// Numbas version: finer_feedback_settings
{"name": "Min_max_v1", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"": {"language": "jme", "type": "number", "parameters": [], "definition": ""}, "poly1": {"language": "javascript", "type": "html", "parameters": [["a1", "number"], ["a2", "number"], ["a3", "number"], ["a4", "number"], ["maxy_poly", "number"]], "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('600px','400px', {boundingbox:[-2,100,10,-10], axis:false});\n        var brd=div.board;\n        \n        // Initial function term\n         var poly = function(x){ return a1*x*x*x-a2*x*x+a3*x+a4; };\n        //var poly = function(x){ return a1*Math.sin(x)*Math.exp(3*x)+a2*Math.cos(x)*Math.exp(3*x); };\n        //var poly = function(x){ return a1*Math.exp(x)*a2*Math.log(2*x, 2.71); };\n      //var poly = function(x){ return a1*x*x*x*Math.exp(x/3)-a2*x*x*Math.exp(x/3)+a3*x*Math.exp(x/3)+a4*Math.exp(x/3); };\n        var graph_poly = function(x) { return poly(x); };\n        \n        // Start value\n        var s = 2;\n         \n        \n        \n        var i;\n        var ax = brd.create('axis', [[0,0], [1,0]], {strokeColor: 'black'});\n        var ay = brd.create('axis', [[0,0], [0,1]], {strokeColor: 'black'});\n         \n        var g = brd.create('functiongraph', [function(x){return graph_poly(x);}],{strokeWidth: 2, dash:0});\n       \n        \t\n        return div;"}, "tan": {"language": "javascript", "type": "html", "parameters": [], "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('600px','400px', {boundingbox:[-3.5,5,3.5,-5], axis:false});\n        var brd=div.board;\n\n// boundingbox\n\n        // Initial function term\n         //var poly = function(x){ return a1*x*x*x-a2*x*x+a3*x+a4; };\n        var func = function(x){ return Math.tan(x); };\n        //var poly = function(x){ return a1*Math.exp(x)*a2*Math.log(2*x, 2.71); };\n      //var poly = function(x){ return a1*x*x*x*Math.exp(x/3)-a2*x*x*Math.exp(x/3)+a3*x*Math.exp(x/3)+a4*Math.exp(x/3); };\n        var graph_func = function(x) { return func(x); };\n   \n        var i;\n        var ax = brd.create('axis', [[0,0], [1,0]], {strokeColor: 'black'});\n        var ay = brd.create('axis', [[0,0], [0,1]], {strokeColor: 'black'});\n         \n        var g = brd.create('functiongraph', [function(x){return graph_func(x);}],{strokeWidth: 2, dash:0});\n       \n        \t\n        return div;"}, "fun": {"language": "jme", "type": "number", "parameters": [["m", "number"], ["b", "number"], ["a", "number"], ["c", "number"]], "definition": "((m*c-1)*e^(m*c)+a)/(m*e^(m*c)+b)"}, "sincos": {"language": "javascript", "type": "html", "parameters": [["as1", "number"], ["as2", "number"], ["as3", "number"], ["minysincos", "number"], ["maxysincos", "number"]], "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('600px','400px', {boundingbox:[-3.5,maxysincos,3.5,minysincos], axis:false});\n        var brd=div.board;\n\n// boundingbox\n\n        // Initial function term\n         //var poly = function(x){ return a1*x*x*x-a2*x*x+a3*x+a4; };\n        var func = function(x){ return as2*Math.sin(x)*Math.exp(x/as1)-as3*Math.cos(x)*Math.exp(x/as1); };\n        //var poly = function(x){ return a1*Math.exp(x)*a2*Math.log(2*x, 2.71); };\n      //var poly = function(x){ return a1*x*x*x*Math.exp(x/3)-a2*x*x*Math.exp(x/3)+a3*x*Math.exp(x/3)+a4*Math.exp(x/3); };\n        var graph_func = function(x) { return func(x); };\n        \n        // Start value\n        var s = 2;\n         \n        \n        \n        var i;\n        var ax = brd.create('axis', [[0,0], [1,0]], {strokeColor: 'black'});\n        var ay = brd.create('axis', [[0,0], [0,1]], {strokeColor: 'black'});\n         \n        var g = brd.create('functiongraph', [function(x){return graph_func(x);}],{strokeWidth: 2, dash:0});\n       \n        \t\n        return div;"}, "nr": {"language": "jme", "type": "list", "parameters": [["m", "number"], ["b", "number"], ["a", "number"], ["c", "number"], ["n", "number"], ["l", "list"]], "definition": "if(n=5,l+[fun(m,b,a,c)]+[fun(m,b,a,fun(m,b,a,c))],nr(m,b,a,fun(m,b,a,c),n-1,l+[c]))"}, "test": {"language": "javascript", "type": "html", "parameters": [["m", "number"], ["b", "number"], ["a", "number"], ["maxy", "number"]], "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('600px','400px', {boundingbox:[0,maxy,3,-30], axis:false});\n        var brd=div.board;\n        // Initial function term\n        var term = function(x) { return Math.exp(m*x)+b*x-a; };\n        var graph = function(x) { return term(x); };\n        // Recursion depth\n        var steps = 4;\n        // Start value\n        var s = 2;\n         \n        //for (i = 0; i < steps; i++) {\n         //document.write('<tr><td><nobr>x<sub>' + i + '</sub> = </nobr></td><td><font id=\"xv' + i + '\"></font></td></tr>');\n        //}\n        \n        var i;\n        var ax = brd.create('axis', [[0,0], [1,0]], {strokeColor: 'black'});\n        var ay = brd.create('axis', [[0,0], [0,1]], {strokeColor: 'black'});\n         \n        var g = brd.create('functiongraph', [function(x){return graph(x);}],{strokeWidth: 2, dash:0});\n       // var x = brd.create('glider',[s,0,ax], {name: 'x_{0}', strokeColor: 'magenta', fillColor: 'yellow'});\n         \n       // newton(x, steps, brd);\t\n         \n        //function xval() {\n       //for (i = 0; i < steps; i++)\n      //document.getElementById('xv' + i).innerHTML = (brd.select('x_{' + i + '}').X()).toFixed(14);\n        //}\n         \n        //brd.addHook(xval);\n         \n        function newton(p, i, board) {\t\n        board.suspendUpdate();\t\n        if(i>0) {\n        var f = board.create('glider',[function(){return p.X();}, function(){return graph(p.X())},g], {name: '', style: 3, strokeColor: 'green', fillColor: 'yellow'});\n        var l = board.create('line', [p,f],{strokeWidth: 0.5, dash: 1, straightFirst: false, straightLast: false, strokeColor: 'black'});\n       // var t = board.create('tangent',[f],{strokeWidth: 0.5, strokeColor: '#0080c0', dash: 0});\n        //var x = board.create('intersection',[ax,t,0],{name: 'x_{'+(steps-i+1) + '}', style: 4, strokeColor: 'magenta', fillColor: 'yellow'});\n      //  newton(x,--i, board);\n        }\n        board.unsuspendUpdate(); \n      \n      \n        }\t\n        return div;"}, "poly2": {"language": "javascript", "type": "number", "parameters": [], "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('600px','200px',{boundingBox:[0,2,0,1],grid:false});\nvar board = div.board;\nvar ap1 = Numbas.jme.unwrapValue(scope.variables.a1);\nvar ap2 = Numbas.jme.unwrapValue(scope.variables.a2);\nvar ap3 = Numbas.jme.unwrapValue(scope.variables.a3);\nvar ap4 = Numbas.jme.unwrapValue(scope.variables.a4);\n\nvar graph_poly2 = board.create('functiongraph', function(x){return Math.ap1*x^3-ap2*x^2+ap3*x+ap4});\nreturn div;\n"}, "funfornr": {"language": "javascript", "type": "html", "parameters": [], "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('600px','200px',{boundingBox:[0,10,1,-8],grid:false});\n        var board = div.board;\n        var m = Numbas.jme.unwrapValue(scope.variables.m);\n        