeReduced": false, "showFeedbackIcon": true, "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "customName": "", "maxValue": "m", "variableReplacementStrategy": "originalfirst"}], "useCustomName": false, "customName": "", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "sortAnswers": false}, {"showCorrectAnswer": true, "customMarkingAlgorithm": "", "prompt": "<p>Use this gradient and the coordinates of the points to calculate the $y$-intercept, $c$.</p>\n<p>$c=$&nbsp;[[0]]</p>", "unitTests": [], "scripts": {}, "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "type": "gapfill", "marks": 0, "gaps": [{"correctAnswerFraction": false, "unitTests": [], "scripts": {}, "adaptiveMarkingPenalty": 0, "correctAnswerStyle": "plain", "minValue": "c", "marks": 1, "mustBeReducedPC": 0, "useCustomName": false, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showFractionHint": true, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "showFeedbackIcon": true, "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "customName": "", "maxValue": "c", "variableReplacementStrategy": "originalfirst"}], "useCustomName": false, "customName": "", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "sortAnswers": false}, {"showCorrectAnswer": true, "customMarkingAlgorithm": "", "prompt": "<p>Give the equation of the straight line through these points in the form $y=mx+c$.&nbsp;</p>\n<p>$\\displaystyle y=$ [[0]]</p>\n<p>Use the graph to plot your answer and check that it goes through these points.</p>", "unitTests": [], "scripts": {"mark": {"order": "after", "script": "this.question.lines.l.setAttribute({strokeColor: this.credit==1 ? 'green' : 'red'});\nthis.question.lines.c.setAttribute({visible: this.credit==1});\n"}}, "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "type": "gapfill", "marks": 0, "gaps": [{"showPreview": true, "vsetRangePoints": 5, "scripts": {}, "unitTests": [], "checkingType": "absdiff", "vsetRange": [0, 1], "failureRate": 1, "answerSimplification": "fractionNumbers", "useCustomName": false, "answer": "{m}*x+{c}", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "notallowed": {"message": "<p>You must input your answer in the form y = mx +c where m and c are numbers.</p>", "showStrings": false, "partialCredit": 0, "strings": ["c", "m"]}, "checkVariableNames": true, "checkingAccuracy": 0.001, "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "type": "jme", "valuegenerators": [{"name": "x", "value": ""}], "customName": "", "marks": 1, "variableReplacementStrategy": "originalfirst"}], "useCustomName": false, "customName": "", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "sortAnswers": false}], "functions": {"correctPoints": {"type": "html", "definition": "//point coordinate variables\nvar xa = Numbas.jme.unwrapValue(scope.variables.xa);\nvar xb = Numbas.jme.unwrapValue(scope.variables.xb);\nvar ya = Numbas.jme.unwrapValue(scope.variables.ya);\nvar yb = Numbas.jme.unwrapValue(scope.variables.yb);\nvar m = Numbas.jme.unwrapValue(scope.variables.m);\nvar c = Numbas.jme.unwrapValue(scope.variables.c);\n\n//make board\nvar div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',{boundingBox:[Math.min(-1,xa-2),Math.max(2,yb+2,c+1),Math.max(2,xb+2),Math.min(-1,ya-2,c-1)],grid: true});\nvar board = div.board;\nquestion.board = board;\n\n\n//points (with nice colors)\nvar a = board.create('point',[xa,ya],{name: 'A', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow', fixed: true, showInfobox: true});\nvar b = board.create('point',[xb,yb],{name: 'B', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow',fixed: true, showInfobox: true});\n\n\n//ans(was tree) is defined at the end and nscope looks important\n//but they're both variables\n\nvar correct_line = board.create('functiongraph',[function(x){ return m*x+c},-22,22], {strokeColor:\"green\",setLabelText:'mx+c',visible: true, strokeWidth: 4, highlightStrokeColor: 'green'} )\n\n\n\nquestion.signals.on('HTMLAttached',function(e) {\nko.computed(function(){\n//define ans as this \ncorrect_line.updateCurve();\nboard.update();\n});\n  });\n\n\nreturn div;", "parameters": [], "language": "javascript"}, "plotPoints": {"type": "html", "definition": "//point coordinate variables\nvar xa = Numbas.jme.unwrapValue(scope.variables.xa);\nvar xb = Numbas.jme.unwrapValue(scope.variables.xb);\nvar ya = Numbas.jme.unwrapValue(scope.variables.ya);\nvar yb = Numbas.jme.unwrapValue(scope.variables.yb);\nvar m = Numbas.jme.unwrapValue(scope.variables.m);\nvar c = Numbas.jme.unwrapValue(scope.variables.c);\n\n//make board\nvar div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',{boundingBox:[Math.min(-1,xa-2),Math.max(2,yb+2,c+1),Math.max(2,xb+2),Math.min(-1,ya-2,c-1)],grid: true});\nvar board = div.board;\nquestion.board = board;\n\n//points (with nice colors)\nvar a = board.create('point',[xa,ya],{name: 'A', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow', fixed: true, showInfobox: true});\nvar b = board.create('point',[xb,yb],{name: 'B', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow',fixed: true, showInfobox: true});\n\n\n//ans(was tree) is defined at the end and nscope looks important\n//but they're both variables\n  var ans;\n  var nscope = new Numbas.jme.Scope([scope,{variables:{x:new Numbas.jme.types.TNum(0)}}]);\n//this is the beating heart of whatever plots the function,\n//I've changed this from being curve to functiongraph\n  var line = board.create('functiongraph',[function(x){\nif(ans) {\n  try {\nnscope.variables.x.value = x;\n  var val = Numbas.jme.evaluate(ans,nscope).value;\n  return val;\n  }\n  catch(e) {\nreturn 13;\n  }\n}\nelse\n  return 13;\n  },-12,12]\n                          , {strokeColor:\"blue\",strokeWidth: 4}                    );\n \nvar correct_line = board.create('functiongraph',[function(x){ return m*x+c},-22,22], {strokeColor:\"green\",setLabelText:'mx+c',visible: false, strokeWidth: 4, highlightStrokeColor: 'green'} )\n\nquestion.lines = {\n  l:line, c:correct_line\n}\n\n  question.signals.on('HTMLAttached',function(e) {\nko.computed(function(){\nvar expr = question.parts[2].gaps[0].display.studentAnswer();\n\n//define ans as this \ntry {\n  ans = Numbas.jme.compile(expr,scope);\n}\ncatch(e) {\n  ans = null;\n}\nline.updateCurve();\ncorrect_line.updateCurve();\nboard.update();\n});\n  });\n\n\nreturn div;", "parameters": [], "language": "javascript"}}, "rulesets": {}}, {"name": "Conversions - Decimals and Percentages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z", "aa", "bb", "cc", "dd", "ee", "ff", "gg", "hh", "ii", "jj", "kk", "ll"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"distractors": ["", "", "", "", "", "", "", ""], "prompt": "<p>Select the answer that is equal to $\\var{a}$%</p>", "matrix": ["1", 0, 0, 0, 0, 0, 0, 0], "shuffleChoices": true, "variableReplacements": [], "choices": ["<p>$\\var{b}$</p>", "<p>$\\var{c}$</p>", "<p>$\\var{d}$</p>", "<p>$\\var{f}$</p>", "<p>$\\var{g}$</p>", "<p>$\\var{h}$</p>", "<p>$\\var{j}$</p>", "<p>$\\var{k}$</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": "1", "scripts": {}, "marks": 0, "displayColumns": "0", "showCorrectAnswer": true, "type": "1_n_2", "minMarks": "1"}, {"distractors": ["", "", "", "", "", "", "", ""], "prompt": "<p>Select the answer that is equal to $\\var{l}$%</p>", "matrix": ["1", 0, 0, 0, 0, 0, 0, 0], "shuffleChoices": true, "variableReplacements": [], "choices": ["<p>$\\var{m}$</p>", "<p>$\\var{n}$</p>", "<p>$\\var{o}$</p>", "<p>$\\var{p}$</p>", "<p>$\\var{q}$</p>", "<p>$\\var{r}$</p>", "<p>$\\var{s}$</p>", "<p>$\\var{t}$</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": "1", "scripts": {}, "marks": 0, "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": "1"}, {"distractors": ["", "", "", "", "", "", "", ""], "prompt": "<p>Select the answer that is equal to $\\var{u}$</p>", "matrix": ["1", 0, 0, 0, 0, 0, 0, 0], "shuffleChoices": true, "variableReplacements": [], "choices": ["<p>$\\var{v}$ %</p>", "<p>$\\var{w}$ %</p>", "<p>$\\var{x}$ %</p>", "<p>$\\var{y}$ %</p>", "<p>$\\var{z}$ %</p>", "<p>$\\var{aa}$ %</p>", "<p>$\\var{bb}$ %</p>", "<p>$\\var{cc}$ %</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": "1", "scripts": {}, "marks": 0, "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": "1"}, {"distractors": ["", "", "", "", "", "", "", ""], "prompt": "<p>Select the answer that is equal to $\\var{dd}$</p>", "matrix": ["1", 0, 0, 0, 0, 0, 0, 0], "shuffleChoices": true, "variableReplacements": [], "choices": ["<p>$\\var{ee}$ %</p>", "<p>$\\var{ff}$ %</p>", "<p>$\\var{gg}$ %</p>", "<p>$\\var{hh}$ %</p>", "<p>$\\var{ii}$ %</p>", "<p>$\\var{jj}$ %</p>", "<p>$\\var{kk}$ %</p>", "<p>$\\var{ll}$ %</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": "1", "scripts": {}, "marks": 0, "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": "1"}, {"maxAnswers": 0, "prompt": "<p>Match up the equivalent decimals and percentages</p>", "matrix": [["1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "shuffleAnswers": false, "minAnswers": 0, "variableReplacements": [], "answers": ["<p>$50$ %</p>", "<p>$25$ %</p>", "<p>$20$ %</p>", "<p>$10$ %</p>", "<p>$12.5$ %</p>", "<p>$5$ %</p>", "<p>$4$ %</p>", "<p>$1$ %</p>", "<p>$33.