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This question tests ability to calculate differences using negative numbers in context.

The temperature in Stockholm is $\\var{stockholm}^\\circ\\mbox{C}$. In Plymouth, it is $\\var{rise}^\\circ\\mbox{C}$ warmer. What is the temperature in Plymouth?

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$\\simplify{{stockholm}-{rise}}^\\circ\\mbox{C}$

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$\\simplify{{stockholm}+2*{rise}}^\\circ\\mbox{C}$

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$\\simplify{{stockholm}+{rise}}^\\circ\\mbox{C}$

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$\\var{rise}^\\circ\\mbox{C}$

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This question tests ability to calculate differences using negative numbers in context.

Round $\\var{round_me}$ to the nearest whole number.

Answer: [[0]]

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Work out $\\var{base_1}^2+\\var{base_2}^2$.

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$\\simplify{{base_1}^2}$

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$\\simplify{{base_1}^2+{base_2}}$

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$\\simplify{{base_1}+{base_2}^2}$

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$\\simplify{{base_1}^2+{base_2}^2}$

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If $\\var{const_2}-x=\\var{const_1}$, what is the value of $x$?

Answer: [[0]]

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The following diagram shows a cuboid which has width $\\var{width}$ cm, height $\\var{height}$ cm and depth $\\var{depth}$ cm. What is the volume of the cube?

Answer: [[0]] $\\mbox{cm}^3$

Understanding the concept of the highest common factor and least common multiple of two positive integers.

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What is the highest common factor of $\\var{const_1}$ and $\\var{const_2}$?

Answer: [[0]]

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You need to find the largest whole number that goes into both of the original numbers exactly. For example, $\\var{const_1}$ and $\\var{const_2}$ have a common factor of $\\var{hint}$, but this is not the highest common factor.

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What is the least common multiple of $\\var{const_2}$ and $\\var{const_3}$?

Answer: [[0]]

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You need to find the smallest whole number that is a multiple of both $\\var{const_2}$ and $\\var{const_3}$. For example, $\\var{const_2}\\times\\var{const_3}=\\simplify{{const_2}*{const_3}}$ is a common multiple of $\\var{const_2}$ and $\\var{const_3}$, but it is not the least common multiple.

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Tests basic arithmetic and the concept of perimeter.

The following shape has two sides of lengths $\\var{seed_side}$ cm and $\\var{side_3}$ cm. The other two sides have length $\\var{side_1}$ and $\\var{side_2}$cm. Work out the perimeter of the shape.

Answer: [[0]] cm

The perimeter of the shape is the total length of all its sides added together $\\var{seed_side}+\\var{side_2}+\\var{side_2}+\\var{side_3}$.

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Test ability to calculate the difference between two times.

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Gabriel wakes up at $\\var{wake_hour}:\\var{wake_minutes}$ am and goes to sleep at $\\var{sleep_hour}:\\var{sleep_minutes}$ pm. How long is Gabriel awake?

Answer: [[0]] hours [[1]] minutes

It is $\\simplify{12-({wake_hour}+1)}$ hours and $\\simplify{60-{wake_minutes}}$ minutes from when Gabriel wakes up until 12 noon. Add this time in hours and minutes to the time Gabriel goes to sleep. If the sum of the minutes is more than sixty, then the total number of hours increases by 1 and the total number of minutes decreases by 60.

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Find percentages and valculate percentages of values.

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These questions are all about finding percentages and calculating percentages of things.

In general, to find a percentage, you need to calculate

$\\frac{n}{\\text{total}} * 100$

For example, if you are interesting in finding the percentage of people who voted for the Labour party in a general election you must calculate

$\\frac{\\text{# number of votes for Labour}}{\\text{total # of votes}} * 100$.

In contrast, if you are asked to calculate $x\\%$ of a number, $n$, then you must calculate $\\frac{x}{100}*n$

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A survey {total} individuals' Body Mass Index (BMI) are recorded in the table below.

$\"What$

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

BMI	<18.5	18.5-24.9	25-29.9	30-34.9	>35
Freq	{freq1}	{freq2}	{freq3}	{freq4}	{freq5}

What is the percentage of individuals who are considered to have a \"normal\" BMI, that is, those between 18.5 and 24.9 BMI?

[[0]]$\\%$

What is the percentage of individuals who have a BMI strictly less than 30?

[[1]] $\\%$

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Raheem has opened a savings account which he wishes to put {saving}$\\%$ of his earnigns into each month.

Raheem earns £{income} per month. $\"Piggy$

Calculate the amount of money Raheem will deposit into his savings account per month.

Answer: £[[0]]

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The price of a TV was £{x} . It will be decreased by {y}% for the upcoming sales period. What will be reduced price?

(Round your answer to 2 decimal places).

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A store has a closing down sale where all items are 30% off their retail price.

$\"Sales$

Jenny wants to buy

1 x frying pan whose retail price is £{pan}

4 x Mugs whose retail price are £{mug} each.

1 x dinner set whose retail price is £{dset}

How much does Jenny's shopping list come to?

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To calculate a discount you need to subtract the % discount of the item from the original price.

