// Numbas version: exam_results_page_options {"name": "Practice questions", "metadata": {"description": "

Twenty questions which can be used by Initial Teacher Education students preparing for the Australian LANTITE numeracy test. The questions are grouped in content strands and each question is randomised. Questions are either multiple choice, true/false or type the answer in a box. The questions are chosen from a menu and there is no time limit. They are different to the questions in Timed Practice Quiz v2.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": true, "showstudentname": true, "question_groups": [{"name": "Number and Algebra strand", "pickingStrategy": "all-ordered", "pickQuestions": "10", "questionNames": ["Working out days hired (10+)", "Emergency call centre (4)", "Calculate tax payable (10+)", "Booksellers commission (10+)", "Find the larger share (10+)"], "questions": [{"name": "NA Working out days hired from total cost (10+)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE", "Western Sydney MESH"], "metadata": {"description": "

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students are given the total cost, insurance fee and daily hire charge (all randomly generated). They need to calculate the number of days hired.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

{names[index]} hired a bike during his holiday. The insurance cost was \\${insurance} regardless of the number of hire days and the hire fee was an additional \\${hire_per_day} per day.

", "advice": "

The total cost of \\${total_cost} includes both the insurance (\\${insurance}) and the cost per day.

If we subtract the insurance from the total cost we will have the cost per day.

\\${total_cost} - \\${insurance} = \\${total_cost-insurance}

The bike cost \\${hire_per_day} to hire each day.

If we divide the total amount paid for the hire component by the daily cost we will get the number of days that the bike was hired.

{total_cost-insurance} ÷ {hire_per_day} = {days}

{names[index]} hired the bike for {days} days.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"insurance": {"name": "insurance", "group": "Ungrouped variables", "definition": "random(11 .. 27#1)", "description": "

The one-off fee for insurance.

", "templateType": "randrange", "can_override": false}, "days": {"name": "days", "group": "Ungrouped variables", "definition": "random(4 .. 9#1)", "description": "

The number of days that the bike is hired.

", "templateType": "randrange", "can_override": false}, "hire_per_day": {"name": "hire_per_day", "group": "Ungrouped variables", "definition": "random(22 .. 34#1)", "description": "

The dollar cost to hire the bike per day.

", "templateType": "randrange", "can_override": false}, "index": {"name": "index", "group": "Ungrouped variables", "definition": "random(0 .. 7#1)", "description": "

Index for list of names.

", "templateType": "randrange", "can_override": false}, "names": {"name": "names", "group": "Ungrouped variables", "definition": "[ \"Sam\", \"Joseph\", \"Mark\", \"Jim\", \"Tarin\", \"Luke\", \"Ali\", \"Ben\" ]", "description": "

List of boys names for bike hire.

", "templateType": "list of strings", "can_override": false}, "total_cost": {"name": "total_cost", "group": "Ungrouped variables", "definition": "{insurance}+{hire_per_day}*{days}", "description": "

Total cost of hiring the bike over the time period.

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["days", "hire_per_day", "insurance", "total_cost", "index", "names"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "prompt": "

If the total cost of the bike was \\${total_cost}, how many days did {names[index]} hire the bike for?

", "minValue": "{days}", "maxValue": "{days}", "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": "NA Emergency call centre infographic percentages (4)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/national_Emergency-Call-Centre_FA.jpg", "/srv/numbas/media/question-resources/national_Emergency-Call-Centre_FA.jpg"], ["question-resources/national_Emergency-Call-Centre_FA_550.jpg", "/srv/numbas/media/question-resources/national_Emergency-Call-Centre_FA_550.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE", "Western Sydney MESH"], "metadata": {"description": "

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students need to calculate the proportion of calls for one given emergency, after reading the number of calls, and total number of calls from the supplied infographic. There are 4 different versions of this question.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

The National Emergency Call Centre was established by the Australian Government in July 2006 to serve as a first point of contact for Australians in the event of an emergency or disaster of national significance. It provides a coordinated whole of government response to the delivery and gathering of information.

The infographic below shows the number of calls taken for four of the biggest emergencies in the first five years of the centre's operation.

^{http://mediahub.humanservices.gov.au/news/emergency-call-centre-celebrates-10-years/}

", "advice": "

There were {fullnumcalls} calls received regarding {incident}.

The infographic shows 410 000 calls in total.

We need to find what percentage {fullnumcalls} is of 410 000.

Divide {fullnumcalls} by 410 000, then multiply by 100%.

{fullnumcalls} ÷ 410 000 x 100% = {precround(numcalls/410*100,4)}...%.

This should be rounded to the nearest whole number.

{precround({numcalls/410*100},0)}% of the calls shown were about {incident}.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"incident": {"name": "incident", "group": "Ungrouped variables", "definition": "incidents[index]", "description": "

The name of the randomly selected incident.

", "templateType": "anything", "can_override": false}, "incidents": {"name": "incidents", "group": "Ungrouped variables", "definition": "['the Victorian bushfires','Cyclone Yasi','the North Queensland floods','the Hunter Floods']", "description": "

The list of the four incidents.

", "templateType": "anything", "can_override": false}, "index": {"name": "index", "group": "Ungrouped variables", "definition": "random(0 .. 3#1)", "description": "

The index to both the incident and calls lists.

", "templateType": "randrange", "can_override": false}, "numcalls": {"name": "numcalls", "group": "Ungrouped variables", "definition": "calls[index]", "description": "

The number of calls divided by 1000, for the randomly selected incident.

", "templateType": "anything", "can_override": false}, "calls": {"name": "calls", "group": "Ungrouped variables", "definition": "[80,240,60,30]", "description": "

The number of calls (divided by 1000) for each corresponding incident

", "templateType": "anything", "can_override": false}, "fullnumcalls": {"name": "fullnumcalls", "group": "Ungrouped variables", "definition": "formatnumber(numcalls*1000,'si-en')", "description": "

The actual number of calls for the randomly selected incident, in spaced format. This variable cannot be used in calculations as it is a string. It is used in the Advice section.

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["index", "incidents", "incident", "calls", "numcalls", "fullnumcalls"], "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": "

What proportion of these four emergencies were the calls about {incident}?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["

\n{precround({numcalls*100/410},0)}%", "80%", "30%", "60%"], "matrix": ["1", 0, 0, 0], "distractors": ["Well done!", "You need to work out the proportion of calls, out of the total number of calls, then multiply by 100%.", "You need to work out the proportion of calls, out of the total number of calls, then multiply by 100%.", "You need to work out the proportion of calls, out of the total number of calls, then multiply by 100%."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NA Use tax table to calculate tax payable (10+)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/tax_table_image.png", "/srv/numbas/media/question-resources/tax_table_image.png"], ["question-resources/tax_table_image_3.png", "/srv/numbas/media/question-resources/tax_table_image_3.png"], ["question-resources/tax_table_image_4.png", "/srv/numbas/media/question-resources/tax_table_image_4.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE", "Western Sydney MESH"], "metadata": {"description": "

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students are shown a personal income tax table and given a randomly generated taxable income. They are required to calculate the tax payable.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

The table below shows the tax rates for Australian residents in the 2019-2020 financial year.

^{https://www.ato.gov.au/Rates/Individual-income-tax-rates/}

", "advice": "

First, determine which row of the table you should use, based on the taxable income given.

The taxable income is \\${formatnumber(TaxableIncome,\"si-en\")}, so you should use the {RowNumber[BracketIndex]} row in the given tax table.

This row says that no tax is payable on taxable incomes below \\$18 201 therefore the tax payable on \\${formatnumber(TaxableIncome,\"si-en\")} is \\$0.

This row says that the tax payable is worked out by:

{Rate[BracketIndex]*100} cents for each \\$1 over \\${formatnumber(Level[BracketIndex],\"si-en\")}.

Next, calculate how many dollars are above \\${formatnumber(Level[BracketIndex],\"si-en\")}:

\\${formatnumber(TaxableIncome,\"si-en\")} - \\${formatnumber(Level[BracketIndex],\"si-en\")} = \\${formatnumber(TaxableIncome-Level[BracketIndex],\"si-en\")}

Finally, multiply the cents in the dollar rate (as a decimal) by this amount:

{Rate[BracketIndex]} x \\${formatnumber(TaxableIncome-Level[BracketIndex],\"si-en\")} = \\${trim(dpformat(Rate[BracketIndex]*(TaxableIncome-Level[BracketIndex]),2,\"si-en\"))}

The amount of tax payable is \\${trim(dpformat(TaxDue,0,\"si-en\"))} to the nearest dollar.

This row says that the tax payable is worked out by:

\\${formatnumber(BaseAmount[BracketIndex],\"si-en\")} plus {Rate[BracketIndex]*100} cents for each \\$1 over \\${formatnumber(Level[BracketIndex],\"si-en\")}.

Secondly calculate how many dollars are above \\${formatnumber(Level[BracketIndex],\"si-en\")}:

\\${formatnumber(TaxableIncome,\"si-en\")} - \\${formatnumber(Level[BracketIndex],\"si-en\")} = \\${formatnumber(TaxableIncome-Level[BracketIndex],\"si-en\")}

Thirdly, multiply the cents in the dollar rate (as a decimal) by this amount:

{Rate[BracketIndex]} x \\${formatnumber(TaxableIncome-Level[BracketIndex],\"si-en\")} = \\${trim(dpformat(Rate[BracketIndex]*(TaxableIncome-Level[BracketIndex]),2,\"si-en\"))}

Finally, add this to the base amount:

\\${formatnumber(BaseAmount[BracketIndex],\"si-en\")} + \\${trim(dpformat(Rate[BracketIndex]*(TaxableIncome-Level[BracketIndex]),2,\"si-en\"))} = \\${trim(dpformat(TaxDue,2,\"si-en\"))}

The amount of tax payable is \\${trim(dpformat(TaxDue,0,\"si-en\"))} to the nearest dollar.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"IncomeBrackets": {"name": "IncomeBrackets", "group": "Ungrouped variables", "definition": "[random(18201..37000),random(37001..90000),random(90001..180000),random(180001..280000)]", "description": "

A list containing the five income brackets.

", "templateType": "anything", "can_override": false}, "RowNumber": {"name": "RowNumber", "group": "Ungrouped variables", "definition": "['second','third','fourth','fifth']", "description": "

Which row of the tax table the student should be looking at.

", "templateType": "anything", "can_override": false}, "TaxDue": {"name": "TaxDue", "group": "Ungrouped variables", "definition": "TaxPayable[BracketIndex]", "description": "

This is the tax payable for the randomly generated TaxableIncome.

", "templateType": "anything", "can_override": false}, "NamesIndex": {"name": "NamesIndex", "group": "Ungrouped variables", "definition": "random(0 .. 6#1)", "description": "

The random number used to index the list of names.

", "templateType": "randrange", "can_override": false}, "TaxPayable": {"name": "TaxPayable", "group": "Ungrouped variables", "definition": "[0.19*(TaxableIncome-18200),3572+0.325*(TaxableIncome-37000),20797+0.37*(TaxableIncome-90000),54097+0.45*(TaxableIncome-180000)]", "description": "

This variable is used in the Marking section to calculate the taxpayable, using the Taxable Income. However, more variables are required for the Advice section, in order to be able to print all values in the relevant row of the tax table.

", "templateType": "anything", "can_override": false}, "names": {"name": "names", "group": "Ungrouped variables", "definition": "[ \"Jay\", \"Lucy\", \"Sue\", \"Tim\", \"Mark\", \"Ahmad\", \"Neera\" ]", "description": "

The list of possible names for this question.

", "templateType": "list of strings", "can_override": false}, "TaxableIncome": {"name": "TaxableIncome", "group": "Ungrouped variables", "definition": "IncomeBrackets[BracketIndex]", "description": "

A randomly selected number from the tax bracket indicated by BracketIndex.

", "templateType": "anything", "can_override": false}, "Rate": {"name": "Rate", "group": "Ungrouped variables", "definition": "[0.19,0.325,0.37,0.45]", "description": "

This is the second number given in the tax table calculation, for each row in the table.

", "templateType": "anything", "can_override": false}, "BaseAmount": {"name": "BaseAmount", "group": "Ungrouped variables", "definition": "[0,3572,20797,54097]", "description": "

This is the first number given in the tax table calculation, for each row in the table.

", "templateType": "anything", "can_override": false}, "Level": {"name": "Level", "group": "Ungrouped variables", "definition": "[18200,37000,90000,180000]", "description": "

This is the third number given in the tax table calculation, for each row in the table.

", "templateType": "anything", "can_override": false}, "BracketIndex": {"name": "BracketIndex", "group": "Ungrouped variables", "definition": "random(0 .. 3#1)", "description": "

The random number used to index the IncomeBrackets. It also indexes the lists for BaseAmount, Rate, Level, RowNumber and TaxPayable, so that the correct figures are used based on the tax bracket.

", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["names", "NamesIndex", "BracketIndex", "IncomeBrackets", "TaxableIncome", "TaxPayable", "TaxDue", "BaseAmount", "Rate", "Level", "RowNumber"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "prompt": "

{names[NamesIndex]} has a taxable income of \\${formatnumber(TaxableIncome,\"si-en\")} in 2019-2020. How much tax will {names[NamesIndex]} be required to pay? Round your answer to the nearest whole dollar. Do not type a comma and do not type the \\$ sign.

", "minValue": "int(TaxDue)", "maxValue": "int(TaxDue)", "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": "NA Booksellers commission (10+)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE", "Western Sydney MESH"], "metadata": {"description": "

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students are given sales and years of service. They read the retainer and commission from two tables, then calculate before-tax income. The sales and years of service are randomly generated.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

An educational book seller pays its sales staff a monthly retainer (base level of pay) depending on their years of service. The retainer is given in Table 1 below.

They also pay a commission based on the sales person's total sales for the month. If sales are below \\$500, no commission is paid. Otherwise, the commission is given in Table 2 below.

