// Numbas version: exam_results_page_options {"name": "Introductory Maths from GCSE", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": "0", "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", ""], "variable_overrides": [[], [], [], []], "questions": [{"name": "Line Graphs: Sketching - DNA Melting Temperature", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Evi Papadaki", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18113/"}], "tags": [], "metadata": {"description": "

Practicing skills required for sketching line graphs depicting DNA melting temperature according to the percentage of GC content. The question includes: a) identifying the  vertical intercept, b) choosing the accurate sketch from a list, and c) interpreting elements of the sketch in context. 

", "licence": "None specified"}, "statement": "

The melting temperature of DNA, $T$ degrees Celsius, depends on the percentage of GC content of the DNA, $G~$%, according to the formula:

\n

$T=\\simplify[fractionNumbers]{{a}G+{b}} $

\n

Sketch the function T for $0\\leq G \\leq \\var{G_max}$  and then answer the questions below.

", "advice": "

a) The vertical axis shows possible values for $T$. In order to find the intersection of the graph with the vertical axis, we need to find the value of $T$ when $G=0$. 

\n

Therefore, 

\n

\\[T=\\simplify[fractionNumbers]{{a}*0+{b}} \\]

\n

\\[T=\\simplify[!zeroTerm]{{a*0}+{b}} \\]

\n

\\[T=\\simplify{{a*0}+{b}} \\]

\n

So, the intersection of the graph with the vertical axis is the point $(0,\\var{b})$.

\n

\n

b)  We need to consider the gradient of the graph. The gradient here is $\\simplify[fractionNumbers]{{a}}$ which is a positive number. Therefore, the graph is going upwards. We also know that the intersection of the graph with the veritcal axis is $(0,\\var{b})$ from part (a).

\n

Therefore, our graph should look like the one below:

\n

{geogebra_applet('https://www.geogebra.org/m/a9wf5jjk', defs)}

\n

\n

c) The intersection point $(0,\\var{b})$ tells us that when the GC content (G) is $0$, the melting temperature (T) is $\\var{b}$.

\n

So, the correct answer is \"The melting temperature of DNA with 0% GC content\".

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..5)/random(3..9)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(10..15)", "description": "", "templateType": "anything", "can_override": false}, "G_max": {"name": "G_max", "group": "Ungrouped variables", "definition": "random(35..50 #5)", "description": "", "templateType": "anything", "can_override": false}, "G_1": {"name": "G_1", "group": "Ungrouped variables", "definition": "random(10..50 #5)", "description": "", "templateType": "anything", "can_override": false}, "T_1": {"name": "T_1", "group": "Ungrouped variables", "definition": "random(b..a*g_max+b #5)", "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(g_max,a*g_max+b)", "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}, "GeopointA2": {"name": "GeopointA2", "group": "Unnamed group", "definition": "vector(0,0)", "description": "", "templateType": "anything", "can_override": false}, "GeopointB2": {"name": "GeopointB2", "group": "Unnamed group", "definition": "vector(g_max,a*g_max)", "description": "", "templateType": "anything", "can_override": false}, "defs2": {"name": "defs2", "group": "Unnamed group", "definition": "[\n ['A',geopointa2],\n ['B',geopointb2]\n ]", "description": "", "templateType": "anything", "can_override": false}, "GeopointB3": {"name": "GeopointB3", "group": "Unnamed group", "definition": "Vector (g_max,3)", "description": "", "templateType": "anything", "can_override": false}, "defs3": {"name": "defs3", "group": "Unnamed group", "definition": "[\n ['A',geopointa1],\n ['B',geopointb3]\n ]", "description": "", "templateType": "anything", "can_override": false}, "GeopointA4": {"name": "GeopointA4", "group": "Unnamed group", "definition": "vector(5,b)", "description": "", "templateType": "anything", "can_override": false}, "defs4": {"name": "defs4", "group": "Unnamed group", "definition": "[\n ['A',geopointa4],\n ['B',geopointb1]\n ]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "(a<=0.5)and(g_1<=g_max)and(t_1>b)", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "G_max", "G_1", "T_1"], "variable_groups": [{"name": "Unnamed group", "variables": ["GeoPointA1", "GeoPointB1", "defs", "GeopointA2", "GeopointB2", "defs2", "GeopointB3", "defs3", "GeopointA4", "defs4"]}], "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": "

Find the intersection of the graph with the vertical axis.

\n

The intersection is the point $(0,$ [[0]] $)$.

", "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], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "1_n_2", "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": "

Choose the graph which looks most like your sketch.