var be = Numbas.jme.unwrapValue(scope.variables.b);\n        var al = Numbas.jme.unwrapValue(scope.variables.a);\n        var ans = Numbas.jme.unwrapValue(scope.variables.ans1)\n        var a = board.create('point',[ans,0],'$A$');\n        \n        var graph = board.create('functiongraph',function(x){return Math.exp(m*x)+be*x-al});\n        \n        return div;\n        "}}, "ungrouped_variables": ["a", "maxy", "ans1", "m", "results", "b", "tol", "ans", "tans", "a1", "a2", "a3", "a4", "maxy_poly", "maxysincos", "as1", "as2", "as3", "minysincos", "ANSas2", "ANSas3", "inv_tan_sol1", "inv_tan_sol2", "inv_tan_sol3", "inv_tan_sol4", "f_min", "f_max"], "extensions": ["jsxgraph"], "preamble": {"css": "", "js": ""}, "advice": "", "tags": [], "variable_groups": [], "statement": "<p>Test for&nbsp;${e^{x/\\var{as1}}}({\\var{as2}}sin(x)-{\\var{as3}cos(x))}$</p>\n<p>Find local extrema in the range&nbsp;$-\\pi \\le x \\le \\pi$</p>\n<p>Think about constants as they are important for the stationary points (unless it is possible to put a condition (whether to add&nbsp;or substract pi - see below)&nbsp;</p>\n<p>Check whether the ymin and ymax work</p>\n<p></p>\n<p></p>", "parts": [{"marks": 0, "useCustomName": false, "choices": ["Choice 1<br/>{sincos(as1,as2,as3,minysincos,maxysincos)}", "Choice 2<br/>{sincos(-as1,-as2,-as3,minysincos,maxysincos)}", "Choice 3<br/>{sincos(as1,1/as2,as3,minysincos,maxysincos)}", "Choice 4<br/>{sincos(as1,as2,1/as3,minysincos,maxysincos)}"], "maxMarks": 0, "showFeedbackIcon": true, "variableReplacements": [], "minMarks": 0, "stepsPenalty": 0, "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "prompt": "<p>Which of the following graphs represent the function</p>\n<p>${e^{x/\\var{as1}}}({\\var{as2}}sin(x)-{\\var{as3}cos(x))}$</p>\n<p>Notes:</p>\n<ol>\n<li>Make sure min/max is ok with current definitions</li>\n<li>Add some hints</li>\n</ol>\n<p></p>", "customMarkingAlgorithm": "", "unitTests": [], "shuffleChoices": false, "showCellAnswerState": true, "displayType": "radiogroup", "matrix": ["1", 0, 0, 0], "type": "1_n_2", "variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacements": [], "unitTests": [], "marks": 0, "useCustomName": false, "showFeedbackIcon": true, "type": "information", "variableReplacementStrategy": "originalfirst", "scripts": {}, "prompt": "<p>Give an advice about calculating some points...</p>", "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "customName": "", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true}], "displayColumns": 0, "scripts": {}, "distractors": ["", "", "", ""], "customName": "", "extendBaseMarkingAlgorithm": true}, {"marks": 0, "useCustomName": false, "maxMarks": 0, "showFeedbackIcon": true, "variableReplacements": [], "minMarks": 0, "choices": ["Choice 1<br/>${\\frac{df(x)}{dx}=\\frac{1}{\\var{as1}}e^{x/\\var{as1}}}({\\var{as2}}cos(x)-{\\var{as3}sin(x))}$", "Choice 2 - should be correct (no simplification)<br/>${\\frac{df(x)}{dx}=\\frac{1}{\\var{as1}}e^{x/\\var{as1}}}({\\var{as2}}sin(x)-{\\var{as3}cos(x))}+e^{x/\\var{as1}}({\\var{as2}}cos(x)+{\\var{as3}sin(x))}$", "Choice 3 - I am proposing to put the simplified version here which could (should) also be correct<br/>${\\frac{df(x)}{dx}=e^{x/\\var{as1}}({\\frac{\\var{ANSas3}}{\\var{as1}}sin(x)}+{\\frac{\\var{ANSas2}}{\\var{as1}}}cos(x))}$", "Choice 4<br/>Another incorrect choice"], "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "prompt": "<p>(In order to find minumum and/or maximum) Calculate the derivative of the function</p>\n<p>${f(x)=e^{x/\\var{as1}}}({\\var{as2}}sin(x)-{\\var{as3}cos(x))}$</p>\n<p>Note:</p>\n<ol>\n<li>Prompt - you must use the product rule</li>\n<li>Use the table?