// Numbas version: exam_results_page_options
{"question_groups": [{"name": "Group", "pickQuestions": 1, "pickingStrategy": "all-ordered", "questions": [{"name": "Calculating a simple rate of pay", "extensions": ["random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}], "tags": ["compound units", "Compound units", "rate of pay", "taxonomy"], "metadata": {"description": "<p>Calculate a rate of pay (in pounds per week) given the total pay over a given period of time.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>{pname} gets paid a total of $&pound;\\var{payment}$ at the end of {their} summer job; {they} work{s} for $\\var{weeks}$ weeks.</p>", "advice": "<p>We are told that {pname} gets paid a total of&nbsp;$&pound;\\var{payment}$&nbsp;at the end of {their} summer job and that {they} work{s} at {their} job for $\\var{weeks}$ weeks.</p>\n<p>To calculate the amount of money {pname} gets paid per week, we divide the total amount of money that {they} earn{s} at the end of {their} job by how many weeks that {they} work{s} for.</p>\n<p>\\[&pound;\\displaystyle\\frac{\\var{payment}}{\\var{weeks}} = &pound;\\var{{payment/weeks}}.\\]</p>\n<p>Therefore {pname} gets paid $&pound;\\var{{payment/weeks}}$/week.</p>\n<p>Note that in compound measures, a forward slash symbol / is often used instead of the word 'per'. So $&pound;\\var{{payment/weeks}}$/week means the same as $&pound;\\var{{payment/weeks}}$ per week.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"person": {"name": "person", "group": "A person", "definition": "random_person()", "description": "<p>A random person</p>", "templateType": "anything", "can_override": false}, "weeks": {"name": "weeks", "group": "Ungrouped variables", "definition": "random(5,8)", "description": "<p>Number of weeks person works for</p>", "templateType": "anything", "can_override": false}, "payment": {"name": "payment", "group": "Ungrouped variables", "definition": "random(1400,1600,1800)", "description": "<p>amount person gets paid</p>", "templateType": "anything", "can_override": false}, "pname": {"name": "pname", "group": "A person", "definition": "person[\"name\"]", "description": "", "templateType": "anything", "can_override": false}, "they": {"name": "they", "group": "A person", "definition": "person[\"pronouns\"][\"they\"]", "description": "", "templateType": "anything", "can_override": false}, "their": {"name": "their", "group": "A person", "definition": "person[\"pronouns\"][\"their\"]", "description": "", "templateType": "anything", "can_override": false}, "theirs": {"name": "theirs", "group": "A person", "definition": "person[\"pronouns\"][\"theirs\"]", "description": "", "templateType": "anything", "can_override": false}, "s": {"name": "s", "group": "A person", "definition": "if(person[\"gender\"]=\"neutral\",\"\",\"s\")", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["payment", "weeks"], "variable_groups": [{"name": "A person", "variables": ["person", "pname", "they", "their", "theirs", "s"]}], "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>How much does {pname} get paid per week?</p>\n<p>&pound;[[0]]/week</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": "{payment}/{weeks}", "maxValue": "{payment}/{weeks}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Rounding and estimating calculations - adding up prices in a shop", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "type": "question", "tags": ["random names", "taxonomy"], "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"cash": {"templateType": "anything", "name": "cash", "description": "<p>Amount of cash we have.</p>", "definition": "if(can_afford,\n  ceil(total_rounded_up)\n  ,\n  ceil(sum(p)+ice_cream)-1\n)\n  ", "group": "Randoms"}, "can_afford": {"templateType": "anything", "name": "can_afford", "description": "<p>Can we afford all three items?</p>", "definition": "random(true,false)", "group": "Randoms"}, "total_rounded_up": {"templateType": "anything", "name": "total_rounded_up", "description": "<p>Total price of the three items when&nbsp;rounding up.</p>", "definition": "precround(p[0]+0.05,1) + precround(p[1]+0.05,1) + precround(ice_cream,1)", "group": "Randoms"}, "flavour": {"templateType": "anything", "name": "flavour", "description": "<p>Flavour of the ice cream.</p>", "definition": "random(\"strawberry cheesecake\", \"cookie dough\", \"mint chocolate chip\", \"vanilla\", \"raspberry\", \"Neapolitan\")", "group": "Randoms"}, "ice_cream": {"templateType": "anything", "name": "ice_cream", "description": "<p>Price of the ice cream</p>", "definition": "(random(100..380#10)+9)/100", "group": "Randoms"}, "p": {"templateType": "anything", "name": "p", "description": "<p>Prices of the first two items.</p>", "definition": "repeat((random(30..200 #10) + random(1..9))/100,2)", "group": "Randoms"}}, "functions": {"pounds": {"parameters": [["n", "number"]], "type": "string", "language": "jme", "definition": "if(n>=1,currency(n,\"\u00a3\",\"\"), \"\u00a3\"+dpformat(n,2))"}}, "statement": "<p>Imagine you are shopping&nbsp;at the&nbsp;supermarket. You only have &pound;{cash}&nbsp;in cash.&nbsp;There are&nbsp;two items in your&nbsp;basket so far, costing {currency(p[0],\"&pound;\",\"p\")} and {currency(p[1],\"&pound;\",\"p\")}.</p>\n<p>Just before checkout, you notice a tasty&nbsp;{flavour}&nbsp;ice cream on the shelf. It costs {currency(ice_cream,\"&pound;\",\"p\")}. Can you put this in your&nbsp;basket without going over your limit?</p>", "variable_groups": [{"name": "Randoms", "variables": ["p", "ice_cream", "total_rounded_up", "can_afford", "cash", "flavour"]}, {"name": "Answers", "variables": []}], "parts": [{"scripts": {}, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "gaps": [{"displayColumns": 0, "minMarks": 0, "distractors": ["", ""], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "choices": ["<p>Round up.</p>", "<p>Round down.</p>"], "showFeedbackIcon": true, "shuffleChoices": false, "matrix": ["1", "0"], "variableReplacements": [], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "maxMarks": 0, "type": "1_n_2"}], "showCorrectAnswer": true, "prompt": "<p>If we don't want to underestimate the total price of these items, do&nbsp;we round the individual prices up, or down?