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["{geogebra_applet('https://www.geogebra.org/m/a9wf5jjk', defs)}", "{geogebra_applet('https://www.geogebra.org/m/a9wf5jjk', defs2)}", "{geogebra_applet('https://www.geogebra.org/m/a9wf5jjk', defs3)}", "{geogebra_applet('https://www.geogebra.org/m/a9wf5jjk', defs4)}"], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "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": "

What does the intersection of the graph with the vertical axis represent?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["The melting temperature of DNA with $0$% GC content.", "The percentage of GC content when $T=0 ^\\circ C$.", "The maximum melting temperature of DNA.", "Nothing, it is just a point on the graph."], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Line Graphs: Interesting Graphs - DNA Melting Temperature", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Evi Papadaki", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18113/"}], "tags": [], "metadata": {"description": "

Interpreting line graphs depicting the melting temperature of DNA depending on the percentage of GC content. Estimating the melting temperature given a GC percentage and vice versa.

", "licence": "None specified"}, "statement": "

The melting temperature of DNA, $T$ degrees Celsius, depends on the percentage of GC content of the DNA, $G~$%. The following graph depicts the relation between T and G, for $0\\leq G \\leq \\var{G_max}$:

\n

{geogebra_applet('https://www.geogebra.org/m/rcx6wdzu', defs)}

", "advice": "

a) We need to find the point on the $T$-axis where $G=\\var{g_1}$ . So, we first need to find the point on the $G$-axis where $G=\\var{g_1}$. From that point, we draw a line vertically to find a point on the graph. From the point on the graph, we need to draw a horizontal line, and then estimate the value on $T$. 

\n

Here, a good estimate could be $\\var{roundedA} ^\\circ C$.

\n

{geogebra_applet('https://www.geogebra.org/m/z8gwsgjk', defsadvice1)}

\n

b) We need to find the point on the $G$-axis where $T=\\var{t_1}$. So, we first need to estimate the point on the $T$-axis where $T=\\var{t_1}$. From here, we draw horizontally to find a point on the graph. From the point on the graph, we draw a vertical line, and then estimate the value on G. 

\n

Here, a good estimate could be $\\var{roundedB}$%.

\n

{geogebra_applet('https://www.geogebra.org/m/z8gwsgjk', defsadvice2)}

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..5)/random(3..9)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(10..15)", "description": "", "templateType": "anything", "can_override": false}, "G_max": {"name": "G_max", "group": "Ungrouped variables", "definition": "random(35..50 #5)", "description": "", "templateType": "anything", "can_override": false}, "G_1": {"name": "G_1", "group": "Ungrouped variables", "definition": "random(10..36 #5)", "description": "", "templateType": "anything", "can_override": false}, "T_1": {"name": "T_1", "group": "Ungrouped variables", "definition": "random(b..a*g_max+b #5)", "description": "", "templateType": "anything", "can_override": false}, "ans_a": {"name": "ans_a", "group": "Ungrouped variables", "definition": "a*g_1+b", "description": "", "templateType": "anything", "can_override": true}, "ans_b": {"name": "ans_b", "group": "Ungrouped variables", "definition": "(t_1-b)*(1/a) ", "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({g_max},{a}*{g_max}+{b})", "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({g_1},{a}*{g_1}+{b})", "description": "", "templateType": "anything", "can_override": false}, "DefsAdvice1": {"name": "DefsAdvice1", "group": "Unnamed group", "definition": "[\n ['A',geopointa1],\n ['B',geopointb1],\n ['C',geopointc1]\n ]", "description": "", "templateType": "anything", "can_override": false}, "RoundedA": {"name": "RoundedA", "group": "Ungrouped variables", "definition": "round({ans_a})", "description": "", "templateType": "anything", "can_override": false}, "RoundedB": {"name": "RoundedB", "group": "Ungrouped variables", "definition": "round({ans_b})", "description": "", "templateType": "anything", "can_override": false}, "GeopointC2": {"name": "GeopointC2", "group": "Unnamed group", "definition": "vector((t_1-b)*(1/a),t_1)", "description": "", "templateType": "anything", "can_override": false}, "Defsadvice2": {"name": "Defsadvice2", "group": "Unnamed group", "definition": "[\n ['A',geopointa1],\n ['B',geopointb1],\n ['C',geopointc2]\n ]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "(a<=0.5)and(g_1<=g_max)and(t_1>b)", "maxRuns": 100}, "ungrouped_variables": ["b", "a", "G_1", "G_max", "ans_b", "T_1", "RoundedA", "ans_a", "RoundedB"], "variable_groups": [{"name": "Unnamed group", "variables": ["GeoPointA1", "GeoPointB1", "defs", "GeopointC1", "DefsAdvice1", "GeopointC2", "Defsadvice2"]}], "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": "

Estimate the melting temperature of DNA with $\\var{G_1}$% GC content.

\n

The melting temperature in this case is [[0]] $ ^\\circ C$.

", "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_a}", "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": "

Estimate the percentage GC content of DNA with a melting temperature of $\\var{T_1}^\\circ C$.

\n

The percentage GC content of DNA is [[0]] %.

", "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_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}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Line Graphs: Sketching - Reaction Temperature", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Evi Papadaki", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18113/"}], "tags": [], "metadata": {"description": "

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. 

