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PISA Reading PISA Mathematics

PISA Maths Questions 1

Table of Contents

Question Sets

Poppies 2

Decorating 5

The Wedding Planner 9

Tsunami 15

Baking Takes Off 17

Wheel Size 20

Tandem Speed 25

Freezing Cold 27

Correct Answers

Poppies 30

Decorating 32

The Wedding Planner 34

Tsunami 37

Baking Takes Off 38

Wheel Size 39

Tandem Speed 42

Freezing Cold 44


Poppies

Read the text about 'Blood Swept Lands and Seas of Red'

The major art installation 'Blood Swept Lands and Seas of Red' at the Tower of London

marked one hundred years since the first full day of Britain's involvement in the First

World War. Created by ceramic artist Paul Cummins, with setting by stage designer Tom

Piper, 888,246 ceramic poppies filled the Tower's famous moat over the summer of

2014. Each poppy represented a British military fatality during the war.

The poppies encircled the iconic landmark, creating not only a spectacular display

visible from all around the Tower but also a location for personal reflection. The scale of

the installation reflects the magnitude of such an important centenary, creating a

powerful visual commemoration.

The Times reported on Friday 17th October 2014 that:

For each poppy sold, £9 out of £25 went to charity

The money was shared equally amongst 6 service charities

90 tonnes of steel was used to make the rods supporting the poppies

5 million individual parts were used to make all of the poppies

The total land covered was 16 acres of grass

The volunteers could plant approximately 15,000 poppies a day

It took volunteers 2 minutes to plant each poppy


1. In the text, it is stated that Paul Cummins created poppies to represent the

number of British military fatalities during the First World War. How many

poppies were sold?

a. Eighty-eight million, eight thousand, two hundred and forty-six

b. Eighty-eight thousand, two hundred and forty-six

c. Eight hundred and eighty-eight thousand, two hundred and forty-six

d. Eight million, eight hundred and eighty thousand two hundred and forty-six

2. In the text, it is stated that the number of poppies made was 888,246. What place

value does the underlined 8 in 888,246 stand for?

a. Eight million

b. Eighty thousand

c. Eight hundred thousand

d. Eight thousand

3. The monies raised by selling all of the poppies was divided equally between

charities. How much did each charity receive?

a. £1,332,369

b. £7,994,214

c. £3,701,025

d. £1,579,104

4. Use the information in the text to estimate the number of parts for each poppy.


5. How many grams of steel are needed to support each poppy? Note that 1

tonne = 1,000 kilograms.

a. 0.1 grams

b. 101 grams

c. 9.87 grams

d. 987 grams

6. The text gives a rounded number of individual poppy parts used to make all

888,246 poppies. What is the range of possible values for the actual number of

poppy parts created? Give your answer in the form of an inequality.

7. Using the figures from the text, estimate how many poppy volunteers are needed

to plant the poppies each day.


Decorating

Read the following information about decorating

Helen and Josh have decided to decorate a bedroom. They are getting a new carpet and

painting the walls. The rectangular room is 3.5 metres wide and 405 centimetres long.

1. Carpet is generally sold by area in metres squared (m2). Convert 405 centimetres to

metres.

a. 4.5m

b. 4,050m

c. 4.05m

d. 40.5m

Before going to buy the carpet for the room, Helen and Josh have to calculate the area

of the floor to be carpeted. The room is a rectangle with the following dimensions:


2. What is the area of the floor in square metres (m2)?

a. 15.1m2

b. 12.3525m2

c. 15.75m2

d. 14.175m2

Helen and Josh used the internet to compare prices on a variety of carpets. They have

decided that they would like a blue carpet to cover the floor area of 14.175m2

Carpet Name Price per m2

Regency Blue £9.99

Oxford Blue £10.99

Royal Blue £8.50

Brogden Blue £12.99

3. Helen and Josh have a budget of £150 for the carpet – show that they can't afford

to buy the Brogden Blue carpet at £12.99 per m2


Carpet is bought in either four metre or five metre widths. Helen and Josh have decided to

buy a carpet which is four metre wide. The room is a rectangle with the following

dimensions:

4. The carpet has no pattern, so can be laid either way round and is 4 metres wide.

How much waste carpet is there when the carpet has been laid?

a. 3.5m2

b. 4.25m2

c. 1.075m2

d. 2.025m2

5. What percentage of the carpet was waste?

a. 12.5%

b. 8%

c. 14.3%

d. 8.75%

Helen and Josh have also decided to paint the walls of the room. The room is 2.5 metres

high and has a door and a window.

