// Numbas version: exam_results_page_options
{"name": "Creating formulas", "metadata": {"description": "<p>A quick practice set of problems for education students to take in preparation for their numeracy test.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], []], "questions": [{"name": "Formulas (dots)", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Daniel Sutherland", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/16947/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Consider the various stages of dots in the following diagram:</p>\n<p>{GGB_DIAGRAM}</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"ggb_diagram": {"name": "ggb_diagram", "group": "Ungrouped variables", "definition": "geogebra_applet('ac6nz8x6',[m: step, b: start])", "description": "", "templateType": "anything", "can_override": false}, "start": {"name": "start", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "", "templateType": "anything", "can_override": false}, "step": {"name": "step", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "", "templateType": "anything", "can_override": false}, "stage": {"name": "stage", "group": "Ungrouped variables", "definition": "random(5..20)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["ggb_diagram", "start", "step", "stage"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Identify the formula", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Think about how many dots are present at each stage of the diagram, and complete the following formula:</p>\n<p>Number of dots in a given stage = [[0]] $+$ (stage number) $\\times$ [[1]].</p>", "stepsPenalty": "2", "steps": [{"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>Notice we start with $\\var{start}$ dots. From that stage on, we take the dots from the previous stage and add $\\var{step}$ dots. Since we are repeatedly adding $\\var{step}$ dots, at each stage we can think of adding multiples of $\\var{step}$ to $\\var{start}$.&nbsp;</p>\n<table style=\"height: 126px; width: 302px;\" border=\"1\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 67.25px; text-align: center; height: 18px;\"><strong>Stage</strong></td>\n<td style=\"width: 201.75px; text-align: center; height: 18px;\"><strong>Number of dots</strong></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 67.25px; text-align: center; height: 18px;\">$0$</td>\n<td style=\"width: 201.75px; text-align: center; height: 18px;\">$\\var{start}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 67.25px; text-align: center; height: 18px;\">$1$</td>\n<td style=\"width: 201.75px; text-align: center; height: 18px;\">$\\var{start}$ plus one lot of $\\var{step}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 67.25px; text-align: center; height: 18px;\">$2$</td>\n<td style=\"width: 201.75px; text-align: center; height: 18px;\">$\\var{start}$ plus two lots of $\\var{step}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 67.25px; text-align: center; height: 18px;\">$3$</td>\n<td style=\"width: 201.75px; text-align: center; height: 18px;\">$\\var{start}$ plus three lots of $\\var{step}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 67.25px; text-align: center; height: 18px;\">$\\vdots$</td>\n<td style=\"width: 201.75px; text-align: center; height: 18px;\">$\\vdots$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 67.25px; text-align: center; height: 18px;\">$n$</td>\n<td style=\"width: 201.75px; text-align: center; height: 18px;\">$\\var{start}$ plus $n$ lots of $\\var{step}$</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>So in general we can say,</p>\n<p>Number of dots in a given stage $=$ $\\var{start}$ $+$ (stage number) $\\times$ $\\var{step}$.</p>"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "start", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "start", "maxValue": "start", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "step", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "step", "maxValue": "step", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "numberentry", "useCustomName": true, "customName": "Use the formula", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Hence, predict the number of dots in the diagram for Stage {stage}:</p>", "stepsPenalty": "1", "steps": [{"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>We know that</p>\n<p>Number of dots in a given stage $=$ $\\var{start}$ $+$ (stage number) $\\times$ $\\var{step}$,</p>\n<p>so at stage {stage}:</p>\n<p>Number of dots in stage {stage} is $\\var{start}+\\var{stage}\\times\\var{step}=\\var{start+stage*step}$.