// Numbas version: exam_results_page_options
{"name": "1: Linear Graphs: Sediment age vs. Thickness", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "parts": [{"showFeedbackIcon": true, "variableReplacements": [], "type": "gapfill", "marks": 0, "showCorrectAnswer": true, "prompt": "<p>Which type of sediment was being deposited approximately {an1} million years ago?</p>\n<p style=\"text-align: left;\">[[0]]</p>", "variableReplacementStrategy": "originalfirst", "gaps": [{"showCorrectAnswer": true, "variableReplacements": [], "answer": "{lith_an1}", "marks": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "matchMode": "regex", "type": "patternmatch", "scripts": {}, "displayAnswer": "{lith_an1}"}], "scripts": {}}, {"showFeedbackIcon": true, "variableReplacements": [], "type": "gapfill", "marks": 0, "showCorrectAnswer": true, "prompt": "<p style=\"text-align: left;\">Approximately how many metres of this sediment had already been deposited at this point?</p>\n<p style=\"text-align: left;\">[[0]]metre(s)</p>\n<p></p>", "variableReplacementStrategy": "originalfirst", "gaps": [{"variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerFraction": false, "scripts": {}, "correctAnswerStyle": "plain", "allowFractions": false, "minValue": "thck_an1-0.5", "maxValue": "thck_an1+0.5", "marks": 1, "variableReplacementStrategy": "originalfirst"}], "scripts": {}}, {"showCorrectAnswer": true, "stepsPenalty": 0, "type": "gapfill", "prompt": "<p>On average, what is the rate of sediment deposition in the studied&nbsp;{enviro} location over the timescale shown in the graph?</p>\n<p>[[0]]metre<span style=\"line-height: 32px;\">(s)</span>&nbsp;every&nbsp;million years.</p>", "marks": 0, "gaps": [{"variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerFraction": false, "scripts": {}, "correctAnswerStyle": "plain", "allowFractions": false, "minValue": "m*0.9", "maxValue": "m*1.1", "marks": 1, "variableReplacementStrategy": "originalfirst"}], "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "scripts": {}, "steps": [{"showCorrectAnswer": true, "variableReplacements": [], "type": "information", "marks": 0, "prompt": "<p>This question effectively asks how many metres of sediment are deposited for every million years that pass. It is the gradient. This can be read directly from the graph as how many units up (y axis)&nbsp;the line of points moves for each unit to the right (x axis).</p>", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "scripts": {}}]}, {"showCorrectAnswer": true, "stepsPenalty": 0, "type": "gapfill", "prompt": "<p style=\"text-align: left;\">Write a mathematical expression for the linear relationship between age of deposition layer ($t$) and cumulative thickness ($d$) found in this study:</p>\n<p style=\"text-align: left;\">$d=$[[0]]$t +$[[1]]</p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\"><em>Note: If the coefficient of $t$ is 1, this question still requires that you enter the number although this wouldn't be necessary when written.</em></p>", "marks": 0, "gaps": [{"variableReplacements": [{"part": "p2g0", "must_go_first": true, "variable": "m"}], "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerFraction": false, "scripts": {}, "correctAnswerStyle": "plain", "allowFractions": false, "minValue": "m", "maxValue": "m", "marks": 1, "variableReplacementStrategy": "alwaysreplace"}, {"variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerFraction": false, "scripts": {}, "correctAnswerStyle": "plain", "allowFractions": false, "minValue": "c-0.5", "maxValue": "c+0.5", "marks": 1, "variableReplacementStrategy": "originalfirst"}], "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "scripts": {}, "steps": [{"showCorrectAnswer": true, "variableReplacements": [], "type": "information", "marks": 0, "prompt": "<p>As you may have noticed, the 'linear relationship' is described by the equation of the line. This follows the typical structure: $y=mx+c$ where $y$ is the&nbsp;cumulative thickness (metres), $m$ is the gradient of the line, $x$ is the age (Ma) and $c$ is the point where the line intercepts the y-axis.