// Numbas version: exam_results_page_options
{"name": "Line Graphs: Interpreting Graphs - 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: Interpreting Graphs - Reaction Temperature", "tags": [], "metadata": {"description": "<p>Interpreting line graphs depicting the decrease of temperature in a mixture over time. Estimating the temperature of the mixture at a given time point and vice versa.</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, as shown on the graph:&nbsp;</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/frzwhq9u', defs)}</p>", "advice": "<p>a) To find the initial temperature of the mixture, we need to find the point on the $T$-axis where $t=0$. So, we need to find the point where the line intersects with the $T$-axis.&nbsp;</p>\n<p>Here, a good estimate could be $\\var{b} ^\\circ C$.</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/evvd3nua', defadvice1)}</p>\n<p>b) We need to find the point on $T$-axis where the temperature $t=\\var{t_1}$. So we first need to estimate the point on the $t$-axis where $t=\\var{t_1}$. From there, we draw a vertical line to find the point on the graph. From the point on the graph, we draw a horizontal line and estimate the value on the $T$-axis where the horizontal line and the axis intersect.&nbsp;</p>\n<p>Here, a good estimate could be $ \\var{ans_c_estimate} ^\\circ C$.</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/evvd3nua', defadvice2)}</p>\n<p>c) We need to find the point on $t$-axis where the temperature $T=\\var{temp_1}$. So we first need to estimate the point on the $T$-axis where $T=\\var{temp_1}$. From there, we draw a horizontal line to find the point on the graph. From the point on the graph, we draw a vertical line and estimate the value on the $T$-axis where the vertical line and the axis intersect.</p>\n<p>Here, a good estimate could be $ \\var{ans_d_estimate}$ minutes.</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/evvd3nua', defadvice3)}</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": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(36..49)", "description": "", "templateType": "anything", "can_override": false}, "t_max": {"name": "t_max", "group": "Ungrouped variables", "definition": "random(15..30 #5)", "description": "", "templateType": "anything", "can_override": false}, "t_1": {"name": "t_1", "group": "Ungrouped variables", "definition": "random(5..({t_max}-1))", "description": "", "templateType": "anything", "can_override": false}, "Temp_1": {"name": "Temp_1", "group": "Ungrouped variables", "definition": "ceil(\nrandom(b-a*t_max..b #5)\n)", "description": "", "templateType": "anything", "can_override": false}, "ans_c": {"name": "ans_c", "group": "Ungrouped variables", "definition": "precround ((b-a*t_1),2)", "description": "", "templateType": "anything", "can_override": true}, "ans_d": {"name": "ans_d", "group": "Ungrouped variables", "definition": "precround((b-temp_1)*(1/a),2)", "description": "", "templateType": "anything", "can_override": false}, "GeoPointA1": {"name": "GeoPointA1", "group": "Unnamed group", "definition": "Vector(0,b)", "description": "", "templateType": "anything", "can_override": false}, "GeoPointB1": {"name": "GeoPointB1", "group": "Unnamed group", "definition": "vector({t_max},{b}-{a}*{t_max})", "description": "", "templateType": "anything", "can_override": false}, "defs": {"name": "defs", "group": "Unnamed group", "definition": "[\n  ['A',geopointa1],\n  ['B',geopointb1]\n  ]", "description": "", "templateType": "anything", "can_override": false}, "GeopointC1": {"name": "GeopointC1", "group": "Unnamed group", "definition": "vector(0,b)", "description": "", "templateType": "anything", "can_override": false}, "defAdvice1": {"name": "defAdvice1", "group": "Unnamed group", "definition": "[\n  ['A',geopointa1],\n  ['B',geopointb1],\n  ['C',geopointc1]\n  ]", "description": "", "templateType": "anything", "can_override": false}, "GeopointC2": {"name": "GeopointC2", "group": "Unnamed group", "definition": "vector(t_1,{b}-{a}*{t_1})", "description": "", "templateType": "anything", "can_override": false}, "defAdvice2": {"name": "defAdvice2", "group": "Unnamed group", "definition": "[\n  ['A',geopointa1],\n  ['B',geopointb1],\n  ['C',geopointc2]\n  ]", "description": "", "templateType": "anything", "can_override": false}, "ans_c_estimate": {"name": "ans_c_estimate", "group": "Ungrouped variables", "definition": "round(ans_c)", "description": "", "templateType": "anything", "can_override": false}, "ans_d_estimate": {"name": "ans_d_estimate", "group": "Ungrouped variables", "definition": "round(ans_d)", "description": "", "templateType": "anything", "can_override": false}, "GeopointC3": {"name": "GeopointC3", "group": "Unnamed group", "definition": "vector((b-temp_1)*(1/a),temp_1)", "description": "", "templateType": "anything", "can_override": false}, "defAdvice3": {"name": "defAdvice3", "group": "Unnamed group", "definition": "[\n  ['A',geopointa1],\n  ['B',geopointb1],\n  ['C',geopointc3]\n  ]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "(t_1<t_max)and(temp_1<b)and(b-a*t_max>0)", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "t_max", "t_1", "Temp_1", "ans_c", "ans_d", "ans_c_estimate", "ans_d_estimate"], "variable_groups": [{"name": "Unnamed group", "variables": ["GeoPointA1", "GeoPointB1", "defs", "GeopointC1", "defAdvice1", "GeopointC2", "defAdvice2", "GeopointC3", "defAdvice3"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Use the graph to estimate 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": "1", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Use the graph to estimate the temperature of the mixture after $\\var{t_1}$ minutes.</p>\n<p>The temperature after $\\var{t_1}$ minutes is [[0]] $ ^\\circ C$.</p>\n<p></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": "{ans_c}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": "1", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", 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1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Evi Papadaki", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18113/"}]}]}], "contributors": [{"name": "Evi Papadaki", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18113/"}]}