// Numbas version: exam_results_page_options
{"name": "Algebra: solving equations graphically. Version 4", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "tags": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Simple procedures are given and student is asked to carry them out or un-do them.</p>\n<p>Version 1: i and ii have the same answer. iii and iv both have two answers.</p>\n<p>Version 2: i and ii have different answers. iii has two answers,biv has one answer.</p>\n<p>Version 3: i and ii have different answer. iii has one answer, iv has two answers.</p>\n<p>Version 4: i and ii have the same answer. iii has one answer, iv has two answers.</p>"}, "variable_groups": [{"variables": ["add2", "sub2", "ymax", "ymin", "shift", "gy"], "name": "part a"}], "name": "Algebra: solving equations graphically. Version 4", "ungrouped_variables": [], "extensions": ["jsxgraph"], "variables": {"sub2": {"templateType": "anything", "name": "sub2", "definition": "random(1..3)", "description": "", "group": "part a"}, "add2": {"templateType": "anything", "name": "add2", "definition": "random(1..5)", "description": "", "group": "part a"}, "shift": {"templateType": "anything", "name": "shift", "definition": "vector(shuffle(1..3)+[0])", "description": "", "group": "part a"}, "ymin": {"templateType": "anything", "name": "ymin", "definition": "vector(-add2,-add2,-add2,-add2)-shift", "description": "", "group": "part a"}, "gy": {"templateType": "anything", "name": "gy", "definition": "vector((ymax[0]+add2)^2-sub2,(ymax[1]+add2)^2-sub2,(ymax[2]+add2)^2-sub2,(ymax[3]+add2)^2-sub2)", "description": "", "group": "part a"}, "ymax": {"templateType": "anything", "name": "ymax", "definition": "vector(-add2,-add2,-add2,-add2)+shift", "description": "", "group": "part a"}}, "preamble": {"css": "", "js": ""}, "functions": {"eqnline": {"type": "html", "language": "javascript", "definition": "// This functions plots a quadratic graph of the form y = (x+a)^2 - b\n\n\n// Max and min x and y values for the axis.\nvar x_min = -10;\nvar x_max = 4;\nvar y_min = -6;\nvar y_max = 10;\n\n\n// First, make the JSXGraph board.\nvar div = Numbas.extensions.jsxgraph.makeBoard(\n  '500px',\n  '600px',\n {\n   boundingBox: [x_min,y_max,x_max,y_min],\n   axis: false,\n   showNavigation: true,\n   grid: true\n }\n);\n\n\n\n\n// div.board is the object created by JSXGraph, which you use to \n// manipulate elements\nvar board = div.board; \n\n// create the x-axis and y-axis\nvar xaxis = board.create('axis',[[0,0],[1,0]]);\n\n// create the y-axis\nvar yaxis = board.create('axis',[[0,0],[0,1]], );\n\n\n\n\n// Plot the function.\n    board.create('functiongraph',\n             [function(x){ return (x+a)*(x+a)-b},x_min,x_max]);\n\n\n\nreturn div;", "parameters": [["a", "number"], ["b", "number"]]}}, "advice": "", "parts": [{"type": "gapfill", "sortAnswers": false, "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "gaps": [{"type": "numberentry", "maxValue": "gy[0]", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "scripts": {}, "correctAnswerFraction": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "minValue": "gy[0]", "correctAnswerStyle": "plain", "showFeedbackIcon": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "customMarkingAlgorithm": "", "mustBeReduced": false, "marks": "1", "mustBeReducedPC": 0}, {"type": "numberentry", "maxValue": "gy[0]", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "scripts": {}, "correctAnswerFraction": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "minValue": "gy[0]", "correctAnswerStyle": "plain", "showFeedbackIcon": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "customMarkingAlgorithm": "", "mustBeReduced": false, "marks": "1", "mustBeReducedPC": 0}, {"type": "matrix", "tolerance": 0, "correctAnswer": "matrix([ymin[3]])", "correctAnswerFractions": false, "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "numRows": 1, "showFeedbackIcon": true, "allowFractions": false, "markPerCell": false, "variableReplacementStrategy": "originalfirst", "allowResize": true, "variableReplacements": [], "customMarkingAlgorithm": "", "marks": 1, "numColumns": "1"}, {"type": "matrix", "tolerance": 0, "correctAnswer": "matrix([ymin[2],ymax[2]])", "correctAnswerFractions": false, "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "numRows": 1, "showFeedbackIcon": true, "allowFractions": false, "markPerCell": false, "variableReplacementStrategy": "originalfirst", "allowResize": true, "variableReplacements": [], "customMarkingAlgorithm": "", "marks": 1, "numColumns": "1"}], "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "prompt": "<p></p>\n<p>Below is the graph of the function $f(x)$.</p>\n<p>{eqnline(add2,sub2)}</p>\n<p></p>\n<p>What is $f(\\var{ymax[0]})$? [[0]]</p>\n<p>What is&nbsp;&nbsp;$f(\\var{ymin[0]})$? [[1]]</p>\n<p>Solve the equation $f(x)=\\var{gy[3]}$?</p>\n<p>[[2]]</p>\n<p></p>\n<p>Solve&nbsp;$f(x) = \\var{gy[2]}$?</p>\n<p>[[3]]</p>\n<p></p>", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "customMarkingAlgorithm": "", "marks": 0}], "statement": "<p>If a question has more than one answer, increase the number of&nbsp;<strong>COLUMNS</strong> and list your answers in&nbsp;<strong>ASCENDING ORDER.</strong></p>", "variablesTest": {"maxRuns": 100, "condition": ""}, "type": "question", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}