</li>\n<li>This could be as a choice question or&nbsp;gapfill (the other below)</li>\n<li>I don't understand how choices work...</li>\n</ol>", "customMarkingAlgorithm": "", "unitTests": [], "shuffleChoices": false, "showCellAnswerState": true, "displayType": "radiogroup", "matrix": [0, "1", "1", 0], "type": "1_n_2", "variableReplacementStrategy": "originalfirst", "displayColumns": 0, "scripts": {}, "distractors": ["", "", "", ""], "customName": "", "extendBaseMarkingAlgorithm": true}, {"variableReplacements": [], "unitTests": [], "marks": 0, "useCustomName": false, "sortAnswers": false, "gaps": [{"marks": 1, "useCustomName": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "variableReplacements": [], "valuegenerators": [{"value": "", "name": "x"}], "checkVariableNames": false, "answerSimplification": "all", "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "unitTests": [], "failureRate": 1, "type": "jme", "showPreview": true, "checkingAccuracy": 0.001, "scripts": {}, "vsetRangePoints": 5, "answer": "e^(x/{as1})({{ANSas2}/{as1}}cos(x)+{{ANSas3}/{as1}}sin(x))", "customName": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1]}], "showFeedbackIcon": true, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "scripts": {}, "prompt": "<p>(In order to find minumum and/or maximum) Calculate the derivative of the function</p>\n<p>${f(x)=e^{x/\\var{as1}}}({\\var{as2}}sin(x)-{\\var{as3}cos(x))}$</p>\n<p>Simplify your answer and present it in a form: (what form would be the best?)</p>\n<p>${\\frac{df(x)}{dx}=\\frac{A}{B}e^{x/\\var{as1}}(Csin(x)+Dcos(x))}$, where A, B, C and D are any real constants</p>\n<p>[[0]]</p>\n<p>(there's something wrong with this gap number) - if does not compile - change the number to 0 or 1, compile again, maybe change agian</p>\n<p></p>", "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "customName": "", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true}, {"marks": 0, "useCustomName": false, "choices": ["Choice 1<br/>There are two stationary points for $-\\pi \\le x \\le \\pi$:<br/>${x_1=\\var{inv_tan_sol1}, x_2=\\var{inv_tan_sol2}}$<br/>Note: how can we limit this to 3-4 sf?", "Choice 2<br/>There are three stationary points for $-\\pi \\le x \\le \\pi$:<br/>${x_1=-\\pi ,x_2=0, x_2=\\pi}$<br/>Note: add more choices", "Choice 3<br/>There are two stationary points for $-\\pi \\le x \\le \\pi$:<br/>${x_1=\\var{inv_tan_sol3}, x_2=\\var{inv_tan_sol4}}$<br/>Note: how can we limit this to 3-4 sf?"], "maxMarks": 0, "showFeedbackIcon": true, "variableReplacements": [], "minMarks": 0, "stepsPenalty": 0, "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "prompt": "<p>What are the stationary points of $f(x)$?</p>\n<p></p>", "customMarkingAlgorithm": "", "unitTests": [], "shuffleChoices": false, "showCellAnswerState": true, "displayType": "radiogroup", "matrix": ["2", 0, 0], "type": "1_n_2", "variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacements": [], "unitTests": [], "marks": 0, "useCustomName": false, "showFeedbackIcon": true, "type": "information", "variableReplacementStrategy": "originalfirst", "scripts": {}, "prompt": "<p>In order to find the stationary points you must solve the following equation</p>\n<p>${\\frac{df(x)}{dx}=0}$</p>\n<p>Once you solve this you might find the graph of $g(x) = tan(x)$ useful</p>\n<p>{tan()}</p>", "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "customName": "", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true}], "displayColumns": 