Table 1

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Full years of service	Retainer
0 - 2	\\$600
3 - 5	\\$700
6 - 8	\\$800
9 and above	\\$900

Table 2

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Monthly sales	Commission
\\$500 - \\$799	15%
\\$800 - \\$899	18%
\\$900 - \\$999	21%
\\$1000 and over	24%

", "advice": "

Retainer

{name1} has been working as a book seller for {years} years. According to Table 1, the retainer is \\${retainer}.

Commission

{name1}'s sales for the month were \\${trim(dpformat(sales,0,\"si-en\"))}, so no commission is payable.

{name1}'s sales for the month were \\${trim(dpformat(sales,0,\"si-en\"))}. According to Table 2, the commission rate is {commissionrate*100}%.

The commission earnt is {commissionrate*100}% of \\${trim(dpformat(sales,0,\"si-en\"))}.

{commissionrate*100}% of \\${trim(dpformat(sales,0,\"si-en\"))} = {commissionrate*100} ÷100 x \\${trim(dpformat(sales,0,\"si-en\"))} = \\${trim(split(dpformat(commissionrate*sales,2,\"si-en\"),\".00\")[0])}

Income

Income = Retainer + Commission = \\${trim(split(dpformat(retainer,2,\"si-en\"),\".00\")[0])} + \\${trim(split(dpformat(commissionrate*sales,2,\"si-en\"),\".00\")[0])} = \\${trim(split(dpformat(retainer+commissionrate*sales,2,\"si-en\"),\".00\")[0])}

{name1}'s income is \\${trim(dpformat(income,0,\"si-en\"))}.

Rounded to the nearest dollar, {name1}'s income is \\${trim(dpformat(income,0,\"si-en\"))}.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"years": {"name": "years", "group": "Ungrouped variables", "definition": "random(1 .. 10#0.5)", "description": "

The number of years that the bookseller has been working for the company.

", "templateType": "randrange", "can_override": false}, "income": {"name": "income", "group": "Ungrouped variables", "definition": "retainer+commissionrate*sales", "description": "

The income, based on retainer plus commission.

", "templateType": "anything", "can_override": false}, "retainer": {"name": "retainer", "group": "Ungrouped variables", "definition": "switch({years}<3,600,{years}<6,700,{years}<9,800,900)", "description": "

The retainer paid, based on the years of service.

", "templateType": "anything", "can_override": false}, "name1": {"name": "name1", "group": "Ungrouped variables", "definition": "random(\"Maria\",\"Frances\",\"Maysa\",\"Gia\",\"Lin\",\"Yousif\",\"James\")", "description": "

The name of the book seller.

", "templateType": "anything", "can_override": false}, "sales": {"name": "sales", "group": "Ungrouped variables", "definition": "random(250 .. 1650#10)", "description": "

The dollar value of the sales for the given month.

", "templateType": "randrange", "can_override": false}, "commissionrate": {"name": "commissionrate", "group": "Ungrouped variables", "definition": "switch({sales}<500,0,{sales}<800,0.15,{sales}<900,0.18,{sales}<1000,0.21,0.24)", "description": "

The commission rate as a decimal, based on the monthly sales amount.

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["name1", "years", "retainer", "sales", "commissionrate", "income"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "prompt": "

{name1} has been working for the book selling company for {years} years. Last month, {name1} sold books worth a total of \\${trim(dpformat(sales,0,\"si-en\"))}.

Calculate {name1}'s before-tax income for the month. Enter your answer, rounded to the nearest dollar. Do not type the \\$ sign.

", "minValue": "precround(income,0)", "maxValue": "precround(income,0)", "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": "NA Find the larger share for a given ratio (10+)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE", "Western Sydney MESH"], "metadata": {"description": "

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students are given a ratio, and the total number of dancers. They must calculate the number of girls (the larger share). The ratio, and total number are randomly generated.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

The ratio of boys to girls at a dance school is {boysratio} : {girlsratio}.

There are {classsize} pupils enrolled in the dance school altogether.

", "advice": "

The ratio of boys as to girls at the dance school is {boysratio} : {girlsratio}.

We can divide the dance students into {boysratio + girlsratio} equal groups, with {boysratio} of the groups for boys, and {girlsratio} of the groups for girls.

How many dance students would be in each group?

{classsize} ÷ {boysratio + girlsratio} = {scalefactor}. There are {scalefactor} students in each group.

There are {girlsratio} x {scalefactor} = {scalefactor*girlsratio} girls, as there are {girlsratio} groups of girls.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"girlsratio": {"name": "girlsratio", "group": "Ungrouped variables", "definition": "boysratio+increment", "description": "

The number of girls in the ratio.

", "templateType": "anything", "can_override": false}, "classsize": {"name": "classsize", "group": "Ungrouped variables", "definition": "scalefactor*(boysratio+girlsratio)", "description": "

The total number of pupils in the dance school.

", "templateType": "anything", "can_override": false}, "scalefactor": {"name": "scalefactor", "group": "Ungrouped variables", "definition": "random(5 .. 16#1)", "description": "

The factor by which the ratio sum is multiplied to get the class size.

", "templateType": "randrange", "can_override": false}, "boysratio": {"name": "boysratio", "group": "Ungrouped variables", "definition": "random(2 .. 4#1)", "description": "

The number of boys in the ratio.

", "templateType": "randrange", "can_override": false}, "increment": {"name": "increment", "group": "Ungrouped variables", "definition": "random(2..6 except boysratio except 2*boysratio except 3*boysratio except 1.5*boysratio except 0.5*boysratio)", "description": "

The increment which is added to boysratio to ensure that there are more girls.

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["boysratio", "increment", "girlsratio", "scalefactor", "classsize"], "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": "

How many girls are there in the dance school?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["{boysratio*scalefactor}", "{girlsratio*scalefactor}", "{trunc(((girlsratio+boysratio)*scalefactor)/2)}", "{girlsratio+boysratio}"], "matrix": ["0", "1", 0, 0], "distractors": ["", "Well done!", "How many more girls than boys were there?", "Have you found the difference between the number of girls and boys?"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Measurement and Geometry strand", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["Bus timetable (7)", "Two-person compass directions (7)", "Nutrition label calculations (7)", "Area by subtraction (10+)", "Thermometer degrees celsius (8)"], "questions": [{"name": "MG Reading a bus timetable (7)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/bus_timetable.png", "/srv/numbas/media/question-resources/bus_timetable.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE", "Western Sydney MESH"], "metadata": {"description": "

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. The bus timetable is shown, and one multiple choice question asked. There are seven potential questions (scenarios).

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

The timetable below shows the stops and times for Route 12 between Yarralumla and the Patents Office at Barton.

^{https://www.flickr.com/photos/lukeorourke/13448688984/}

", "advice": "

Take some time to examine the timetable. Then read the question carefully to determine what is required.

{explanation}

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"scenario": {"name": "scenario", "group": "Ungrouped variables", "definition": "random(scenarios)", "description": "

The randomly selected scenario.

", "templateType": "anything", "can_override": false}, "wrong3": {"name": "wrong3", "group": "Ungrouped variables", "definition": "scenario[\"distractor3\"]", "description": "

The third incorrect answer for the randomly selected scenario.

", "templateType": "anything", "can_override": false}, "correct": {"name": "correct", "group": "Ungrouped variables", "definition": "scenario[\"answer\"]", "description": "

The correct answer for the randomly selected scenario.

", "templateType": "anything", "can_override": false}, "wrong1": {"name": "wrong1", "group": "Ungrouped variables", "definition": "scenario[\"distractor1\"]", "description": "

The first incorrect answer for the randomly selected scenario.

", "templateType": "anything", "can_override": false}, "scenarios": {"name": "scenarios", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n{\\n\\\"question\\\":\\\"Tom arrived at the Deakin shops bus stop at 8:26 am on a Tuesday. How many minutes did he have to wait for the next bus?\\\",\\n\\\"answer\\\":16,\\n\\\"distractor1\\\":14,\\n\\\"distractor2\\\":18,\\n\\\"distractor3\\\":26,\\n\\\"advice\\\":\\\"The next bus after 8:26 am is due at 8:42 am.
There are 16 minutes from 8:26 am until 8:42 am.
So Tom needs to wait 16 minutes.\\\"\\n},\\n{\\n\\\"question\\\":\\\"Jim arrived at the Deakin Shops bus stop at 9:56 am on a Sunday. How many minutes did he have to wait for the next bus?\\\",\\n\\\"answer\\\":76,\\n\\\"distractor1\\\":16,\\n\\\"distractor2\\\":18,\\n\\\"distractor3\\\":56,\\n\\\"advice\\\":\\\"Notice that the 10:12 am bus service from Deakin Shops does not operate on Sundays.
Therefore Jim will have to wait for the 11:12 am service.
This is 1 hour and 16 minutes after 9:56 am, or 76 minutes.
Jim had to wait 76 minutes for the next bus.\\\"\\n},\\n{\\n\\\"question\\\":\\\"How many hours are there between the first bus at Hopetoun Circuit on Monday, and the last bus at Hopetoun Circuit on Monday?\\\",\\n\\\"answer\\\":15,\\n\\\"distractor1\\\":3,\\n\\\"distractor2\\\":13,\\n\\\"distractor3\\\":10,\\n\\\"advice\\\":\\\"The first bus at Hopetoun Circuit on Monday arrives at 7:10 am.
The last bus at Hopetoun Circuit on Monday is at 10:10 pm.
There are 12 hours between 7:10 am and 7:10 pm, then another 3 hours until 10:10 pm.
So there are 15 hours between the first bus and the last bus .\\\"\\n},\\n{\\n\\\"question\\\":\\\"How many buses stop at the Patents Office bus stop on Thursdays?\\\",\\n\\\"answer\\\":14,\\n\\\"distractor1\\\":17,\\n\\\"distractor2\\\":8,\\n\\\"distractor3\\\":12,\\n\\\"advice\\\":\\\"Count all of the buses which stop at the Patents Office stop. Do not include the services marked with a --.
There are 14 services which stop at the Patents Office bus stop on Thursdays.\\\"\\n},\\n{\\n\\\"question\\\":\\\"Mia catches the 10:04 am bus from Yarralumla. She gets off at Manuka Shops to do some shopping. The shopping takes her 1 hour and 50 minutes. She then catches the next bus from the Manuka Shops bus stop to the Kingston Shops. What time will she arrive at the Kingston Shops stop?\\\",\\n\\\"answer\\\":\\\"12 23 pm\\\",\\n\\\"distractor1\\\":\\\"11:23 am\\\",\\n\\\"distractor2\\\":\\\"1:23 pm\\\",\\n\\\"distractor3\\\":\\\"12:28 pm\\\",\\n\\\"advice\\\":\\\"Mia arrives at the Manuka Shops stop at 10:20 am.
After shopping for 1 hour and 50 minutes, it is 12:10 pm.
The next bus arrives at Manuka shops at 12:20 pm, and this bus then arrives at the Kingston Shops bus stop at 12:23 pm.\\\"\\n},\\n{\\n\\\"question\\\":\\\"A bus driver starts her Wednesday shift driving the 7:34 am bus from Yarrumla. Her last route of the day is the 2:04 pm bus from Yarralumla, which she drives to the end of the route. How long was her shift that day?\\\",\\n\\\"answer\\\":\\\"6 hours 54 minutes\\\",\\n\\\"distractor1\\\":\\\"5 hours 6 minutes\\\",\\n\\\"distractor2\\\":\\\"7 hours 2 minutes\\\",\\n\\\"distractor3\\\":\\\"7 hours 6 minutes\\\",\\n\\\"advice\\\":\\\"The bus driver\\'s day starts at 7:34 am and ends at 2:28 pm.
From 7:34 am until 8 am is 26 minutes.
From 8 am until 2 pm is 6 hours.
From 2 pm until 2:28 pm is 28 minutes.
6 hours + 26 minutes + 28 minutes = 6 hours and 54 minutes.
Her shift that day was 6 hours 54 minutes.\\\"\\n},\\n{\\n\\\"question\\\":\\\"What is the shortest time between buses at the Melbourne Avenue bus stop?\\\",\\n\\\"answer\\\":\\\"26 minutes\\\",\\n\\\"distractor1\\\":\\\"30 minutes\\\",\\n\\\"distractor2\\\":\\\"28 minutes\\\",\\n\\\"distractor3\\\":\\\"24 minutes\\\",\\n\\\"advice\\\":\\\"The closest times are 7:45 am and 8:11 am. These times are 26 minutes apart.\\\"\\n}\\n]\"))", "description": "

The 7 possible questions, each along with their correct answer, 3 distractors and the Advice.

", "templateType": "json", "can_override": false}, "Prompt": {"name": "Prompt", "group": "Ungrouped variables", "definition": "scenario[\"question\"]", "description": "

The question for the randomly selected scenario.

", "templateType": "anything", "can_override": false}, "wrong2": {"name": "wrong2", "group": "Ungrouped variables", "definition": "scenario[\"distractor2\"]", "description": "

The second incorrect answer for the randomly selected scenario.

", "templateType": "anything", "can_override": false}, "explanation": {"name": "explanation", "group": "Ungrouped variables", "definition": "scenario[\"advice\"]", "description": "

The customised advice for the given scenario.

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["scenarios", "scenario", "Prompt", "correct", "wrong1", "wrong2", "wrong3", "explanation"], "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": "

Use the timetable to answer the following question.