The dimensions of the door are 1,981 millimetres by 838 millimetres.

The dimensions of the window are 105 centimetres by 120 centimetres.


6. One 2.5 litre tin of paint can cover 32m2 of wall. Helen and Josh are going to use

two coats of paint as they need to cover a previous colour. How many 2.5 litre

tins of paint will they need to paint the walls of the room?


The Wedding Planner

Look at the following menu

1. All guests attending the wedding of Nerys and Rhys Jones were asked to order a

starter, a main and a dessert. How many different combinations of starter, main and

dessert are there?


2. Based on the information in the bar chart, how many guests attended the wedding?

a. 32 guests

b. 30 guests

c. 16 guests

d. 15 guests

3. What fraction of the guests had soup?

a. 1

3

b. 3

16

c. 14

18

d. 3

8


Look at the pie chart on the next page. It shows the main courses eaten by the 32

guests.

4. How many people ate beef as their main course?


5. Based on the two-way table, what is the probability that a person who had a main

course of tortellini had pâté for a starter?

a. 8

18

b. 8

32

c. 8

10

d. 10

32


Look at the following menu prices

Starter

Gravadlax of Scottish Salmon £6.25

Sweet Potato & Chive Soup £4.50

Chicken Liver Pâté £5.50

Main

Roast Beef with Yorkshire Pudding £12.95

Pork Fillet Wrapped in Pancetta £12.95

Grilled Fillet of Salmon £13.95

Asparagus & Ricotta Tortellini £12.35

Dessert

Sticky Toffee Pudding £4.50

Teacup Trifle with Damson Preserve £4.75

Rhubarb & Ginger Crumble £4.95

6. To work out the total cost per meal, the owners find the mean of the three starters,

the mean of the three main courses and the mean of the three desserts. They then

add these together and add 5% for service and staff as they are closing the

restaurant for the evening. Work out the total meal cost for the 30 guests and the

bride and groom.


Read the following information

The restaurant owner prepares a total bill for £770. The total bill includes a 10% profit for

the restaurant. The profit is calculated by adding it to the total cost of ingredients and

wages to arrive at the final bill of £770.

7. How much profit is added on to make the final bill?

a. £77

b. £70

c. £63

d. £87


Tsunami

Read the following information about tsunamis

A tsunami is a huge wave caused by earthquakes or volcanic eruptions. As a tsunami

hits shallow water, often near the coast, it slows down but increases in height. In March

2011, the Tohoku earthquake off the eastern coast of Japan caused a tsunami that did a

lot of damage. The tsunami waves created by the Tohoku earthquake reached heights

of over 40 metres (131 feet) in some areas, wiping out coastal towns and causing a

number of nuclear accidents.

Tsunamis move very quickly. Their speed is calculated using the following formula:

𝑣 = √𝑔 × 𝑑

In this formula:

𝑔 = 9.8𝑚𝑠⁻²

𝑑 = the depth of the ocean in metres

1. Based on the information provided in the text, one metre is approximately how

many feet?

a. 0.31 feet

b. 3.275 feet

c. 5.24 feet

d. 3 feet


2. An earthquake 5,000m deep in the ocean causes a tsunami. How fast is the

tsunami moving?

a. 221ms⁻¹

b. 70ms⁻¹

c. 22.1ms⁻¹

d. 70ms⁻¹

3. A tsunami is travelling at 150ms⁻¹. How deep is the water?

a. 150m

b. 2,343m

c. 1,200m

d. 2,296m


Baking Takes Off

Read the following information about a baking website

Brilliant Baking is a website. Its members pay a small annual subscription fee of £2, which

gives them access to exclusive recipes, offers, competitions, baking forums and use of a

mobile/tablet app that they can use to record their favourite recipes and tips.