\\dot{3}$ %</p>", "<p>$11.\\dot{1}$ %</p>", "<p>$60$ %</p>", "<p>$30$ %</p>", "<p>$85$ %</p>", "<p>$66.\\dot{6}$ %</p>", "<p>$45$ %</p>"], "choices": ["<p>$0.5$</p>", "<p>$0.25$</p>", "<p>$0.2$</p>", "<p>$0.1$</p>", "<p>$0.125$</p>", "<p>$0.05$</p>", "<p>$0.04$</p>", "<p>$0.01$</p>", "<p>$0.3\\dot{3}$</p>", "<p>$0.1\\dot{1}$</p>", "<p>$0.6$</p>", "<p>$0.3$</p>", "<p>$0.85$</p>", "<p>$0.6\\dot{6}$</p>", "<p>$0.45$</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "marks": 0, "warningType": "none", "showCorrectAnswer": true, "type": "m_n_x", "shuffleChoices": false, "minMarks": 0, "layout": {"expression": "", "type": "all"}}], "statement": "<p>Here you just need to pick out the solution that is equivalent to the value in the question.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"aa": {"definition": "u*2", "templateType": "anything", "group": "Ungrouped variables", "name": "aa", "description": ""}, "jj": {"definition": "dd*2", "templateType": "anything", "group": "Ungrouped variables", "name": "jj", "description": ""}, "cc": {"definition": "u*20", "templateType": "anything", "group": "Ungrouped variables", "name": "cc", "description": ""}, "gg": {"definition": "dd/100", "templateType": "anything", "group": "Ungrouped variables", "name": "gg", "description": ""}, "ll": {"definition": "dd*20", "templateType": "anything", "group": "Ungrouped variables", "name": "ll", "description": ""}, "ee": {"definition": "dd*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ee", "description": ""}, "bb": {"definition": "u*200", "templateType": "anything", "group": "Ungrouped variables", "name": "bb", "description": ""}, "dd": {"definition": "random(0..1#0.001)", "templateType": "anything", "group": "Ungrouped variables", "name": "dd", "description": ""}, "hh": {"definition": "dd*1000\n", "templateType": "anything", "group": "Ungrouped variables", "name": "hh", "description": ""}, "ff": {"definition": "dd*10", "templateType": "anything", "group": "Ungrouped variables", "name": "ff", "description": ""}, "a": {"definition": "random(1..100) //random percentage between 1 and 100", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "ii": {"definition": "dd/10", "templateType": "anything", "group": "Ungrouped variables", "name": "ii", "description": ""}, "c": {"definition": "a/10", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "a/100", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "a*100", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "a*10", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "a/1000", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "kk": {"definition": "dd*200", "templateType": "anything", "group": "Ungrouped variables", "name": "kk", "description": ""}, "h": {"definition": "a/2", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "a/20", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "a/200", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "l/100", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random(1..100#0.1) //random decimal percentage", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "o": {"definition": "l*100", "templateType": "anything", "group": "Ungrouped variables", "name": "o", "description": ""}, "n": {"definition": "l/10", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "q": {"definition": "l*10", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "p": {"definition": "l/1000", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "s": {"definition": "l/200", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "r": {"definition": "l/2", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "u": {"definition": "random(0..1#0.01) //random decimal to become a percentage", "templateType": "anything", "group": "Ungrouped variables", "name": "u", "description": ""}, "t": {"definition": "l/20", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}, "w": {"definition": "u*10", "templateType": "anything", "group": "Ungrouped variables", "name": "w", "description": ""}, "v": {"definition": "u*100", "templateType": "anything", "group": "Ungrouped