</p>\n<p>[[0]]<em></em></p>", "type": "gapfill"}, {"scripts": {}, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "gaps": [{"correctAnswerFraction": false, "precisionMessage": "You have not given your answer to the correct precision.", "precisionPartialCredit": 0, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "precision": "2", "precisionType": "dp", "maxValue": "total_rounded_up", "showFeedbackIcon": true, "minValue": "total_rounded_up", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "showPrecisionHint": false, "marks": 1, "variableReplacements": [], "strictPrecision": false, "showCorrectAnswer": true}], "showCorrectAnswer": true, "prompt": "<p>Estimate the total price if we buy the ice cream, rounding the price of each item to <strong>1 decimal place</strong>.</p>\n<p>&pound; [[0]]</p>\n<p></p>", "type": "gapfill"}, {"scripts": {}, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "gaps": [{"displayColumns": 0, "minMarks": 0, "type": "1_n_2", "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "choices": ["<p>Yes, we do have enough cash.</p>", "<p>No, we may not have enough.</p>"], "showFeedbackIcon": true, "shuffleChoices": false, "matrix": "if(can_afford,[1,0],[0,1])", "variableReplacements": [], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "maxMarks": 0}], "showCorrectAnswer": true, "prompt": "<p>Can&nbsp;we be sure that we&nbsp;have enough cash to pay for all three items?</p>\n<p>[[0]]</p>", "type": "gapfill"}], "ungrouped_variables": [], "rulesets": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Estimate whether you can afford an extra item in a shop by rounding prices to the nearest 10p.</p>"}, "preamble": {"css": "", "js": ""}, "advice": "<h4>a)</h4>\n<p>We want to ensure we won't go over the limit, so it is better to overestimate. If we underestimated, we could potentially think we have enough money when we don't.</p>\n<p>To overestimate our total, we round each price&nbsp;<strong>up</strong>.</p>\n<h4>b)</h4>\n<p><em></em>We round up all our values to 1 decimal place:</p>\n<table>\n<tbody>\n<tr>\n<th>Original prices</th>\n<td>&pound;{p[0]}</td>\n<td>&pound;{p[1]}</td>\n<td>&pound;{ice_cream}</td>\n</tr>\n<tr>\n<th>Rounded up</th>\n<td>{pounds(precround(p[0]+0.05,1))}</td>\n<td>{pounds(precround(p[1]+0.05,1))}</td>\n<td>{pounds(precround(ice_cream,1))}</td>\n</tr>\n</tbody>\n</table>\n<p>Now we calculate the total of these rounded numbers:</p>\n<p>\\[ \\var{pounds(precround(p[0]+0.05,1))} + \\var{pounds(precround(p[1]+0.05,1))} + \\var{pounds(precround(ice_cream,1))} = \\var{pounds(total_rounded_up)}&nbsp;\\]</p>\n<h4>c)</h4>\n<p><em></em>As the estimated&nbsp;total, &pound;{dpformat(total_rounded_up,2)}, is {if(can_afford,'lower','higher')} than &pound;{cash}, we {if(can_afford,'do have','may not have')} enough money to purchase the {flavour} ice cream.</p>"}, {"name": "Partial sum of an arithmetic sequence - birthday money", "extensions": ["random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Hannah Aldous", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1594/"}], "variable_groups": [{"variables": ["person", "pronouns"], "name": "A person"}], "functions": {}, "rulesets": {}, "ungrouped_variables": ["m", "n", "c", "ci", "ni", "b", "first"], "metadata": {"description": "<p>The amount of money a person gets on their birthday&nbsp;follows an arithmetic sequence.</p>\n<p>Calculate the amount&nbsp;on a given birthday, then calculate the sum up to that point.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "advice": "<p>We are told that {person['name']}'s parents&nbsp;deposit a uniformly&nbsp;increasing&nbsp;amount of money into&nbsp;a savings account&nbsp;for {person['name']} every&nbsp;year on&nbsp;{person['name']}'s&nbsp;birthday.</p>\n<p>We are&nbsp;also given the amount of money that&nbsp;{person['pronouns']['their']} parents deposit into the account&nbsp;on&nbsp;{person['pronouns']['their']} first $3$ birthdays:</p>\n<ul>\n<li>On {person['pronouns']['their']}&nbsp;$1^{st}$ birthday, they deposited $&pound;\\var{first}$ into the account.</li>\n<li>On {person['pronouns']['their']}&nbsp;$2^{nd}$ birthday, they deposited $&pound;\\var{b[1]+first}$ into the account.</li>\n<li>On {person['pronouns']['their']}&nbsp;$3^{rd}$ birthday, they deposited $&pound;\\var{b[1]*2+first}$ into the account.</li>\n</ul>\n<h4>a)</h4>\n<p>To calculate the&nbsp;amount of money&nbsp;{person['name']}'s parents&nbsp;would deposit&nbsp;into the savings account on&nbsp;{person['pronouns']['their']} 21<sup>st</sup>&nbsp;birthday, if {pronouns['their']} parents maintained this pattern, we&nbsp;use the equation</p>\n<p>\\[a_n=a_1+(n-1)d\\text{,}\\]</p>\n<p>where</p>\n<ul>\n<li>$a_1$ is the first&nbsp;term;</li>\n<li>$a_n$ is the $n^{\\text{th}}$ term;</li>\n<li>$d$ is the common difference between consecutive terms.</li>\n</ul>\n<p>To identify the first term and common difference of the sequence we can use a table like the one below.</p>\n<table border=\"1\">\n<thead></thead>\n<tbody>\n<tr>\n<th>$n$</th>\n<td>$1$</td>\n<td>$2$</td>\n<td>$3$</td>\n</tr>\n<tr>\n<th>$a_n$</th>\n<td>$\\mathbf{\\var{first}}$</td>\n<td>$\\var{b[1]+first}$</td>\n<td>$\\var{b[1]*2+first}$</td>\n</tr>\n<tr>\n<th>First differences</th>\n<td></td>\n<td>$\\mathbf{\\var{b[1]}}$</td>\n<td>$\\mathbf{\\var{b[1]}}$</td>\n</tr>\n</tbody>\n</table>\n<p>The first term&nbsp;and common difference have been highlighted in bold: $a_1 = \\var{first}$ and $d = \\var{b[1]}$.</p>\n<p>Now we&nbsp;can use these to calculate $a_{21}$, giving us</p>\n<p>\\begin{align}<br/>a_{21}&amp;=\\var{first}+\\var{b[1]} \\times (21-1) \\\\<br/>&amp;=\\var{first+b[1]*(20)}\\text{.} \\\\<br/>\\end{align}</p>\n<p>So, assuming that {person['name']}'s parents do maintain this pattern, on {pronouns['their']}&nbsp;21<sup>st</sup>&nbsp;birthday {pronouns['their']} parents will&nbsp;deposit $&pound;\\var{first+b[1]*(20)}$ into the savings account.</p>\n<h4>b)</h4>\n<p>We are now asked to calculate&nbsp;the total&nbsp;amount of&nbsp;money that {person['name']}'s&nbsp;parents will&nbsp;have added to this savings account over 21 years, including the money that&nbsp;{pronouns['their']} parents will&nbsp;deposit into the account on {pronouns['their']} 21<sup>st</sup>&nbsp;birthday.</p>\n<p>This question involves calculating the sum using the equation</p>\n<p>\\[\\sum\\limits_{i=1}^n{a_i}=\\frac{n}{2}(a_1+a_n)\\text{.}\\]</p>\n<p>We know from part <strong>a) </strong>that</p>\n<p>\\begin{align}<br/>a_1&amp;=\\var{first},\\\\<br/>n&amp;=21,\\\\<br/>a_{21}&amp;= \\var{first+b[1]*(20)}.<br/>\\end{align}</p>\n<p>Using&nbsp;our formula for the sum,</p>\n<p>\\begin{align}<br/>\\sum\\limits_{i=1}^n{a_i}&amp;=\\frac{n}{2}(a_1+a_n)\\\\<br/>&amp;=\\frac{\\var{21}}{2}(\\var{first}+\\var{first+b[1]*(21-1)})\\\\<br/>&amp;=\\var{21*(first+first+b[1]*(20))/2}\\text{.