{Prompt}

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["

\n{correct}", "{wrong1}", "{wrong2}", "{wrong3}"], "matrix": ["1", 0, 0, 0], "distractors": ["You're correct. Well done!", "Read the question carefully and try again.", "Read the question carefully and try again.", "Read the question carefully and try again."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "MG Two-person compass directions (7)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Compass_Ben_150.png", "/srv/numbas/media/question-resources/Compass_Ben_150.png"], ["question-resources/Compass_Ben_200.png", "/srv/numbas/media/question-resources/Compass_Ben_200.png"], ["question-resources/compass_Isaac_225.png", "/srv/numbas/media/question-resources/compass_Isaac_225.png"], ["question-resources/Compass_Ben_Isaac_250.png", "/srv/numbas/media/question-resources/Compass_Ben_Isaac_250.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE", "Western Sydney MESH"], "metadata": {"description": "

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. Two people walk away from a central flagpole, in different directions. The multiple choice question asks for the angle between them. There are seven potential scenarios.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

{name1}, {name2} and {name3} are all standing next to a flagpole.

{direc1}

{direc2}

{name3} turns to look at {name1}. Then {name3} turns in a clockwise direction until {pronoun} is looking at {name2}.

", "advice": "

The example below shows one way of approaching these kinds of questions. Read it through and see if you can then apply the reasoning to the given problem.

Sample question:

Isaac, Ben and Madi are all standing next to a flagpole.

Isaac walks 25 metres in a southerly direction, then turns and walks 25 metres in a westerly direction, then stops.
Ben walks 10 metres in an easterly direction, then turns and walks 10 metres in a southerly direction, then stops.

Madi turns to look at Isaac. Then Madi turns in a clockwise direction until she is looking at Ben.

How many degrees did Madi turn through between looking at Isaac and looking at Ben?

Solution:

Imagine that the flagpole is at the centre of the compass rose below.

The solid yellow lines show the path that Isaac took - south and then west. Effectively, Isaac has travelled in a south-westerly direction because both sections of his walk were the same length (25 metres each).

The solid red lines on the diagram below show the path that Ben took - east and then south. Effectively, Ben has travelled in a south-easterly direction because both sections of his walk were the same length (10 metres each).

Now imagine that Madi is at the centre of the compass rose. She looks first at Isaac, then turns clockwise to look at Ben (see the curved black arrow). It does not matter that Ben and Isaac travelled different distances. We are interested in the angle between them.

How many degrees has she turned through? In this case, she has turned through 3 x 90 degrees.

Madi turned through 270 degrees between looking at Isaac and looking at Ben.

^{Images adapted from https://en.wikipedia.org/wiki/File:Compass_rose_simple.svg}

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"scenarios": {"name": "scenarios", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n{\\n\\\"dir1\\\":\\\"Tim walks 35 metres in a northerly direction, then turns and walks 35 metres in a westerly direction, then stops.\\\",\\n\\\"dir2\\\":\\\"Mick walks 25 metres in a southerly direction, then turns and walks 25 metres in a westerly direction, then stops.\\\",\\n\\\"n1\\\":\\\"Tim\\\",\\n\\\"n2\\\":\\\"Mick\\\",\\n\\\"n3\\\":\\\"Luke\\\",\\n\\\"pnoun\\\":\\\"he\\\",\\n\\\"answer\\\":270,\\n\\\"wrong1\\\":\\\"90\\\",\\n\\\"wrong2\\\":\\\"180\\\",\\n\\\"wrong3\\\":\\\"45\\\"\\n},\\n{\\n\\\"dir1\\\":\\\"Angie walks 25 metres in a northerly direction, then turns and walks 25 metres in an easterly direction, then stops.\\\",\\n\\\"dir2\\\":\\\"Jake walks 30 metres in a westerly direction, then turns and walks 30 metres in a southerly direction, then stops.\\\",\\n\\\"n1\\\":\\\"Angie\\\",\\n\\\"n2\\\":\\\"Jake\\\",\\n\\\"n3\\\":\\\"Liam\\\",\\n\\\"pnoun\\\":\\\"he\\\",\\n\\\"answer\\\":180,\\n\\\"wrong1\\\":\\\"90\\\",\\n\\\"wrong2\\\":\\\"270\\\",\\n\\\"wrong3\\\":\\\"45\\\"\\n},\\n{\\n\\\"dir1\\\":\\\"Brad walks 15 metres in an easterly direction, then turns and walks 15 metres in a southerly direction, then stops.\\\",\\n\\\"dir2\\\":\\\"Subah walks 20 metres in a southerly direction, then turns and walks 20 metres in a westerly direction, then stops.\\\",\\n\\\"n1\\\":\\\"Brad\\\",\\n\\\"n2\\\":\\\"Subah\\\",\\n\\\"n3\\\":\\\"Lisa\\\",\\n\\\"pnoun\\\":\\\"she\\\",\\n\\\"answer\\\":90,\\n\\\"wrong1\\\":\\\"180\\\",\\n\\\"wrong2\\\":\\\"270\\\",\\n\\\"wrong3\\\":\\\"135\\\"\\n},\\n{\\n\\\"dir1\\\":\\\"Maria walks 20 metres in an easterly direction, then turns and walks 20 metres in a northerly direction, then stops.\\\",\\n\\\"dir2\\\":\\\"Tony walks 30 metres in a westerly direction, then turns and walks 30 metres in a northerly direction, then stops.\\\",\\n\\\"n1\\\":\\\"Maria\\\",\\n\\\"n2\\\":\\\"Tony\\\",\\n\\\"n3\\\":\\\"Lara\\\",\\n\\\"pnoun\\\":\\\"she\\\",\\n\\\"answer\\\":270,\\n\\\"wrong1\\\":\\\"180\\\",\\n\\\"wrong2\\\":\\\"90\\\",\\n\\\"wrong3\\\":\\\"135\\\"\\n},\\n{\\n\\\"dir1\\\":\\\"Sue walks 35 metres in an easterly direction, then turns and walks 35 metres in a southerly direction, then stops.\\\",\\n\\\"dir2\\\":\\\"Mark walks 15 metres in an easterly direction, then turns and walks 15 metres in a northerly direction, then stops.\\\",\\n\\\"n1\\\":\\\"Sue\\\",\\n\\\"n2\\\":\\\"Mark\\\",\\n\\\"n3\\\":\\\"Lily\\\",\\n\\\"pnoun\\\":\\\"she\\\",\\n\\\"answer\\\":270,\\n\\\"wrong1\\\":\\\"180\\\",\\n\\\"wrong2\\\":\\\"90\\\",\\n\\\"wrong3\\\":\\\"135\\\"\\n},\\n{\\n\\\"dir1\\\":\\\"Will walks 45 metres in a northerly direction, then stops.\\\",\\n\\\"dir2\\\":\\\"Hana walks 15 metres in a westerly direction, then turns and walks 15 metres in a southerly direction, then stops.\\\",\\n\\\"n1\\\":\\\"Will\\\",\\n\\\"n2\\\":\\\"Hana\\\",\\n\\\"n3\\\":\\\"Li\\\",\\n\\\"pnoun\\\":\\\"she\\\",\\n\\\"answer\\\":225,\\n\\\"wrong1\\\":\\\"180\\\",\\n\\\"wrong2\\\":\\\"90\\\",\\n\\\"wrong3\\\":\\\"135\\\"\\n},\\n{\\n\\\"dir1\\\":\\\"Sara walks 20 metres in a westerly direction, then stops.\\\",\\n\\\"dir2\\\":\\\"John walks 40 metres in a southerly direction, then turns and walks 40 metres in a westerly direction, then stops.\\\",\\n\\\"n1\\\":\\\"Sara\\\",\\n\\\"n2\\\":\\\"John\\\",\\n\\\"n3\\\":\\\"Laz\\\",\\n\\\"pnoun\\\":\\\"he\\\",\\n\\\"answer\\\":315,\\n\\\"wrong1\\\":\\\"45\\\",\\n\\\"wrong2\\\":\\\"270\\\",\\n\\\"wrong3\\\":\\\"135\\\"\\n}\\n]\"))", "description": "

The list of all possible directions, and the number of degrees between the two people (the answer).

", "templateType": "json", "can_override": false}, "direc1": {"name": "direc1", "group": "Ungrouped variables", "definition": "scenario[\"dir1\"]", "description": "

The directions and distances that name1 walks for the chosen scenario.

", "templateType": "anything", "can_override": false}, "index": {"name": "index", "group": "Ungrouped variables", "definition": "random(0 .. 6#1)", "description": "

The index which selects the scenario for the question.

", "templateType": "randrange", "can_override": false}, "scenario": {"name": "scenario", "group": "Ungrouped variables", "definition": "scenarios[index]", "description": "

The selected scenario for the question.

", "templateType": "anything", "can_override": false}, "direc2": {"name": "direc2", "group": "Ungrouped variables", "definition": "scenario[\"dir2\"]", "description": "

The directions and distances that name2 walks for the chosen scenario.

", "templateType": "anything", "can_override": false}, "degrees": {"name": "degrees", "group": "Ungrouped variables", "definition": "scenario[\"answer\"]", "description": "

The correct answer in degrees for the chosen scenario.

", "templateType": "anything", "can_override": false}, "option2": {"name": "option2", "group": "Ungrouped variables", "definition": "scenario[\"wrong1\"]", "description": "

The first wrong answer (distractor).

", "templateType": "anything", "can_override": false}, "option3": {"name": "option3", "group": "Ungrouped variables", "definition": "scenario[\"wrong2\"]", "description": "

The second wrong answer (distractor).

", "templateType": "anything", "can_override": false}, "option4": {"name": "option4", "group": "Ungrouped variables", "definition": "scenario[\"wrong3\"]", "description": "

The third wrong answer (distractor).

", "templateType": "anything", "can_override": false}, "name3": {"name": "name3", "group": "Ungrouped variables", "definition": "scenario[\"n3\"]", "description": "

The name of the third person.

", "templateType": "anything", "can_override": false}, "pronoun": {"name": "pronoun", "group": "Ungrouped variables", "definition": "scenario[\"pnoun\"]", "description": "

Either \"he\" or \"she\" depending on the gender of name3.

", "templateType": "anything", "can_override": false}, "name1": {"name": "name1", "group": "Ungrouped variables", "definition": "scenario[\"n1\"]", "description": "

The name of the first person.

", "templateType": "anything", "can_override": false}, "name2": {"name": "name2", "group": "Ungrouped variables", "definition": "scenario[\"n2\"]", "description": "

The name of the second person.

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["scenarios", "index", "scenario", "name1", "name2", "name3", "pronoun", "direc1", "direc2", "degrees", "option2", "option3", "option4"], "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": "

How many degrees did {name3} turn through between looking at {name1} and looking at {name2}?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["{degrees}", "{option2}", "{option3}", "{option4}"], "matrix": ["1", 0, 0, 0], "distractors": ["Well done - you are correct!", "Read the question carefully and try again.", "Read the question carefully and try again.", "Read the question carefully and try again."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "MG Mass calculations from a nutrition label (7)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/FDA_Nutrition_Facts_Label_2016_300.png", "/srv/numbas/media/question-resources/FDA_Nutrition_Facts_Label_2016_300.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE", "Western Sydney MESH"], "metadata": {"description": "

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. A nutrition label is shown, and one multiple choice question asked. There are seven potential questions (scenarios).

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

The nutrition facts for a snack food are given on the nutrition panel below.

^{https://commons.wikimedia.org/wiki/File:FDA_Nutrition_Facts_Label_2016.png}

", "advice": "

{advice}

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"scenarios": {"name": "scenarios", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n {\\n \\\"question\\\":\\\"Dan eats three servings of the snack. How many grams of sodium does he consume in total?\\\",\\n \\\"answer\\\":\\\"0.48\\\",\\n \\\"distractor1\\\":\\\"0.048\\\",\\n \\\"distractor2\\\":\\\"4.8\\\",\\n \\\"distractor3\\\":\\\"48\\\",\\n \\\"feedback\\\":\\\"Each serving contains 160 milligrams of sodium.
Three servings would contain 3 x 160 = 480 mg of sodium.
To convert mg to grams, divide by 1000, as there are 1000 mg in a gram.
480 \u00f7 1000 = 0.48 so Dan consumes 0.48 grams of sodium in total.\\\"\\n },\\n {\\n \\\"question\\\":\\\"How many serves of the snack would be needed if I wanted to consume 1 gram of Calcium?\\\",\\n \\\"answer\\\":4,\\n \\\"distractor1\\\":2,\\n \\\"distractor2\\\":3,\\n \\\"distractor3\\\":5,\\n \\\"feedback\\\":\\\"One serving contains 260 milligrams of Calcium.
There are 1000 mg in one gram. 1000 \u00f7 260 = 3.85 (to 2 decimal places).
Therefore 4 servings would be needed to reach the required amount of Calcium .\\\"\\n },\\n {\\n \\\"question\\\":\\\"What percentage (by weight) of one serving, is Potassium?\\\",\\n \\\"answer\\\":\\\"0.4%\\\",\\n \\\"distractor1\\\":\\\"4%\\\",\\n \\\"distractor2\\\":\\\"2.35%\\\",\\n \\\"distractor3\\\":\\\"6%\\\",\\n \\\"feedback\\\":\\\"One serving weighs 55 g.
Convert this to milligrams by multiplying by 1000. One serving weighs 55 000 mg.
What proportion of 55 000 mg is 235 mg?
235 \u00f7 55 000 x 100 = 0.427%.
The closest answer is therefore 0.4%.\\\"\\n },\\n {\\n \\\"question\\\":\\\"What percentage (by weight) of one serving, is Added Sugar?\\\",\\n \\\"answer\\\":\\\"18%\\\",\\n \\\"distractor1\\\":\\\"20%\\\",\\n \\\"distractor2\\\":\\\"5.5%\\\",\\n \\\"distractor3\\\":\\\"10%\\\",\\n \\\"feedback\\\":\\\"Added Sugars are 10 g out of the 55 g serving.
To convert this proportion to a percentage, calculate 10 \u00f7 55 x 100 = 18.18.
Therefore around 18% of the snack is Added Sugar.\\\"\\n },\\n {\\n \\\"question\\\":\\\"How many times more Iron, by weight, is there in one serving of the snack, compared to Vitamin D? Note that there are 1000 micrograms in 1 milligram, and microgram can be abbreviated to mcg.\\\",\\n \\\"answer\\\":\\\"4000\\\",\\n \\\"distractor1\\\":\\\"400\\\",\\n \\\"distractor2\\\":\\\"45\\\",\\n \\\"distractor3\\\":\\\"4.5\\\",\\n \\\"feedback\\\":\\\"Convert 8 mg of Iron to micrograms.
8 x 1000 = 8000.
There are 8000 micrograms of Iron in one serving.
Then divide 8000 micrograms (Iron) by 2 micrograms (Vitamin D).
8000 \u00f7 2 = 4000.
There is 4000 times more Iron, by weight, in the snack, than Vitamin D.\\\"\\n },\\n {\\n \\\"question\\\":\\\"Which of the following contributes the largest mass to one serving of the snack?\\\",\\n \\\"answer\\\":\\\"Protein\\\",\\n \\\"distractor1\\\":\\\"Sodium\\\",\\n \\\"distractor2\\\":\\\"Calcium\\\",\\n \\\"distractor3\\\":\\\"Saturated Fat\\\",\\n \\\"feedback\\\":\\\"Protein and Saturated Fat are measured in grams. Sodium and Calcium are measured in milligrams.
One milligram is one thousand times smaller than a gram.
Therefore the largest weight in one serving, from the options given, is Protein at 3 grams.\\\"\\n },\\n {\\n \\\"question\\\":\\\"In one serving, what is the total mass of Vitamin D, Calcium and Iron? Note that there are 1000 micrograms in 1 milligram, and microgram can be abbreviated to mcg.\\\",\\n \\\"answer\\\":\\\"268.002 mg\\\",\\n \\\"distractor1\\\":\\\"268.02 mg\\\",\\n \\\"distractor2\\\":\\\"26 802 micrograms\\\",\\n \\\"distractor3\\\":\\\"2 682 micrograms\\\",\\n \\\"feedback\\\":\\\"Convert the Vitamin D mass to milligrams.
2 \u00f7 1000 = 0.002.
Add the three masses in milligrams. 0.002 + 260 + 8 = 268.002.
The total mass of the three vitamins and minerals is 268.002 mg.\\\"\\n }\\n]\"))", "description": "