</p>", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "scripts": {}}]}], "name": "1: Linear Graphs: Sediment age vs. Thickness", "statement": "<p>In this question, sediment stratification is studied in a<span data-jme-visible=\"{enviro}=&quot;aluvial fan&quot;\">n</span> {enviro} succession. Three strata are found, their thicknesses are measured and their age ranges calculated:</p>\n<table width=\"436\" height=\"182\" style=\"height: 182px;\" border=\"black\">\n<tbody>\n<tr>\n<td style=\"border-color: black;\">\n<p style=\"text-align: center;\"><span style=\"text-decoration: underline;\"><strong>Stratum</strong></span></p>\n</td>\n<td style=\"border-color: black;\">\n<p><span style=\"text-decoration: underline;\"><strong>Thickness </strong>(m)</span></p>\n</td>\n<td style=\"border-color: black;\">\n<p><span style=\"text-decoration: underline;\"><strong>&nbsp; Age range </strong>(Ma)</span></p>\n</td>\n</tr>\n<tr>\n<td style=\"border-color: black;\">{lith1}</td>\n<td style=\"border-color: black;\">{lith1_thck}</td>\n<td style=\"border-color: black;\">{lith1_age}</td>\n</tr>\n<tr>\n<td style=\"border-color: black;\">{lith2}</td>\n<td style=\"border-color: black;\">{lith2_thck}</td>\n<td style=\"border-color: black;\">{lith2_age}</td>\n</tr>\n<tr>\n<td style=\"border-color: black;\">{lith3}</td>\n<td style=\"border-color: black;\">{lith3_thck}</td>\n<td style=\"border-color: black;\">{lith3_age}</td>\n</tr>\n</tbody>\n</table>\n<p>When the lower age bounds&nbsp;are plotted against the cumulative thickness of the sediment, a linear relationship is apparent. <em>(Note that the graph converts age into 'time from present', where an age of $6\\text{Ma}$ from the table would be $-6\\text{Ma}$ from the present on the graph. This is to give a more intuitive sense of the linear trend over time from left to right)</em>:</p>\n<p style=\"text-align: center;\">{lngraph()}</p>", "ungrouped_variables": ["m", "x", "c", "enviro", "lithlist", "lith1", "lith2", "lith3", "x0", "x1", "x2", "y0", "y1", "y2", "lith1_thck", "lith2_thck", "lith3_thck", "lith1_age", "lith2_age", "lith3_age", "ya", "an1", "lith_an1", "thck_an1"], "variables": {"y0": {"description": "", "definition": "m*x0+c", "name": "y0", "group": "Ungrouped variables", "templateType": "anything"}, "m": {"description": "", "definition": "random(1..4#1)", "name": "m", "group": "Ungrouped variables", "templateType": "randrange"}, "lith3_thck": {"description": "", "definition": "c-y2", "name": "lith3_thck", "group": "Ungrouped variables", "templateType": "anything"}, "lithlist": {"description": "", "definition": "[\"Arenite\",\"Dolomite\",\"Mudstone\",\"Sandstone\",\"Siltstone\"]", "name": "lithlist", "group": "Ungrouped variables", "templateType": "anything"}, "lith2": {"description": "", "definition": "if(enviro=\"deep ocean\" or enviro = \"desert lake\",lithlist[4],lithlist[0])", "name": "lith2", "group": "Ungrouped variables", "templateType": "anything"}, "an1": {"description": "", "definition": "random(0.5..(x0*-1)-0.5#0.5 except [x1*-1,x2*-1])", "name": "an1", "group": "Ungrouped variables", "templateType": "anything"}, "lith1_age": {"description": "", "definition": "\"{x0*-1} to {x1*-1}\"", "name": "lith1_age", "group": "Ungrouped variables", "templateType": "anything"}, "lith3_age": {"description": "", "definition": "\"{x2*-1} to {0}\"", "name": "lith3_age", "group": "Ungrouped variables", "templateType": "anything"}, "lith2_age": {"description": "", "definition": "\"{x1*-1} to {x2*-1}\"", "name": "lith2_age", "group": "Ungrouped variables", "templateType": "anything"}, "y2": {"description": "", "definition": "m*x2+c", "name": "y2", "group": "Ungrouped variables", "templateType": "anything"}, "x0": {"description": "", "definition": "random(-10..-12.5#0.5)", "name": "x0", "group": "Ungrouped variables", "templateType": "anything"}, "c": {"description": "", "definition": "-(m*x0)", "name": "c", "group": "Ungrouped variables", "templateType": "anything"}, "y1": {"description": "", "definition": "m*x1+c", "name": "y1", "group": "Ungrouped variables", "templateType": "anything"}, "lith_an1": {"description": "", "definition": "if(-an1>=x0 and -an1<=x1, lith1,if(-an1>x1 and -an1<=x2, lith2,if(-an1>x2 and -an1<=0, lith3)))", "name": "lith_an1", "group": "Ungrouped variables", "templateType": "anything"}, "thck_an1": {"description": "", "definition": "if(-an1>=x0 and -an1<=x1, (m*(-an1)+c),if(-an1>x1 and -an1<=x2, (m*(-an1)+c)-(m*(x1)+c),if(-an1>x2 and -an1<=0, (m*(-an1)+c)-(m*(x2)+c))))", "name": "thck_an1", "group": "Ungrouped variables", "templateType": "anything"}, "enviro": {"description": "", "definition": "random(\"deep ocean\",\"desert lake\",\"aluvial fan\")", "name": "enviro", "group": "Ungrouped