}<br/>\\end{align}</p>\n<p>Therefore, over 21 years {person['name']}'s&nbsp;parents will&nbsp;have added a total of $&pound;\\var{21*(first+first+b[1]*(20))/2}$&nbsp;to this savings account!</p>", "statement": "<p>{person['name']}'s parents&nbsp;deposit a uniformly&nbsp;increasing&nbsp;amount of money into&nbsp;a savings account&nbsp;for {pronouns['them']} every&nbsp;year on {pronouns['their']}&nbsp;birthday:</p>\n<ul>\n<li>on&nbsp;{pronouns['their']} first&nbsp;birthday&nbsp;{pronouns['their']} parents deposited&nbsp;$&pound;\\var{first}$ into the account;</li>\n<li>on&nbsp;{pronouns['their']} second&nbsp;birthday&nbsp;{person['pronouns']['their']} parents&nbsp;deposited&nbsp;$&pound;\\var{b[1]+first}$ into the account;</li>\n<li>on {pronouns['their']} third&nbsp;birthday&nbsp;{pronouns['their']} parents&nbsp;deposited $&pound;\\var{b[1]*2+first}$ into the account.</li>\n</ul>\n<p>{person['name']} wants to know&nbsp;the total amount&nbsp;of&nbsp;money&nbsp;that will be in&nbsp;this savings account,&nbsp;excluding interest,&nbsp;after&nbsp;{pronouns['their']} 21<sup>st</sup>&nbsp;birthday, if&nbsp;{pronouns['their']} parents maintain this pattern.</p>", "preamble": {"js": "", "css": ""}, "variables": {"c": {"name": "c", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(3..13 except[10]),8)"}, "n": {"name": "n", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(3..9),7)"}, "person": {"name": "person", "description": "<p>A random person</p>", "templateType": "anything", "group": "A person", "definition": "random_person()"}, "m": {"name": "m", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(2..10),5)"}, "first": {"name": "first", "description": "<p>first term in the sequence</p>", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(10..15 #5)"}, "pronouns": {"name": "pronouns", "description": "", "templateType": "anything", "group": "A person", "definition": "person['pronouns']"}, "ni": {"name": "ni", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(19..40),10)"}, "b": {"name": "b", "description": "<p>a</p>", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(10..25 #5), 3)"}, "ci": {"name": "ci", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(6..20),10)"}}, "parts": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p>How much money will&nbsp;{person['name']}'s parents deposit&nbsp;into the savings account on {pronouns['their']} 21<sup>st</sup>&nbsp;birthday,&nbsp;if {pronouns['their']} parents maintain this pattern?&nbsp;</p>\n<p>&pound;[[0]].</p>", "stepsPenalty": 0, "gaps": [{"answer": "{first+b[1]*(20)}", "showpreview": true, "expectedvariablenames": [], "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "checkingtype": "absdiff", "type": "jme", "checkingaccuracy": 0.001, "variableReplacements": [], "vsetrange": [0, 1], "checkvariablenames": false, "showFeedbackIcon": true, "scripts": {}, "marks": 1, "showCorrectAnswer": true}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "steps": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p>Use the arithmetic formula,</p>\n<p>\\[a_n = a_1 + (n-1)d, \\]</p>\n<p>where</p>\n<ul>\n<li>$a_n$ is the $n^\\text{th}$ term;</li>\n<li>$a_1$ is the first&nbsp;term in&nbsp;the sequence;</li>\n<li>$d$ is the common difference between consecutive terms.</li>\n</ul>", "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "information", "marks": 0, "showCorrectAnswer": true}, {"variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "maxValue": "{first}", "allowFractions": false, "prompt": "<p>What is the value of $a_1$?</p>", "mustBeReducedPC": 0, "minValue": "{first}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": "0.2", "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "maxValue": "{b[1]}", "allowFractions": false, "prompt": "<p>What is the value of $d$?</p>", "mustBeReducedPC": 0, "minValue": "{b[1]}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": "0.2", "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "prompt": "<p>Now use the formula to calculate&nbsp;$a_{21}$.</p>", "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "information", "marks": 0, "showCorrectAnswer": true}], "showCorrectAnswer": true}, {"variableReplacementStrategy": "originalfirst", "prompt": "<p>How much money will&nbsp;{person['name']}'s&nbsp;parents have added to this savings account over&nbsp;$21$ years in total, including the money that&nbsp;{person['pronouns']['their']} parents will&nbsp;deposit into the account on {person['pronouns']['their']} $21^{st}$ birthday?</p>\n<p>&pound;[[0]].</p>\n<p></p>", "stepsPenalty": 0, "gaps": [{"variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "maxValue": "{21*(first+first+b[1]*(20))/2}", "allowFractions": false, "mustBeReducedPC": 0, "minValue": "{21*(first+first+b[1]*(20))/2}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 1, "scripts": {}}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "steps": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p>The sum of an arithmetic sequence $a_1, a_2, \\ldots, a_n$ is calculated by the following formula.</p>\n<p>\\[\\sum\\limits_{i=1}^n{a_i}=\\frac{n}{2}(a_1+a_n)\\text{.}\\]</p>", "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "information", "marks": 0, "showCorrectAnswer": true}], "showCorrectAnswer": true}], "tags": ["Arithmetic sequences", "Arithmetic Sequences", "arithmetic sequences", "nth term", "partial sums", "random names", "sequences", "taxonomy"], "variablesTest": {"maxRuns": 100, "condition": ""}}, {"name": "Cumulative percent decrease", "extensions": ["random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}, {"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}], "type": "question", "tags": ["decrease", "percentages", "taxonomy"], "variablesTest": {"condition": "", "maxRuns": "1000"}, "variables": {"test": {"definition": "precround(precround(price*((100-perc)/100)^5, 2)*((100-perc)/100)^(n-5), 2)", "description": "<p>Calculated value of price2 to ensure we mention rounding&nbsp;errors&nbsp;in advice only when needed.</p>", "templateType": "anything", "name": "test", "group": "Part b)"}, "pricee3": {"definition": "precround(price*((100 - perc)/100)^(testn-2),2)", "description": "", "templateType": "anything", "name": "pricee3", "group": "Part b)"}, "person": {"definition": "random_person()", "description": "", "templateType": "anything", "name": "person", "group": "Part b)"}, "testn": {"definition": "random(6..9)", "description": "<p>Number of months in total.</p>", "templateType": "anything", "name": "testn", "group": "Part b)"}, "pricee1": {"definition": "precround(price*((100 - perc)/100)^(testn),2)", "description": "<p>The resulting price after the&nbsp;total of testn months.