The list of all potential questions, answers, distractors and feedback (advice).

", "templateType": "json", "can_override": false}, "scenario": {"name": "scenario", "group": "Ungrouped variables", "definition": "random(scenarios)", "description": "

The particular scenario for the current question.

", "templateType": "anything", "can_override": false}, "prompt": {"name": "prompt", "group": "Ungrouped variables", "definition": "scenario[\"question\"]", "description": "

The randomly selected question.

", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "scenario[\"answer\"]", "description": "

The correct answer for the randomly selected question.

", "templateType": "anything", "can_override": false}, "dis1": {"name": "dis1", "group": "Ungrouped variables", "definition": "scenario[\"distractor1\"]", "description": "

The first incorrect answer for the randomly selected question.

", "templateType": "anything", "can_override": false}, "dis2": {"name": "dis2", "group": "Ungrouped variables", "definition": "scenario[\"distractor2\"]", "description": "

The second incorrect answer for the randomly selected question.

", "templateType": "anything", "can_override": false}, "dis3": {"name": "dis3", "group": "Ungrouped variables", "definition": "scenario[\"distractor3\"]", "description": "

The third incorrect answer for the randomly selected question.

", "templateType": "anything", "can_override": false}, "advice": {"name": "advice", "group": "Ungrouped variables", "definition": "scenario[\"feedback\"]", "description": "

The advice (feedback) for the randomly selected question.

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["scenarios", "scenario", "prompt", "ans", "dis1", "dis2", "dis3", "advice"], "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": "

{prompt}

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["{ans}", "{dis1}", "{dis2}", "{dis3}"], "matrix": ["1", 0, 0, 0], "distractors": ["Well done! You are correct.", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "MG Area by subtraction (10+)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/classroom.png", "/srv/numbas/media/question-resources/classroom.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE", "Western Sydney MESH"], "metadata": {"description": "

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. Students must calculate the area of the classroom excluding the storeroom. The length and width of the classroom and the area of the storeroom are randomly generated.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

A rectangular primary school classroom has dimensions {width} metres by {length} metres. A storeroom in one corner has floor area {area} m².

", "advice": "

The area of a rectangle is given by the formula Area = Length x Breadth.

The area of the rectangular classroom is {width} x {length} = {width*length} square metres (abbreviated to m²) .

The area of the storeroom must be subtracted from this.

{width*length} m² - {area} m² = {width*length-area} m².

The floor area of the classroom is {width*length-area} m².

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"width": {"name": "width", "group": "Ungrouped variables", "definition": "random(5 .. 8#0.5)", "description": "

Width of classroom is between 5m and 8m, in half-metre increments.

", "templateType": "randrange", "can_override": false}, "extrawidth": {"name": "extrawidth", "group": "Ungrouped variables", "definition": "random(1 .. 2.5#0.5)", "description": "

This is how many metres greater the length is, than the width.

", "templateType": "randrange", "can_override": false}, "area": {"name": "area", "group": "Ungrouped variables", "definition": "precround(0.15*width*length,0)", "description": "

Area of storeroom is 15% of area of classroom, rounded to nearest whole number.

", "templateType": "anything", "can_override": false}, "length": {"name": "length", "group": "Ungrouped variables", "definition": "width+extrawidth", "description": "

Length of classroom is between 1 and 2.5 metres more than width.

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["width", "length", "area", "extrawidth"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "prompt": "

What is the floor area of the classroom in square metres, excluding the storeroom? The diagram is not drawn to scale.

", "minValue": "{length}*{width}-{area}", "maxValue": "{length}*{width}-{area}", "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": "MG NC Thermometers degrees celsius (8)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/thermometer_5_degrees.png", "/srv/numbas/media/question-resources/thermometer_5_degrees.png"], ["question-resources/thermometer_19_degrees.png", "/srv/numbas/media/question-resources/thermometer_19_degrees.png"], ["question-resources/thermometer_32_degrees.png", "/srv/numbas/media/question-resources/thermometer_32_degrees.png"], ["question-resources/thermometer_minus_6_degrees.png", "/srv/numbas/media/question-resources/thermometer_minus_6_degrees.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE", "Western Sydney MESH"], "metadata": {"description": "

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. NC = Non-Calculator strand. Students are shown an image of a thermometer calibrated in degrees Celsius. Student must answer a question using the thermometer. The image is randomly selected from a pool of 4. There are two different potential questions for each thermometer. Hence 8 different questions in total.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

This thermometer is calibrated in degrees Celsius. Use the temperature reading on the thermometer to answer the question shown below the thermometer.

{image('resources/question-resources/'+picture)}

^{https://www.math-aids.com/cgi/pdf_viewer_6.cgi?script_name=measurement_reading_thermometers.pl&scale=3&kind=1&language=0&memo=&answer=1&x=78&y=24}

", "advice": "

How to read the thermometer

The major division on this thermometer is 10°C. In other words, the numbers on the labelled graduations increase by 10°C.

The minor division on this thermometer is 2°C. In other words, the space between any two graduation marks represents 2°C.

The reading is halfway between two graduation marks, so you will need to add 1°C to the lower reading.

Use this knowledge to read the temperature on the thermometer.

Some useful things to know about temperatures measured in degrees Celsius:

Water will freeze at 0°C and boil at 100°C.
An air temperature between 18°C and 25°C will feel comfortable to most people.
An air temperature above 30°C will feel hot to most people.
Normal human body temperature is 37°C.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"question": {"name": "question", "group": "Ungrouped variables", "definition": "scenario[\"qn\"]", "description": "

The question for the randomly selected scenario.

", "templateType": "anything", "can_override": false}, "scenarios": {"name": "scenarios", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n{\\n\\\"pic\\\":\\\"thermometer_minus_6_degrees.png\\\",\\n\\\"qn\\\":\\\"Which temperature would be 4 degrees warmer than the temperature shown?\\\",\\n\\\"ans\\\":\\\"-2°C\\\",\\n\\\"wrong1\\\":\\\"2°C\\\",\\n\\\"wrong2\\\":\\\"-12°C\\\",\\n\\\"odd\\\":\\\"n\\\"\\n},\\n{\\n\\\"pic\\\":\\\"thermometer_minus_6_degrees.png\\\",\\n\\\"qn\\\":\\\"Which temperature would be 4 degrees colder than the temperature shown?\\\",\\n\\\"ans\\\":\\\"-10°C\\\",\\n\\\"wrong1\\\":\\\"-2°C\\\",\\n\\\"wrong2\\\":\\\"-12°C\\\",\\n\\\"odd\\\":\\\"n\\\"\\n},\\n{\\n\\\"pic\\\":\\\"thermometer_5_degrees.png\\\",\\n\\\"qn\\\":\\\"If the thermometer displays the outside temperature, the outside air would feel:\\\",\\n\\\"ans\\\":\\\"quite cold\\\",\\n\\\"wrong1\\\":\\\"very hot\\\",\\n\\\"wrong2\\\":\\\"comfortable\\\",\\n\\\"odd\\\":\\\"y\\\"\\n},\\n{\\n\\\"pic\\\":\\\"thermometer_5_degrees.png\\\",\\n\\\"qn\\\":\\\"If the temperature increased by 5°C above the temperature shown, what would the temperature then be?\\\",\\n\\\"ans\\\":\\\"10°C\\\",\\n\\\"wrong1\\\":\\\"0°C\\\",\\n\\\"wrong2\\\":\\\"15°C\\\",\\n\\\"odd\\\":\\\"y\\\"\\n},\\n{\\n\\\"pic\\\":\\\"thermometer_19_degrees.png\\\",\\n\\\"qn\\\":\\\"If the thermometer displays the temperature outside, the outside air would feel:?\\\",\\n\\\"ans\\\":\\\"comfortable\\\",\\n\\\"wrong1\\\":\\\"very hot\\\",\\n\\\"wrong2\\\":\\\"very cold\\\",\\n\\\"odd\\\":\\\"y\\\"\\n},\\n{\\n\\\"pic\\\":\\\"thermometer_19_degrees.png\\\",\\n\\\"qn\\\":\\\"If the temperature increased by 3°C above the temperature shown, what would the temperature then be?\\\",\\n\\\"ans\\\":\\\"22°C\\\",\\n\\\"wrong1\\\":\\\"16°C\\\",\\n\\\"wrong2\\\":\\\"25°C\\\",\\n\\\"odd\\\":\\\"y\\\"\\n},\\n{\\n\\\"pic\\\":\\\"thermometer_32_degrees.png\\\",\\n\\\"qn\\\":\\\"If the thermometer displays the temperature outside, it could be a good day for:\\\",\\n\\\"ans\\\":\\\"swimming\\\",\\n\\\"wrong1\\\":\\\"skiing\\\",\\n\\\"wrong2\\\":\\\"long distance running\\\",\\n\\\"odd\\\":\\\"n\\\"\\n},\\n{\\n\\\"pic\\\":\\\"thermometer_32_degrees.png\\\",\\n\\\"qn\\\":\\\"What is the minimum temperature that could be measured using this thermometer?\\\",\\n\\\"ans\\\":\\\"-28°C\\\",\\n\\\"wrong1\\\":\\\"-24°C\\\",\\n\\\"wrong2\\\":\\\"-16°C\\\",\\n\\\"odd\\\":\\\"n\\\"\\n}\\n]\"))", "description": "

The list of images with corresponding question, answer, two distractors and the odd/even status of the reading.

", "templateType": "json", "can_override": false}, "scenario": {"name": "scenario", "group": "Ungrouped variables", "definition": "random(scenarios)", "description": "

The randomly selected scenario.

", "templateType": "anything", "can_override": false}, "picture": {"name": "picture", "group": "Ungrouped variables", "definition": "scenario[\"pic\"]", "description": "

The image for the randomly selected scenario.

", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "scenario[\"ans\"]", "description": "

The correct answer for the randomly selected scenario.

", "templateType": "anything", "can_override": false}, "dis1": {"name": "dis1", "group": "Ungrouped variables", "definition": "scenario[\"wrong1\"]", "description": "

The first incorrect answer for the randomly selected scenario.

", "templateType": "anything", "can_override": false}, "dis2": {"name": "dis2", "group": "Ungrouped variables", "definition": "scenario[\"wrong2\"]", "description": "

The second incorrect answer for the randomly selected scenario.

", "templateType": "anything", "can_override": false}, "midway": {"name": "midway", "group": "Ungrouped variables", "definition": "scenario[\"odd\"]", "description": "

The odd/even status for the randomly selected scenario (used in Advice).

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["scenarios", "scenario", "picture", "question", "answer", "dis1", "dis2", "midway"], "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": "

{question}

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["{answer}", "{dis1}", "{dis2}"], "matrix": ["1", 0, 0], "distractors": ["Well done! ", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Statistics and Probability strand", "pickingStrategy": "all-ordered", "pickQuestions": "10", "questionNames": ["Water usage (7)", "Pie chart for LANTITE (7)", "Mens health infographic (7)", "Comfort zone (5)", "Airline chart distance vs cost (7)", "African literacy bar chart (7)"], "questions": [{"name": "SP Water usage column charts (7)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/How_does_your_home_compare.png", "/srv/numbas/media/question-resources/How_does_your_home_compare.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE", "Western Sydney MESH"], "metadata": {"description": "

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. Students are asked a multiple choice question based on a series of bar charts. The question is randomly selected from a pool of seven questions.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Percentage of grade 6 pupils reaching reading proficiency levels— Southern and Eastern Africa Consortium for Monitoring Educational Percentage of grade 6 pupils reaching reading proficiency levels— Southern and Eastern Africa Consortium for Monitoring Educational

The chart below shows the average amount of water used per household per day in Sydney.

These amounts depend upon the number of people in the household, the size of the property in square metres, and the billing quarter (three month period).

