// Numbas version: exam_results_page_options
{"name": "Graphical solution of simultaneous linear equations", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Graphical solution of simultaneous linear equations", "tags": [], "metadata": {"description": "<p>Studnents are asked to write down equations for cost and income for a business.</p>\n<p>They are then asked to graph the two lines.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>A&nbsp;{shop} owner sells&nbsp;{item}s for {currency(msell,\"\\\\$\",\"\")} each. It costs {currency(mcost,\"\\\\$\",\"\")} to make each {item} and {currency(bcost,\"\\\\$\",\"\")} for the equipment needed to make the {item}s.</p>", "advice": "<p>The income received from selling the {item}s is the selling cost of each item multiplied by the number of items sold.</p>\n<p>That is, $I = \\var{msell} \\times n$.</p>\n<p>The equation for income is a straight line of the form $y = mx +b$, where $m$ is the gradient of the line and $b$ is the $y$-intercept.</p>\n<p>In this equation, the&nbsp;constant $b = 0$ as, when 0 units are sold, $I=\\$0$, so the line passes through the point $(0,0)$.</p>\n<p>The cost to make the {item}s is the cost to make each item multiplied by the number of items made plus the fixed costs.</p>\n<p>That is, $C = \\var{mcost} \\times n + \\var{bcost}$.</p>\n<p>This is also a straight line of the form $y=mx+b$</p>\n<p>When we graph the two functions, we get the following:</p>\n<p>{geogebra_applet(\"https://www.geogebra.org/m/srpxwjnu\",defs)}</p>\n<p>Your graph needs:</p>\n<ul>\n<li>to start at (0,0) in the bottom left hand corner.</li>\n<li>to show the cost line and the revenue line.</li>\n<li>labels and arrows on both axes.</li>\n<li>a scale on each axis.</li>\n<li>to include the break-even point, where the two lines meet.</li>\n</ul>\n<p>You may have chosen different scales for your axes. This is fine.</p>\n<p></p>", "rulesets": {}, "extensions": ["geogebra"], "variables": {"shoptypes": {"name": "shoptypes", "group": "Ungrouped variables", "definition": "['bakery','bakery','bakery','craft shop','craft shop','craft shop']", "description": "", "templateType": "anything"}, "itemidx": {"name": "itemidx", "group": "Ungrouped variables", "definition": "random(0..5)", "description": "", "templateType": "anything"}, "itemtypes": {"name": "itemtypes", "group": "Ungrouped variables", "definition": "['muffin','cake','pie','handmade paper','figurine','bandanna']", "description": "", "templateType": "anything"}, "msell": {"name": "msell", "group": "Ungrouped variables", "definition": "random(30..100)/10", "description": "", "templateType": "anything"}, "mcost": {"name": "mcost", "group": "Ungrouped variables", "definition": "round(random(10..msell*20/3))/10", "description": "", "templateType": "anything"}, "bcost": {"name": "bcost", "group": "Ungrouped variables", "definition": "random(1..10)*100", "description": "", "templateType": "anything"}, "defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[\n  ['b1',0],['m1',msell],['b2',bcost],['m2',mcost],\n  ['xmin',-1],['xmax',2*x],['ymin',-1],['ymax',2*y]\n  ]", "description": "", "templateType": "anything"}, "shop": {"name": "shop", "group": "Ungrouped variables", "definition": "shoptypes[itemidx]", "description": "", "templateType": "anything"}, "item": {"name": "item", "group": "Ungrouped variables", "definition": "itemtypes[itemidx]", "description": "", "templateType": "anything"}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "bcost/(msell-mcost)", "description": "<p>break-even point x-value</p>", "templateType": "anything"}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "msell * x", "description": "<p>break even point y-value</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["shoptypes", "itemidx", "itemtypes", "msell", "mcost", "bcost", "defs", "shop", "item", "x", "y"], "variable_groups": [], "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>Write an equation to relate the income, $I$, that is made from selling the {item}s, to the $n$, the number of {item}s sold.</p>\n<p>Don't enter any dollar signs, just numbers.</p>\n<p>$I = $ [[0]]$\\times n +$[[1]]</p>", "gaps": [{"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": "msell", "maxValue": "msell", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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>Write an equation to relate the cost, $C$,&nbsp;of producing&nbsp;the {item}s, to the $n$, the number of {item}s sold.</p>\n<p>Don't enter any dollar signs, just numbers.</p>\n<p>$C = $&nbsp;[[0]]$\\times n +$[[1]]</p>", "gaps": [{"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": "mcost", "maxValue": "mcost", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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": "bcost", "maxValue": "bcost", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "information", "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>Draw up a table of values for each equation and plot the two lines on the same graph.</p>\n<p>You can check your graph yourself by clicking on the \"reveal answers\" button at the end of the question.</p>\n<p>Warning: Don't do this until you have finished the question, because it has answers for all of the question parts!</p>"}], "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/"}]}