</p>"}], "minValue": "start+stage*step", "maxValue": "start+stage*step", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Formulas (matchsticks)", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Daniel Sutherland", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/16947/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Consider the various stages of matchsticks in the following diagram:</p>\n<p>{GGB_DIAGRAM}</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"ggb_diagram": {"name": "ggb_diagram", "group": "Ungrouped variables", "definition": "geogebra_applet('rknzd4dq',[n: boxes])", "description": "", "templateType": "anything", "can_override": false}, "stage": {"name": "stage", "group": "Ungrouped variables", "definition": "random(5..20)", "description": "", "templateType": "anything", "can_override": false}, "boxes": {"name": "boxes", "group": "Ungrouped variables", "definition": "random(1..6)", "description": "", "templateType": "anything", "can_override": false}, "start": {"name": "start", "group": "Ungrouped variables", "definition": "1+3*boxes", "description": "", "templateType": "anything", "can_override": false}, "step": {"name": "step", "group": "Ungrouped variables", "definition": "1+2*boxes", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["ggb_diagram", "stage", "boxes", "start", "step"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Identify the formula", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Think about how many matchsticks are present at each stage of the diagram, and complete the following formula:</p>\n<p>Number of matchsticks in a given stage = [[0]] $+$ (stage number) $\\times$ [[1]].</p>", "stepsPenalty": "2", "steps": [{"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>Notice we start with $\\var{start}$ matchsticks. From that stage on, we take the matchsticks from the previous stage and add $\\var{step}$ matchsticks. Since we are repeatedly adding $\\var{step}$ matchsticks, at each stage we can think of adding multiples of $\\var{step}$ to $\\var{start}$.&nbsp;</p>\n<table style=\"height: 126px; width: 302px;\" border=\"1\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 67.25px; text-align: center; height: 18px;\"><strong>Stage</strong></td>\n<td style=\"width: 201.75px; text-align: center; height: 18px;\"><strong>Number of matchsticks</strong></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 67.25px; text-align: center; height: 18px;\">$0$</td>\n<td style=\"width: 201.75px; text-align: center; height: 18px;\">$\\var{start}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 67.25px; text-align: center; height: 18px;\">$1$</td>\n<td style=\"width: 201.75px; text-align: center; height: 18px;\">$\\var{start}$ plus one lot of $\\var{step}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 67.25px; text-align: center; height: 18px;\">$2$</td>\n<td style=\"width: 201.75px; text-align: center; height: 18px;\">$\\var{start}$ plus two lots of $\\var{step}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 67.25px; text-align: center; height: 18px;\">$3$</td>\n<td style=\"width: 201.75px; text-align: center; height: 18px;\">$\\var{start}$ plus three lots of $\\var{step}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 67.25px; text-align: center; height: 18px;\">$\\vdots$</td>\n<td style=\"width: 201.75px; text-align: center; height: 18px;\">$\\vdots$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 67.25px; text-align: center; height: 18px;\">$n$</td>\n<td style=\"width: 201.75px; text-align: center; height: 18px;\">$\\var{start}$ plus $n$ lots of $\\var{step}$</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>So in general we can say,</p>\n<p>Number of matchsticks in a given stage $=$ $\\var{start}$ $+$ (stage number) $\\times$ $\\var{step}$.</p>"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "start", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "start", "maxValue": "start", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "step", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "step", "maxValue": "step", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "numberentry", "useCustomName": true, "customName": "Use the formula", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Hence, predict the number of matchsticks in the diagram for Stage {stage}:</p>", "stepsPenalty": "1", "steps": [{"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>We know that</p>\n<p>Number of matchsticks in a given stage $=$ $\\var{start}$ $+$ (stage number) $\\times$ $\\var{step}$,</p>\n<p>so at stage {stage}:</p>\n<p>Number of matchsticks in stage {stage} is $\\var{start}+\\var{stage}\\times\\var{step}=\\var{start+stage*step}$.