</p>", "templateType": "anything", "name": "pricee1", "group": "Part b)"}, "n": {"definition": "if(pricee2 < threshold, testn-1, testn)", "description": "", "templateType": "anything", "name": "n", "group": "Part b)"}, "threshold": {"definition": "siground(pricee1+5,2)", "description": "", "templateType": "anything", "name": "threshold", "group": "Part b)"}, "price": {"definition": "random(300..800) + 0.99", "description": "<p>The original price.</p>", "templateType": "anything", "name": "price", "group": "Part a)"}, "price2": {"definition": "if(pricee2 < threshold, pricee2, pricee1)", "description": "", "templateType": "anything", "name": "price2", "group": "Part b)"}, "perc": {"definition": "random(2..4 #0.5)", "description": "<p>Percentage decrease per month.</p>", "templateType": "anything", "name": "perc", "group": "Part a)"}, "pricee2": {"definition": "precround(price*((100 - perc)/100)^(testn-1),2)", "description": "", "templateType": "anything", "name": "pricee2", "group": "Part b)"}}, "statement": "<p>A smartphone's value decreases by $\\var{perc}$% every month. The original price when it is released is $&pound;\\var{price}$.</p>", "variable_groups": [{"name": "Part a)", "variables": ["price", "perc"]}, {"name": "Part b)", "variables": ["threshold", "pricee1", "pricee2", "pricee3", "testn", "test", "price2", "n", "person"]}], "parts": [{"showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "stepsPenalty": 0, "gaps": [{"correctAnswerFraction": false, "precisionMessage": "<p>Round your answer to $2$ decimal places.</p>", "precisionPartialCredit": 0, "scripts": {}, "maxValue": "precround(price*((100-perc)/100)^5, 2)", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "precision": "2", "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "minValue": "precround(price*((100-perc)/100)^5, 2)", "showPrecisionHint": true, "marks": "2", "variableReplacements": [], "strictPrecision": false, "showCorrectAnswer": true, "type": "numberentry"}], "showFeedbackIcon": true, "prompt": "<p>How much&nbsp;will the smartphone&nbsp;be worth after&nbsp;$5$ months?</p>\n<p>&pound; [[0]]</p>", "steps": [{"scripts": {}, "variableReplacements": [], "type": "information", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "<p>The original price of the phone is $&pound;\\var{price}$ and we are told that the price decreases&nbsp;by $\\var{perc}$% every month.</p>\n<p></p>", "marks": 0}, {"correctAnswerFraction": false, "scripts": {}, "maxValue": "1-{perc}/100", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "prompt": "<p>What is the decimal multiplier for the decrease in the smartphones each month?</p>", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "minValue": "1-{perc}/100", "variableReplacements": [], "marks": "0.5", "showCorrectAnswer": true, "type": "numberentry"}, {"precisionMessage": "<p>Round your answer to $2$ decimal places.</p>", "precisionPartialCredit": 0, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>Multiply the original&nbsp;price by the decimal multiplier to obtain the price after 1 month.</p>", "mustBeReducedPC": 0, "mustBeReduced": false, "minValue": "{price}*(1-{perc}/100)", "variableReplacements": [], "marks": "0.5", "strictPrecision": false, "showCorrectAnswer": true, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "precision": "2", "maxValue": "{price}*(1-{perc}/100)", "precisionType": "dp", "correctAnswerStyle": "plain", "showPrecisionHint": true}, {"precisionMessage": "<p>Round your answer to $2$ decimal places.</p>", "precisionPartialCredit": 0, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>Multiply your answer above&nbsp;by the decimal multiplier to obtain the price after 2 months.&nbsp;</p>\n<p>Note that this is the same as multiplying the original price by $d^2$, where $d$ is the decimal multiplier.</p>", "mustBeReducedPC": 0, "mustBeReduced": false, "minValue": "{price}*(1-{perc}/100)^2", "variableReplacements": [], "marks": "0.5", "strictPrecision": false, "showCorrectAnswer": true, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "precision": "2", "maxValue": "{price}*(1-{perc}/100)^2", "precisionType": "dp", "correctAnswerStyle": "plain", "showPrecisionHint": true}], "marks": 0}, {"scripts": {}, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "maxValue": "n-5", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "minValue": "n-5", "variableReplacements": [], "marks": "2", "showCorrectAnswer": true, "type": "numberentry"}], "showFeedbackIcon": true, "prompt": "<p>{person['name']} has&nbsp;$&pound;\\var{threshold}$ to spend on a smartphone. After how many <strong>more</strong>&nbsp;full months&nbsp;will {person['pronouns']['they']}&nbsp;be able to afford the smartphone?</p>\n<p>[[0]] months</p>", "marks": 0}], "ungrouped_variables": [], "rulesets": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Given the original price of a smartphone and the rate at which it decreases, calculate its price after a given number of months. In the second part, calculate the time remaining until the price goes below a&nbsp;certain point.</p>"}, "preamble": {"css": "", "js": ""}, "functions": {}, "advice": "<h4>a)</h4>\n<p>We&nbsp;can use the multiplier method to calculate the new price. If the price decreases by {perc}%, this its value is&nbsp;{100-perc}% of the original value after 1 month. The decimal multiplier for {100-perc}% is</p>\n<p>\\[\\frac{\\var{100-perc}}{100} = \\var{(100-perc)/100} \\text{.}\\]</p>\n<p>Each month our smartphone's value can be found by multiplying the previous month's value by the decimal multiplier. For example, after the first month, the value&nbsp;is</p>\n<p>\\[&nbsp;\\var{(100-perc)/100} \\times\\mathrm{&pound;}\\var{price} = \\mathrm{&pound;}\\var{dpformat(price*(100-perc)/100,2)}\\text{.} \\]</p>\n<p>To calculate the price after 5 months, we multiply the original price of the smartphone by our multiplier&nbsp;5 times:</p>\n<p>\\[ \\begin{align}&nbsp;\\text{Final worth} &amp;=&nbsp;\\var{price} \\times \\var{(100-perc)/100}&nbsp;\\times \\var{(100-perc)/100}&nbsp;\\times \\var{(100-perc)/100}&nbsp;\\times \\var{(100-perc)/100}&nbsp;\\times \\var{(100-perc)/100} \\\\&amp;= &nbsp;\\var{price} \\times \\var{(100-perc)/100}^{5} \\\\&amp;= &pound;\\var{precround(price*((100-perc)/100)^5, 2)} {.}&nbsp;\\end{align}\\]</p>\n<h4>b)</h4>\n<p>From part <strong>a)</strong>, the value after 5 months is &nbsp;&pound;$\\var{precround(price*((100-perc)/100)^5, 2)}$.