", "licence": "None specified"}, "statement": "

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: 

\n

$ T=\\var{b}-\\var{a}t $

\n

Sketch the function $T$ for $0\\leq t \\leq \\var{t_max}$ minutes and then answer the questions below.

", "advice": "

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.

\n

\\[  T=\\var{b}-\\var{a} \\times 25\\]

\n

\\[  T=\\var{b}-\\simplify{{{a}*25}}\\]

\n

\\[  T=\\simplify{{b}-{{a}*25}}\\]

\n

Therefore, our sketch should look like the graph below

\n

{geogebra_applet('https://www.geogebra.org/m/cyvdfer7', defs)}

\n

\n

b) To calculate the initial temperature of the mixture we need to find the value of $T$ when $t=0$ seconds. 

\n

\\[  T=\\var{b}-\\var{a}\\times 0\\]

\n

\\[  T=\\var{b}-\\simplify{{{a}*0}}\\]

\n

\\[  T=\\simplify{{b}-{{a}*0}}\\]

\n

Therefore, the initial temperature of the mixture is $T=\\simplify{{b}-{{a}*0}} ^\\circ C$.

", "rulesets": {}, "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..40)", "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}, "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}, "GeopointA2": {"name": "GeopointA2", "group": "Unnamed group", "definition": "vector(0,0)", "description": "", "templateType": "anything", "can_override": false}, "GeopointB2": {"name": "GeopointB2", "group": "Unnamed group", "definition": "vector(t_max,a*t_max)", "description": "", "templateType": "anything", "can_override": false}, "defs2": {"name": "defs2", "group": "Unnamed group", "definition": "[\n ['A',geopointa2],\n ['B',geopointb2]\n ]", "description": "", "templateType": "anything", "can_override": false}, "GeopointB3": {"name": "GeopointB3", "group": "Unnamed group", "definition": "Vector (t_max,a*t_max+b)", "description": "", "templateType": "anything", "can_override": false}, "defs3": {"name": "defs3", "group": "Unnamed group", "definition": "[\n ['A',geopointa1],\n ['B',geopointb3]\n ]", "description": "", "templateType": "anything", "can_override": false}, "GeopointB4": {"name": "GeopointB4", "group": "Unnamed group", "definition": "vector(t_max,0)", "description": "", "templateType": "anything", "can_override": false}, "defs4": {"name": "defs4", "group": "Unnamed group", "definition": "[\n ['A',geopointa1],\n ['B',geopointb4]\n ]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "(t_10)", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "t_max", "t_1", "Temp_1"], "variable_groups": [{"name": "Unnamed group", "variables": ["GeoPointA1", "GeoPointB1", "defs", "GeopointA2", "GeopointB2", "defs2", "GeopointB3", "defs3", "GeopointB4", "defs4"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "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": "

Choose the graph that looks more like your sketch.

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["{geogebra_applet('https://www.geogebra.org/m/cyvdfer7', defs)}", "{geogebra_applet('https://www.geogebra.org/m/cyvdfer7', defs2)}", "{geogebra_applet('https://www.geogebra.org/m/cyvdfer7', defs3)}", "{geogebra_applet('https://www.geogebra.org/m/cyvdfer7', defs4)}"], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}, {"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": "

What is the initial temperature of the mixture? 

\n

\n

The initial temperature of the mixture is [[0]] $ ^\\circ C$.

", "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], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Line Graphs: Interpreting Graphs - Reaction Temperature", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Evi Papadaki", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18113/"}], "tags": [], "metadata": {"description": "

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.

", "licence": "None specified"}, "statement": "

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: 

\n

{geogebra_applet('https://www.geogebra.org/m/frzwhq9u', defs)}

", "advice": "

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. 

\n

Here, a good estimate could be $\\var{b} ^\\circ C$.

\n

{geogebra_applet('https://www.geogebra.org/m/evvd3nua', defadvice1)}

\n

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. 

\n

Here, a good estimate could be $ \\var{ans_c_estimate} ^\\circ C$.

\n

{geogebra_applet('https://www.geogebra.org/m/evvd3nua', defadvice2)}

\n

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.

\n

Here, a good estimate could be $ \\var{ans_d_estimate}$ minutes.

\n

{geogebra_applet('https://www.geogebra.org/m/evvd3nua', defadvice3)}

", "rulesets": {}, "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_10)", "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": "

Use the graph to estimate the initial temperature of the mixture. 

\n

\n

The initial temperature of the mixture is [[0]] $ ^\\circ C$.

", "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": "

Use the graph to estimate the temperature of the mixture after $\\var{t_1}$ minutes.

\n

The temperature after $\\var{t_1}$ minutes is [[0]] $ ^\\circ C$.

\n

", "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": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Use the graph to estimate the time taken for the mixture to reach $\\var{temp_1}^\\circ C$.

\n

The time taken is [[0]] minutes.

\n

", "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_d}", "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}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "end_message": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Evi Papadaki", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18113/"}], "extensions": ["geogebra"], "custom_part_types": [], "resources": []}