2010 Maths Spec.indd

This document is an issue 2.Substantial changes are marked by a sidebar.

Please see page 11.

Edexcel GCSE Sample Assessment Materials © Edexcel Limited 2010in Mathematics A Issue 2

1

ContentsGeneral Marking Guidance 2

Paper 1: Foundation Tier Sample Assessment Material 3Sample Mark Scheme 33

Paper 1: Higher Tier Sample Assessment Material 47Sample Mark Scheme 75

Paper 2: Foundation Tier Sample Assessment Material 91Sample Mark Scheme 121

Paper 2: Higher Tier Sample Assessment Material 133Sample Mark Scheme 155


2

General Marking Guidance

All candidates must receive the same treatment. Examiners must mark the first candidate in exactly the same way as they mark the last.

Mark schemes should be applied positively. Candidates must be rewarded for what they have shown they can do rather than penalised for omissions.

All the marks on the mark scheme are designed to be awarded. Examiners should always award full marks if deserved, i.e. if the answer matches the mark scheme. Examiners should also be prepared to award zero marks if the candidate’s response is not worthy of credit according to the mark scheme.

Where some judgement is required, mark schemes will provide the principles by which marks will be awarded and exemplification may be limited.

Crossed out work should be marked UNLESS the candidate has replaced it with an alternative response.

Mark schemes will indicate within the table where, and which strands of QWC, are being assessed. The strands are as follows:

i) ensure that text is legible and that spelling, punctuation and grammar are accurate so that meaning is clear. Comprehension and meaning is clear by using correct notation and labelling conventions.

ii) select and use a form and style of writing appropriate to purpose and to complex subject matter. Reasoning, explanation or argument is correct and appropriately structured to convey mathematical reasoning.

iii) organise information clearly and coherently, using specialist vocabulary when appropriate. The mathematical methods and processes used are coherently and clearly organised and the appropriate mathematical vocabulary used.

Guidance on the use of codes within this mark scheme M1 – method mark A1 – accuracy mark B1 – working mark C1 – communication mark QWC – quality of written communication oe – or equivalent cao – correct answer only ft – follow through sc - special case


3

Centre Number Candidate Number

Write your name hereSurname Other names

Total Marks

Paper Reference

Turn over

*S37707A0130*

Edexcel GCSE

Mathematics APaper 1 (Non-Calculator)

Foundation Tier

Sample Assessment MaterialTime: 1 hour 45 minutes

You must have:

Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser.

1MA0/1F

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 must not be used.

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 – you should take particular care on these questions with your spelling, punctuation

and grammar, as well as the clarity of expression.

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.

S37707A©2010 Edexcel Limited.

2/2/2/2/3/2/


4

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 = (a + b)h

Volume of prism = area of cross section × length

b

a

h

length

crosssection

12

GCSE Mathematics 1MA0


5

Answer ALL questions.

Write your answers in the spaces provided.

You must write down all stages in your working.

1 (a) Write down the reading on this scale.(1)

km/h

3040

50 60 7080

90

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . km/h

The scale shows the weight of Sam’s dog.

0

15

kg

24

3

Sam’s baby brother weighs 5 kg.

(b) Work out the difference in weight between Sam’s baby brother and Sam’s dog.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kg

(Total for Question 1 = 3 marks)


6

2 A bus seats 47 people. Another 6 people can stand.

There are 44 people on the bus. The bus stops.

8 people get off the bus. 19 people want to get on the bus.

Can the bus hold all the people who want to get on the bus? Explain your answer.



7

3 Here is a coordinate grid.

P

Q

x

y

7

7

6

6

8

5

5

4

4

3

3

2

2

1

1O

(a) Write down the coordinates of the point P.(1)

(…………, …………)

R is the midpoint of PQ.

(b) Write down the coordinates of the point R.(2)

(…………, …………)

The point B is on the x-axis. The line BP is parallel to the y-axis.

(c) Write down the coordinates of the point B.(2)

(…………, …………)



8

4 Ben is planning to make some blocks for a child.

The diagram shows some 3-D shapes.

A B C

D E

(a) Write down the mathematical name of the 3-D shape C.(1)

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

(b) Write down the number of edges on the 3-D shape D.(1)

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

(c) Write down the letters of all the 3-D shapes that have 5 faces.(1)

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


9

Ben is going to make one of the boxes, the 3-D shape B. The 3-D shape is to be 4 cm high, 5 cm wide and 6 cm long.

(d) (i) In the space below draw an accurate net of the solid shape B.

(ii) Find the length and width of the smallest rectangle of card needed for the net.(5)

Smallest width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Smallest length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



10

5

A

Shape A has been drawn on a centimetre grid.

(a) Find the perimeter of shape A.(1)

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


11

The diagram shows the plan, the front elevation and the side elevation of a 3-D solid made from one centimetre cubes drawn full size.