&nbsp;Continuing to multiply the price by the decimal multiplier,</p>\n<p><span data-jme-visible=\"n&gt;5\">\\[&pound;\\var{precround(price*((100-perc)/100)^5, 2)} \\times \\var{(100-perc)/100} = &pound;\\var{precround(precround(price*((100-perc)/100)^5, 2)*(100-perc)/100, 2)}\\]</span></p>\n<p><span data-jme-visible=\"n&gt;6\">\\[&pound;\\var{precround(price*((100-perc)/100)^5, 2)} \\times \\var{(100-perc)/100}^2 = &pound;\\var{precround(precround(price*((100-perc)/100)^6, 2)*(100-perc)/100, 2)}\\]</span></p>\n<p><span data-jme-visible=\"n&gt;7\">\\[&pound;\\var{precround(price*((100-perc)/100)^5, 2)} \\times \\var{(100-perc)/100}^3 = &pound;\\var{precround(precround(price*((100-perc)/100)^7, 2)*(100-perc)/100, 2)}\\]</span></p>\n<p><span data-jme-visible=\"n&gt;8\">\\[&pound;\\var{precround(price*((100-perc)/100)^5, 2)} \\times \\var{(100-perc)/100}^4 = &pound;\\var{precround(precround(price*((100-perc)/100)^8, 2)*(100-perc)/100, 2)}\\]</span></p>\n<p></p>\n<p>The smartphone's value&nbsp;will be below $&pound;\\var{threshold}$ after&nbsp;<strong>{n-5}</strong> more&nbsp;month<span data-jme-visible=\"n&gt;6\">s</span> ({n} months in total since&nbsp;its release).</p>"}, {"name": "Applied y-intercepts: Investing in boats", "extensions": ["geogebra", "random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Bradley Bush", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1521/"}], "metadata": {"description": "<p>This question provides an example of&nbsp;an initial bank account investment with a fixed return and tests the student's understanding of an application of intercepts.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "ungrouped_variables": ["p", "friend", "m", "c", "bal"], "type": "question", "advice": "<h4>a)</h4>\n<p>The balance increases by &pound;{m} each year, so $m = \\var{m}$.</p>\n<p>We know that&nbsp;at $x = 9$ years, $y = \\var{bal}$. Substituting these values into the equation, we obtain</p>\n<p>\\[ \\var{bal} = \\var{m} \\times 9 + c \\]</p>\n<p>Rearrange this to find $c$:</p>\n<p>\\begin{align}<br/>c &amp;= \\var{bal} - \\var{m} \\times 9 \\\\ <br/>&amp;= \\var{bal}&nbsp;- \\var{m*9} \\\\<br/>&amp;= \\var{c}&nbsp;<br/>\\end{align}</p>\n<p>So the formula for the account balance is</p>\n<p>\\[y = \\var{m}x+\\var{c}\\text{.}\\]</p>\n<h4>b)</h4>\n<p>The constant term $\\var{c}$ determines the point at which the line crosses the $y$-axis. This point is&nbsp;called the <em>$y$-intercept</em>.</p>\n<h4>c)</h4>\n<p>The initial investment is the value of $y$ at $x = 0$, so it's &pound;{c}$.</p>\n<h4>d)</h4>\n<p>It is useful to plot the graph of {friend['name']}'s savings account against your own for comparison ({friend['name']}'s balance is shown as a dashed line):</p>\n<p>{geogebra_applet('gpFmg3Ex',[[\"p\",p],[\"m\",m],[\"c\",c]])}</p>\n<p>Using this graph,&nbsp;we can see that only two of the statements are true:</p>\n<ul>\n<li>The two lines are parallel. This is because they both increase by &pound;{m} each year.</li>\n<li>The plot of {friend['name']}'s balance has a higher $y$-intercept because {friend['pronouns']['their']} initial balance is higher.</li>\n</ul>\n<p>As the gradients of the two lines on the graph are the same, we can eliminate the other two statements about the lines converging and&nbsp;about having a higher gradient.</p>", "variable_groups": [], "rulesets": {}, "statement": "<p>You are a forgetful investor set on saving enough money to buy a new fishing boat for when you retire.</p>\n<p>Your savings account manager tells you your savings account is worth &pound;{formatnumber(bal,\"en\")}.&nbsp;</p>\n<p>You have forgotten&nbsp;the principal amount you started with the account with; however you do know that you have been saving for exactly nine years now and your manager informs you that the bank has been paying you a premium of &pound;{m} per year.</p>\n<p>Your account manager shows you this graph, which plots account balance over time for a given principal amount.</p>\n<p><em>The line on the graph below can be&nbsp;repositioned by dragging the slider.</em></p>\n<p>{geogebra_applet('HtnCWSSQ',[[\"p\",p],[\"m\",m],[\"c\",c]])}&nbsp;</p>", "parts": [{"scripts": {}, "gaps": [{"showpreview": true, "vsetrangepoints": 5, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "checkingaccuracy": 0.001, "showFeedbackIcon": true, "checkvariablenames": false, "type": "jme", "answer": "{m}x+{c}", "scripts": {}, "variableReplacements": [], "checkingtype": "absdiff", "vsetrange": [0, 1], "marks": 1, "expectedvariablenames": []}], "type": "gapfill", "showCorrectAnswer": true, "marks": 0, "variableReplacements": [], "showFeedbackIcon": true, "prompt": "<p>With $y$ representing the account balance and $x$ the&nbsp;number of years the account has been open, give an&nbsp;expression for the balance in the form $y=mx+c$.</p>\n<p>$y=$&nbsp;[[0]]</p>\n<p><em></em></p>", "variableReplacementStrategy": "originalfirst"}, {"shuffleChoices": true, "type": "1_n_2", "minMarks": 0, "showCorrectAnswer": true, "prompt": "<p>Which of the following elements of the graph corresponds to the constant part of the equation?</p>", "showFeedbackIcon": true, "displayColumns": 0, "choices": ["<p>y-intercept</p>", "<p>x-intercept</p>", "<p>z-intercept</p>", "<p>The origin</p>"], "scripts": {}, "distractors": ["", "", "", ""], "maxMarks": 0, "variableReplacementStrategy": "originalfirst", "marks": 0, "variableReplacements": [], "matrix": ["1", 0, 0, 0], "displayType": "dropdownlist"}, {"scripts": {}, "gaps": [{"showpreview": true, "vsetrangepoints": 5, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "checkingaccuracy": 0.001, "showFeedbackIcon": true, "checkvariablenames": false, "type": "jme", "answer": "{c}", "scripts": {}, "variableReplacements": [], "checkingtype": "absdiff", "vsetrange": [0, 1], "marks": 1, "expectedvariablenames": []}], "type": "gapfill", "showCorrectAnswer": true, "marks": 0, "variableReplacements": [], "showFeedbackIcon": true, "prompt": "<p>From your answer to the last question, state the initial investment you made towards saving for your new fishing boat.</p>\n<p>Initial investment $=$ $&pound;$[[0]].</p>", "variableReplacementStrategy": "originalfirst"}, {"shuffleChoices": true, "type": "m_n_2", "maxAnswers": 0, "minMarks": 0, "showCorrectAnswer": true, "minAnswers": 0, "prompt": "<p>Your friend, {friend['name']}, is considerably wealthier than you are, so {friend['pronouns']['they']}&nbsp;{if(friend['gender']='neutral','start','starts')}&nbsp;with twice the investment you did but still {if(friend['gender']='neutral','receive','receives')} the same annual payment of $&pound;\\var{m}$.