^{https://www.sydneywater.com.au/web/groups/publicwebcontent/documents/document/zgrf/mdgw/~edisp/dd_080908.pdf}

", "advice": "

General advice:

Consider how to read this chart:

The three coloured columns show 1-person, 3-person and 5-person households.
Each row is for a particular property size (small, medium or large).
The billing periods are listed at the top of the chart (Nov - Jan, Feb - Apr etc).

Specific Advice:

{advice}

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"correctanswer": {"name": "correctanswer", "group": "Ungrouped variables", "definition": "scenario[\"answer\"]", "description": "

The correct answer for the randomly chosen scenario.

", "templateType": "anything", "can_override": false}, "wrong1": {"name": "wrong1", "group": "Ungrouped variables", "definition": "scenario[\"distractor1\"]", "description": "

The first incorrect answer (distractor) for the randomly chosen scenario.

", "templateType": "anything", "can_override": false}, "scenarios": {"name": "scenarios", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n {\\n \\\"question\\\":\\\"Which property size consistently uses the most water?\\\",\\n \\\"answer\\\":\\\"Large\\\",\\n \\\"distractor1\\\":\\\"Medium\\\",\\n \\\"distractor2\\\":\\\"Small\\\",\\n \\\"feedback\\\":\\\"Every column in the third row of the chart shows a larger number than either of those directly above it.
Therefore large properties consistently use the most water.\\\"\\n },\\n {\\n \\\"question\\\":\\\"What is the average daily water usage for a three-person household in a 550 square metre property during the May-July quarter?\\\",\\n \\\"answer\\\":\\\"447 L\\\",\\n \\\"distractor1\\\":\\\"477 L\\\",\\n \\\"distractor2\\\":\\\"425 L\\\",\\n \\\"feedback\\\":\\\"The property is a medium sized property as it is between 500 and 700 square metres, so look along the second row.
Look at the middle column in the May-July grouping.
The average daily water usage is 447 L.\\\"\\n },\\n {\\n \\\"question\\\":\\\"Which sized property has an average daily water usage of 258 L for a single person during August to October?\\\",\\n \\\"answer\\\":\\\"Large\\\",\\n \\\"distractor1\\\":\\\"Medium\\\",\\n \\\"distractor2\\\":\\\"Small\\\",\\n \\\"feedback\\\":\\\"Look for the 1-person column underneath the Aug-Oct grouping which has an average daily water usage of 258 L.
The required 1-person column is in the Large property row.\\\"\\n },\\n {\\n \\\"question\\\":\\\"What is the average daily water usage during one year for a typical 5-person household on an 800 square metre block?\\\",\\n \\\"answer\\\":\\\"647 L\\\",\\n \\\"distractor1\\\":\\\"2588 L\\\",\\n \\\"distractor2\\\":\\\"2106 L\\\",\\n \\\"feedback\\\":\\\"An 800 square metre block is in the bottom row (>701 square metres).
The average daily water usage for a typical 5-person houshold on this row is calculated by adding the four quarterly readings then dividing the result by 4.
661 + 666 + 619 + 642 = 2588.
Dividing this by 4 gives 647 L.\\\"\\n },\\n {\\n \\\"question\\\":\\\"How many kilolitres of water would an average 3-person household living on a 450 square metre block use in total during the Nov-Jan quarter? There are 92 days in the Nov-Jan quarter.\\\",\\n \\\"answer\\\":\\\"41.952 kL\\\",\\n \\\"distractor1\\\":\\\"22.356 kL\\\",\\n \\\"distractor2\\\":\\\"419.52 kL\\\",\\n \\\"feedback\\\":\\\"From the chart, the average daily water usage for the Nov-Jan quarter for an average 3-person household living on a 450 square metre block is 456 L.
Multiply this by the 92 days in that quarter.
This gives 41952 L.
This then needs to be converted to kilolitres, by dividing by 1000.
The total water usage is 41.952 kL.\\\"\\n },\\n {\\n \\\"question\\\":\\\"An average 5-person household used a total of 55.568 kL of water in the May-July quarter. There are 92 days in the May-July quarter. Which kind of property did they live on?\\\",\\n \\\"answer\\\":\\\" Medium property\\\",\\n \\\"distractor1\\\":\\\"Small property\\\",\\n \\\"distractor2\\\":\\\"Large property\\\",\\n \\\"feedback\\\":\\\"Multiply 55.568 kL by 1000 to convert it to litres. This gives 55 568 L.
Then divide this by 92 to get the average daily water usage of 604 L.
Look in the May-July group for the 5-person household with average daily water usage of 604 L.
The property was a medium property.\\\"\\n },\\n {\\n \\\"question\\\":\\\"The average daily water usage for a 7-person household living in a large property during the Feb-April quarter would be closest to:\\\",\\n \\\"answer\\\":\\\"770 L\\\",\\n \\\"distractor1\\\":\\\"900 L\\\",\\n \\\"distractor2\\\":\\\"850 L kg\\\",\\n \\\"feedback\\\":\\\"The increase in water usage for 5-person households compared to 3-person households is small relative to the increase in water usage for 3-person households compared to 1-person households.
You can assume that the increase in water usage for 7-person households compared to 5-person households is smaller still.
A 5-person household living on a large property uses an average of 666 L of water daily. This is an increase of 168 L from the 3-person household.
666 L + 168 L = 834 L. We are looking for an answer smaller than this.
The average daily water usage for a 7-person household living in a large property during the Feb-April quarter would be closest to 770L.\\\"\\n }\\n]\"))", "description": "

The question statement, correct answer, three distractors and Advice for each of the seven possible questions.

", "templateType": "json", "can_override": false}, "wrong2": {"name": "wrong2", "group": "Ungrouped variables", "definition": "scenario[\"distractor2\"]", "description": "

The second incorrect answer (distractor) for the randomly chosen scenario.

", "templateType": "anything", "can_override": false}, "scenario": {"name": "scenario", "group": "Ungrouped variables", "definition": "random(scenarios)", "description": "

The randomly chosen scenario, consisting of question statement, correct answer, three distractors and Advice.

", "templateType": "anything", "can_override": false}, "questionwording": {"name": "questionwording", "group": "Ungrouped variables", "definition": "scenario[\"question\"]", "description": "

The question statement for the randomly chosen scenario.

", "templateType": "anything", "can_override": false}, "advice": {"name": "advice", "group": "Ungrouped variables", "definition": "scenario[\"feedback\"]", "description": "

The custom advice (feedback) for the selected scenario question.

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["scenarios", "scenario", "questionwording", "correctanswer", "wrong1", "wrong2", "advice"], "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": "

Use the chart to answer the following question:

{questionwording}

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["

\n{correctanswer}", "{wrong1}", "{wrong2}"], "matrix": ["1", 0, 0], "distractors": ["Well done!", "Have you read the question and the axis labels carefully? ", "Have you read the question and the axis labels carefully? "]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SP NC Pie chart for LANTITE test dates (7)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/when_sitting_lantite_test.png", "/srv/numbas/media/question-resources/when_sitting_lantite_test.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE", "Western Sydney MESH"], "metadata": {"description": "

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. NC = Non-Calculator strand. Students are asked a multiple choice question based on a pie chart. The question is randomly selected from a pool of seven questions.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

In April, some Teacher Education students were asked when they were planning to sit the LANTITE numeracy test.

Their responses are shown in the pie chart below.

", "advice": "

{advice}

The question for the randomly selected scenario.

", "templateType": "anything", "can_override": false}, "scenarios": {"name": "scenarios", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n{\\n\\\"qn\\\":\\\"What percentage of students were hoping to sit the test in the May window?\\\",\\n\\\"ans\\\":\\\"6.2%\\\",\\n\\\"wrong1\\\":\\\"18.8%\\\",\\n\\\"wrong2\\\":\\\"266.2%\\\",\\n\\\"wrong3\\\":\\\"7.2%\\\",\\n\\\"feedback\\\":\\\"All of the percentages must add to 100%.
The two May sectors must add to 25%.
25% - 18.8% = 6.2%.
6.2% of students were hoping to sit the test in the May window.\\\"\\n},\\n{\\\"qn\\\":\\\"How many students indicated that they were probably sitting the test in the November test window?\\\",\\n\\\"ans\\\":\\\"2\\\",\\n\\\"wrong1\\\":\\\"1\\\",\\n\\\"wrong2\\\":\\\"3\\\",\\n\\\"wrong3\\\":\\\"4\\\",\\n\\\"feedback\\\":\\\"12.5% of students indicated that they were probably sitting the test in the November test window.
As a fraction this is $\\\\\\\\frac\\\\\\{1\\\\\\}\\\\\\{8\\\\\\}$.
$\\\\\\\\frac\\\\\\{1\\\\\\}\\\\\\{8\\\\\\}$ of 16 = 2.
Therefore 2 students indicated that they were probably sitting the test in the November test window.\\\"\\n},\\n{\\\"qn\\\":\\\"What percentage of students were probably sitting the test in the second half of the year?\\\",\\n\\\"ans\\\":\\\"62.5%\\\",\\n\\\"wrong1\\\":\\\"12.5%\\\",\\n\\\"wrong2\\\":\\\"50%\\\",\\n\\\"wrong3\\\":\\\"25%\\\",\\n\\\"feedback\\\":\\\"August and November are in the second half of the year.
50% + 12.5% = 62.5%.
Therefore 62.5% of students were probably sitting the test in the second half of the year.\\\"\\n},\\n{\\\"qn\\\":\\\"What fraction of students responded in the Other category?\\\",\\n\\\"ans\\\":\\\"$\\\\\\\\frac\\\\\\{1\\\\\\}\\\\\\{8\\\\\\}$\\\",\\n\\\"wrong1\\\":\\\"$\\\\\\\\frac\\\\\\{1\\\\\\}\\\\\\{4\\\\\\}$\\\",\\n\\\"wrong2\\\":\\\"$\\\\\\\\frac\\\\\\{1\\\\\\}\\\\\\{2\\\\\\}$\\\",\\n\\\"wrong3\\\":\\\"$\\\\\\\\frac\\\\\\{1\\\\\\}\\\\\\{5\\\\\\}$\\\",\\n\\\"feedback\\\":\\\"The Other category is 12.5% of the total.
25% is equal to $\\\\\\\\frac\\\\\\{1\\\\\\}\\\\\\{4\\\\\\}$ and 12.5% is half of 25%.
Therefore 12.5% is half of $\\\\\\\\frac\\\\\\{1\\\\\\}\\\\\\{4\\\\\\}$, which gives $\\\\\\\\frac\\\\\\{1\\\\\\}\\\\\\{8\\\\\\}$.
The Other category is $\\\\\\\\frac\\\\\\{1\\\\\\}\\\\\\{8\\\\\\}$ of the total.\\\"\\n},\\n{\\\"qn\\\":\\\"The type of data collected in this survey is:\\\",\\n\\\"ans\\\":\\\"categorical\\\",\\n\\\"wrong1\\\":\\\"quantitative\\\",\\n\\\"wrong2\\\":\\\"numerical\\\",\\n\\\"wrong3\\\":\\\"proportional\\\",\\n\\\"feedback\\\":\\\"A pie chart always represents categorical data.
That is, data where the survey participants select one option from a number of supplied options.\\\"\\n},\\n{\\\"qn\\\":\\\"What percentage of students nominated one or other of the May test window options?\\\",\\n\\\"ans\\\":\\\"25%\\\",\\n\\\"wrong1\\\":\\\"18.8%\\\",\\n\\\"wrong2\\\":\\\"30%\\\",\\n\\\"wrong3\\\":\\\"6.2%\\\",\\n\\\"feedback\\\":\\\"One May option is labelled as 18.8% and the other May option is not labelled.
However, the two May options together make up $\\\\\\\\frac\\\\\\{1\\\\\\}\\\\\\{4\\\\\\}$ of the chart, which is the same as 25%.\\\"\\n},\\n{\\\"qn\\\":\\\"If 1000 students had been asked the same question, could we conclude that 125 of them would probably sit the test in the November test window?\\\",\\n\\\"ans\\\":\\\"No, because the original sample size was very small.\\\",\\n\\\"wrong1\\\":\\\"Yes, because 12.5% of 1000 is 125.\\\",\\n\\\"wrong2\\\":\\\"No, because 12.5% of 1000 is not 125.\\\",\\n\\\"wrong3\\\":\\\"Yes, because the data is proportional.\\\",\\n\\\"feedback\\\":\\\"The original survey only had 16 respondents. This is a very small sample size.
We cannot be sure that the survey responses will be in the same proportions for a much larger sample (number of people).\\\"\\n}\\n]\"))", "description": "

The list of images with corresponding question, answer, two distractors and the odd/even status of the reading.

", "templateType": "json", "can_override": false}, "scenario": {"name": "scenario", "group": "Ungrouped variables", "definition": "random(scenarios)", "description": "

The randomly selected scenario.

", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "scenario[\"ans\"]", "description": "

The correct answer for the randomly selected scenario.

", "templateType": "anything", "can_override": false}, "dis1": {"name": "dis1", "group": "Ungrouped variables", "definition": "scenario[\"wrong1\"]", "description": "

The first incorrect answer for the randomly selected scenario.

", "templateType": "anything", "can_override": false}, "dis2": {"name": "dis2", "group": "Ungrouped variables", "definition": "scenario[\"wrong2\"]", "description": "

The second incorrect answer for the randomly selected scenario.

", "templateType": "anything", "can_override": false}, "dis3": {"name": "dis3", "group": "Ungrouped variables", "definition": "scenario[\"wrong3\"]", "description": "

The third incorrect answer for the randomly selected scenario.

", "templateType": "anything", "can_override": false}, "advice": {"name": "advice", "group": "Ungrouped variables", "definition": "scenario[\"feedback\"]", "description": "

The customised feedback for the Advice section.