In recent years, Brilliant Baking has grown in popularity with a greater number of members

joining each year. This is shown in the following graph:

1. How many male subscribers did the website have in 2012?

a. 327

b. 203

c. 124

d. 176


2. In which year was the difference in the number of male subscribers and female

subscribers smallest?

a. 2010

b. 2011

c. 2012

d. 2013

e. 2014

Brilliant Baking's website developer noticed that there was an increase in subscriptions

in 2013. He believes this was due to a popular television programme shown that year.

He plots the viewing figures for each week in a graph against the number of new

subscribers that week.


3. Brilliant Baking’s website developer makes a series of statements based on the

graph he created. Circle ‘True’ or ‘False’ for each statement.

1

“The more viewers the television programme has, the

more new subscribers we get.”

True

False

2

“This graph shows strong negative correlation”.

True

False

3

“The week we had 81 new subscribers was the week

the television programme had 2.2 million viewers.”

True

False

4

“If 2 million people watched the television

programme, we would expect to have between 50

and 70 new subscribers that week.”

True

False


Wheel Size

Read the following information about tyres

The following information is written on the wall of the tyre in the picture: 195/45 R15

The diagram below shows the different parts of the tyre and wheel.


The first figure 195/45 R15 is the width of the tyre in millimetres. In this case, it is 195

millimetres. This is the part of the tyre in contact with the road.

The second figure 195/45 R15 is the height of the tyre as a percentage of the width of

the tyre. In this case, it is 45%.

The third figure 195/45 R15 is the diameter of the rim in inches. In this case, the

diameter of the rim is 15 inches.

O/D is the total diameter of the wheel and the tyre.

1. Using the information from the text, how high is the tyre wall in millimetres?

2. What is the diameter of the wheel in millimetres? Use the following conversion:

1 inch = 25.4mm


3. What is the diameter of the wheel and tyre? Give your answer to the nearest

millimetre.

a. 469mm

b. 576mm

c. 557mm

d. 255mm

4. To the nearest revolutions, how many revolutions does the wheel make as the

car travels one kilometre?

a. 1,142 revolutions

b. 571 revolutions

c. 743 revolutions

d. 429 revolutions

Garage mechanics use tables like this one to make sure that the wheel and tyre

combinations is correct for the car.


(O/D mm – total diameter of wheel and tyre)

At the bottom of the chart is the following information:

"As a rule of thumb, to avoid putting out speedometer calibrations when converting

tyres, don't increase the overall diameter by more than 1.5% or decrease by 2%. This

calculation must be taken from the tyre size fitted originally by the vehicle

manufacturer."

5. The manufacturer recommends a 175/65 R14 wheel for a car that has a diameter

of 584mm. The wheel fitted to the car is 195/45 R15. Explain whether this will

alter the speedometer or not.

6. The car has R15 wheels which take a 195mm tyre. Using the chart, decide which

wheel or wheels could be fitted to the car that fall within the permitted

tolerances when compared to the manufacturer’s recommended 584mm

diameter (O/D mm).


Read the following information about tyres

195/45 R15 (O/D = 557mm)

195/50 R15 (O/D = 577mm)

7. The car is currently fitted with 195/45 R15 (O/D = 557mm) tyres, and these are to

be replaced by 195/50 R15 (O/D = 577mm) tyres. What is the percentage change

in the number of revolutions completed by the wheel in a kilometre using the old

tyre as the starting point?

a. An increase of 3.5%

b. A decrease of 5.4 %

c. An increase of 5.4%

d. A decrease of 3.5%


Tandem Speed


In 2014 Guy Martin and James Miles cycled a purpose built tandem for 24 hours covering

565 miles to set a new world records.