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Calculate the following and give your answer as a fraction (enter your answer in the form $a/b$ using the slash symbol).

$\\frac{{\\var{num1}}}{{\\var{denominator}}}+\\frac{{\\var{num2}}}{\\simplify{{denominator}+1}}=$ [[0]]

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To add the fractions, you need to find a common denominator. This is a whole number which is a multiple of both $\\var{denominator}$ and $\\simplify{{denominator}+1}$. The easiest choice is $\\var{common_denominator}$. Then rewrite the calcuation as

$\\dfrac{\\Box}{\\var{common_denominator}}+\\dfrac{\\Box}{\\var{common_denominator}}$

where you need to work out the new numerators to fill in the boxes. For example, $\\dfrac{\\var{num1}}{\\var{denominator}}=\\dfrac{\\simplify{{num1}*({denominator}+1)}}{\\var{common_denominator}}$ and this tells you what to enter in the first box.

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Tests the addition rule for fractions.

", "licence": null}, "tags": [], "type": "question"}, {"name": "Comparing cost per item_spare", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/496/"}, {"name": "Marta Emmett", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/11961/"}], "tags": [], "metadata": {"description": "

This application of arithmetic tests division as a method to compare cost per item, in order to determine value for money.

", "licence": "None specified"}, "statement": "

Supermarket A has an offer for $\\var{num1}$ gala apples for £$\\var{cost1_string}$. Supermarket B has an offer for $\\var{num2}$ gala apples for £$\\var{cost2_string}$.

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What is the cost per apple at the cheapest supermarket (answer in pence)?

Answer: [[0]] pence

First work out the cost per apple in supermarket A in pence, that is, $\\simplify{{cost1}*100}\\div\\var{num1}$. Then you will need to do a similar calculation for supermarket B. Compare your answers to find the cheapest cost per apple.

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A group of people were asked to vote for their favourite British film of all time from a selection of six taken from the the BFI top 100. The following bar chart shows the results of the survey.

", "advice": "

Click \"Show Steps\" above to see how to answer this question.

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How many people voted for {film1}?

Answer: [[0]]

Find the bar for {film1}. Use the scale on the Y-axis to find how many people voted for it.

How many people voted for either {film1} or {film2}?

Answer: [[0]]

What percentage of people surveyed voted for {film2}?

Answer: [[0]]

To find an exact percentage, if $n$ is the number of votes for {film2}, then you need to calculate

$\\frac{n}{\\text{total # of votes}} * 100$

Since there are 50 votes in total, you will be able to simplify this and give your answer as a whole number.

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Tests understanding of scatter plots and related concepts.

", "licence": "None specified"}, "statement": "

The scatter plot below shows the relationship between an employee’s height in centimetres and how long it takes them to walk to work in minutes.

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

time (mins)	{drawgraph()}
	height (cm)

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p6y

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\n var xaxis=brd.createElement('axis', [[minx,0],[maxx,0]]);\n var yaxis=brd.createElement('axis', [[minx+5,miny],[minx+5,maxy]]);\n var li1=brd.create('line',[[minx,regy1],[maxx,regy2]],{fixed:true,withLabel:false});\n var pt1=brd.create('point',[p1x,p1y],{visible:true,withLabel:false}); \n var pt2=brd.create('point',[p2x,p2y],{visible:true,withLabel:false}); \n var pt3=brd.create('point',[p3x,p3y],{visible:true,withLabel:false}); \n var pt4=brd.create('point',[p4x,p4y],{visible:true,withLabel:false}); \n var pt5=brd.create('point',[p5x,p5y],{visible:true,withLabel:false}); \n var pt6=brd.create('point',[p6x,p6y],{visible:true,withLabel:false}); \nreturn div;\n "}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the height of the tallest person in the sample?

Answer: [[0]] cm

What is the maximum difference in time taken to walk to work for people in the sample?

Answer: [[0]] minutes

Mark the statement that best describes what this scatter plot shows.

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In general, there is a positive correlation between a person's height and how long it takes them to walk to work.

", "

There is a positive correlation between the variables for the sample.

", "

In general, there is a negative correlation between a person's height and how long it takes them to walk to work.

", "

There is a negative correlation between the variables for the sample.

", "

In general, there is a no correlation between a person's height and how long it takes them to walk to work.

", "

There is a no correlation between the variables for the sample.

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This question tests ability to deal with measures of central tendancy for a small data set. The mode or median is required at random.