0, "scripts": {}, "distractors": ["", "", ""], "customName": "", "extendBaseMarkingAlgorithm": true}, {"variableReplacements": [], "unitTests": [], "marks": 0, "useCustomName": false, "sortAnswers": false, "gaps": [{"marks": 1, "useCustomName": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "mustBeReduced": false, "unitTests": [], "showFractionHint": true, "correctAnswerStyle": "plain", "minValue": "inv_tan_sol1 - 0.2", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "scripts": {}, "maxValue": "inv_tan_sol1 + 0.2", "customName": "", "extendBaseMarkingAlgorithm": true}, {"marks": 1, "useCustomName": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "mustBeReduced": false, "unitTests": [], "showFractionHint": true, "correctAnswerStyle": "plain", "minValue": "f_min - 0.2", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "scripts": {}, "maxValue": "f_min + 0.2", "customName": "", "extendBaseMarkingAlgorithm": true}], "showFeedbackIcon": true, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "scripts": {}, "prompt": "<p>The&nbsp;function has a minimum point at: $x = $ [[0]]&nbsp;and the value of the function is : $f(x) = $&nbsp;[[1]]</p>\n<p>Note (correct answer):&nbsp;${\\var{f_min}}$ - to be deleted</p>", "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "customName": "", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true}, {"variableReplacements": [], "unitTests": [], "marks": 0, "useCustomName": false, "sortAnswers": false, "gaps": [{"marks": 1, "useCustomName": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "mustBeReduced": false, "unitTests": [], "showFractionHint": true, "correctAnswerStyle": "plain", "minValue": "inv_tan_sol2 - 0.2", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "scripts": {}, "maxValue": "inv_tan_sol2 + 0.2", "customName": "", "extendBaseMarkingAlgorithm": true}, {"marks": 1, "useCustomName": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "mustBeReduced": false, "unitTests": [], "showFractionHint": true, "correctAnswerStyle": "plain", "minValue": "f_max - 0.2", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "scripts": {}, "maxValue": "f_max + 0.2", "customName": "", "extendBaseMarkingAlgorithm": true}], "showFeedbackIcon": true, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "scripts": {}, "prompt": "<p>The&nbsp;function has a maximum point at: $x = $ [[0]]&nbsp;and the value of the function is $f(x)=$&nbsp;[[1]]</p>\n<p>Note (correct answer):&nbsp;${\\var{f_max}}$ - to be deleted</p>", "showCorrectAnswer": true, "adaptiveMarkingPenalty": 0, "customName": "", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true}], "metadata": {"description": "<p>Calculate the local extrema of a function&nbsp;${f(x) = e^{x/C1}(C2sin(x)-C3cos(x))}$</p><p>The graph of f(x) has to be identified.</p><p>The first derivative of f(x) has to be calculated.&nbsp;</p><p>The min max points have to be identified using the graph and/or calculated using the first derivative method.&nbsp; Requires solving trigonometric equation</p>", "licence": "Creative Commons Attribution 4.0 International"}, "name": "Min_max_v1", "rulesets": {"std": ["all", "!collectNumbers", "!noLeadingMinus"]}, "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"maxy_poly": {"definition": "ceil({a1}^3)+5", "templateType": "anything", "description": "<p>{\\var{a1}}x^3-{\\var{a2}}x^2+{\\var{a3}}x-{\\var{a4}}</p>", "name": "maxy_poly", "group": "Ungrouped variables"}, "a4": {"definition": "random(0.1 .. 