</p>\n<p>Which of the following statements comparing&nbsp;the graph of {friend['name']}'s&nbsp;account balance&nbsp;to yours are true?</p>", "showFeedbackIcon": true, "displayColumns": "1", "choices": ["<p>The gradient is equal and hence {friend['pronouns']['their']}&nbsp;line would be parallel to yours.</p>", "<p>The plot of {friend['pronouns']['their']} balance&nbsp;crosses the $y$-axis at a higher point than yours.</p>", "<p>The plot of {friend['pronouns']['their']} balance has a higher gradient.</p>", "<p>The plots of your balance and&nbsp;{friend['pronouns']['theirs']} cross at some point.</p>"], "scripts": {}, "distractors": ["", "", "", ""], "maxMarks": 0, "variableReplacementStrategy": "originalfirst", "marks": 0, "variableReplacements": [], "matrix": ["1", "1", 0, 0], "displayType": "checkbox", "warningType": "none"}], "tags": ["applications of y-intercepts", "taxonomy", "y-intercept"], "preamble": {"css": "", "js": ""}, "functions": {}, "variables": {"bal": {"description": "", "group": "Ungrouped variables", "definition": "m*9+c", "name": "bal", "templateType": "anything"}, "c": {"description": "", "group": "Ungrouped variables", "definition": "random(995,1005,1010,1015,1020,1025)", "name": "c", "templateType": "anything"}, "p": {"description": "<p>not intercept, starting intercept</p>", "group": "Ungrouped variables", "definition": "1100", "name": "p", "templateType": "anything"}, "friend": {"description": "", "group": "Ungrouped variables", "definition": "random_person()", "name": "friend", "templateType": "anything"}, "m": {"description": "", "group": "Ungrouped variables", "definition": "random(15,30,45)", "name": "m", "templateType": "anything"}}, "variablesTest": {"maxRuns": 100, "condition": ""}}, {"name": "Using compound units - room hire price per hour and per minute", "extensions": ["random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["taxonomy"], "metadata": {"description": "<p>Given the cost of hiring a room for a given number of hours, compare with competing prices given per hour and per minute.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>{pname} has been tasked with booking a room for a {hours}-hour meeting.</p>", "advice": "<h4>a)</h4>\n<p>The price per hour is the total price divide by the number of hours.</p>\n<p>\\[ \\text{Price per hour} = \\frac{\\var{block_price_per_hour*hours}}{\\var{hours}} = &pound;\\var{dpformat(block_price_per_hour,2)} \\text{ per hour} \\]</p>\n<h4>b)</h4>\n<p>The price is given in pence per minute. To convert to pounds per&nbsp;minute, divide by $100$:</p>\n<p>\\[ \\var{100*competitor_price_per_minute} \\text{ p/minute} = &pound;\\var{dpformat(competitor_price_per_minute,2)} \\text{ per minute} \\]</p>\n<p>Then to convert to pounds per hour, multiply by $60$:</p>\n<p>\\[ &pound;\\var{dpformat(competitor_price_per_minute,2)} \\text{ per minute} = &pound;\\var{dpformat(competitor_price_per_minute*60,2)} \\text{ per hour} \\]</p>\n<h4>c)</h4>\n<p>{pname} should choose the method with the lowest cost per hour, which is {best_method}.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"competitor_price_per_minute": {"name": "competitor_price_per_minute", "group": "Ungrouped variables", "definition": "floor(100*block_price_per_hour/60*(1+random(0.1..0.3#0)*random(-1,1)))/100", "description": "<p>Price of booking at RoomCo, the competitor, in pounds per minute</p>", "templateType": "anything", "can_override": false}, "pronouns": {"name": "pronouns", "group": "Person", "definition": "person['pronouns']", "description": "", "templateType": "anything", "can_override": false}, "best_method": {"name": "best_method", "group": "Ungrouped variables", "definition": "switch(\n  min(prices)=block_price_per_hour,\n    'paying in advance at ACME',\n  min(prices)=single_price_per_hour,\n    'pay-as-you-go at ACME',\n    'paying per minute at RoomCo'\n)", "description": "<p>A description of the cheapest method.</p>", "templateType": "anything", "can_override": false}, "block_price_per_hour": {"name": "block_price_per_hour", "group": "Ungrouped variables", "definition": "random(10..25#0.25)", "description": "<p>Price of&nbsp;booking the room at ACME in advance, in pounds per hour</p>", "templateType": "anything", "can_override": false}, "hours": {"name": "hours", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "<p>Length of the meeting in hours</p>", "templateType": "anything", "can_override": false}, "pname": {"name": "pname", "group": "Person", "definition": "person['name']", "description": "", "templateType": "anything", "can_override": false}, "marking_matrix": {"name": "marking_matrix", "group": "Ungrouped variables", "definition": "let(best,min(prices),\n  map(if(x=best,1,0),x,prices)\n)", "description": "<p>Marking matrix for the \"which method is best\" part.</p>", "templateType": "anything", "can_override": false}, "single_price_per_hour": {"name": "single_price_per_hour", "group": "Ungrouped variables", "definition": "block_price_per_hour+random(0.5..2#0.25)*random(-1,1)", "description": "<p>Pay-as-you-go price at ACME, in pounds per hour</p>", "templateType": "anything", "can_override": false}, "verbs": {"name": "verbs", "group": "Person", "definition": "if(person['gender']='neutral','','s')", "description": "", "templateType": "anything", "can_override": false}, "prices": {"name": "prices", "group": "Ungrouped variables", "definition": "[block_price_per_hour,single_price_per_hour,60*competitor_price_per_minute]", "description": "", "templateType": "anything", "can_override": false}, "person": {"name": "person", "group": "Person", "definition": "random_person()", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "100"}, "ungrouped_variables": ["hours", "block_price_per_hour", "single_price_per_hour", "competitor_price_per_minute", "marking_matrix", "prices", "best_method"], "variable_groups": [{"name": "Person", "variables": ["person", "pronouns", "pname", "verbs"]}], "functions": {"pounds": {"parameters": [["n", "number"]], "type": "string", "language": "jme", "definition": "currency(n,\"\u00a3\",\"p\")"}}, "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>{pname} is quoted a price of {pounds(block_price_per_hour*hours)} by ACME Office Services to book a room in advance for {hours} hours, or {pounds(single_price_per_hour)} per hour in a pay-as-you-go scheme.</p>\n<p>To compare the two prices, {pronouns['they']} decide{verbs} to convert the advance booking price to a price per hour.