", "licence": "None specified"}, "statement": "

Calculating averages:

", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"median": {"name": "median", "group": "Ungrouped variables", "definition": "random(91..100)", "description": "", "templateType": "anything", "can_override": false}, "x4": {"name": "x4", "group": "Ungrouped variables", "definition": "median+random(11..20)", "description": "", "templateType": "anything", "can_override": false}, "x3": {"name": "x3", "group": "Ungrouped variables", "definition": "median-random(21..30)", "description": "", "templateType": "anything", "can_override": false}, "mean": {"name": "mean", "group": "Ungrouped variables", "definition": "precround(total/7,2)", "description": "", "templateType": "anything", "can_override": false}, "x1": {"name": "x1", "group": "Ungrouped variables", "definition": "median-random(1..10)", "description": "", "templateType": "anything", "can_override": false}, "x2": {"name": "x2", "group": "Ungrouped variables", "definition": "median-random(11..20)", "description": "", "templateType": "anything", "can_override": false}, "mode": {"name": "mode", "group": "Ungrouped variables", "definition": "median+random(1..10)", "description": "", "templateType": "anything", "can_override": false}, "total": {"name": "total", "group": "Ungrouped variables", "definition": "median+2*mode+x1+x2+x3+x4", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["median", "mode", "x1", "x2", "x3", "x4", "total", "mean"], "variable_groups": [{"name": "Unnamed group", "variables": []}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Seven children's heights in centimetres are recorded as follows: $\\var{mode},\\var{median},\\var{mode},\\var{x2},\\var{x3},\\var{x4},\\var{x1}$.

What is the mean height of the group of children in centimetres?

Answer: [[0]] cm

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To find the mean of the set of numbers, first add all the numbers together ($\\var{total}$) and then divide by how many numbers there are. So, you need to calculate $\\var{total}\\div 7$.

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What is the median for this sample of measurements?

Answer: [[0]] cm

\"The median is the middle number when all of the numbers are placed in order.\"

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What is the mode for this sample of measurements?

Answer: [[0]] cm

\"The mode is the most commonly occuring value.\"

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This question tests the method of expanding a pair of brackets.

Expand and simplify the following algebraic expression:

$(x+\\var{const1})(x+\\var{const2})$

You need to multiply everything in the first bracket by the second bracket. That is,

$x (x + \\var{const2}) + \\var{const1} (x + \\var{const2})=x^2+\\var{const2}x+\\var{const1}x+(\\var{const1}\\times\\var{const2})$

and then simplify your answer.

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You need to simplify your solution as far as possible.

"}, "valuegenerators": [{"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Missing side in a right-angled triangle_to_delete", "extensions": [], "custom_part_types": [], "resources": [["question-resources/triangle_yeq6Xd0_wpRhdOT.png", "/srv/numbas/media/question-resources/triangle_yeq6Xd0_wpRhdOT.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/496/"}, {"name": "Marta Emmett", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/11961/"}], "tags": [], "metadata": {"description": "

This question tests ability to use Pythagoras' theorem.

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The following triangle has two sides of length $\\var{short_side}$ cm and $\\var{long_side}$ cm.

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

$\\var{long_side}$ cm
	$\\var{short_side}$ cm

What is the length of the longest side correct to 1 decimal place?

If the longest side has length $x$ cm, then $x$ needs to satisfy Pythagoras' theorem:

$x^2=\\var{short_side}^2+\\var{long_side}^2=\\simplify{{short_side}^2+{long_side}^2}$.

Depending on the accuracy of $x$, this relationship may only be approximate.

You need to check which of the choices best satisfies this relationship.

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

$\\simplify{{hypotenuse}-0.4}$ cm

", "

$\\var{sum_of_squares}$ cm

", "

$\\var{hypotenuse}$ cm

", "

$\\simplify{{hypotenuse}+0.5}$ cm

"], "matrix": [0, 0, "3", 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Interpreting tables_to_delete", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/496/"}, {"name": "Marta Emmett", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/11961/"}], "tags": [], "metadata": {"description": "

This question tests the ability to read and interpret numerical data summarised in a table and make predictions based on algebraic skills.

", "licence": "None specified"}, "statement": "

The following table shows monthly financial data for a small business.

\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\n\n

	budget forecast (£)	actual (£)	actual - forecast (£)
Revenue	{revenue_forecast}	{revenue}	$\\simplify{{revenue}-{revenue_forecast}}$
Materials	{materials_forecast}	{materials}	$\\simplify{{materials}-{materials_forecast}}$
Overheads	{overheads_forecast}	{overheads}	$\\simplify{{overheads}-{overheads_forecast}}$
Net profit	{net_profit_forecast}	?	$\\simplify{{net_profit}-{net_profit_forecast}}$

", "advice": "

Click \"Show Steps\" above to see how to answer this question.

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Calculate the actual net profit.

Answer: £[[0]]

We can see from the table that the actual net profit subtract the forcast is {{net_profit}-{net_profit_forecast}}.

Therefore \"actual net profit\" - {net_profit_forecast} = {{net_profit}-{net_profit_forecast}}

So the number we want is {{net_profit}-{net_profit_forecast}}+{net_profit_forecast} = {{{net_profit}-{net_profit_forecast}}+{net_profit_forecast}}

What would the actual material costs need to be so that the actual net profit is the same as the forecast?

Answer: £[[0]]

From the table, we can see that

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

Net profit = Revenue - Materials - Overheads.

Since the overheads are the same for the forecast and in reality, for the the actual net profit to be equal to that of the forecast, we need

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

Forecast Revenue - Forecast Materials = Actual Revenue - Actual Materials

If the actual materials are considered to be an unknown ($x$), then we can fill in all the other values from the table and rearrange the equation to find $x$.

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