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["scenarios", "scenario", "question", "answer", "dis1", "dis2", "dis3", "advice"], "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": "

{question}

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["{answer}", "{dis1}", "{dis2}", "{dis3}"], "matrix": ["1", 0, 0, 0], "distractors": ["Well done! ", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SP Mens health infographic using birth year (7)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/air_force_medical_infographic.png", "/srv/numbas/media/question-resources/air_force_medical_infographic.png"], ["question-resources/air_force_medical_infographic_550.png", "/srv/numbas/media/question-resources/air_force_medical_infographic_550.png"], ["question-resources/air_force_medical_infographic_500.png", "/srv/numbas/media/question-resources/air_force_medical_infographic_500.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE"], "metadata": {"description": "

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. Students are shown an infographic, given the details of one man and asked how many routine screenings they should have. There are seven possible questions.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

The infographic below shows the recommended routine health screenings for males.

^{https://www.airforcemedicine.af.mil/News/Art/igphoto/2001546026/}

", "advice": "

{names[index]} was born in {year[index]}.

In the year 2019 he is 2019 - {year[index]} = {2019 - year[index]} years old.

He has normal blood pressure, so will not require diabetes screening. He has no symptoms of depression.

He {smoker[index]}.

Based on these facts, use the infographic to determine the number of screenings he needs.

{names[index]} should have {screenings[index]} health {plural[index]}.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"smoker": {"name": "smoker", "group": "Ungrouped variables", "definition": "['is a current smoker','is a current smoker','is a current smoker','is a former smoker','is a former smoker','has never smoked','has never smoked','has never smoked','has never smoked']", "description": "

The list which states the smoking status of each person.

", "templateType": "anything", "can_override": false}, "names": {"name": "names", "group": "Ungrouped variables", "definition": "['Joe','Wayne','Yan','Costa','Jose','Tim','Bruce','Steve','Lee']", "description": "

The list of all potential names.

", "templateType": "anything", "can_override": false}, "plural": {"name": "plural", "group": "Ungrouped variables", "definition": "['screenings','screenings','screenings','screening','screenings','screenings','screenings','screening','screenings']", "description": "

The list which has the correct word - 'screening' if only 1 screening is recommended, and 'screenings' for 2 or more recommended screenings. Used in the Advice section. This could also have been done with conditional statements.

", "templateType": "anything", "can_override": false}, "year": {"name": "year", "group": "Ungrouped variables", "definition": "[1962,1969,1953,1985,1983,1969,1973,1991,1951]", "description": "

The list of all potential birth years.

", "templateType": "anything", "can_override": false}, "screenings": {"name": "screenings", "group": "Ungrouped variables", "definition": "[4,3,4,1,2,3,2,1,2]", "description": "

The list containing the number of recommended screenings (the answer).

", "templateType": "anything", "can_override": false}, "index": {"name": "index", "group": "Ungrouped variables", "definition": "random(0 .. 8#1)", "description": "

The index to select one person's name, their birth year, their smoking status, the correct screening/screenings word, and the number of screenings recommended (the answer).

", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["index", "names", "year", "screenings", "smoker", "plural"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "prompt": "

{names[index]} was born in {year[index]}. He {smoker[index]}. He had his blood pressure checked last year and it is in the normal range. He is not African-American. He has no symptoms of depression.

According to the infographic, how many routine screenings are recommended in 2019 for {names[index]}?

", "minValue": "screenings[index]", "maxValue": "screenings[index]", "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": "SP Comfort zone (5)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Comfort_chart.png", "/srv/numbas/media/question-resources/Comfort_chart.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE", "Western Sydney MESH"], "metadata": {"description": "

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. Students are asked two true/false questions based on a chart. The pair of true/false questions are randomly selected from a pool of five pairs of questions.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

The chart below can be used to determine whether a room will feel comfortable, for a given temperature and level of relative humidity.

Points inside the shaded area should feel comfortable for most people.

Points outside of the shaded area will not feel comfortable for most people.

Use the chart to decide whether each statement below is True or False:

", "advice": "

Examine the chart, in particular noting the axis labels and scales, and read the question carefully.

For the first statement:

{explanation1}

For the second statement:

{explanation2}

The randomly selected scenario.

", "templateType": "anything", "can_override": false}, "correct1": {"name": "correct1", "group": "Ungrouped variables", "definition": "scenario[\"answer1\"]", "description": "

The first correct answer for the randomly selected scenario.

", "templateType": "anything", "can_override": false}, "scenarios": {"name": "scenarios", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n{\\n\\\"question1\\\":\\\"A room with temperature $25$°C and relative humidity $60\\\\\\\\%$ would feel comfortable to most people.\\\",\\n\\\"answer1\\\":\\\"True\\\",\\n\\\"advice1\\\":\\\"The intersection of the $25$°C horizontal line and the $60\\\\\\\\%$ vertical line lies within the shaded area.
Therefore the room would feel comfortable to most people, so the statement is true.\\\",\\n\\\"question2\\\":\\\"Raising the relative humidity in a room at $21$°C from $30\\\\\\\\%$ to $60\\\\\\\\%$ would improve the comfort level for most people.\\\",\\n\\\"answer2\\\":\\\"True\\\",\\n\\\"advice2\\\":\\\"The intersection of the $21$°C horizontal line and the $30\\\\\\\\%$ vertical line lies just outside of the shaded area.
Raising the relative humidity to $60\\\\\\\\%$ places the intersection just inside the shaded area, so the statement is true.\\\"\\n},\\n{\\n\\\"question1\\\":\\\"According to the chart, a room with temperature $31$°C could not be made to feel comfortable for most people, regardless of the humidity level.\\\",\\n\\\"answer1\\\":\\\"True\\\",\\n\\\"advice1\\\":\\\"The $31$°C horizontal line never passes within the shaded area.
Therefore the room could not be made to feel comfortable for most people regardless of the humidity level, so the statement is true.\\\",\\n\\\"question2\\\":\\\"According to the chart, lower room temperatures require lower relative humidity levels in order to feel comfortable for most people.\\\",\\n\\\"answer2\\\":\\\"False\\\",\\n\\\"advice2\\\":\\\"A temperature of $21$°C requires humidity levels around $50\\\\\\\\%$ to $70\\\\\\\\%$ for comfort, whereas a temperature of $27$°C requires humidity levels around $30\\\\\\\\%$ to $60\\\\\\\\%$ for comfort
The statement is therefore false.\\\"\\n},\\n{\\n\\\"question1\\\": \\\"According to the chart, a room with humidity level $65\\\\\\\\%$ could not be made to feel comfortable for most people, regardless of the temperature.\\\",\\n\\\"answer1\\\": \\\"False\\\",\\n\\\"advice1\\\": \\\"The $65\\\\\\\\%$ humidity vertical line passes through the shaded area.
Therefore the statement is false.\\\",\\n\\\"question2\\\":\\\"According to the chart, higher room temperatures require lower relative humidity levels in order to feel comfortable for most people.\\\",\\n\\\"answer2\\\":\\\"True\\\",\\n\\\"advice2\\\":\\\"A temperature of $21$°C requires humidity levels around $50\\\\\\\\%$ to $70\\\\\\\\%$ for comfort, whereas a temperature of $27$°C requires humidity levels around $30\\\\\\\\%$ to $60\\\\\\\\%$ for comfort
The statement is therefore true.\\\"\\n},\\n{\\n\\\"question1\\\": \\\"At a relative humidity level of $50$%, the temperatures that result in a comfortable room lie within a range of $7$°C.\\\",\\n \\\"answer1\\\": \\\"True\\\",\\n \\\"advice1\\\": \\\"The $50\\\\\\\\%$ vertical line enters the shaded area at $21$°C and exits it at $28$°C.
The difference between these two temperatures is $7$°C.
Therefore the statement is true.\\\",\\n\\\"question2\\\":\\\"Raising the temperature of a room with temperature $21$°C and relative humidity $40\\\\\\\\%$ by $2$°C would improve the comfort level for most people.\\\",\\n\\\"answer2\\\":\\\"True\\\",\\n\\\"advice2\\\":\\\"A room with relative humidity $40\\\\\\\\%$ and temperature $21$°C is just below the shaded area on the chart.
Increasing the temperature by $2$°C would move the intersection point into the shaded area.
The statement is therefore true.\\\"\\n},\\n{\\n\\\"question1\\\": \\\"A room with temperature $27$°C and relative humidity $70\\\\\\\\%$ would feel comfortable to most people.\\\",\\n \\\"answer1\\\": \\\"False\\\",\\n \\\"advice1\\\": \\\"The intersection of the $27$°C horizontal line and the $70\\\\\\\\%$ vertical line lies outside of the shaded area.
Therefore the room would not feel comfortable to most people, and the statement is false.\\\",\\n\\\"question2\\\":\\\"According to the chart, rooms with lower humidity levels have a larger range of comfortable room temperatures than rooms with higher humidity levels.\\\",\\n\\\"answer2\\\":\\\"True\\\",\\n\\\"advice2\\\":\\\"A room with a humidity level of $30\\\\\\\\%$ is comfortable between $22$°C and $30$°C. This is a range of $8$°C.
A room with humidity level at $70\\\\\\\\%$ is comfortable between $20$°C and $26$°C. This is a range of only $6$°C.
The statement is therefore true.\\\"\\n}\\n]\"))", "description": "

The 7 possible T/F question pairs, each along with their correct answer, distractor and the Advice.

", "templateType": "json", "can_override": false}, "prompt1": {"name": "prompt1", "group": "Ungrouped variables", "definition": "scenario[\"question1\"]", "description": "

The first question for the randomly selected scenario.

", "templateType": "anything", "can_override": false}, "explanation1": {"name": "explanation1", "group": "Ungrouped variables", "definition": "scenario[\"advice1\"]", "description": "

The customised advice for the first question in the given scenario.

", "templateType": "anything", "can_override": false}, "prompt2": {"name": "prompt2", "group": "Ungrouped variables", "definition": "scenario[\"question2\"]", "description": "

The second question for the randomly selected scenario.

", "templateType": "anything", "can_override": false}, "correct2": {"name": "correct2", "group": "Ungrouped variables", "definition": "scenario[\"answer2\"]", "description": "

The second correct answer for the randomly selected scenario.

", "templateType": "anything", "can_override": false}, "explanation2": {"name": "explanation2", "group": "Ungrouped variables", "definition": "scenario[\"advice2\"]", "description": "

The customised advice for the second question in the given scenario.

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["scenarios", "scenario", "prompt1", "prompt2", "correct1", "correct2", "explanation1", "explanation2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "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": "

Below are some statements about the chart provided above.

Select 'True or 'False' for each statement.

", "minMarks": 0, "maxMarks": "1", "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": false, "shuffleAnswers": false, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["{prompt1}", "{prompt2}"], "matrix": [["if(correct1=\"True\",0.5,0)", "if(correct1=\"False\",0.5,0)"], ["if(correct2=\"True\",0.5,0)", "if(correct2=\"False\",0.5,0)"]], "layout": {"type": "all", "expression": ""}, "answers": ["True", "False"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SP Airline chart distance vs cost (7)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Long_haul_flights_vs_cost_chart.png", "/srv/numbas/media/question-resources/Long_haul_flights_vs_cost_chart.png"], ["question-resources/InkedLong_haul_flights_vs_cost_chart_advice1_small.jpg", "/srv/numbas/media/question-resources/InkedLong_haul_flights_vs_cost_chart_advice1_small.jpg"], ["question-resources/InkedLong_haul_flights_vs_cost_chart_advice2_LI_small.jpg", "/srv/numbas/media/question-resources/InkedLong_haul_flights_vs_cost_chart_advice2_LI_small.jpg"], ["question-resources/InkedLong_haul_flights_vs_cost_chart_advice3_LI_small.jpg", "/srv/numbas/media/question-resources/InkedLong_haul_flights_vs_cost_chart_advice3_LI_small.jpg"], ["question-resources/InkedLong_haul_flights_vs_cost_chart_advice4_LI_small.jpg", "/srv/numbas/media/question-resources/InkedLong_haul_flights_vs_cost_chart_advice4_LI_small.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE"], "metadata": {"description": "

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. Students are shown an unuaual chart and asked one of seven possible questions. The Advice for this question is general in nature.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

The chart below shows the distance and change in cost of a number of common flight routes.

^{https://www.economist.com/graphic-detail/2018/12/08/why-ticket-prices-on-long-haul-flights-have-plummeted}

", "advice": "

First, read the notes below to identify and understand the axes on this unusual chart:

The distance travelled for each flight can be worked out by examining where the dot for each route is, relative to the white curved lines, and reading the distance from the upper or lower straight edges of the sector. For example, the distance travelled on the London-Dubai route is around 5 200 km (see the pink arrow on the diagram below, then refer to the larger diagram above to read the numbers).

The percentage change in cost can be worked out by extending along the straight grey or blue line to the curved percentage scale at the right hand side. For example, the cost on the London-Dubai route has decreased by around 33% (see the yellow arrow on the diagram below, then refer to the larger diagram above to read the numbers).

Secondly, read the notes below to investigate how two routes might be related:

If two routes have the same distance, they will lie on the same white curved line (or be the same distance from the same curved line). For example, the London-Dubai route has the same distance as the New York - Paris route (see the green line on the diagram below, then refer to the larger diagram above for more detail).

If two routes have the same percentage change in cost, they will lie on the same straight line radiating from the left-hand side of the sector. For example, the Boston - Dallas route has the same percentage change in cost as the New York - Los Angeles route (see the brown line on the diagram below, then refer to the larger diagram above for more detail).

Once you have undestood how to read this chart, read the question carefully, to determine what is required. Sometimes the answer can be read straight from the chart.

However, you might then be asked to increase or decrease an amount by a percentage. For example:

Find the 2018 fare if the 2014 fare was $1 600 and it had decreased by 20% between 2014 and 2018.

The quickest way is to multiply $1 600 by 0.8 (which is equivalent to finding 100% - 20%).