</p>\n<p>Price per hour: &pound; [[0]]</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": "block_price_per_hour", "maxValue": "block_price_per_hour", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": 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>A competitor, RoomCo, is offering meeting rooms charged by the minute, at {pounds(competitor_price_per_minute)} per minute.</p>\n<p>To compare this price to ACME's offer, {pname} decide{verbs} to convert it to a price per hour.</p>\n<p>Price per hour: &pound;&nbsp;[[0]]</p>\n<p></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": "60*competitor_price_per_minute", "maxValue": "60*competitor_price_per_minute", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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": "<p>How should {pname} book the room?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": ["<p>Pay in advance at ACME</p>", "<p>Pay-as-you-go at ACME</p>", "<p>Pay per minute at RoomCo</p>"], "matrix": "marking_matrix"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Using compound units: price/weight of sweets", "extensions": ["random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}], "tags": ["Compound units", "compound units", "conversion", "measurements", "rate of pay", "speed", "taxonomy", "unit pricing", "using compound units"], "metadata": {"description": "<p>This question assesses the students ability to calculate and convert between different types of compound units, including rates of pay, speed and unit pricing.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>{pname} goes to {pronouns['their']} local shop and buys a bag containing $\\var{weight}$g of sweets for &pound;$\\var{cost}$.</p>", "advice": "<h4>a)</h4>\n<p>We are given the price of a bag of $\\var{weight}$ grams of sweets.</p>\n<p>To find the price per 100g of sweets we divide the price of a bag of sweets by its weight in grams and then multiply this by $100$.</p>\n<p><span data-jme-visible=\"(100*cost/weight) = precround((100*cost)/weight,2)\">\\[\\displaystyle\\frac{\\var{cost}}{\\var{weight}} \\times 100 = \\var{(100*cost/weight)}.\\]&nbsp;</span></p>\n<p><span data-jme-visible=\"(100*cost)/weight &lt;&gt; precround((100*cost)/weight,2)\">\\begin{align} <br/>\\displaystyle\\frac{\\var{cost}}{\\var{weight}} \\times 100 &amp;= \\var{(100*cost/weight)}\\\\ &amp;= \\var{dpformat(100*cost/weight,2)} \\; (\\text{rounded to $2$ decimal places}).<br/>\\end{align}</span></p>\n<p>The sweets cost {pounds(100*cost/weight)}&nbsp;per 100g.</p>\n<h4>b)</h4>\n<p>To convert the cost from pounds per $100$ grams to pounds per kilogram we need to use the fact that $1\\text{g} = \\displaystyle\\frac{1}{1000}\\text{kg}$.</p>\n<p>This means that $100\\text{g} = \\displaystyle\\frac{1}{10}\\text{kg}$.</p>\n<p>We know from<strong>&nbsp;a)</strong>&nbsp;that sweets cost {pounds(100*cost/weight)}&nbsp;per 100g, which is the same as {pounds(100*cost/weight)} per $\\frac{1}{10}$kg.</p>\n<p>We want the price per <strong>one</strong>&nbsp;kilogram of sweets, so we multiply by $10$.</p>\n<p>Note that we use the actual value of $\\displaystyle\\frac{\\var{cost}}{\\var{weight}} \\times 100 = \\var{100*cost/weight}$ here to ensure that our final answer is accurate.</p>\n<p>\\begin{align}<br/>\\var{100*cost/{weight}} \\times 10 &amp;= \\var{dpformat(1000*{cost}/{weight},2)} \\; (2 \\; \\text{d.p})<br/>\\end{align}</p>\n<p>So, the sweets cost {pounds(1000*cost/weight)} per kg.</p>\n<h4>c)</h4>\n<p>We worked out in part&nbsp;<strong>a)</strong> that&nbsp;sweets cost {pounds(100*cost/weight)} per 100g when bought in the bag, so at {pounds(pick_n_mix_cost)} per 100g the Pick'n'Mix is {if(pick_n_mix_cost&lt;100*cost/weight,'cheaper','more expensive')} than buying the bag.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"pronouns": {"name": "pronouns", "group": "Ungrouped variables", "definition": "person['pronouns']", "description": "", "templateType": "anything", "can_override": false}, "cost": {"name": "cost", "group": "Ungrouped variables", "definition": "precround(cost_per_g*weight,1)-0.01", "description": "<p>Cost of a bag of sweets - always ends in .x9 to look like a real price.</p>", "templateType": "anything", "can_override": false}, "max_kg_cost": {"name": "max_kg_cost", "group": "Ungrouped variables", "definition": "max(precround(1000*cost/weight,2), precround(100*cost/weight,2)*10)", "description": "<p>Minimum acceptable cost per kg -&nbsp;using the rounded cost per 100g can introduce an error.</p>", "templateType": "anything", "can_override": false}, "pname": {"name": "pname", "group": "Ungrouped variables", "definition": "person['name']", "description": "", "templateType": "anything", "can_override": false}, "pick_n_mix_cost": {"name": "pick_n_mix_cost", "group": "Ungrouped variables", "definition": "precround(100*cost/weight,2)+random(-15..15 except -2..2)*0.01", "description": "<p>Cost of the sweets at the Pick'n'Mix, per 100g.</p>", "templateType": "anything", "can_override": false}, "min_kg_cost": {"name": "min_kg_cost", "group": "Ungrouped variables", "definition": "min(precround(1000*cost/weight,2), precround(100*cost/weight,2)*10)", "description": "<p>Minimum acceptable cost per kg -&nbsp;using the rounded cost per 100g can introduce an error.</p>", "templateType": "anything", "can_override": false}, "weight": {"name": "weight", "group": "Ungrouped variables", "definition": "random(150..200)", "description": "<p>Weight of a bag of sweets, in grams</p>", "templateType": "anything", "can_override": false}, "person": {"name": "person", "group": "Ungrouped variables", "definition": "random_person()", "description": "", "templateType": "anything", "can_override": false}, "cost_per_g": {"name": "cost_per_g", "group": "Ungrouped variables", "definition": "random(0.005..0.02#0)", "description": "<p>Cost of the sweets per gram, in pounds.</p>\n<p>Between 50p and &pound;2 per 100g.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "10000"}, "ungrouped_variables": ["weight", "cost_per_g", "cost", "min_kg_cost", "max_kg_cost", "person", "pname", "pronouns", "pick_n_mix_cost"], "variable_groups": [], "functions": {"pounds": {"parameters": [["n", "number"]], "type": "string", "language": "jme", "definition": "currency(n,\"\u00a3\",\"p\")"}}, "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>How much do the sweets cost per $100$ grams?</p>\n<p>&pound;[[0]]&nbsp;per $100$g</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": "100*cost/weight", "maxValue": "100*cost/weight", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "<p>Round your answer to $2$ decimal places.</p>", "strictPrecision": false, "showPrecisionHint": false, "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>How much is this in pounds per kilogram?