// Numbas version: exam_results_page_options
{"name": "Line Graphs: Sketching - Reaction Temperature", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Line Graphs: Sketching - Reaction Temperature", "tags": [], "metadata": {"description": "<p>Practicing skills required for sketching line graphs depicting the temperature of a mixture according to time. The question includes: a) choosing the accurate sketch from a list, and b) identifying the initial temperature of the mixture.&nbsp;</p>", "licence": "None specified"}, "statement": "<p>Zinc is mixed with an acid in an insulated container. After the initial temperature rise, the temperature of the mixture, $T$ $^\\circ$ C, falls over time, $t$ minutes, according to the formula:&nbsp;</p>\n<p>\\[ T=\\var{b}-\\var{a}t \\]</p>\n<p>Sketch the function $T$ for $0\\leq t \\leq \\var{t_max}$ minutes and then answer the questions below.</p>", "advice": "<p>a) To sketch the graph, one thing we need to consider is the gradient. Here the gradient is $-\\var{a}$ which is a negative number. So, the line graph will go downwords over time. We only have two options showing graphs with negative gradient. The difference between the two graphs is the last point shown on the graph. Therefore, we need to calculate the value of $T$ when $t=25$ seconds.</p>\n<p>\\[&nbsp; T=\\var{b}-\\var{a} \\times 25\\]</p>\n<p>\\[&nbsp; T=\\var{b}-\\simplify{{{a}*25}}\\]</p>\n<p>\\[&nbsp; T=\\simplify{{b}-{{a}*25}}\\]</p>\n<p>Therefore, our sketch should look like the graph below</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/cyvdfer7', defs)}</p>\n<p></p>\n<p>b) To calculate the initial temperature of the mixture we need to find the value of $T$ when $t=0$ seconds.&nbsp;</p>\n<p>\\[&nbsp; T=\\var{b}-\\var{a}\\times 0\\]</p>\n<p>\\[&nbsp; T=\\var{b}-\\simplify{{{a}*0}}\\]</p>\n<p>\\[&nbsp; T=\\simplify{{b}-{{a}*0}}\\]</p>\n<p>Therefore, the initial temperature of the mixture is $T=\\simplify{{b}-{{a}*0}} ^\\circ C$.</p>", "rulesets": {}, "extensions": ["geogebra"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random (0.4 .. 0.8 #0.05)", "description": "", 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"extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the initial temperature of the mixture?&nbsp;</p>\n<p></p>\n<p>The initial temperature of the mixture is [[0]] $ ^\\circ$ C.</p>", "gaps": [{"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": "{b}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], 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