The 2018 fare was $1 280.

OR Find the 2014 fare if the fare decreased by 20% between 2014 and 2018, and the 2018 fare was $900.

This is a little more complicated, because $900 is 80% of the 2014 fare.

To find 100% of the 2014 fare, divide $900 by 0.8. Note that this is NOT the same as multiplying by 1.2.

The 2014 fare was $1 125.

", "rulesets": {}, "variables": {"answer": {"name": "answer", "group": "Ungrouped variables", "definition": "scenario[\"correctanswer\"]", "description": "

The correct answer from the randomly selected scenario.

", "templateType": "anything"}, "question": {"name": "question", "group": "Ungrouped variables", "definition": "scenario[\"questiontext\"]", "description": "

The question from the randomly selected scenario.

", "templateType": "anything"}, "scenario": {"name": "scenario", "group": "Ungrouped variables", "definition": "random(scenarios)", "description": "

The randomly selected scenario.

", "templateType": "anything"}, "wrong2": {"name": "wrong2", "group": "Ungrouped variables", "definition": "scenario[\"distractor2\"]", "description": "

The second incorrect answer from the randomly selected scenario.

", "templateType": "anything"}, "wrong1": {"name": "wrong1", "group": "Ungrouped variables", "definition": "scenario[\"distractor1\"]", "description": "

The first incorrect answer from the randomly selected scenario.

", "templateType": "anything"}, "wrong3": {"name": "wrong3", "group": "Ungrouped variables", "definition": "scenario[\"distractor3\"]", "description": "

The third incorrect answer from the randomly selected scenario.

", "templateType": "anything"}, "scenarios": {"name": "scenarios", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n{\\n\\\"questiontext\\\":\\\"Which flight of less than 3000 km had the largest percentage reduction in price?\\\",\\n\\\"correctanswer\\\":\\\"Amsterdam - London\\\",\\n\\\"distractor1\\\":\\\"Boston - Dallas\\\",\\n\\\"distractor2\\\":\\\"Hong-Kong - Singapore\\\",\\n\\\"distractor3\\\":\\\"London - Frankfurt\\\"\\n},\\n{\\n\\\"questiontext\\\":\\\"Which two routes had the largest percentage reduction in price?\\\",\\n\\\"correctanswer\\\":\\\"Los Angeles - Paris and Los Angeles - London\\\",\\n\\\"distractor1\\\":\\\"San Francisco - Beijing and Los Angeles - Seoul\\\",\\n\\\"distractor2\\\":\\\"Singapore - Sydney and Orlando - Seattle\\\",\\n\\\"distractor3\\\":\\\"Orlando - London and New York - Paris\\\"\\n},\\n{\\n\\\"questiontext\\\":\\\"Any route longer than 5000 km is classified as long-haul. How many long-haul routes are shown on this chart?\\\",\\n\\\"correctanswer\\\":12,\\n\\\"distractor1\\\":8,\\n\\\"distractor2\\\":10,\\n\\\"distractor3\\\":6\\n},\\n{\\n\\\"questiontext\\\":\\\"Which statement is not true?\\\",\\n\\\"correctanswer\\\":\\\"Hong-Kong - Singapore and Hong-Kong - Beijing were the only two routes with prices that decreased by the same percentage.\\\",\\n\\\"distractor1\\\":\\\"As a general trend, the longer flights decreased by a larger percentage than the shorter flights.\\\",\\n\\\"distractor2\\\":\\\"The Singapore - Sydney route became more expensive.\\\",\\n\\\"distractor3\\\":\\\"Trans-Atlantic flights generally decreased by a higher percentage than other flights.\\\"\\n},\\n{\\n\\\"questiontext\\\":\\\"Prior to 2014, an economy-class ticket on the Los Angeles - Seoul route cost an average of $1 600. How much would it cost on average at the end of 2018?\\\",\\n\\\"correctanswer\\\":\\\"$1 280\\\",\\n\\\"distractor1\\\":\\\"$80\\\",\\n\\\"distractor2\\\":\\\"$320\\\",\\n\\\"distractor3\\\":\\\"$1 580\\\"\\n},\\n{\\n\\\"questiontext\\\":\\\"If John travelled Dubai - Singapore then Singapore - Sydney, how far approximately did he travel?\\\",\\n\\\"correctanswer\\\":\\\"12 100 km\\\",\\n\\\"distractor1\\\":\\\"5 800 km\\\",\\n\\\"distractor2\\\":\\\"6 300 km\\\",\\n\\\"distractor3\\\":\\\"12 500 km\\\"\\n},\\n{\\n\\\"questiontext\\\":\\\"After 2018, a ticket on the Los Angeles - Seoul route cost an average of $900. What was the average price prior to 2014?\\\",\\n\\\"correctanswer\\\":\\\"$1 125\\\",\\n\\\"distractor1\\\":\\\"$1 080\\\",\\n\\\"distractor2\\\":\\\"$920\\\",\\n\\\"distractor3\\\":\\\"$720\\\"\\n}\\n]\"))", "description": "

The 7 different scenarios. Each consists of the question, the correct answer, and three incorrect options.

", "templateType": "json"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["scenarios", "scenario", "question", "answer", "wrong1", "wrong2", "wrong3"], "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": "

{question}

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["

\n{answer}", "{wrong1}", "{wrong2}", "{wrong3}"], "matrix": ["1", 0, 0, 0], "distractors": ["Well done!", "Make sure you have studied the axis labels on the chart, then re-read the question.", "Make sure you have studied the axis labels on the chart, then re-read the question.", "Make sure you have studied the axis labels on the chart, then re-read the question."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SP African literacy stacked bar chart (7)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/African_reading_bar_chart.png", "/srv/numbas/media/question-resources/African_reading_bar_chart.png"], ["question-resources/African_reading_bar_chart_800.png", "/srv/numbas/media/question-resources/African_reading_bar_chart_800.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE"], "metadata": {"description": "

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. Students are shown a stacked bar chart and asked one of seven possible questions.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

The Southern and Eastern African Consortium for Monitoring Educational Quality reported on the percentage of Grade 6 pupils reaching reading proficiency levels from six African nations. Their findings are illustrated in the stacked bar chart below.

", "advice": "

General advice

First, make sure you check the percentage scale and the Key carefully.

Then, read the question carefully and identify which part of the chart it is referring to. Read the question again, to double-check that you have interpreted it correctly.

Specific advice

{explanation}

", "rulesets": {}, "variables": {"questionwording": {"name": "questionwording", "group": "Ungrouped variables", "definition": "scenario[\"question\"]", "description": "

The question statement for the randomly chosen scenario.

", "templateType": "anything"}, "wrong2": {"name": "wrong2", "group": "Ungrouped variables", "definition": "scenario[\"distractor2\"]", "description": "

The second incorrect answer (distractor) for the randomly chosen scenario.

", "templateType": "anything"}, "scenario": {"name": "scenario", "group": "Ungrouped variables", "definition": "random(scenarios)", "description": "

The randomly chosen scenario, consisting of question statement, correct answer, three distractors and feedback.

", "templateType": "anything"}, "wrong3": {"name": "wrong3", "group": "Ungrouped variables", "definition": "scenario[\"distractor3\"]", "description": "

The third incorrect answer (distractor) for the randomly chosen scenario.

", "templateType": "anything"}, "correctanswer": {"name": "correctanswer", "group": "Ungrouped variables", "definition": "scenario[\"answer\"]", "description": "

The correct answer for the randomly chosen scenario.

", "templateType": "anything"}, "scenarios": {"name": "scenarios", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n {\\n \\\"question\\\":\\\"Which country had the highest percentage of pupils in the Desirable range for reading?\\\",\\n \\\"answer\\\":\\\"Zimbabwe\\\",\\n \\\"distractor1\\\":\\\"Kenya\\\",\\n \\\"distractor2\\\":\\\"Mauritius\\\",\\n \\\"distractor3\\\":\\\"Malawi\\\",\\n \\\"advice\\\":\\\"To determine which country had the highest percentage of pupils in the Desirable range, look for the longest light-grey bar. Zimbabwe is the country with the highest percentage of pupils in the Desirable range for reading.\\\"\\n },\\n {\\n \\\"question\\\":\\\"Which country had the lowest percentage of pupils who were Below Minimum standard in reading?\\\",\\n \\\"answer\\\":\\\"Kenya\\\",\\n \\\"distractor1\\\":\\\"Zimbabwe\\\",\\n \\\"distractor2\\\":\\\"Mauritius\\\",\\n \\\"distractor3\\\":\\\"Zambia\\\",\\n \\\"advice\\\":\\\"To find the country with the lowest percentage of pupils who were Below Minimum standard, look for the shortest black bar. Kenya is the country with the lowest percentage of pupils who were Below Minimum standard in reading.\\\"\\n },\\n {\\n \\\"question\\\":\\\"Which two countries had the most similar profiles?\\\",\\n \\\"answer\\\":\\\"Malawi and Zambia\\\",\\n \\\"distractor1\\\":\\\"Kenya and Zambia\\\",\\n \\\"distractor2\\\":\\\"Mauritius and Zimbabwe\\\",\\n \\\"distractor3\\\":\\\"Malawi and Namibia\\\",\\n \\\"advice\\\":\\\"To find the two countries with the most similar profiles, look for the two countries which have black bars of a similar length AND mid-grey bars of a similar length AND light-grey bars of a similar length. Malawi and Zambia have the most similar profiles, as there is the least difference between the length of their bars. \\\"\\n },\\n {\\n \\\"question\\\":\\\"Which country had the highest percentage of pupils whose results were outside of the Desirable range for reading?\\\",\\n \\\"answer\\\":\\\"Malawi\\\",\\n \\\"distractor1\\\":\\\"Zimbabwe\\\",\\n \\\"distractor2\\\":\\\"Mauritius\\\",\\n \\\"distractor3\\\":\\\"Zambia\\\",\\n \\\"advice\\\":\\\"A simple way to answer this particular question is to look for the country with the lowest percentage of pupils in the Desirable range for reading. Malawi is the country with the shortest light-grey bar, so it is therefore the country with the highest percentage of pupils whose results were outside of the Desirable range for reading.\\\"\\n },\\n {\\n \\\"question\\\":\\\"Which country had the highest percentage of pupils who were not Below Minimum standard for reading?\\\",\\n \\\"answer\\\":\\\"Kenya\\\",\\n \\\"distractor1\\\":\\\"Zambia\\\",\\n \\\"distractor2\\\":\\\"Mauritius\\\",\\n \\\"distractor3\\\":\\\"Malawi\\\",\\n \\\"advice\\\":\\\"A simple way to answer this particular question is to look for the country with the lowest percentage of pupils who were Below Minimum standard for reading. The country with the shortest black bar is Kenya, so Kenya has the highest percentage of pupils who were not Below Minimum standard for reading.\\\"\\n },\\n {\\n \\\"question\\\":\\\"What proportion of Namibian pupils reached the Minimum standard for reading, but were not above it?\\\",\\n \\\"answer\\\":\\\"18%\\\",\\n \\\"distractor1\\\":\\\"26%\\\",\\n \\\"distractor2\\\":\\\"8%\\\",\\n \\\"distractor3\\\":\\\"74%\\\",\\n \\\"advice\\\":\\\"To answer this particular question, we need to find the proportion of Namibian students represented by the mid-grey bar. This bar starts at approximately 8% and ends at approximately 26%. Subtracting these gives 18%, so approximately 18% of Namibian pupils reached the Minimum standard for reading, but were not above it.\\\"\\n },\\n {\\n \\\"question\\\":\\\"What proportion of Kenyan pupils were Below Minimum standard for reading?\\\",\\n \\\"answer\\\":\\\"35%\\\",\\n \\\"distractor1\\\":\\\"65%\\\",\\n \\\"distractor2\\\":\\\"45%\\\",\\n \\\"distractor3\\\":\\\"55%\\\",\\n \\\"advice\\\":\\\"To find the proportion of Kenyan pupils who were Below Minimum standard, we need to find the proportion of Kenyan students represented by the black bar. This bar starts at approximately 65% and ends at 100%. Subtracting these gives 35%, so approximately 35% of Kenyan pupils were Below Minimum standard for reading.\\\"\\n }\\n]\"))", "description": "

The question statement, correct answer, three distractors and feedback for each of the seven possible questions.

", "templateType": "json"}, "wrong1": {"name": "wrong1", "group": "Ungrouped variables", "definition": "scenario[\"distractor1\"]", "description": "

The first incorrect answer (distractor) for the randomly chosen scenario.

", "templateType": "anything"}, "explanation": {"name": "explanation", "group": "Ungrouped variables", "definition": "scenario[\"advice\"]", "description": "

This is the detailed advice (feedback) given to explain the correct answer for the randomly selected scenario.

", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["scenarios", "scenario", "questionwording", "correctanswer", "wrong1", "wrong2", "wrong3", "explanation"], "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": "

{questionwording}

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["

\n{correctanswer}", "{wrong1}", "{wrong2}", "{wrong3}"], "matrix": ["1", 0, 0, 0], "distractors": ["Well done!", "Make sure you check the percentage scale and the Key carefully.", "Make sure you check the percentage scale and the Key carefully.", "Make sure you check the percentage scale and the Key carefully."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Non Calculator strand", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["Write an algebraic expression (10+)", "Fraction multiplication (9)", "Use proportional reasoning (10+)", "Sydney water usage (7)"], "questions": [{"name": "NC NA Write an algebraic expression from a word problem (overtime) (10+)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE"], "metadata": {"description": "

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are given the total hours of work (randomised) and overtime (randomised) and asked to write an expression for the amount of pay earned.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

$H$ is used to represent a standard hourly rate of pay in dollars.

", "advice": "

First work out how many hours were worked at the standard hourly rate. {total_hours} - {over_time} = {normal_hours}

{normal_hours} is multiplied by H to give the amount earned during standard hours. {normal_hours} x H = {normal_hours}H

{normal_hours}H is earned during the standard hours.