</p>"}], "minValue": "start+stage*step", "maxValue": "start+stage*step", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Creating formulas: spreadsheet cost", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"cost1": {"name": "cost1", "group": "Ungrouped variables", "definition": "list[0][1]", "description": "", "templateType": "anything", "can_override": false}, "cost2": {"name": "cost2", "group": "Ungrouped variables", "definition": "list[1][1]", "description": "", "templateType": "anything", "can_override": false}, "cost3": {"name": "cost3", "group": "Ungrouped variables", "definition": "list[2][1]", "description": "", "templateType": "anything", "can_override": false}, "item1": {"name": "item1", "group": "Ungrouped variables", "definition": "list[0][0]", "description": "", "templateType": "anything", "can_override": false}, "item2": {"name": "item2", "group": "Ungrouped variables", "definition": "list[1][0]", "description": "", "templateType": "anything", "can_override": false}, "item3": {"name": "item3", "group": "Ungrouped variables", "definition": "list[2][0]", "description": "", "templateType": "anything", "can_override": false}, "list": {"name": "list", "group": "Ungrouped variables", "definition": "[[\"15MM RED GRANITE\", random(65..75)],\n[\"30MM ORNAMENTAL\", random(65..75)],\n[\"TENNIS COURT GRAVEL\", random(65..75)],\n[\"BLENDED SANDY TOPSOIL\", random(49..55#0.25)],\n[\"WASHED RIVER STONE 10MM\", random(75..80#0.25)],\n[\"WASHED RIVER STONE 20MM\", random(75..80#0.5)], \n[\"VENM (VIRGIN EXCAVATED NATURAL MATERIAL)\", random(15..20)],\n  [\"THERMAL SAND\", random(67..70#0.25)],\n  [\"SUB BASE GRAVEL\", random(30..40)]\n][0..3]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["cost1", "cost2", "cost3", "item1", "item2", "item3", "list"], "variable_groups": [], "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": "<p>A spreadsheet is used to find the total cost of an order. The quantity of each material ordered is entered into cells B2, B4 and B6. The spreadsheet then calculates the total cost in cell B9.</p>\n<table style=\"height: 371px; width: 525px; border-style: solid;\" border=\"1\">\n<tbody>\n<tr style=\"height: 18px;\" bgcolor=\"#ddd\">\n<td style=\"width: 28.1875px; text-align: center; height: 18px;\"></td>\n<td style=\"width: 112.531px; text-align: center; height: 18px;\">A</td>\n<td style=\"width: 119.562px; text-align: center; height: 18px;\">B</td>\n<td style=\"width: 99.4688px; text-align: center; height: 18px;\">C</td>\n<td style=\"width: 84.25px; text-align: center; height: 18px;\">D</td>\n</tr>\n<tr style=\"height: 90px;\">\n<td style=\"width: 28.1875px; text-align: center; height: 90px;\" bgcolor=\"#ddd\">1</td>\n<td style=\"width: 112.531px; text-align: center; height: 90px;\"><strong>Material</strong></td>\n<td style=\"width: 119.562px; text-align: center; height: 90px;\">\n<p><strong>Quantity (cubic metres)</strong></p>\n</td>\n<td style=\"width: 99.4688px; text-align: center; height: 90px;\"><strong>Cost&nbsp;</strong><br/><strong>per cubic metres ($)</strong></td>\n<td style=\"width: 84.25px; text-align: center; height: 90px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 28.1875px; text-align: center; height: 18px;\" bgcolor=\"#ddd\">2</td>\n<td style=\"width: 112.531px; height: 18px; text-align: left;\">{item1}</td>\n<td style=\"width: 119.562px; text-align: center; height: 18px; border: 2px solid black;\"></td>\n<td style=\"width: 99.4688px; text-align: center; height: 18px;\">$\\var{cost1}$</td>\n<td style=\"width: 84.25px; text-align: center; height: 18px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 28.1875px; text-align: center; height: 18px;\" bgcolor=\"#ddd\">3</td>\n<td style=\"width: 112.531px; height: 18px; text-align: left;\"></td>\n<td style=\"width: 119.562px; text-align: center; height: 18px;\"></td>\n<td style=\"width: 99.4688px; text-align: center; height: 18px;\"></td>\n<td style=\"width: 84.25px; text-align: center; height: 18px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 28.1875px; text-align: center; height: 18px;\" bgcolor=\"#ddd\">4</td>\n<td style=\"width: 112.531px; height: 18px; text-align: left;\">{item2}</td>\n<td style=\"width: 119.562px; text-align: center; height: 18px; border: 2px solid black;\"></td>\n<td style=\"width: 99.4688px; text-align: center; height: 18px;\">$\\var{cost2}$</td>\n<td style=\"width: 84.25px; text-align: center; height: 18px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 28.1875px; text-align: center; height: 18px;\" bgcolor=\"#ddd\">5</td>\n<td style=\"width: 112.531px; height: 18px; text-align: left;\"></td>\n<td style=\"width: 119.562px; text-align: center; height: 18px;\"></td>\n<td style=\"width: 99.4688px; text-align: center; height: 18px;\"></td>\n<td style=\"width: 84.25px; text-align: center; height: 18px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 28.1875px; text-align: center; height: 18px;\" bgcolor=\"#ddd\">6</td>\n<td style=\"width: 112.531px; height: 18px; text-align: left;\">{item3}</td>\n<td style=\"width: 119.562px; text-align: center; height: 18px; border: 2px solid black;\"></td>\n<td style=\"width: 99.4688px; text-align: center; height: 18px;\">$\\var{cost3}$</td>\n<td style=\"width: 84.25px; text-align: center; height: 