variables", "name": "v", "description": ""}, "y": {"definition": "u*1000", "templateType": "anything", "group": "Ungrouped variables", "name": "y", "description": ""}, "x": {"definition": "u/100", "templateType": "anything", "group": "Ungrouped variables", "name": "x", "description": ""}, "z": {"definition": "u/10", "templateType": "anything", "group": "Ungrouped variables", "name": "z", "description": ""}}, "metadata": {"description": "<p>This question concentrates on converting between decimals and percentages</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Conversions - Fractions and Percentages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "m", "n"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>Insert a fraction that has the same value as the following percentages:</p>\n<p>$\\var{a}$ % = [[0]]</p>\n<p>$\\var{b}$ % = [[1]]</p>\n<p>$\\var{c}$ % = [[2]]</p>\n<p>$\\var{d}$ % = [[3]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "a/100", "minValue": "a/100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "b/100", "minValue": "b/100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "c/100", "minValue": "c/100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "d/100", "minValue": "d/100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Insert the correct percentage for each of these fractions</p>\n<p>$\\frac{\\var{f}}{\\var{g}}$ = [[0]]</p>\n<p>$\\frac{\\var{h}}{\\var{j}}$ = [[1]]</p>\n<p>$\\frac{\\var{k}}{\\var{l}}$ = [[2]]</p>\n<p>$\\frac{\\var{m}}{\\var{n}}$ = [[3]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "(f/g)*100", "minValue": "(f/g)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "(h/j)*100", "minValue": "(h/j)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "(k/l)*100", "minValue": "(k/l)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "(m/n)*100", "minValue": "(m/n)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"maxAnswers": "15", "prompt": "<p>Match up commonly used fractions and percentages</p>", "matrix": [["1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "shuffleAnswers": true, "minAnswers": "10", "variableReplacements": [], "answers": ["<p>$\\frac{1}{2}$</p>", "<p>$\\frac{1}{4}$</p>", "<p>$\\frac{1}{5}$</p>", "<p>$\\frac{1}{10}$</p>", "<p>$\\frac{1}{8}$</p>", "<p>$\\frac{1}{20}$</p>", "<p>$\\frac{1}{25}$</p>", "<p>$\\frac{1}{100}$</p>", "<p>$\\frac{1}{3}$</p>", "<p>$\\frac{1}{9}$</p>", "<p>$\\frac{3}{4}$</p>", "<p>$\\frac{2}{5}$</p>", "<p>$\\frac{1}{11}$</p>", "<p>$\\frac{1}{6}$</p>", "<p>$\\frac{1}{45}$</p>"], "choices": ["<p>$50$ %</p>", "<p>$25$ %</p>", "<p>$20$ %</p>", "<p>$10$ %</p>", "<p>$12.5$ %</p>", "<p>$5$ %</p>", "<p>$4$ %</p>", "<p>$1$ %</p>", "<p>$33.\\dot{3}$ %</p>", "<p>$11.\\dot{1}$ %</p>", "<p>$60$ %</p>", "<p>$30$ %</p>", "<p>$85$ %</p>", "<p>$66.\\dot{6}$ %</p>", "<p>$45$ %</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": "10", "scripts": {}, "marks": 0, "warningType": "none", "showCorrectAnswer": true, "type": "m_n_x", "shuffleChoices": true, "minMarks": "10", "layout": {"expression": "", "type": "all"}}], "statement": "<p>This question allows you to practice converting between fractions and percentages.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(0..100#10 except [0,100])", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(0..100 except [0,100])", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(0..100#5 except [0,100])", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(1..200)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random([2,4,5,10,20,25,50,100])", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(1..g-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random(0..j-1#2 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(0..l-1#4 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random([4,5,10,20,25,40,50,100,200])", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "random(1..n)", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random([8,16,20,40,80,100,200,400])", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "n": {"definition": "random([3,6,9])", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}}, "metadata": {"description": "<p>This question will help you practice converting between fractions and percentages</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}], "type": "exam", "contributors": [{"name": "aine whelan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2156/"}], "extensions": ["jsxgraph"], "custom_part_types": [], "resources": []}