H is multiplied by 1.5 for each overtime hour, which is paid at time and a half. There are {over_time} overtime hours, so {over_time} x 1.5 x H = {1.5*over_time}H

{1.5*over_time}H is earned during the overtime hours.

Then the standard pay and the overtime pay are added: {normal_hours}H + {1.5*over_time}H = {normal_hours+1.5*over_time}H

{normal_hours+1.5*over_time}H represents the amount earned after {total_hours} hours work.

", "rulesets": {}, "variables": {"normal_hours": {"name": "normal_hours", "group": "Ungrouped variables", "definition": "random(4 .. 8#1)", "description": "

Number of hours paid at the standard rate. Student are required to work this out. It is set up to be greater than or equal to over_time.

", "templateType": "randrange"}, "over_time": {"name": "over_time", "group": "Ungrouped variables", "definition": "random(2 .. 4#1)", "description": "

Overtime hours worked. This is stated in the question. It is set up to be less than or equal to normal_hours.

", "templateType": "randrange"}, "total_hours": {"name": "total_hours", "group": "Ungrouped variables", "definition": "over_time+normal_hours", "description": "

Total hours worked. This is stated in the question, but calculated from the other two variables.

", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["total_hours", "over_time", "normal_hours"], "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": "

Which one of the following expressions would represent the amount of pay earned for {total_hours} hours work, where {over_time} of those hours were worked at time-and-a-half (that is at 1.5 times the standard rate of pay)?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$\\var{total_hours+over_time}H$", "$\\var{normal_hours+1.5*over_time}H$", "$ \\frac{\\var{total_hours}}{1.5}H$", "$\\var{total_hours+1.5*over_time}H$"], "matrix": [0, "1", 0, 0], "distractors": ["How many hours were worked at the normal rate? Click on Reveal Answer and scroll down for Advice regarding this question.", "Well done!", "Does dividing by 1.5 increase the amount paid? Click on Reveal Answer and scroll down for Advice regarding this question.", "How many hours were worked at the normal rate? Click on Reveal Answer and scroll down for Advice regarding this question."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NC NA Fraction multiplication - a proportion of a partially eaten chocolate bar (9)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE"], "metadata": {"description": "

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are asked to find a fraction of a fraction. There are 9 different versions of this question.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

On Monday, {name1} bought a chocolate bar and ate one {frac1name} of it.

On Tuesday, {name1} ate one {frac2name} of the remaining part of the chocolate bar.

", "advice": "

On Monday, {name1} bought a chocolate bar and ate one {frac1name} of it.

We need to subtract this fraction from one whole to find the fraction remaining.

1 - $ \\frac{1}{\\var{frac1denom}} $ = $ \\frac {\\var{monleftfracnum}} {\\var{monleftfracden}} $

On Tuesday, {name1} ate one {frac2name} of the fraction remaining.

We need to find one {frac2name} of $ \\frac {\\var{monleftfracnum}} {\\var{monleftfracden}} $.

$ \\frac{1}{\\var{frac2denom}} $ x $ \\frac {\\var{monleftfracnum}} {\\var{monleftfracden}} $ = $ \\frac {\\var{monleftfracnum}} {\\var{frac2denom*monleftfracden}} $

This fraction cannot be simplified.

So {name1} ate $ \\frac {\\var{monleftfracnum}} {\\var{frac2denom*monleftfracden}} $ of the chocolate bar on Tuesday.

This fraction needs to be simplified. Divide both numerator and denominator by {gcd(monleftfracnum,frac2denom*monleftfracden)}.

$ \\frac {\\var{monleftfracnum}} {\\var{frac2denom*monleftfracden}} $ = $ \\frac {\\var{answernumerator}} {\\var{answerdenominator}}$

So {name1} ate $ \\frac {\\var{answernumerator}} {\\var{answerdenominator}}$ of the chocolate bar on Tuesday.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"frac1name": {"name": "frac1name", "group": "Ungrouped variables", "definition": "frac1[\"name\"]", "description": "

The randomly selected Monday fraction - in word form.

", "templateType": "anything", "can_override": false}, "fractioneaten": {"name": "fractioneaten", "group": "Ungrouped variables", "definition": "rational_approximation(decimaleaten)", "description": "

The proportion of the chocolate bar eaten on Tuesday. It is the answer as a fraction.

", "templateType": "anything", "can_override": false}, "answernumerator": {"name": "answernumerator", "group": "Ungrouped variables", "definition": "fractioneaten[0]", "description": "

The numerator of the proportion of the chocolate bar eaten on Tuesday (fraction not yet simplified)

", "templateType": "anything", "can_override": false}, "decimaleaten": {"name": "decimaleaten", "group": "Ungrouped variables", "definition": "(1-(1/frac1denom))*(1/frac2denom)", "description": "

The proportion of the chocolate bar eaten on Tuesday. It is the answer as a decimal.

", "templateType": "anything", "can_override": false}, "frac2": {"name": "frac2", "group": "Ungrouped variables", "definition": "random(frac2options)", "description": "

The randomly selected Tuesday fraction - in both word and numerical form.

", "templateType": "anything", "can_override": false}, "monleftfrac": {"name": "monleftfrac", "group": "Ungrouped variables", "definition": "rational_approximation(monleft)", "description": "

The proportion of the chocolate bar remaining on Monday, as a fraction.

", "templateType": "anything", "can_override": false}, "name1": {"name": "name1", "group": "Ungrouped variables", "definition": "random(\"Tyler\",\"Emma\",\"Lachlan\",\"Bella\",\"Mario\",\"Jia\")", "description": "

A randomly selected name from the list.

", "templateType": "anything", "can_override": false}, "frac1denom": {"name": "frac1denom", "group": "Ungrouped variables", "definition": "frac1[\"denom\"]", "description": "

The denominator of the randomly selected Monday fraction.

", "templateType": "anything", "can_override": false}, "monleftfracden": {"name": "monleftfracden", "group": "Ungrouped variables", "definition": "monleftfrac[1]", "description": "

The denominator of the proportion of the chocolate bar remaining on Monday.

", "templateType": "anything", "can_override": false}, "frac2denom": {"name": "frac2denom", "group": "Ungrouped variables", "definition": "frac2[\"denom\"]", "description": "

The denominator of the randomly selected Tuesday fraction.

", "templateType": "anything", "can_override": false}, "frac2options": {"name": "frac2options", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n {\\\"name\\\":\\\"half\\\",\\n \\\"denom\\\":2\\n },\\n {\\\"name\\\":\\\"third\\\",\\n \\\"denom\\\":3\\n },\\n {\\\"name\\\":\\\"quarter\\\",\\n \\\"denom\\\":4\\n }\\n]\"))", "description": "

The denominator of the Tuesday fraction in both word and numerical form. List of three possible scenarios.

", "templateType": "json", "can_override": false}, "frac2name": {"name": "frac2name", "group": "Ungrouped variables", "definition": "frac2[\"name\"]", "description": "

The randomly selected Tuesday fraction - in word form.

", "templateType": "anything", "can_override": false}, "monleft": {"name": "monleft", "group": "Ungrouped variables", "definition": "(1-1/frac1denom)", "description": "

The proportion of the chocolate bar remaining on Monday, as a decimal.

", "templateType": "anything", "can_override": false}, "frac1options": {"name": "frac1options", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n {\\n \\\"name\\\": \\\"half\\\",\\n \\\"denom\\\": 2\\n },\\n {\\n \\\"name\\\": \\\"third\\\",\\n \\\"denom\\\": 3\\n },\\n {\\n \\\"name\\\": \\\"quarter\\\",\\n \\\"denom\\\": 4\\n }\\n]\"))", "description": "

The denominator of the Monday fraction in both word and numerical form. List of three possible scenarios.

", "templateType": "json", "can_override": false}, "answerdenominator": {"name": "answerdenominator", "group": "Ungrouped variables", "definition": "fractioneaten[1]", "description": "

The denominator of the proportion of the chocolate bar eaten on Tuesday (fraction not yet simplified)

", "templateType": "anything", "can_override": false}, "frac1": {"name": "frac1", "group": "Ungrouped variables", "definition": "random(frac1options)", "description": "

The randomly selected Monday fraction - in both word and numerical form.

", "templateType": "anything", "can_override": false}, "monleftfracnum": {"name": "monleftfracnum", "group": "Ungrouped variables", "definition": "monleftfrac[0]", "description": "

The numerator of the proportion of the chocolate bar remaining on Monday.

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["name1", "frac1options", "frac1", "frac1name", "frac1denom", "frac2options", "frac2", "frac2name", "frac2denom", "decimaleaten", "fractioneaten", "answernumerator", "answerdenominator", "monleft", "monleftfrac", "monleftfracnum", "monleftfracden"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "prompt": "

What fraction of the whole bar did {name1} eat on Tuesday?

Use the / key to enter your anwer as a fraction in simplest form.

", "minValue": "decimaleaten", "maxValue": "decimaleaten", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NC NA Use proportional reasoning to scale up rice recipe (10+)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE"], "metadata": {"description": "

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are given the number of people that are fed with 200g of rice (randomised), and the total number of people to be fed (randomised). They need to calculate the weight of rice using proportional reasoning.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Mr Sims teaches Year 6. His class is responsible for cooking the rice for a Multicultural Day banquet. They need to cook the right amount of rice for {num_people} people.

One cup of uncooked rice weighs 200 g and will serve {per_cup} people.

", "advice": "

One cup of uncooked rice will serve {per_cup} people, and there are {num_people} people to be served.

Dividing {num_people} by {per_cup} will give the number of cups of rice required.

{num_people} ÷ {per_cup} = {(num_people)/(per_cup)}

So they will need {(num_people)/(per_cup)} cups of uncooked rice.

Each cup of uncooked rice weighs 200 grams. So every 5 cups of uncooked rice will weigh 1 kilogram (or 1000 grams).

5 cups of uncooked rice weigh 1 kilogram.

{(num_people)/(per_cup)} cups of uncooked rice weigh {kilos} kilograms. (Scale up by a factor of {kilos})

They will need {kilos} kilograms of uncooked rice to feed {num_people} people.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"num_people": {"name": "num_people", "group": "Ungrouped variables", "definition": "per_cup*kilos*5", "description": "

This is the total number of people to be fed. It is stated in the question, but calculated by multiplying the number of people fed per cup by the the number of kilograms of rice then by 5 to convert from 200grams to kg.

", "templateType": "anything", "can_override": false}, "per_cup": {"name": "per_cup", "group": "Ungrouped variables", "definition": "random(3 .. 6#1)", "description": "

This is the number of people fed per uncooked cup. It is stated in the question.

", "templateType": "randrange", "can_override": false}, "kilos": {"name": "kilos", "group": "Ungrouped variables", "definition": "random(5 .. 10#1)", "description": "

The number of kilograms of rice required. This is the answer.

", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["num_people", "per_cup", "kilos"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "prompt": "

How many kilograms of uncooked rice will they need? Just enter the number, not the kg symbol.

", "minValue": "{kilos}", "maxValue": "{kilos}", "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": "NC NA Sydney water usage percentages to fraction approximation (7)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Sydney_water_usage.png", "/srv/numbas/media/question-resources/Sydney_water_usage.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}], "tags": ["LANTITE"], "metadata": {"description": "

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are asked to obtain a percentage from an infographic, then choose the fraction which is closest. There are 7 different versions of this question.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Sydney Water advises that the water consumption for a typical household is distributed as follows:

^{https://www.sydneywater.com.au/web/groups/publicwebcontent/documents/document/zgrf/mjew/~edisp/dd_210924.pdf}

", "advice": "

There are a few different ways to approach this type of question. For some questions, one method may be better than another.

Notice that the question says 'closest to' which indicates that the percentage may not be exactly equal to any of the fractions listed.

METHOD 1

You could convert the percentage to a fraction, by putting it over 100 and then simplifying. Sometimes this fraction will be one of the given options. eg 20% = $ \\frac{20} {100} $ = $ \\frac{1} {5} $.

Sometimes you may need to round it first. eg round 49% to 50% then $ \\frac{50} {100} $ = $ \\frac{1} {2} $

METHOD 2

Alternatively, convert each of the given fractions to a percentage by dividing the numerator by the denominator then multiplying by 100. Then compare them to see which is closest to the given percentage.

eg $ \\frac{1} {8} $ = 1 ÷ 8 x 100 = 12.5%

METHOD 3

It is helpful to memorise the most common fraction/percentage relationships.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Fraction	Percentage
$ \\frac{1} {2} $	50%
$ \\frac{1} {3} $	33.333..%
$ \\frac{1} {4} $	25%
$ \\frac{1} {5} $	20%
$ \\frac{1} {8} $	12.5%
$ \\frac{1} {10} $	10%

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List of description of each category in the infographic. Includes prepositions to make sentences work.

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This is the correct answer for each appliance.

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This is the third incorrect answer for each appliance.

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This randomly generated index is used to select the appliance, correct fraction answer and all 3 distractors.

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Which fraction is closest to the percentage of water used {Appliance[Index]}?

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Your time has expired. You are welcome to try this test again, or practise with the untimed version.

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You have 5 minutes remaining.

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These practice questions are grouped into strands.

You can select which questions you want to practise. You can do as many or as few as you like. You may choose to concentrate on just one strand, for example.

Click on any question to try it. Click on the Go back to the menu button at the top of the screen when you are finished with a question.

You may use a basic calculator for the questions in the first three strands.

You should not use a calculator for the non-calculator strand, which is located at the end.

This is not a test and it is not timed. You will not get an overall mark, although you will be told whether you are correct each time you submit an answer. You can make full use of the following features at the bottom of each question to help you to improve your numeracy skills:

Try another question like this one (the number after the question title tells you how many different versions of the question there are)
Reveal Answers (make sure that you scroll down to see the fully worked solution)

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