0.9#0.1)", "templateType": "randrange", "description": "", "name": "a4", "group": "Ungrouped variables"}, "ans1": {"definition": "precround(results[6],4)", "templateType": "anything", "description": "", "name": "ans1", "group": "Ungrouped variables"}, "a2": {"definition": "random(11 .. 19#1)", "templateType": "randrange", "description": "", "name": "a2", "group": "Ungrouped variables"}, "inv_tan_sol1": {"definition": "arctan(-ANSas2/ANSas3)", "templateType": "anything", "description": "<p>Solution to stationary points&nbsp;</p>", "name": "inv_tan_sol1", "group": "Ungrouped variables"}, "inv_tan_sol2": {"definition": "inv_tan_sol1+3.14", "templateType": "anything", "description": "", "name": "inv_tan_sol2", "group": "Ungrouped variables"}, "minysincos": {"definition": "floor(-{as2})-5", "templateType": "anything", "description": "", "name": "minysincos", "group": "Ungrouped variables"}, "m": {"definition": "random(1.5..2#0.1)", "templateType": "anything", "description": "", "name": "m", "group": "Ungrouped variables"}, "ANSas3": {"definition": "as2+as3*as1", "templateType": "anything", "description": "", "name": "ANSas3", "group": "Ungrouped variables"}, "as2": {"definition": "random(2..9 except as3)", "templateType": "anything", "description": "", "name": "as2", "group": "Ungrouped variables"}, "a": {"definition": "random(2..15)", "templateType": "anything", "description": "", "name": "a", "group": "Ungrouped variables"}, "a3": {"definition": "random(11 .. 19#1)", "templateType": "randrange", "description": "", "name": "a3", "group": "Ungrouped variables"}, "results": {"definition": "nr(m,b,a,2,10,[])", "templateType": "anything", "description": "", "name": "results", "group": "Ungrouped variables"}, "a1": {"definition": "random(2 .. 9#0.1)", "templateType": "randrange", "description": "", "name": "a1", "group": "Ungrouped variables"}, "f_min": {"definition": "e^(inv_tan_sol1/as1)(as2*sin(inv_tan_sol1)-as3*cos(inv_tan_sol1))", "templateType": "anything", "description": "", "name": "f_min", "group": "Ungrouped variables"}, "as1": {"definition": "random(2 .. 9#1)", "templateType": "randrange", "description": "", "name": "as1", "group": "Ungrouped variables"}, "ANSas2": {"definition": "-as3+as2*as1", "templateType": "anything", "description": "", "name": "ANSas2", "group": "Ungrouped variables"}, "maxy": {"definition": "ceil(e^(2*m)+2*b-a)+5", "templateType": "anything", "description": "", "name": "maxy", "group": "Ungrouped variables"}, "f_max": {"definition": "e^(inv_tan_sol2/as1)(as2*sin(inv_tan_sol2)-as3*cos(inv_tan_sol2))", "templateType": "anything", "description": "", "name": "f_max", "group": "Ungrouped variables"}, "as3": {"definition": "random(2..9 except as1)", "templateType": "anything", "description": "", "name": "as3", "group": "Ungrouped variables"}, "tol": {"definition": "0", "templateType": "anything", "description": "", "name": "tol", "group": "Ungrouped variables"}, "ans": {"definition": "precround(tans,4)", "templateType": "anything", "description": "", "name": "ans", "group": "Ungrouped variables"}, "tans": {"definition": "((2*m-1)*exp(2*m)+a)/(m*exp(2*m)+b)", "templateType": "anything", "description": "", "name": "tans", "group": "Ungrouped variables"}, "b": {"definition": "random((a+1)..9)", "templateType": "anything", "description": "", "name": "b", "group": "Ungrouped variables"}, "maxysincos": {"definition": "ceil({as2}*3)", "templateType": "anything", "description": "", "name": "maxysincos", "group": "Ungrouped variables"}, "inv_tan_sol3": {"definition": "arctan(as3/as2)", "templateType": "anything", 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