18px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 28.1875px; text-align: center; height: 18px;\" bgcolor=\"#ddd\">7</td>\n<td style=\"width: 112.531px; height: 18px; text-align: left;\"></td>\n<td style=\"width: 119.562px; text-align: center; height: 18px;\"></td>\n<td style=\"width: 99.4688px; text-align: center; height: 18px;\"></td>\n<td style=\"width: 84.25px; text-align: center; height: 18px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 28.1875px; text-align: center; height: 18px;\" bgcolor=\"#ddd\">8</td>\n<td style=\"width: 112.531px; height: 18px; text-align: left;\"></td>\n<td style=\"width: 119.562px; text-align: center; height: 18px;\"></td>\n<td style=\"width: 99.4688px; text-align: center; height: 18px;\"></td>\n<td style=\"width: 84.25px; text-align: center; height: 18px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 28.1875px; text-align: center; height: 18px;\" bgcolor=\"#ddd\">9</td>\n<td style=\"width: 112.531px; height: 18px; text-align: left;\"><strong>Total cost ($)</strong></td>\n<td style=\"width: 119.562px; text-align: center; height: 18px; border: 2px solid black;\"></td>\n<td style=\"width: 99.4688px; text-align: center; height: 18px;\"></td>\n<td style=\"width: 84.25px; text-align: center; height: 18px;\"></td>\n</tr>\n</tbody>\n</table>\n<p><strong>About spreadsheets:<br/></strong>Each cell is referred to by the column letter and row number.<br/>For example, REFER TO A CELL.<br/>The symbol * stands for multiplication.<br/>The symbol / stands for division.</p>\n<p></p>\n<p>Which formula can be used to find the total cost in cell B9?</p>", "stepsPenalty": "1", "steps": [{"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>Consider the first material. Each cubic metre of it costs $\\$\\var{cost1}$. If we order 2 cubic metres, it will cost $2\\times\\$\\var{cost1}$. If we order 3 cubic metres, it will cost $3\\times\\$\\var{cost1}$. In general, the cost will be \"the number of cubic metres\" multiplied by \"the cost per cubic metre\".</p>\n<p>The same can be said about the other materials.&nbsp;</p>\n<p>We can then add up those three costs.</p>\n<p>Therefore, in cell B9 we would input</p>\n<p>&nbsp;= B2*C2+B4*C4+B6*C6</p>"}], "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": ["&nbsp;= B2*C2+C3*D3+D4*E4", "&nbsp;= (B2+B4+B6)*(C2+C4+C6)", "&nbsp;= C2+C4+C6", "&nbsp;= B2*C2+B4*C4+B6*C6", "I'm not sure"], "matrix": [0, 0, 0, "1", 0], "distractors": ["These are not the cells you are looking for", "", "This would be the cost of one cubic metre of each", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Creating formula: Cost of phone calls", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"list": {"name": "list", "group": "Ungrouped variables", "definition": "shuffle([\n  [\"BANGLADESH\",0.40, 1.96, 2.26], \n  [\"HAITI\", 0.40, 2.93, 2.93],\n  [\"SWITZERLAND\", 0.40, 0.75, 1.31],\n  [\"FRANCE\", 0.40, 0.75, 1.31],\n  [\"BRAZIL\", 0.40, 1.31, 1.58],\n  [\"ARGENTINA\", 0.40 ,1.31, 1.58],\n  [\"IRAN\", 0.40 ,1.39, 1.61],\n  [\"GERMANY\", 0.40, 0.75, 1.31],\n  [\"UNITED KINGDOM\", 0.40, 0.55 ,1.13],\n  [\"NEW ZEALAND\", 0.40 , 0.44,  1.03],\n  [\"KOREA REPUBLIC OF\", 0.40, 1.01, 1.31],\n  [\"JAPAN\", 0.40, 0.75, 1.31],\n  [\"SINGAPORE\", 0.40, 0.69 ,1.04],\n  [\"BARBADOS\", 0.40, 1.96, 1.97],\n[\"HAWAII\", 0.40, 0.44, 0.45],\n[\"IRAQ\", 0.40, 2.32, 2.33],\n[\"CANADA\", 0.40, 0.64, 0.65],\n[\"SPAIN\", 0.40, 2.52 ,2.53],\n[\"COSTA RICA\", 0.40, 2.10, 2.12],\n[\"ANTARCTICA\", 0.40, 0.81, 0.82]\n])[0..4]", "description": "<p>https://www.telstra.com.au/mobile-phones/calling-overseas-from-australia</p>", "templateType": "anything", "can_override": false}, "type": {"name": "type", "group": "Ungrouped variables", "definition": "if(type_seed=2, 'fixed line', 'international (non-roaming) mobile')", "description": "", "templateType": "anything", "can_override": false}, "country": {"name": "country", "group": "Ungrouped variables", "definition": "random(list)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "len(country[0])+1", "description": "", "templateType": "anything", "can_override": false}, "type_seed": {"name": "type_seed", "group": "Ungrouped variables", "definition": "random(2,3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["list", "country", "type_seed", "type", "n"], "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>A phone company charges the following rates for the following destinations.