// Numbas version: exam_results_page_options
{"showstudentname": true, "duration": 0, "question_groups": [{"pickingStrategy": "all-ordered", "name": "Group", "pickQuestions": 1, "questions": [{"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": "Calculate the original price before a decrease", "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/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}], "tags": ["decrease", "percentages", "taxonomy"], "metadata": {"description": "<p>Find the original price before a discount by dividing the new price by the percentage discount.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>{name1} and {name2} are friends. {name1} noticed {name2}'s new {item} when he came over to visit her house. He immediately knew he wanted to buy the same model. When he got home, he bought the {item} online for &pound;{newprice}.</p>", "advice": "<p>We need to find the original price paid by {name2}. This value represents 100%.</p>\n<p>By the time {name1} bought the {item}, the price had decreased by {percentage}%.</p>\n<p>{name1} therefore paid {100-percentage}% of the price {name2} paid.</p>\n<p></p>\n<p>We use the unitary method to find the original price. We know the price paid by {name1}.</p>\n<p>\\[\\var{100-percentage}\\text{%} = \\var{newprice} \\text{.}\\]</p>\n<p>Divide both sides&nbsp;by {100-percentage} to get</p>\n<p>\\[\\begin{align} 1\\text{%} &amp;= \\var{newprice} \\div \\var{100-percentage} \\\\&amp;= \\var{newprice/(100-percentage)} \\text{.} \\end{align}\\]</p>\n<p>Multiply&nbsp;both sides&nbsp;by&nbsp;100 to get</p>\n<p>\\[\\begin{align} 100\\text{%} &amp;= \\var{newprice/(100-percentage)} \\times&nbsp;100 \\\\&amp;= \\var{newprice/(100-percentage)*100} \\\\&amp;= \\var{oldprice}\\text{.} \\end{align}\\]</p>\n<p>This is the original price paid by {name2} before the {percentage}% decrease.</p>\n<p>We can check our answer with a different method.</p>\n<p>\\[\\begin{align} \\var{100-percentage}\\text{% of } \\var{oldprice} &amp;= \\var{(100-percentage)/100} \\times \\var{oldprice}&nbsp;\\\\&amp;= &nbsp;\\var{(100-percentage)/100*oldprice} \\\\&amp;= \\var{precround((100-percentage)/100*oldprice, 2)}&nbsp;&nbsp;\\text{.} \\end{align}\\]</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"newprice": {"name": "newprice", "group": "Ungrouped variables", "definition": "precround(oldprice*(100-percentage)/100,2)", "description": "", "templateType": "anything", "can_override": false}, "name2": {"name": "name2", "group": "Ungrouped variables", "definition": "random(\"Emily\", \"Kate\", \"Michaela\", \"Susan\", \"Sophie\")", "description": "<p>A female name.</p>", "templateType": "anything", "can_override": false}, "name1": {"name": "name1", "group": "Ungrouped variables", "definition": "random(\"Josh\", \"Adam\", \"Mike\", \"Trevor\", \"Alex\")", "description": "<p>A male name.</p>", "templateType": "anything", "can_override": false}, "oldprice": {"name": "oldprice", "group": "Ungrouped variables", "definition": "switch(\n  item = \"TV\", random(179.99..1199.99 #10), \n  item = \"laptop\", random(209.99..799.99 #10),\n  item = \"smartphone\", random(109.99..799.99 #10),\n  item = \"PC\", random(209.99..969.99 #10),\n  item = \"gaming console\", random(89.99..349.99 #10),\n  399.99)", "description": "", "templateType": "anything", "can_override": false}, "percentage": {"name": "percentage", "group": "Ungrouped variables", "definition": "random(5..30)", "description": "<p>Discount percentage.</p>", "templateType": "anything", "can_override": false}, "item": {"name": "item", "group": "Ungrouped variables", "definition": "random(\"TV\", \"laptop\", \"smartphone\", \"PC\", \"gaming console\")", "description": "<p>The bought item.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "precround(precround(oldprice*(100-percentage)/100,2)*100/(100-percentage),2) = oldprice", "maxRuns": "1000"}, "ungrouped_variables": ["item", "name1", "percentage", "name2", "oldprice", "newprice"], "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>When {name1} told {name2} how much he had paid for the {item}, {name2} said the price had decreased by {percentage}% since she bought it.</p>\n<p>How much did&nbsp;{name2} pay for the {item}?