Applications of Mathematics

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P45897RRA©2015 Pearson Education Ltd.

6/6/6/6/6/3/6/6/1/

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Applications of MathematicsUnit 2: Applications 2For Approved Pilot Centres ONLY

Foundation TierFriday 6 November 2015 – MorningTime: 1 hour 45 minutes 5AM2F/01You must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

Instructions

• Use black ink or ball-point pen.• Fill in the boxes at the top of this page with your name, centre number and candidate number.• Answer all questions.• Answer the questions in the spaces provided

– there may be more space than you need.• Calculators may be used.• If your calculator does not have a button, take the value of to be

3.142 unless the question instructs otherwise.

Information

• The total mark for this paper is 100• The marks for each question are shown in brackets

– use this as a guide as to how much time to spend on each question.• Questions labelled with an asterisk (*) are ones where the quality of your

written communication will be assessed.

Advice

• Read each question carefully before you start to answer it.• Keep an eye on the time.• Try to answer every question.• Check your answers if you have time at the end.

Pearson Edexcel GCSE

2

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GCSE Mathematics 2AM01

Formulae: Foundation Tier

You must not write on this formulae page.Anything you write on this formulae page will gain NO credit.

Area of trapezium = 12 (a + b)h

Volume of prism = area of cross section × length

b

a

h

length

sectioncross

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Answer ALL questions.

Write your answers in the spaces provided.

You must write down all stages in your working.

1 Jim has these coins in his pocket.

(a) How much money does he have altogether?

£.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

Peter changes a £10 note for 20p coins.

(b) Work out how many 20p coins he gets.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

Alice has to pay for parking her car. She can pay with ten 20p coins or she can pay with 50p coins.

(c) How many 50p coins does she need to make the same total value as ten 20p pieces?

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

(Total for Question 1 is 6 marks)

Two pounds

Fifty pence

Fifty pence

Ten pence

One pound

Twenty pence

Twenty pence

Five pence

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2 The table shows the numbers of papers sold on 15 April 2012 and on 14 April 2013

Number of papers sold

Newspaper 15 April 2012 14 April 2013

The Sun on Sunday 2297441 1905772

Sunday Mirror 1088354 1033801

Mail on Sunday 1800674 1697982

Sunday Express 529510 459808

Sunday Times 955248 882497

Data taken from Wikipedia and www.abc.org.uk

On 14 April 2013 the number of papers sold for one newspaper was less than five hundred thousand.

(a) Write down the name of this newspaper.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) Work out the difference between the number sold for the Sunday Times on 14 April 2013 and on 15 April 2012

... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

There were 48 pages in the Sun on Sunday on 14 April 2013

Larry says,

‘There was a total of over 72 million pages in all of the Sun on Sunday papers sold on 14 April 2013’

*(c) Is Larry correct? You must show your working.

(3)


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3 Here is a lake shown on a grid of centimetre squares.

Lake

(a) Estimate the area of the lake shown on the grid.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm2

(2)

Each square on the grid represents an area of 100 m2 for the real lake.

(b) Work out an estimate for the area of the real lake.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m2

(1)


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4 The diagram shows 5 stations on a train line. It also shows how long it takes a train to go from each station to the next station.

LutonHendonFarringdonTulse Hill

Morden South

24 mins 22 mins 23 mins 34 mins

It takes a train more time to go from Hendon to Luton than it does to go from Morden South to Tulse Hill.

(a) How much more time?

... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . minutes(1)

(b) How long does it take a train to go from Tulse Hill to Luton? Give your answer in hours and minutes.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . hours .. . . . . . . . . . . . . . . . . . . . . . . . . . minutes(2)

Jim catches a train from Farringdon at 09 12

(c) What time does this train get to Luton?

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

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Alice has to get to Hendon station by 1100 She catches a train from Morden South at 0924

(d) Will the train get to Hendon station by 1100? You must show your working.

(2)


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5 Billy sees this special offer in a shop.

Special Offer

3 for the price of 2

Buy any 3 items - get the cheapest item free.

Here are the items in the special offer.

Calculator £6.99 Exam set £2.99 Pack of pens £4.99

Billy buys a calculator, an exam set and a pack of pens. He uses the special offer.

(a) Work out how much he has to pay.

£ .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

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There is also a special offer on all books in the shop.

Special Offer on Books

Buy 2 books - get the cheaper book for half price

The full price of ‘The White Princess’ is £13.20 The full price of ‘Save with Jamie’ is £13

Hannah buys both of these books. She uses the special offer.

Hannah pays with a £50 note.

(b) How much change should she get?

£ .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(3)


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6 Here is a sketch of Jill’s garden.

16m

10m

60°

Diagram NOT accurately drawn

D

A B

C

(a) Make an accurate scale drawing of Jill’s garden.

Use a scale of 1cm represents 2m.

The side AB has already been drawn for you.

(3)

A B

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Jill wants to put fencing all around the edges of the garden. Fencing is sold in packs. There is 4m of fencing in each pack.

(b) Work out how many packs of fencing Jill needs to buy.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(3)


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*7 Angus wants to send some Christmas foods to a friend. He is going to pack these foods in a box.

Christmas pudding 1.1kg

Jar of jam 340grams

Jar of apple sauce 145grams

Cake 200grams

Angus does not want the total weight of the box and the foods to be more than 2 kg.

What is the greatest weight of a box he can use?


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*8 Mr Smith is planning a school trip.

240 students are going on the trip. 10 teachers are going on the trip.

Mr Smith is going to hire buses for the trip. There are 49 seats for passengers on each bus. It costs £385 to hire each bus.