</p>\n<p></p>\n<table class=\"table\" style=\"height: 162px; width: 620px;\">\n<tbody>\n<tr style=\"height: 36px;\">\n<th rowspan=\"2\" style=\"width: 171.312px; height: 90px;\">Destination</th>\n<th rowspan=\"2\" style=\"width: 114.938px; height: 90px;\">Connection Fee<br/>(inc GST)</th>\n<th colspan=\"2\" style=\"width: 284.75px; height: 36px;\">Voice Call Rates<br/>(per minute)<a class=\"close\" onclick=\"tcom.callratecalc.removeCountry('BARBADOS'); return false;\" href=\"https://www.telstra.com.au/mobile-phones/calling-overseas-from-australia#\"></a></th>\n</tr>\n<tr style=\"height: 54px;\">\n<th style=\"width: 137.078px; height: 54px;\">to Fixed Line<br/>(inc GST)</th>\n<th style=\"width: 131.672px; height: 54px;\">to an International<br/>(non-roaming) Mobile<br/>(inc GST)</th>\n</tr>\n<tr style=\"height: 18px;\">\n<td class=\"heading-shade-2\" style=\"width: 171.312px; height: 18px; text-align: left;\"><strong>{list[0][0]}</strong></td>\n<td style=\"width: 114.938px; height: 18px; text-align: left;\">\\${list[0][1]}</td>\n<td style=\"width: 137.078px; height: 18px; text-align: left;\">\\${list[0][2]}</td>\n<td style=\"width: 131.672px; height: 18px; text-align: left;\">\\${list[0][3]}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td class=\"heading-shade-2\" style=\"width: 171.312px; height: 18px; text-align: left;\"><strong>{list[1][0]}</strong></td>\n<td style=\"width: 114.938px; height: 18px; text-align: left;\">\\${list[1][1]}</td>\n<td style=\"width: 137.078px; height: 18px; text-align: left;\">\\${list[1][2]}</td>\n<td style=\"width: 131.672px; height: 18px; text-align: left;\">\\${list[1][3]}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 171.312px; height: 18px; text-align: left;\"><strong>{list[2][0]}</strong></td>\n<td style=\"width: 114.938px; height: 18px; text-align: left;\">\\${list[2][1]}</td>\n<td style=\"width: 137.078px; height: 18px; text-align: left;\">\\${list[2][2]}</td>\n<td style=\"height: 18px; width: 131.672px; text-align: left;\">\\${list[2][3]}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 171.312px; height: 18px; text-align: left;\"><strong>{list[3][0]}</strong></td>\n<td style=\"width: 114.938px; height: 18px; text-align: left;\">\\${list[3][1]}</td>\n<td style=\"width: 137.078px; height: 18px; text-align: left;\">\\${list[3][2]}</td>\n<td style=\"height: 18px; width: 131.672px; text-align: left;\">\\${list[3][3]}</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>In the field below, enter the formula for the cost, $C$, of a phone call (in dollars) to a<span data-jme-visible=\"type_seed=3\">n</span> {type} in {country[0][0]+lower(country[0][1..n])} for $m$ minutes.&nbsp;</p>\n<p></p>\n<p>[[0]]</p>\n<p><strong>Note 1:</strong> The warning \"Not enough arguments for operation ...\" simply means you haven't finished yet!&nbsp;</p>\n<p><strong>Note 2:</strong> You shouldn't leave off the first zero of a decimal</p>\n<p><strong>Note 3:</strong> You can use * for multiplication</p>", "stepsPenalty": "1", "steps": [{"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>You need to make sense of the table.</p>\n<p>Find the row that corresponds to {country[0][0]+lower(country[0][1..n])}. Notice that there is a connection fee of $\\$\\var{country[1]}$.</p>\n<p>Find the column for the type of phone to be rung, i.e. {type}. The cell at the intersection of the row and column of interest is the charge per minute, in your case $\\$\\var{country[type_seed]}$ per minute. Since for each minute, we get another $\\$\\var{country[type_seed]}$ charge, it should make sense that we multiply the charge per minute and the number of minutes ($m$).</p>\n<p></p>\n<p>Generally, we would write something like</p>\n<p>$C=\\var{country[1]}+\\var{country[type_seed]}m$.</p>\n<p>Entering into a computer, we would generally write something like&nbsp;</p>\n<p>$C=\\var{country[1]}+\\var{country[type_seed]}^* m$.</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": "C={country[1]}+{country[type_seed]}m", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "m", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Creating formulas: taxi fare", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>A taxi fare is made up of different charges.</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"peak_b": {"name": "peak_b", "group": "part b", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}, "night_b": {"name": "night_b", "group": "part b", "definition": "if(peak_b=1, 1, random(0,1))", "description": "<p>in urban, peak is always night</p>", "templateType": "anything", "can_override": false}, "second_distance_rate": {"name": "second_distance_rate", "group": "part a", "definition": "if(type_a=0,3.23, 3.85)", "description": "<ul>\n<li><span data-jme-visible=\"urban=1\"><strong>Hire&nbsp;charge:</strong> \\$3.60</span></li>\n<li><span data-jme-visible=\"urban=1\"><strong>Peak time hire charge:</strong> \\$2.50&nbsp;(in addition to the hire charge,&nbsp;10pm&nbsp;&ndash;&nbsp;6am on Friday's, Saturday's, and evening prior to&nbsp;Public Holidays),&nbsp;</span></li>\n<li><span data-jme-visible=\"urban=1\"><strong>Distance rate:</strong> \\$2.29 per kilometre</span></li>\n<li><span data-jme-visible=\"urban=1\"><strong>Night distance rate:</strong> \\$2.73 per kilometre (trips between&nbsp;10pm &ndash; 6am)</span></li>\n<li><span data-jme-visible=\"urban=1\"><strong>Waiting time:</strong> \\$56.68 per hour while vehicle speed is less than 26 km/h</span></li>\n<li><span data-jme-visible=\"urban=1\"><strong>Cleaning fee:&nbsp;</strong>if you dirty the taxi, you may be charged up to \\$120</span></li>\n<li><span data-jme-visible=\"urban=1\"><strong>Passenger Service Levy:</strong> \\$1.32 will be added to your fare if the service provider elects to pass on the cost of the levy to their passengers.