variables", "templateType": "anything"}, "x": {"description": "", "definition": "shuffle(-10..0#0.5)", "name": "x", "group": "Ungrouped variables", "templateType": "anything"}, "ya": {"description": "", "definition": "if(c_oddoreven(c), c+1, c+2)", "name": "ya", "group": "Ungrouped variables", "templateType": "anything"}, "lith1_thck": {"description": "", "definition": "y1", "name": "lith1_thck", "group": "Ungrouped variables", "templateType": "anything"}, "lith1": {"description": "", "definition": "if(enviro=\"deep ocean\" or enviro = \"desert lake\",lithlist[3],lithlist[1])", "name": "lith1", "group": "Ungrouped variables", "templateType": "anything"}, "lith3": {"description": "", "definition": "if(enviro=\"deep ocean\" or enviro = \"desert lake\",lithlist[2],lithlist[4])", "name": "lith3", "group": "Ungrouped variables", "templateType": "anything"}, "x1": {"description": "", "definition": "x0+random(4..7#0.5)", "name": "x1", "group": "Ungrouped variables", "templateType": "anything"}, "lith2_thck": {"description": "", "definition": "y2-y1", "name": "lith2_thck", "group": "Ungrouped variables", "templateType": "anything"}, "x2": {"description": "", "definition": "random(x1+0.5..-0.5#0.5)", "name": "x2", "group": "Ungrouped variables", "templateType": "anything"}}, "tags": [], "metadata": {"description": "<p>A question to practise the following skills in the context of Earth Sciences:</p>\n<ul>\n<li>graph-reading skills</li>\n<li>using a graph to find the equation of a line</li>\n<li>used adpative marking</li>\n</ul>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "variable_groups": [], "extensions": ["jsxgraph"], "variablesTest": {"maxRuns": "100", "condition": ""}, "functions": {"lngraph": {"type": "html", "definition": "x0 = Numbas.jme.unwrapValue(scope.variables.x0);\ny0 = Numbas.jme.unwrapValue(scope.variables.y0);\nx1 = Numbas.jme.unwrapValue(scope.variables.x1);\ny1 = Numbas.jme.unwrapValue(scope.variables.y1);\nx2 = Numbas.jme.unwrapValue(scope.variables.x2);\ny2 = Numbas.jme.unwrapValue(scope.variables.y2);\nya = Numbas.jme.unwrapValue(scope.variables.ya);\nc = Numbas.jme.unwrapValue(scope.variables.c);\nlith1 = Numbas.jme.unwrapValue(scope.variables.lith1);\nlith2 = Numbas.jme.unwrapValue(scope.variables.lith2);\nlith3 = Numbas.jme.unwrapValue(scope.variables.lith3);\n\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-13,ya,3,-3], grid:true, axis: false});\nvar board = div.board;\n\n\n// create the x-axis.\nvar xaxis = board.create('line',[[0,0],[1,0]], { strokeColor: 'black', fixed: true, withlabel: true, name: function () {return \"Time from present (Ma)\"}, label: {offset:[110,15]}});\nvar xticks = board.create('ticks',[xaxis,1],{\n  drawLabels: true,\n  label: {offset: [-4, -15]},\n  minorTicks: 0\n});\n\n// create the y-axis\nvar yaxis = board.create('line',[[0,0],[0,1]], { strokeColor: 'black', fixed: true, withlabel: true, name: function () {return \"Cumulative thickness (metres)\"}, label: {offset:[20,300]} });\nvar yticks = board.create('ticks',[yaxis,2],{\ndrawLabels: true,\nlabel: {offset: [-20, 0]},\nminorTicks: 0\n});\n\n\n//board.create('point',[x0,y0],{fixed:true});\n//board.create('point',[x1,y1],{fixed:true});\nboard.create('line',[[x1,y1],[x2,y2]],{strokeColor:'black', strokeWidth:2, fixed:true});\nboard.create('line',[[0,10],[0,20]],{strokeColor:'black', strokeWidth:2, fixed:true});\nboard.create('segment',[[x0,y0],[x1,y1]],{strokeColor:'blue', strokeWidth:3, fixed:true, withlabel: true, name: function () {return lith1}, label: {offset:[-50,20]}});\nboard.create('segment',[[x1,y1],[x2,y2]],{strokeColor:'yellow', strokeWidth:3, fixed:true, withlabel: true, name: function () {return lith2}, label: {offset:[-50,20]}});\nboard.create('segment',[[x2,y2],[0,c]],{strokeColor:'red', strokeWidth:3, fixed:true, withlabel: true, name: function () {return lith3}, label: {offset:[-50,10]}});\n\n\nreturn div;", "language": "javascript", "parameters": []}, "c_oddoreven": {"type": "boolean", "definition": "return (num % 2 == 0);", "language": "javascript", "parameters": [["num", "number"]]}}, "preamble": {"css": "", "js": ""}, "advice": "<p>Click 'Try another question like this one' and re-do the question as many times as you wish until you are comfortable with the concepts and methods.</p>", "type": "question", "contributors": [{"name": "Luke Park", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/826/"}]}]}], "contributors": [{"name": "Luke Park", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/826/"}]}