Plan

FrontElevation

SideElevation

(b) Find the volume of the 3-D shape.(4)

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



12

6 Laura and Jaz were worried about the amount of traffic in their town.

The town council aims to reduce the percentage of lorries to 25% of the total number of vehicles.

Laura and Jaz carried out a survey of the types of vehicles passing Laura’s house during 10 minutes one Saturday morning.

Here is a list of the vehicles they saw.

Car Van Lorry Motorbike Bus Car

Van Car Car Van Lorry Motorbike

Motorbike Motorbike Van Lorry Motorbike Car

Car Bus Lorry Car Lorry Motorbike

Laura and Jaz were going to give a talk about the results of their survey.

* (a) Design a suitable chart or table Laura could use and a different chart or table that Jaz could use to make a summary of the list of vehicles they saw.

Use the space below or the grid provided.(6)


13

The council’s aim was to reduce the percentage of lorries in the town to be less than 25%.

(b) Did the council succeed? You must explain your answer.(2)

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

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

Laura and Jaz’s survey was not a good one.

(c) Explain how Laura and Jaz could design a better survey to investigate the council’s plan.

(2)

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

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



14

7 Here are some patterns made from sticks.

Pattern number 1 Pattern number 2 Pattern number 3

(a) Draw Pattern number 4 in the space below.(1)

(b) How many sticks are used for Pattern number 10?(2)

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

Jim says there is a pattern with 123 sticks in it.

(c) Is Jim correct? You must explain your answer.(2)

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

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

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



15

8 These triangles have been drawn on a centimetre grid.

A

BC

D E F

(a) Write down the letters of the two triangles that are congruent.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . and . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) Write down the letters of two different triangles that are similar.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . and . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c) Find the area of triangle D.(1)

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



16

9

mirror line

(a) Reflect the shaded shape in the mirror line.(1)

Here is a pattern made with squares.

(b) Shade one square to make a black and white pattern with only one line of symmetry.(1)


17

Here is another pattern made with squares.

(c) Shade three more squares to make a pattern with rotational symmetry of order 2.(1)



18

10 (a) Simplify 7x + 3x – 4x(1)

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

(b) Solve 3y – 2 – 8(2)

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



19

11 Chris owns a clothes shop. He bought 50 shirts at £12 for each shirt. He chose the selling price of each shirt so that he would make a profit of 30% on

each shirt. He sold 20 shirts at this price.

Chris then reduced the selling price of each shirt by 15%. He then sold the remaining shirts at this reduced selling price.

Has Chris made a profit or loss? You must explain your answer clearly.


*


20

12 Here are two fair 4-sided spinners. One is a Blue spinner and one is a Red spinner.

2

4

6

8

2

4

6

8

Blue Spinner Red Spinner

Each spinner has four sections numbered 2, 4, 6 and 8.

Each spinner is to be spun once.

Total score = Blue spinner score + Red spinner score

(a) List the different ways that the total score can be 8(2)

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


21

Ali and Shazia play a game. In each round of the game, Ali spins the Blue spinner once and Shazia spins the

Red spinner once. Ali wins when the Blue spinner score is greater than the Red spinner score.

(b) Work out the probability that Ali will win the first round.(4)

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



22

13 Parul has £1.70

She wants to buy a drink and something to eat.

(a) What are the different combinations she can buy?(2)

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

Burgers

Single burger £0.85

Single burger with cheese £0.95

Double burger £1.55Double burger with cheese £1.70

Fries Cola

Regular £0.65 Regular £0.85Large £0.99 Large £1.10

Meal Deals

Regular

Single burger with £2.09

regular fries and regular cola

LargeDouble burger with cheese £3.49large fries and large cola


23

Ken buys

2 double burgers with cheese, 1 large fries and 1 large cola.

He pays with a £10 note.

(b) He gets the best price. What change should he get?

(3)

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



24

14 Simon is a salesman. He gets paid expenses of 40p for every mile that he drives during work. He also gets £12 expenses as a meal allowance for any day that he drives during work. The table gives information about the number of miles Simon drove on 5 days

in one week.

Day Number of miles

Monday 48

Tuesday 37

Wednesday 0

Thursday 78

Friday 21

(a) Work out Simon’s total expenses.(4)

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


25

Sasha works for the same company. She gets paid expenses of 40p for each mile she drives during work.

Last year she worked for 48 weeks.

Her total expenses for driving for the year were £2116.80

(b) Work out an estimate for the average number of miles Sasha drove during work each week last year.

(3)

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



26

15 Emma says

“Since 3 is half way between 2 and 4 then 13 will be half way between

12

and 14

”

Emma is wrong.

Show that 13 is not half way between

12

and 14

Show your working here.


