// Numbas version: exam_results_page_options
{"name": "2.1.3 Task 1", "extensions": [], "custom_part_types": [], "resources": [["question-resources/helm2_1_fig4.png", "/srv/numbas/media/question-resources/helm2_1_fig4.png"], ["question-resources/helm2_1_fig5.png", "/srv/numbas/media/question-resources/helm2_1_fig5.png"], ["question-resources/helm2_1_fig6.png", "/srv/numbas/media/question-resources/helm2_1_fig6.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "2.1.3 Task 1", "tags": [], "metadata": {"description": "<p>Evaluate a composition of functions for a randomised numerical input. The functions are 3t+2 and t+3. This is part of HELM Book 2.1.3.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Given the two functions $g(t) = \\var{a[0]}t + \\var{a[1]}$ and $h(t) = t + \\var{a[2]}$ as in Example 4 above, obtain an expression for the composition $h(g(t))$.</p>", "advice": "<p>We have $h(g(t)) = h(\\var{a[0]}t + \\var{a[1]})$</p>\n<p>$h(\\var{a[0]}t + \\var{a[1]}) = (\\var{a[0]}t+\\var{a[1]}) + \\var{a[2]} = \\var{simplify(expression(a[0]+\"*t+\"+a[1]+\"+\"+a[2]),\"all\")}$.</p>\n<p>Note that $h(g(t))\\neq g(h(t))$</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "repeat(random(1..9),3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a"], "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": "{a[0]}t+{a[1]}+{a[2]}", "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": [{"name": "t", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}