Mr Smith is going to charge each student £9 for the trip. The teachers will not pay.

Is Mr Smith going to charge each student enough money so that he can hire all the buses needed?

You must show your working.


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9 You can use this graph to change between kilometres and miles.

kilometres

miles

40

30

20

10

2 4 6 8 10 12 14 16 18 200

0

(a) Change 12 miles to kilometres.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilometres(1)

(b) Change 26 kilometres to miles.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . miles(1)

Jean’s home is 220 km from Paris. She has to drive from her home to Paris.

Jean drives 60 miles towards Paris. She stops for fuel.

*(c) Work out how far Jean still has to drive.

(3)


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10 Here is part of a child’s toy.


The part of the toy is a prism made of centimetre cubes.

(a) Work out the volume of the prism.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

(b) On the grid, draw a side elevation of the prism from the direction of the arrow.(2)


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11 The total cost of 6 pens and 2 pencils is £5 The total cost of 4 pencils is 88p.

Ellie buys 4 pens and 4 pencils.

Work out the total cost.

£ .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


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12 Ali uses this rule to work out the total cost of using his telephone for a single call.

Total cost = 9p × number of minutes used + 15p

Ali used his telephone to talk to his sister for 20 minutes.

(a) Use the rule to work out the total cost of the phone call.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p(2)

On a different day, Ali used the telephone to talk to his dad. Ali used the rule and worked out that the total cost of the call was £2.40

Ali talked to his dad for more minutes than he talked to his sister.

(b) How many more minutes?

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . minutes(3)


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13 Here is a formula for a child’s dose, d ml, of medicine when the adult dose is D ml.

d a D= + ×( )124

a is the age of the child in years.

Marta is 5 years old. An adult dose of medicine is 20 ml.

(a) Find the dose of medicine Marta should have.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ml(2)

(b) How old is a child when the child’s dose of medicine is half the adult dose of medicine?

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . years(2)


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14 Here is a solid shape.

The solid shape is the base of a small statue.

Volume of solid shape in cm3 = 4 83

6 4 6 4 3 2 3 22 2. ( . . . . )× + × +

Work out the volume in cm3.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm3


3.2cm

6.4cm

4.8cm


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15

Carton

100cm

40cm

30cm

5cm

5cm5cm


Box

Emily fills a carton with boxes.

The carton is a cuboid with

length 100 cm width 40 cm height 30 cm

Each box is a cube of side 5cm.

Work out the number of boxes Emily needs to fill one carton completely.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


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16 Here is a map showing two ports.

(a) Find the distance of Deerham from Seaburn.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . km(2)

(b) Find the bearing of Deerham from Seaburn.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . °

(1)

There is a lighthouse at Deerham. The lighthouse can be seen from ships up to 20 km away.

(c) On the scale drawing, show by shading the region of the sea from where the lighthouse can be seen.

(3)


Scale 1cm represents 5km

Deerham

N

Seaburn

Land

Land

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17 A school is having a fete on Saturday.

The weather forecast says,

“There is an even chance of rain on Saturday.”

(a) On the probability scale, mark with a cross (×) the probability that it will rain on Saturday.

12

0 1

(1)

Megan is planning a game to raise money for charity. She is going to use a fair spinner.

4

2

31

Megan spins the spinner once.

(b) On the probability scale, mark with a cross (×) the probability that the spinner lands on 2

12

0 1

(1)

23


Megan spins the spinner twice.

The score is the sum of the numbers the spinner lands on.

(c) Complete the table to show the possible scores.

2nd spin1st spin

1 2 3 4

1

2 3 5

3 5

4 8

(1)

Here are the rules for Megan’s game.

Pay 50p to spin the spinner twice. When the score is 7 or more, get £1.50

*(d) If this game is played 100 times should Megan expect to make a profit?

(5)


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18 Three students test the same coin for bias. Each student throws the coin a number of times.

The table gives information about the results.

Ben Sammi Ellie

Number of heads 32 73 102

Number of throws 50 100 150

The coin is going to be thrown once more.

(a) Using Ben’s results, work out an estimate for the probability that the coin will land on heads.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) The results of which student should give the most reliable estimate for the probability that the coin will land on heads?

You must give a reason for your answer.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(c) Use all the results to get the best estimate for the probability that the coin will land on heads.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)


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19 The diagram shows two prisms.

A B

All the measurements are in cm.

The volume of prism A is 55 cm3 greater than the volume of prism B.

(a) Show that x3 – 12x = 55

(2)

(b) The equation

x3 – 12x = 55

has a solution between x = 4 and x = 5

Use a trial and improvement method to find this solution. Give your answer correct to one decimal place. You must show ALL your working.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(4)



2x

xx x

8

3

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20 Here is a travel graph.

The travel graph gives information about Andy’s journey from the shops to the library. It also gives information about Kate’s journey from the library to the shops along the

same road.

(a) What time did Andy start his journey?

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) How many minutes did Andy stop for on his journey?

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . minutes(1)

(c) How far had Kate travelled when she met Andy?

... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . km(2)


20

15

10

5

1200 1400 1600

Distance from the shops (km)

Time1300 1500 1700

25

Kate Andy

0

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21 On average, Coopers sell 3000 fridges each year.

The probability that a new fridge will stop working in its first year is 0.015

It costs Coopers £385 to replace any fridge that stops working in its first year.

Work out an estimate for the total cost each year to Coopers of replacing all the fridges that stop working in their first year.

£ .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


TOTAL FOR PAPER IS 100 MARKS

28

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