*


27

16 (a) Solve 5p – 16 = 4(2)

p = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) Solve 2q – 4 = 5q + 5(2)

q = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

y = 3(2x – 1) – 2(5 + 3x)

(c) Find the value of y.(2)

y = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



28

17 A bag contains red, yellow and blue balls.

The probability of drawing a red ball at random is 12

.

The probability of drawing a yellow ball at random is x. The probability of drawing a blue ball at random is 4x .

Work out the probability that a blue ball is selected. Give your answer as a numerical value.

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



29

18

1

2

3

4

5

O

y

T

1 2 3 4 5 6 7 8 9 10–1–2 x–1

–2

–3

–4

–5

The shape T is rotated by 180° about the point (3, 0) to give the shape U.

The shape U is rotated by 180° about the point (6, 0) to give the shape V.

Describe fully the single transformation that will map shape T to shape V.

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

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



30

19 This spinner is used at a fairground.

When the spinner lands on a W, the customer wins a prize.

L

LL

LLW

W

W Diagram NOTaccurately drawn

The fairground owner expects a 1000 customers to have a go. Estimate the number of prizes the owner should buy. Give reasons for your answer.



31

20 (a) Factorise 5x – 10y(1)

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

(b) Factorise fully 3pq – 12p 2

(2)

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



32

21

Diagram NOTaccurately drawn

6 m

8 m

4 m

8 m

The diagram is a plan of the floor of Nikola’s room. All the angles are right angles. Nikola is going to lay flooring to cover all the floor.

She can choose either carpet tiles or wood strips.

Carpet tiles come in packs of 32 and are square. They measure 50 cm by 50 cm. Wood strips come in packs of 10 and are rectangular. They measure 2 m by 25 cm.

She only wants to use one type of flooring and buy as few packs as she can. Which type of flooring should she choose?

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


TOTAL FOR PAPER = 100 MARKS


33

Spec

ific

atio

n A

: Pa

per

1 Fo

unda

tion

Tie

r

1MA

0/1F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 1.

(a

)

65

1 B1

cao

(b

) 5

–3.

81.

2 2

M1

5 –

3.8

A1

cao

To

tal f

or Q

uest

ion:

3 m

arks

2.

44 –

8 =

36

36 +

19

= 55

47

+ 3

= 5

3 O

R44

+ 1

9 –

8 =

55

47 +

6 =

53

OR

47–

44 =

3

3 +

8 =

11

19–

11 –

6=

2

2 (w

ith

appr

opri

ate

reas

on)

2 M

1 Cl

ear

atte

mpt

to

find

the

num

ber

of s

pace

s av

aila

ble

on t

he b

us

afte

r th

e bu

s st

ops

A1 r

easo

n fo

r an

swer

whi

ch m

ust

com

men

t on

the

dif

fere

nce

betw

een

55 a

nd 5

3

Tota

l for

Que

stio

n: 2

mar

ks


34

1MA

0/1F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 3.

(a

)

(6,

7)

1 B1

cao

(b

)

(3,

5.5)

2

M1

Clea

r at

tem

pt t

o fi

nd t

he m

ean

of e

ithe

r x

or y

coo

rdin

ates

of

P an

d Q A1

cao

O

RM

1 id

enti

fies

the

mid

poin

t of

PQ

on

the

diag

ram

A1

cao

SC

B1

for

exac

tly

one

coor

dina

te c

orre

ct

(c

)

(6,

0)

2 M

1 fo

r B

corr

ectl

y pl

aced

on

the

x ax

is

A1 f

or (

6, 0

)

Tota

l for

Que

stio

n: 5

mar

ks

4. FE(a

)

cylin

der

1 B1

cao

(b

)

9 1

B1 c

ao

(c

)

D,

E 1

B1 c

ao

(d

)(i)

(ii)

Net

14 c

m

18

cm

5B3

ful

ly c

orre

ct

(B2

5 co

rrec

t fa

ces)

(B

1 a

net

of a

cub

oid)

B1,

B1 f

t on

d(i

) To

tal f

or Q

uest

ion:

8 m

arks

5.

(a

)

16 c

m

1 B1

cao

(un

its

incl

uded

)

(b

)

48 c

m3

4 M

1 3-

D d

raw

ing

or s

ketc

h M

1 4

4

2 a

nd 2

2

4

/ 4

4

4

and

2

2

4

M1

addi

ng o

r su

btra

ctin

g A1

cao

(un

its

incl

uded

) To

tal f

or Q

uest

ion:

5 m

arks


35

1MA

0/1F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 6. FE

(a)