</span></li>\n</ul>\n<p><span data-jme-visible=\"urban=0\">Here are the maximum amounts that rank and hail taxi's can charge when travelling in <em>country areas</em>.</span></p>\n<ul>\n<li><span data-jme-visible=\"urban=0\"><strong>Hire charge:</strong> \\$4.10</span></li>\n<li><span data-jme-visible=\"urban=0\"><strong>Distance rate:</strong> \\$2.36 per kilometre for the first 12km, then \\$3.23 per kilometre thereafter</span></li>\n<li><span data-jme-visible=\"urban=0\"><strong>Night distance rate:</strong> \\$2.81 per kilometre for the first 12km, then \\$3.85 per kilometre thereafter from 10pm &ndash; 6am)</span></li>\n<li><span data-jme-visible=\"urban=0\"><strong>Holiday distance rate:</strong> \\$2.81 per kilometre for the first 12km, then \\$3.85 per kilometre thereafter (6am to 10pm on Sundays and Public Holidays.)</span></li>\n<li><span data-jme-visible=\"urban=0\"><strong>Waiting time:</strong> \\$57.65 per hour while vehicle speed is less than 26 km/h</span></li>\n<li><span data-jme-visible=\"urban=0\"><strong>Cleaning fee:&nbsp;</strong>if you dirty the taxi, you may be charged up to \\$120</span></li>\n<li><span data-jme-visible=\"urban=0\"><strong>Passenger Service Levy:</strong> \\$1.32 will be added to your fare if the service provider elects to pass on the cost of the levy to their passengers.</span></li>\n</ul>", "templateType": "anything", "can_override": false}, "first_distance_rate": {"name": "first_distance_rate", "group": "part a", "definition": "if(type_a=0,2.36, 2.81)", "description": "", "templateType": "anything", "can_override": false}, "mess_a": {"name": "mess_a", "group": "part a", "definition": "random(0,0,0,0,1)", "description": "", "templateType": "anything", "can_override": false}, "type_a": {"name": "type_a", "group": "part a", "definition": "random(0,1,2)", "description": "<p>0 = standard</p>\n<p>1 = night</p>\n<p>2 = holiday</p>", "templateType": "anything", "can_override": false}, "mess_b": {"name": "mess_b", "group": "part b", "definition": "if(night_b=1, random(0,1),0)", "description": "", "templateType": "anything", "can_override": false}, "distance_rate_b": {"name": "distance_rate_b", "group": "part b", "definition": "if(night_b=0, 2.29, 2.73)", "description": "", "templateType": "anything", "can_override": false}, "cleaning_fee_b": {"name": "cleaning_fee_b", "group": "part b", "definition": "if(mess_b=0,0,random(60,90,120))", "description": "", "templateType": "anything", "can_override": false}, "cleaning_fee_a": {"name": "cleaning_fee_a", "group": "part a", "definition": "if(mess_a=0,0,random(60,90,120))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "part a", "variables": ["type_a", "first_distance_rate", "second_distance_rate", "mess_a", "cleaning_fee_a"]}, {"name": "part b", "variables": ["peak_b", "night_b", "mess_b", "distance_rate_b", "cleaning_fee_b"]}], "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>Here are the amounts a rank and hail taxi can charge when travelling in <em>urban&nbsp;areas</em>.</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<td>\n<ul>\n<li style=\"text-align: left;\"><strong>Hire&nbsp;charge:</strong> \\$3.60</li>\n<li style=\"text-align: left;\"><strong>Peak time hire charge:</strong> \\$2.50 (in addition to the hire charge, 10 pm &ndash; 6 am on Fridays, Saturdays, and evenings prior to Public Holidays),&nbsp;</li>\n<li style=\"text-align: left;\"><strong>Distance rate:</strong> \\$2.29 per kilometre</li>\n<li style=\"text-align: left;\"><strong>Night distance rate:</strong> \\$2.73 per kilometre (trips between 10 pm &ndash; 6 am)</li>\n<li style=\"text-align: left;\"><strong>Waiting time:</strong> \\$56.68 per hour while vehicle speed is less than 26 km/h</li>\n<li style=\"text-align: left;\"><strong>Cleaning fee:&nbsp;</strong>if you dirty the taxi, you may be charged up to \\$120</li>\n<li style=\"text-align: left;\"><strong>Passenger Service Levy:</strong> \\$1.32 will be added to your fare if the service provider elects to pass on the cost of the levy to their passengers.