// Numbas version: finer_feedback_settings
{"name": "HELM Book 2.1.3 Exercises", "metadata": {"description": "<p>HELM book 2.1.3 exercises</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", ""], "variable_overrides": [[], [], []], "questions": [{"name": "2.1.3.1 Evaluate a composite function version 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Given 2 randomised functions f (linear) and g (quadratic), find one of f(f), f(g), g(f) or g(g)</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Find $\\var{latex(fn[0])}(\\var{latex(fn[1])}(x))$ when $f(x)=\\var{fe}$ and $g(x)=\\var{ge}$.</p>", "advice": "<p>When $f(x)=\\var{fe}$ and $g(x)=\\var{ge}$</p>\n<p>\\[\\var{latex(fn[0])}(\\var{latex(fn[1])}(x))=\\var{ans}=\\var{simplified}\\]</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"fe": {"name": "fe", "group": "Ungrouped variables", "definition": "simplify(expression(\n  c[0]+\"*x+\"+c[1]\n),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "ge": {"name": "ge", "group": "Ungrouped variables", "definition": "simplify(expression(\n  c[2]+\"*x^2+\"+c[3]\n),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "fn": {"name": "fn", "group": "Ungrouped variables", "definition": "[[\"f\",\"f\"],[\"f\",\"g\"],[\"g\",\"f\"],[\"g\",\"g\"]][idx]", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "[random(1..9),random(-9..9),random(1..9),random(-9..9)]", "description": "", "templateType": "anything", "can_override": false}, "fof": {"name": "fof", "group": "Ungrouped variables", "definition": "simplify(expression(\n  c[0]+\"*(\"+c[0]+\"*x+\"+c[1]+\")+\"+c[1]\n),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "fog": {"name": "fog", "group": "Ungrouped variables", "definition": "simplify(expression(\n  c[0]+\"*(\"+c[2]+\"*x^2+\"+c[3]+\")+\"+c[1]\n),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "gof": {"name": "gof", "group": "Ungrouped variables", "definition": "simplify(expression(\n  c[2]+\"*(\"+ c[0]+\"*x+\"+c[1] +\")^2+\"+c[3]\n),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "gog": {"name": "gog", "group": "Ungrouped variables", "definition": "simplify(expression(\n  c[2]+\"*(\"+ c[2]+\"*x^2+\"+c[3] +\")^2+\"+c[3]\n),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "[fof, fog, gof, gog][idx]", "description": "", "templateType": "anything", "can_override": false}, "simplified": {"name": "simplified", "group": "Ungrouped variables", "definition": "simplify(expression([\n  c[0]+\"*(\"+c[0]+\"*x+\"+c[1]+\")+\"+c[1],\n  c[0]+\"*(\"+c[2]+\"*x^2+\"+c[3]+\")+\"+c[1],\n    c[2]+\"*(\"+ c[0]+\"*x+\"+c[1] +\")*(\"+ c[0]+\"*x+\"+c[1]+ \")+\"+c[3],\n    c[2]+\"*(\"+ c[2]+\"*x*x+\"+c[3] +\")*(\"+ c[2]+\"*x*x+\"+c[3] +\")+\"+c[3]\n  ][idx]),[\"expandBrackets\",\"all\"])", "description": "", "templateType": "anything", "can_override": false}, "idx": {"name": "idx", "group": "Ungrouped variables", "definition": "random(0..3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["c", "fe", "ge", "idx", "fn", "fof", "fog", "gof", "gog", "ans", "simplified"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{ans}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "2.1.3.2 Evaluate a composite function version 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Given 2 randomised functions f(x) (linear) and g(x) (quadratic), find one of f(f), f(g), g(f) or g(g) at a randomised integer x-value</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Find $\\var{latex(fn[0])}(\\var{latex(fn[1])}(\\var{val}))$ when $f(x)=\\var{fe}$ and $g(x)=\\var{ge}$.