1. Calculate the average speed of their world records, giving your answer correct to

one decimal place, using the following formula: speed = distance

time


1. To convert miles to kilometres you can use the fact that 5 miles is approximately

equal to 8 kilometres. 5 miles ≈ 8 kilometres. How far did they cycle in kilometres?

a. 353.125 kilometres

b. 113 kilometres

c. 870.625 kilometres

d. 904 kilometres

2. Assuming that one of the tandem’s wheels had a diameter if 716mm, how many

revolutions would it take to cover a journey of 904 kilometres (to the nearest 10

revolutions?

a. 4,020 revolutions

b. 401,880 revolutions

c. 4,018,840 revolutions

d. 40, 190 revolutions


A cyclist training for a cycle race reduced her weight from 65kg to 60kg.

3. What percentage of her weight did the cyclist lose (to one decimal place)?

a. 7.7%

b. 92.3%

c. 8.3%

d. 91.7%


Freezing Cold

Read the following information about measuring temperature

Water freezes at 0°C (°C = Celsius) and boils at 100°C.

However this is not the only scale used to measure temperature. Another scale that is used

to measure temperature is Fahrenheit (°F).

The following graph shows a conversion from Celsius (°C) to Fahrenheit (°F).

1. Use the conversion graph to find the freezing point of water in °F

a. 32°F

b. -18°F

c. 30°F

d. -20°F

As well as using a conversion graph, it is possible to convert between Celsius (°C) and

Fahrenheit (°F) using the following formula:

𝐹 = 9

5 𝐶 + 32


2. Mercury is the only elemental metal that is liquid at room temperature. Mercury

melts at approximately -39°C. What is the melting point of mercury in Fahrenheit (°F)

to the nearest whole number?

a. 38.2°F

b. -102.2°F

c. -38°F

d. -102°F

3. Fahrenheit 451 is the title of a book by Ray Bradbury. The title of the book is a

reference to the approximate temperature in Fahrenheit when paper will start to

burn. What is 451°F in Celsius °C, to one decimal place?

a. 268.3°C

b. 745.2°C

c. 232.8°C

d. 869.4°C

4. Oxygen freezes at approximately -362°F. How many degrees Fahrenheit is that

below the freezing point of water, which is 32°F?

a. 330°F

b. -330°F

c. -394°F

d. 394°F

The formula to covert Celsius (°C) to Fahrenheit (°F) is:

𝐹 = 9

5 𝐶 + 32


5. At what temperature is the value for Celsius the same as that for Fahrenheit?

Express your answer as a set of coordinates.


Correct Answers

Poppies

1. The correct answer is C. The number of poppies created and sold was 888,246 which is

eight hundred and eighty-eight thousand, two hundred and forty-six.

2. The correct answer is B. The underlined 8 in 888,246 stands for eighty thousand. The

place value headings are:

3. The correct answer is A. £9 for each poppy goes to charity. There are 888,246 poppies

which raise:

888,246 × £9 = £7,994,214

This is divided equally between 6 charities:

7,994,214 ÷ 6 = £1,332,369

4. In the text, it is stated that 5 million individual parts were used to make the 888,246

poppies.

5,000,000 ÷ 888,246 = 5.629071

As there must be a whole number of parts to make a poppy, this value needs to be

rounded up. Therefore, 6 parts are needed to make 1 poppy.

5. The correct answer is B. 90 tonnes of steel is the same as 90,000 kilograms, which is the

same as 90,000,000 grams of steel.

90,000,000 ÷ 888,246 = 101.3

Therefore the steel supporting each poppy weighs about 101 grams.


6. The text gives the figure of 5 million which can be assumed to be to 1 significant figure.

The upper bound for 5,000,000 is 5,500,000 and the lower bound is 4,500,000, giving the

range of possible values as:

4,500,000 ≤ 𝑥 ≤ 5,500,000

7. It takes 2 minutes per person to plant 1 poppy. This leads to:

15,000 × 2 = 30,000 minutes needed to plant the poppies

Assuming that the volunteers work for 7 hours, the rest of the day is breaks. Minutes

available per person is:

7 × 60 = 420 minutes

30,000 ÷ 420 = 71.4

Therefore approximately 70 people are needed to plant the poppies each day.