</li>\n</ul>\n</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>In the field below, enter the formula for the cost in dollars, $C$, of</p>\n<ul>\n<li>hiring a taxi in an <em>urban area</em>,&nbsp;</li>\n<li><span data-jme-visible=\"peak_b=0\"><em>outside of</em></span> <span data-jme-visible=\"peak_b=1\"><em>during</em></span> peak time</li>\n<li>for a <span data-jme-visible=\"night_b=0\"><em>day</em></span><span data-jme-visible=\"night_b=1\"><em>night</em></span> trip of $D$ km,</li>\n<li>with $W$ <em>minutes</em> of waiting time,</li>\n<li><em>with</em><span data-jme-visible=\"mess_b=0\"><em>out</em></span> a cleaning fee<span data-jme-visible=\"mess_b=1\"> of $\\$\\var{cleaning_fee_b}$</span>,</li>\n<li>and <em>including</em> the passenger service levy.</li>\n</ul>\n<p>[[0]]</p>\n<p><strong>Note:</strong> You can use * for multiplication and / for division.</p>\n<p></p>", "stepsPenalty": "1", "steps": [{"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>The cost will be made up of a hire charge of $\\$3.60$<span data-jme-visible=\"peak_b=1\">, an additional peak time hire charge of $\\$2.50$</span><span data-jme-visible=\"mess_b=1\">, a cleaning fee of $\\$\\var{cleaning_fee_b}$</span>, a passenger levy of $\\$1.32$, a cost of $\\var{distance_rate_b}$ for <i>each kilometre</i>&nbsp;and a cost of $\\$56.68$ for<em> each hour.&nbsp;</em></p>\n<p>Note the number of hours of waiting time is $\\frac{W}{60}$.</p>\n<p>Therefore, the formula can be written as</p>\n<p>$C=\\simplify[all]{3.60+1.32+{peak_b}*2.5+{distance_rate_b}*D+W/60*56.68+{cleaning_fee_b}}$</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": "C=3.60+1.32+{peak_b}*2.5+{distance_rate_b}*D+W/60*56.68+{cleaning_fee_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": [{"name": "c", "value": ""}, {"name": "d", "value": ""}, {"name": "w", "value": ""}]}], "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>Here are the amounts a rank and hail taxi can charge when travelling in <em>country areas</em>.</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<td>\n<ul>\n<li style=\"text-align: left;\"><strong>Hire charge:</strong> \\$4.10</li>\n<li style=\"text-align: left;\"><strong>Distance rate:</strong> \\$2.36 per kilometre for the first 12km, then \\$3.23 per kilometre thereafter</li>\n<li style=\"text-align: left;\"><strong>Night distance rate:</strong> \\$2.81 per kilometre for the first 12km, then \\$3.85 per kilometre thereafter (10 pm to 6 am)</li>\n<li style=\"text-align: left;\"><strong>Holiday distance rate:</strong> \\$2.81 per kilometre for the first 12km, then \\$3.85 per kilometre thereafter (6 am to 10 pm on Sundays and Public Holidays.)</li>\n<li style=\"text-align: left;\"><strong>Waiting time:</strong> \\$57.65 per hour while vehicle speed is less than 26 km/h</li>\n<li style=\"text-align: left;\"><strong>Cleaning fee:&nbsp;</strong>if you dirty the taxi, you may be charged up to \\$120</li>\n<li style=\"text-align: left;\"><strong>Passenger Service Levy:</strong> \\$1.32 will be added to your fare if the service provider elects to pass on the cost of the levy to their passengers.</li>\n</ul>\n</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>In the field below, enter the formula for the cost in dollars, $C$, of</p>\n<ul>\n<li>hiring a taxi in a <em>country area</em>,</li>\n<li>for a <em><span data-jme-visible=\"type_a=0\">standard</span><span data-jme-visible=\"type_a=1\">night</span><span data-jme-visible=\"type_a=2\">holiday</span></em>&nbsp;trip of $D$ km, where we know $D$ is <em>less than</em> $12$ km,</li>\n<li>with $W$ <em>minutes</em> of waiting time,</li>\n<li><em>with</em><span data-jme-visible=\"mess_a=0\"><em>out</em></span> a cleaning fee<span data-jme-visible=\"mess_a=1\"> of $\\$\\var{cleaning_fee_a}$</span>,</li>\n<li>and <em>including</em> the passenger service levy.</li>\n</ul>\n<p>[[0]]</p>\n<p><strong>Note:</strong> You can use * for multiplication and / for division.</p>", "stepsPenalty": "1", "steps": [{"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>The cost will be made up of a hire charge of $\\$4.10$<span data-jme-visible=\"mess_a=1\">, a cleaning fee of $\\$\\var{cleaning_fee_a}$</span>, a passenger levy of $\\$1.32$, a cost of $\\$\\var{first_distance_rate}$ for <i>each kilometre</i>, and a cost of $\\$57.65$ for <em>each hour.&nbsp;</em></p>\n<p>Note the number of hours of waiting time is $\\frac{W}{60}$.</p>\n<p>Therefore, the formula can be written as</p>\n<p>$C=\\simplify[all]{4.1+{first_distance_rate}*D+W/60*57.65+1.32+{cleaning_fee_a}}$</p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "C=4.1+{first_distance_rate}*D+W/60*57.65+1.32+{cleaning_fee_a}", "answerSimplification": "all", "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": "c", "value": ""}, {"name": "d", "value": ""}, {"name": "w", "value": ""}]}], "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>In the field below, enter the formula for the cost in dollars, $C$, of the same scenario as part b above <em>except the distance $D$ is now greater than $12$ km</em>.</p>\n<p>[[0]]</p>\n<p><strong>Note:</strong> You can use * for multiplication and / for division.