</p>\n<p>&pound;&nbsp; [[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "oldprice", "maxValue": "oldprice", "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}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"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": "Simple interest", "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/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}], "metadata": {"description": "<p>Calculate the interest accrued in a savings account, given the initial balance and annual interest rate.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Suppose you put &pound;{money} into a savings account&nbsp;exactly {years} years ago and you haven't touched the money since. The simple interest rate on the account is {perc2}% per year.</p>", "variables": {"perc2": {"name": "perc2", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(0..2.5 #0.05)"}, "money": {"name": "money", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(100..5000 #100)"}, "years": {"name": "years", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(2..6)"}}, "tags": ["interests", "percentages", "taxonomy"], "ungrouped_variables": ["perc2", "money", "years"], "functions": {}, "preamble": {"js": "", "css": ""}, "advice": "<p>This is <em>simple</em> interest, which means the amount added each year is a percentage of the <strong>original</strong> amount. The amount we add is fixed for all {years} years.</p>\n<p>First,&nbsp;we work out the amount of interest for one year:</p>\n<p>\\begin{align} <br/>\\var{perc2} \\text{% of } \\var{money} &amp;= \\frac{\\var{perc2}}{100} \\times \\var{money} \\\\<br/>&amp;= \\var{perc2/100} \\times \\var{money} \\\\<br/>&amp;= &pound;\\var{dpformat(perc2/100*money,2)} \\text{.}&nbsp;<br/>\\end{align}</p>\n<p>The money has been in the account for {years} years, so we multiply $&pound;\\var{dpformat(perc2/100*money,2)}$ by $\\var{years}$.</p>\n<p>\\[ &pound;\\var{dpformat(perc2/100*money,2)} \\times \\var{years} = &pound;\\var{dpformat(perc2/100*money*years,2)} \\text{.} \\]</p>\n<p>Adding this to the original balance:</p>\n<p>\\[ &pound;\\var{money} + &pound;\\var{dpformat(perc2/100*money*years,2)}&nbsp; = &pound;\\var{dpformat(perc2/100*money*years + money,2)} \\text{.} \\]</p>\n<p>This is the amount we would get if we withdrew the whole savings balance today.</p>", "type": "question", "variable_groups": [], "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"scripts": {}, "showCorrectAnswer": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "precision": "2", "variableReplacements": [], "mustBeReducedPC": 0, "precisionPartialCredit": 0, "minValue": "(1 + perc2/100*years)*money", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "allowFractions": false, "correctAnswerStyle": "plain", "precisionType": "dp", "scripts": {}, "maxValue": "(1 + perc2/100*years)*money", "showCorrectAnswer": false, "strictPrecision": true, "type": "numberentry", "showPrecisionHint": true, "mustBeReduced": false, "marks": "2", "showFeedbackIcon": true, "precisionMessage": "You have not given your answer to the correct precision."}], "type": "gapfill", "marks": 0, "prompt": "<p>&nbsp;If you were to withdraw the money from this account now, how much&nbsp;would you have?</p>\n<p>&pound; [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true}]}]}], "feedback": {"allowrevealanswer": true, "feedbackmessages": [], "intro": "", "showactualmark": true, "showtotalmark": true, "showanswerstate": true, "advicethreshold": 0}, "showQuestionGroupNames": false, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Some questions of relevance to consumers.</p>"}, "name": "Neil's copy of Consumer mathematics", "timing": {"timedwarning": {"message": "", "action": "none"}, "timeout": {"message": "", "action": "none"}, "allowPause": true}, "percentPass": 0, "navigation": {"browse": true, "onleave": {"message": "", "action": "none"}, "allowregen": true, "showfrontpage": true, "reverse": true, "preventleave": true, "showresultspage": "oncompletion"}, "type": "exam", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Neil Anderson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2916/"}], "extensions": ["random_person"], "custom_part_types": [], "resources": []}