Decorating

1. The correct answer is C. There are 100 centimetres in 1 metre. Therefore, to find how

many metres in 405 centimetres, divide by 100 as follows:

405 ÷ 100 = 4.05

2. The correct answer is D. The area of a rectangle is found by using:

area = length × width

In this case:

area = 4.05 × 3.5 = 14.175m2

If you chose the answer A you found the perimeter. Remember, the perimeter is the total

distance around the outside of the shape. The area is the space inside the shape.

3. The area needed is 14.175m2

The cost per metre squared is £12.99

14.175 × 12.99 = £184.13325

Helen and Josh only have £150 to spend, so they are £34.13 short. Therefore, they cannot

afford to buy the Brogden Blue carpet.

4. The correct answer is D. The carpet can be laid so that it is 4 metres by 4.05 metres

which means that there is spare carpet.

Method 1

Area of carpet used: 4 × 4.05 = 16.2m2

Area of floor: 3.5 × 4.05 = 14.175m2

Waste: 16.2 − 14.175 = 2.025m2

Method 2

The carpet is 0.5m too wide therefore the waste is:

0.5 × 4.05 = 2.025m2

5. The correct answer is A.

The amount of waste is given as 2.025m2

The total amount of carpet bought is 4 × 4.05 = 16.2m2


The percentage of waste is:

2.025

16.2× 100 = 12.5%

6. The total area of the walls can be calculated by finding the area of each wall and adding

them together.

4.05 × 2.5 + 3.5 + 2.5 + 4.05 × 2.5 + 3.5 × 2.5 =

10.125 + 8.75 + 10.125 + 8.75 = 37.75m2

The area of the door: 1.981 × 0.838 = 1.660078m2

The area of the window: 1.05 × 1.2 = 1.26m2

Therefore the total area of walls that Helen and Josh are painting is:

37.75 − 1.660078 − 1.26 = 34.829922 ≈ 34.8m2

They would have to buy three tins of paint as one tin only covers 32m2 and they want to

paint the walls twice.


The Wedding Planner

1. There are 36 possible three course dinners that can be ordered.

Method 1

There are three starters, four mains and three desserts. Multiply these to get the number

of meal combinations.

3 × 4 × 3 = 36

Method 2

Listing all the possibilities as follows:

Starter Main Desert

Salmon Beef Sticky toffee pudding

Salmon Beef Trifle

Salmon Beef Crumble

Salmon Pork Sticky toffee pudding

Salmon Pork Trifle

Salmon Pork Crumble

Salmon Salmon Sticky toffee pudding

Salmon Salmon Trifle

Salmon Salmon Crumble

Salmon Tortellini Sticky toffee pudding

Salmon Tortellini Trifle

Salmon Tortellini Crumble

Soup Beef Sticky toffee pudding

Soup Beef Trifle

Soup Beef Crumble

Soup Pork Sticky toffee pudding

Soup Pork Trifle

Soup Pork Crumble

Soup Salmon Sticky toffee pudding

Soup Salmon Trifle

Soup Salmon Crumble

Soup Tortellini Sticky toffee pudding

Soup Tortellini Trifle

Soup Tortellini Crumble

Pâté Beef Sticky toffee pudding

Pâté Beef Trifle

Pâté Beef Crumble

Pâté Pork Sticky toffee pudding

Pâté Pork Trifle

Pâté Pork Crumble

Pâté Salmon Sticky toffee pudding

Pâté Salmon Trifle

Pâté Salmon Crumble


Pâté Tortellini Sticky toffee pudding

Pâté Tortellini Trifle

Pâté Tortellini Crumble


The bar chart shows that:

12 guests had salmon

12 guests had soup

8 guests had pâté

12 + 12 + 8 = 32 guests.

3. The correct answer is D.

There are 32 possible starters as there are 32 guests.

12 guests chose soup.

Therefore the fraction choosing soup is 12

32 =

3

8


There are 32 guests. The number of guests eating each main is shown below.