</p>", "stepsPenalty": "1", "steps": [{"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>The cost will be made up of a hire charge of $\\$4.10$<span data-jme-visible=\"mess_a=1\">, a cleaning fee of $\\$\\var{cleaning_fee_a}$</span>, a passenger levy of $\\$1.32$, a cost of $\\$\\var{first_distance_rate}$ for $12$ kilometres, a cost of $\\$\\var{second_distance_rate}$ for the <em>remaining</em> kilometres, and a cost of $\\$57.65$ for <em>each hour.&nbsp;</em></p>\n<p>Note the number of hours of waiting time is $\\frac{W}{60}$.</p>\n<p>Note the <em>remaining</em> kilometres would be $D-12$.</p>\n<p>Therefore, the formula can be written as</p>\n<p>$C=\\simplify[all]{4.1+{first_distance_rate}*12+{second_distance_rate}*(D-12)+W/60*57.65+1.32+{cleaning_fee_a}}$</p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "C=4.1+{first_distance_rate}*12+{second_distance_rate}*(D-12)+W/60*57.65+1.32+{cleaning_fee_a}", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", 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"", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"cpl": {"name": "cpl", "group": "Ungrouped variables", "definition": "190+random(-25..25#0.1)", "description": "", "templateType": "anything", "can_override": false}, "distance": {"name": "distance", "group": "Ungrouped variables", "definition": "random(100..600#100)", "description": "", "templateType": "anything", "can_override": false}, "litres": {"name": "litres", "group": "Ungrouped variables", "definition": "litres_per_100km*distance*0.01", "description": "", "templateType": "anything", "can_override": false}, "litres_per_100km": {"name": "litres_per_100km", "group": "Ungrouped variables", "definition": "random(4..14#0.1)", "description": "", "templateType": "anything", "can_override": false}, "swap": {"name": "swap", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["cpl", "distance", "litres", "litres_per_100km", "swap"], "variable_groups": [], "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": "<p><span data-jme-visible=\"swap=0\">A certain vehicle uses $\\var{litres}$ L of petrol to drive $\\var{distance}$ km. If petrol costs $\\var{cpl}$ cents per litre. Which formula would estimate the cost $C$, in dollars, of driving $d$ kilometres?&nbsp;&nbsp;</span><span data-jme-visible=\"swap=0\"></span></p>\n<p><span data-jme-visible=\"swap=1\">Suppose petrol costs $\\var{cpl}$ c/L and a certain vehicle can drive $\\var{distance}$ km using $\\var{litres}$ L of petrol.</span></p>\n<p><span data-jme-visible=\"swap=1\">Which formula would estimate the cost $C$, in dollars, of driving $d$ kilometres?&nbsp;&nbsp;</span></p>", "stepsPenalty": "1", "steps": [{"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>A certain vehicle uses $\\var{litres}$ L of petrol to drive $\\var{distance}$ km. If petrol costs $\\var{cpl}$ cents per litre. Which formula would estimate the cost $C$, in dollars, of driving $d$ kilometres?&nbsp;</p>\n<p>We want the cost of driving $d$ kilometres.</p>\n<p>If we find the cost of driving $1$ kilometre, then we could multiply that by $d$, to get what we want.</p>\n<p>Since the vehicle uses $\\var{litres}$ L to drive $\\var{distance}$ km, we can divide both numbers by $\\var{distance}$ to find the vehicle uses $\\frac{\\var{litres}}{\\var{distance}}$ L to drive $1$ km. That is, it gets $\\frac{\\var{litres}}{\\var{distance}}$ L/km.</p>\n<p>Note, at this point, we could write</p>\n<p>$\\text{Petrol usage (in litres)} = \\frac{\\var{litres}}{\\var{distance}} \\times d$.</p>\n<p>We want the cost, so we could multiply the petrol usage (in litres) by the cost per litre</p>\n<p>$\\text{Cost (in cents)} = \\var{cpl}\\times \\frac{\\var{litres}}{\\var{distance}} \\times d$,</p>\n<p>but this would be in cents, not dollars! So we divide the cost per litre by $100$ so that it is cost (in dollars) per litre, and we can write</p>\n<p>$C = \\frac{\\var{cpl}}{100} \\times \\frac{\\var{litres}}{\\var{distance}} d$.</p>"}], "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": ["<p>$C = \\frac{\\var{cpl}}{100} \\times \\frac{\\var{litres}}{\\var{distance}} \\times d$</p>", "<p>$C = \\var{cpl}\\times \\frac{\\var{litres}}{\\var{distance}} \\times d$</p>", "<p>$C = \\frac{\\var{cpl}}{100} \\times \\frac{\\var{distance}}{\\var{litres}} \\times d$</p>", "$C = \\var{cpl}\\times \\frac{\\var{distance}}{\\var{litres}} \\times d$", "I'm not sure"], "matrix": ["1", 0, 0, 0, 0], "distractors": ["", "This would result in the cost in cents.", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": false, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": "", "allowAttemptDownload": false, "downloadEncryptionKey": ""}, "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": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "extensions": ["geogebra"], "custom_part_types": [], "resources": []}