</p>", "advice": "<p>When $f(x)=\\var{fe}$ and $g(x)=\\var{ge}$</p>\n<p><span data-jme-visible=\"fn[1]=&quot;f&quot;\">\\[f(\\var{val})=\\var{feval}\\]</span></p>\n<p><span data-jme-visible=\"fn[1]=&quot;g&quot;\">\\[g(\\var{val})=\\var{geval}\\]</span></p>\n<p><span data-jme-visible=\"fn[1]=&quot;f&quot;\">\\[\\var{latex(fn[0])}(\\var{latex(fn[1])}(\\var{val}))=\\var{latex(fn[0])}(\\var{feval})=&nbsp; &nbsp;\\var{ans}\\]</span></p>\n<p><span data-jme-visible=\"fn[1]=&quot;g&quot;\">\\[\\var{latex(fn[0])}(\\var{latex(fn[1])}(\\var{val}))=\\var{latex(fn[0])}(\\var{geval})=&nbsp; &nbsp;\\var{ans}\\]</span></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"fe": {"name": "fe", "group": "Ungrouped variables", "definition": "simplify(expression(\n  c[0]+\"*x+\"+c[1]\n),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "ge": {"name": "ge", "group": "Ungrouped variables", "definition": "simplify(expression(\n  c[2]+\"*x^2+\"+c[3]\n),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "fn": {"name": "fn", "group": "Ungrouped variables", "definition": "[[\"f\",\"f\"],[\"f\",\"g\"],[\"g\",\"f\"],[\"g\",\"g\"]][idx]", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "[random(1..9),random(-9..9),random(1..9),random(-9..9)]", "description": "", "templateType": "anything", "can_override": false}, "fof": {"name": "fof", "group": "Ungrouped variables", "definition": "c[0]*feval+c[1]", "description": "", "templateType": "anything", "can_override": false}, "fog": {"name": "fog", "group": "Ungrouped variables", "definition": "c[0]*geval+c[1]", "description": "", "templateType": "anything", "can_override": false}, "gof": {"name": "gof", "group": "Ungrouped variables", "definition": "c[2]*feval^2+c[3]", "description": "", "templateType": "anything", "can_override": false}, "gog": {"name": "gog", "group": "Ungrouped variables", "definition": "c[2]*geval^2+c[3]", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "[fof, fog, gof, gog][idx]", "description": "", "templateType": "anything", "can_override": false}, "idx": {"name": "idx", "group": "Ungrouped variables", "definition": "random(0..3)", "description": "", "templateType": "anything", "can_override": false}, "val": {"name": "val", "group": "Ungrouped variables", "definition": "random(-9..9)", "description": "", "templateType": "anything", "can_override": false}, "feval": {"name": "feval", "group": "Ungrouped variables", "definition": "c[0]*val+c[1]", "description": "", "templateType": "anything", "can_override": false}, "geval": {"name": "geval", "group": "Ungrouped variables", "definition": "c[2]*val^2+c[3]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["c", "fe", "ge", "idx", "fn", "fof", "fog", "gof", "gog", "ans", "val", "feval", "geval"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{ans}", "maxValue": "{ans}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "2.1.3.3 Evaluate a composite function version 3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Given f(x)=(x+a)/(x+b) and g(x) = 1/x, compute f(g(x)) and g(f(x)).</p>\n<p>a and b are randomised integers.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Given $f(x)=\\var{fe}$ and $g(x)=\\var{ge}$.</p>", "advice": "<p>When $\\displaystyle{f(x)=\\var{fe}}$ and $\\displaystyle{g(x)=\\var{ge}}$</p>\n<p>(a) $\\displaystyle{ f(g(x))= f\\left( \\frac{1}{x} \\right) = \\frac{\\frac{1}{x} \\var{ce[0]}}{\\frac{1}{x} \\var{ce[1]}} }=\\var{fog}$</p>\n<p>(b) $\\displaystyle{ f(g(x))= g\\left( \\var{fe} \\right) = \\frac{1}{\\frac{x \\var{ce[0]}}{x \\var{ce[1]}}}=\\var{gof} }$</p>", 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booklet 2.1, Basic concepts of functions exercises.</p>\n<p>Questions generally have multiple versions, clicking the \"Try another question like this one\" button will generate a new version.</p>", "end_message": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "results_options": {"printquestions": true, "printadvice": true}, "feedbackmessages": [], "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "inreview"}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "type": "exam", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "extensions": [], "custom_part_types": [], "resources": []}