Beef = 7

Pork = 9

Salmon = 10

Tortellini = 6

7 guests had beef.

5. The correct answer is C.

6. There are 10 guests who had tortellini as their main course. Of these, 8 had pâté as a

starter.

The answer is 8

10

7. Find the mean of the three starters, the mean of the three main courses and the mean of

the three desserts.

The mean cost of the starters is:

(6.25+4.50+5.50)

3 = £5.4166

Mean starter price £5.42

The mean cost for the mains is:

(12.95+12.95+13.95+12.35)

4 = £13.05

Mean mains price £13.05

The mean cost for the desserts is:

(4.50+4.75+4.95)

3 = £4.7333


Mean desserts price £4.73

To be very accurate the unrounded mean costs should be added giving:

£5.416667 + £13.05 + £4.733333 = £23.20

Add 5% to give the following:

1.05 × £23.20 = £24.36

The cost per meal is £24.36

Therefore, the total cost for the 30 guests and the bride and groom is:

32 × £24.36 = £779.52

8. The correct answer is B.

The total cost for the ingredients and wages + 10% (of ingredients and wages) = £770

This means that £770 represents 110%

110%

£770

1%

770 ÷ 110 = 7

10 %

7 × 10 = 70

This gives a profit of £70

This is a reverse percentage question.


Tsunami


In the text you are told that 40 metres is 131 feet. Therefore:

1 metre = 131

40 = 3.275 feet


Using the formula:

𝑣 = √𝑔 × 𝑑

where g = 9.8ms⁻² and d = the depth of the ocean in metres.

𝑣 = √9.8 × 5,000 = √49,000

𝑣 = 221𝑚𝑠⁻¹


Using the formula:

𝑣 = √𝑔 × 𝑑

where 𝑔 = 9.8𝑚𝑠⁻² and 𝑑 = the depth of the ocean in metres.

150 = √9.8 × 𝑑

𝑑 = 150²

9.8= 2,296m


Baking Takes Off


As we are only considering male subscribers, we only look at the blue bar for 2012. We

can see that this falls between 100 and 200. The available options are therefore 124 and

176.

Looking more carefully at the axes we can see that the bar is less than halfway between

100 and 200. The correct response is less than 150, so it must be 124.

2. The correct answer is E.

It can be seen that the difference in heights of the male and female bars was smallest in

2014.

3. Statement 1 – True. The graph shows a weak positive correlation so, yes, more TV

viewers means more new subscriptions.

Statement 2 – False. The graph does not show a strong negative correlation.

Statement 3 – False. In the week of 81 new subscribers it can be seen that the

programme had approximately 2.75 million viewers.

Statement 4 – True. You would expect between 50 and 70 new subscribers. This could

be seen by drawing a line of best fit between the plotted points.


Wheel Size

1. The height of the tyre is 45% of 195 millimetres.

Method 1

45

100 × 195 = 87.75mm

Method 2

Convert 45% to a decimal 0.45

0.45 × 195 = 87.75mm

The answer is 87.75mm

2. The wheel rim is 15 inches in diameter

15 × 25.4 = 381mm


The rim has a diameter of:

15 × 25.4 = 381mm

The wall of the tyre is:

0.45 × 195 = 87.75mm

Therefore the total diameter is:

381 + 2 × 87.75 = 556.5mm

The correct answer is 557 millimetres to the nearest millimetre (there are two tyre sides

to be added).


The diameter is 557mm.

This gives a circumference of:

𝐶 = 𝜋 × 557 = 1749.86mm

This is 1.749m

Therefore the number of revolutions in one kilometre is:

1,000 ÷ 1.749m

This is 571 complete revolutions.


5. The recommended diameter is 584mm.

The 195/45 R15 has a diameter of 557mm.

The percentage difference is:

584 − 557

584 × 100 = 4.6

4.6% falls outside the recommended tolerance of 1.5% to 2%. The wheel fitted to the car

will alter the speedometer.