</p>\n<p>&pound;[[0]]&nbsp; per kg</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": "1000*cost/weight", "maxValue": "1000*cost/weight", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "<p>Round your answer to $2$ decimal places.</p>", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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": "<p>{pname} notices that the same sweets are available from the Pick'n'Mix for {pounds(pick_n_mix_cost)} per 100g.</p>\n<p>Should {pronouns['they']} buy {pronouns['their']} sweets from the Pick'n'Mix instead?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>Yes, the Pick'n'Mix is cheaper.</p>", "<p>No, the Pick'n'Mix is more expensive.</p>"], "matrix": "if(pick_n_mix_cost<100*cost/weight,[1,0],[0,1])"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Compound units : shopping for bananas", "extensions": ["random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}], "metadata": {"description": "<p>This question assesses the student's ability to use some given information involving two different units of measurement to&nbsp;rewrite&nbsp;the&nbsp;information&nbsp;as a&nbsp;compound measure.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {}, "type": "question", "ungrouped_variables": ["person", "a", "b", "b_pack", "b_single", "mark_matrix"], "advice": "<h4>a)</h4>\n<p><span data-jme-visible=\"b&gt;=100\">The pack price at Fine Fare supermarket is {b_pack}, which converted to pence is&nbsp;{b}p.</span></p>\n<p>The price per banana at Fine Fare supermarket is</p>\n<p>\\[ \\var{b} \\div 5 = \\var{b_single}\\text{p.}\\]</p>\n<h4>b)</h4>\n<p>As the price at Hintons supermarket is cheaper, {person['pronouns']['they']}&nbsp;should shop there.</p>\n<h4>c)</h4>\n<p>The new price per banana at Fine Fare Supermarket is</p>\n<p>\\begin{align}<br/>\\var{b} \\div 6 &amp;= \\var{if(isint(b/6),b/6,dpformat(b/6,1))}\\text{p.} \\\\<br/>\\end{align}</p>\n<p><span data-jme-visible=\"b/6&gt;a\">Since the price at Hintons Supermarket is still cheaper, {person['name']} should not change {person['pronouns']['their']} decision.</span></p>\n<p><span data-jme-visible=\"b/6&lt;a\">Since the price at Fine Fare Supermarket is now cheaper, {person['name']} should change {person['pronouns']['their']} decision.</span></p>\n<p></p>", "variable_groups": [], "statement": "<p>{person['name']} is shopping for bananas and has two local supermarkets:</p>\n<p>Hintons Supermarket charges {a}p per banana.</p>\n<p>Fine Fare Supermarket&nbsp;charges {b_pack}&nbsp;for a pack of 5 bananas.</p>", "parts": [{"scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>What is the price per banana (in pence) at Fine Fare Supermarket?</p>\n<p>[[0]]p/banana</p>", "variableReplacements": [], "showFeedbackIcon": true, "marks": 0, "gaps": [{"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showFeedbackIcon": true, "marks": 1, "minValue": "b_single", "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "b_single", "mustBeReduced": false, "allowFractions": false, "variableReplacements": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true}]}, {"shuffleChoices": false, "minMarks": 0, "showCorrectAnswer": true, "displayColumns": 0, "variableReplacements": [], "showFeedbackIcon": true, "prompt": "<p>If {person['name']} is interested in getting the best value for money per banana, which supermarket should {person['pronouns']['they']} shop at?</p>", "choices": ["<p>Hintons Supermarket</p>", "<p>Fine Fare Supermarket</p>"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "1_n_2", "maxMarks": 0, "marks": 0, "distractors": ["", ""], "matrix": ["1", 0], "displayType": "radiogroup"}, {"shuffleChoices": false, "minMarks": 0, "showCorrectAnswer": true, "displayColumns": 0, "showFeedbackIcon": true, "prompt": "<p>{person['name']} notices that some of the bags of bananas at Fine Fare Supermarket contain 6 bananas and wonders if that will make a difference to {person['pronouns']['their']}&nbsp;decision. Assuming that {person['pronouns']['they']} can get hold of a pack of 6 bananas at Fine Fare, which supermarket should {person['pronouns']['they']} now shop at?</p>", "choices": ["<p>Hintons Supermarket</p>", "<p>Fine Fare Supermarket</p>"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "1_n_2", "maxMarks": 0, "marks": 0, "variableReplacements": [], "matrix": "mark_matrix", "displayType": "radiogroup"}], "tags": ["compound measures", "Compound measures", "Compound units of measurement", "price", "rate of pay", "taxonomy"], "preamble": {"css": "", "js": ""}, "functions": {}, "variables": {"b_pack": {"description": "<p>formatted price of the pack</p>", "group": "Ungrouped variables", "definition": "currency(b/100,\"\u00a3\",\"p\")", "name": "b_pack", "templateType": "anything"}, "b_single": {"description": "<p>Single banana price at fine fare</p>", "group": "Ungrouped variables", "definition": "b/5", "name": "b_single", "templateType": "anything"}, "a": {"description": "<p>cost&nbsp;per banana in&nbsp;Hintons</p>", "group": "Ungrouped variables", "definition": "random(12..19)", "name": "a", "templateType": "anything"}, "b": {"description": "<p>Price of pack of bananas at Fine Fare</p>", "group": "Ungrouped variables", "definition": "a*5+random(5..20#5 except a)", "name": "b", "templateType": "anything"}, "person": {"description": "", "group": "Ungrouped variables", "definition": "random_person()", "name": "person", "templateType": "anything"}, "mark_matrix": {"description": "", "group": "Ungrouped variables", "definition": "if(b/6>a,[1,0],[0,1])", "name": "mark_matrix", "templateType": "anything"}}, "variablesTest": {"maxRuns": 100, "condition": ""}}]}], "timing": {"timeout": {"action": "none", "message": ""}, "allowPause": true, "timedwarning": {"action": "none", "message": ""}}, "name": "Money", "metadata": {"description": "<p>Questions to do with money.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "exam", "showQuestionGroupNames": false, "navigation": {"browse": true, "onleave": {"action": "none", "message": ""}, "showfrontpage": true, "showresultspage": "oncompletion", "preventleave": true, "reverse": true, "allowregen": true}, "percentPass": 0, "feedback": {"showtotalmark": true, "feedbackmessages": [], "showactualmark": true, "advicethreshold": 0, "intro": "", "showanswerstate": true, "allowrevealanswer": true}, "showstudentname": true, "duration": 0, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "extensions": ["geogebra", "random_person"], "custom_part_types": [], "resources": []}