6. An increase of 1.5% gives a maximum of 592 millimetres to the nearest millimetre.

Method 1

1.5% of 584 = 1.5 × 584 ÷ 100 = 8.76mm

Largest = 584 + 8.76 = 592.76 mm

Therefore a maximum of 592 millimetres to the nearest millimetre.

Method 2

An increase of 1.5% is the same as 1.015 of the original

1.015 × 584 = 592.76mm

Method 3

2% of 584 = 2 × 584 + 100 = 11.68mm

Smallest = 584 − 11.68 = 572.32mm

Therefore a minimum of 593 millimetre to the nearest millimetre.

Method 4

A decrease of 2% is the same as 0.98 of the original

0.98 × 584 = 572.32mm

Therefore a minimum of 593 millimetres (to the nearest millimetre).

Therefore from the table the answer is:

195/50 R15

(O/D = 577mm)


For the 195/45 R15 combination the diameter is given as 557 millimetres.


𝐶 = 𝜋 × 557 = 1,749.86mm


This is 1.749m rounded to the nearest mm.

Using the unrounded answer of:

𝜋 × 557

1,000 = 1.749867108

for the following calculation:

The number of revolutions in one kilometre is:

1,000 ÷ (𝜋 × 557

1,000) = 1,000,000 ÷ (𝜋 × 557) = 571.471968

Using the rounded answer of 1.749 the calculation gives:

1,000 ÷ 1.749 = 571.7552887

Therefore, there are 571 complete revolutions.

For the 195/50 R15 combination:

The diameter is given as 577mm.


𝐶 = 𝜋 × 557 = 1,812.70mm

This is 1.813m

Therefore, the number of revolutions in 1 kilometre is:

1,000 ÷ 1.813 = 551.6

This is 551 complete revolutions.

571 − 551

571 × 100 = 3.5


Tandem Speed

1. The average speed is approximately 23.5mph.

Use the following formula:

speed = distance

time

Substitute in 565 miles and 24 hours:

speed = 565

24= 23.54mph

Their average speed was approximately 23.5mph


Method 1

Using a table:

Miles Kilometres

5 8

1 1.6

565 904

Method 2

Using:

5 miles ≈ 8 kilometers

565 ÷ 5 = 113

113 × 8 = 904 kilometres

Method 3

As above, but in one calculation:

565 × 8

5 = 904


A diameter of 716mm is a circumference of:


𝑐 = 𝜋 × 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟

𝑐 = 𝜋 × 716 = 2,249.38mm

This is approximately 2.24938m

Converting 904km to metres gives 904,000m

The number of revolutions is:

90,400

2.24938= 40,188.4597

This is approximately 40,190 to the nearest 10.

4. The correct answer is A. She started with a weight of 65kg and reduced it to 60kg – a

reduction of 5kg.

This represents:

5

65 × 100 = 7.69. . %

To one decimal place, the cyclise lost 7.7% of her weight.


Freezing Cold


Water freezes at 0°C. Read up the Fahrenheit axis to where the line intersects.

The line intersects at 32°F.


Using the formula:

𝐹 = 9

5 𝐶 + 32

Substitute C with -39 to give:

𝐹 = 9

5 × (−39) + 32 = −38.2

This is -38°F to the nearest whole number.


Substitute F = 451 into the following formula:

𝐹 = 9

5 𝐶 + 32

to give:

451 = 9

5 𝐶 + 32

Rearrange as follows:

451 − 32 = 9

5 𝐶

𝐶 = 5

9 (451 − 32) = 232.7777 …

𝐶 = 232.8°𝐶


32 − (−362) = 394°F

5. The value when the two temperatures are the same is -40°F = -40°C. The coordinates are

(-40, -40).

Method 1

Using the graph it is possible to see that the two lines intersect, which means that there

is a value when Celsius and Fahrenheit are the same.

Method 2


Using the formula, replace F by C to give:

𝐶 = 9

5 𝐶 + 32

This gives:

4

5 𝐶 = −32

𝐶 = −40

Method 3

Using the formula:

𝐹 = 9

5 𝐶 + 32

replace C with F to give:

𝐹 = 9

5 𝐹 + 32

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