Co

rrec

t ta

ble

WIT

H E

ITH

ER

Bar

char

t

OR

Pict

ogra

m

OR

Pie

Char

t

6 B1

Tab

le w

ith

at le

ast

2 co

lum

ns w

ith

car,

lorr

y, v

an,

mot

orbi

ke a

nd

bus

row

s M

1 ta

lly c

olum

n co

mpl

eted

or

head

ed f

requ

ency

col

umn

wit

h at

leas

t tw

o en

trie

s co

rrec

t A1

cor

rect

fre

quen

cies

(7,

4,

5, 6

, 2)

WIT

H E

ITH

ER

B1 la

belle

d ax

es w

ith

a un

ifor

m s

cale

M

1 ba

rs la

belle

d al

l the

sam

e w

idth

A1

bar

s al

l cor

rect

(ft

fro

m a

)

OR

B1 la

belle

d pi

ctog

ram

M

1 5

clas

ses

+ ke

y A1

all

corr

ect

(ft

from

a)

OR

B1 c

ircl

e w

ith

5 se

ctor

s la

belle

d M

1 co

rrec

t ca

lcul

atio

n of

at

leas

t on

e an

gle

A1 a

ll se

ctor

s co

rrec

t (f

t fr

om a

)

(b)

25%

of 2

4 =

6 Ye

s as

5<

6 2

M1

find

ing

25%

of 2

4 A1

Yes

as

5 <

6, (

ft f

rom

a)

(c)

Su

rvey

at

diff

eren

t pl

aces

Su

rvey

at

diff

eren

t ti

mes

D

o a

bigg

er

surv

ey

2B2

2 o

r m

ore

reas

ons

(B

1 1

reas

on)

Ig

nore

irre

leva

nt r

easo

ns

Tota

l for

Que

stio

n: 1

0 m

arks


36

1MA

0/1F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 7.

(a

)

Corr

ect

diag

ram

1

B1 4

iden

tica

l sha

pes

to t

he p

revi

ous

patt

erns

(b

)

60

2 M

1 co

ntin

ues

patt

ern

6, 1

2, 1

8, a

s fa

r as

the

10t

h A1

cao

OR

M1

indi

cate

s th

at t

he n

umbe

r of

sti

cks

is 6

tim

es t

he p

atte

rn n

umbe

r A1

cao

OR

M1

doub

les

30 s

tick

s fo

r pa

tter

n nu

mbe

r 5

A1 c

ao

(c

) 12

3 ÷

6 le

aves

a r

emai

nder

of

3,

so ‘

no’

No

+ ju

stif

icat

ion

2 M

1 At

tem

pts

to d

ivid

e 12

0 by

6

A1 ‘

No’

+ c

omm

ent

on r

emai

nder

O

RM

1 St

arts

at

6 an

d bu

ilds

up t

o 12

0 an

d 12

6 A1

‘N

o’ +

sig

ht o

f 12

0 an

d 12

6

Tota

l for

Que

stio

n: 5

mar

ks

8.

(a)

C

and

D

1 B1

cao

(b)

B

and

E 1

B1 c

ao

(c

)

4.5

cm2

1 B1

cao

Tota

l for

Que

stio

n: 3

mar

ks


37

1MA

0/1F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 9.

(a

)

Corr

ect

refl

ecti

on

1 B1

cao

(b)

Co

rrec

t sq

uare

1 B1

cao

(c)

See

patt

ern

at e

nd

Corr

ect

squa

res

1 B1

cao

Tota

l for

Que

stio

n: 3

mar

ks

10.

(a)

6x

1 B1

cao

(b

)

2y

2 M

1 at

tem

pt t

o is

olat

e y

A1 c

ao

Tota

l for

Que

stio

n: 3

mar

ks

11.

QW

Ci,

ii,

iii

50

shi

rts

at £

12 e

ach

= £6

00

Selli

ng P

rice

for

pro

fit

of 3

0%

= £1

2 1

.3 =

£15

.60

20 s

hirt

s at

£15

.60

= £3

12

Redu

ced

selli

ng p

rice

=

£15.

60

0.8

5 =

£13.

26

30 s

hirt

s at

£13

.26

= £3

97.8

0 £3

97.8

0 +

£312

> £

600

Yes,

tog

ethe

r w

ith

appr

opri

atel

y se

t ou

t w

orki

ngw

hich

supp

orts

an

swer

8 B1

for

pri

ce o

f 50

shi

rts

M1

for

£12

1.3

A1

for

£15

.60

A1 f

or 2

0 sh

irts

= £

312

M1

for

£15.

60

0.8

5A1

for

£13

.26

A1 f

or 3

0 sh

irts

= £

397.

80

C1 Y

es s

tate

d to

geth

er w

ith

a st

atem

ent

whi

ch s

uppo

rts

the

corr

ect

answ

erQ

WC:

Wit

h cl

ear

wor

king

att

ribu

ted

corr

ectl

y

Tota

l for

Que

stio

n: 8

mar

ks


38

1MA

0/1F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 12

. (a

)

(2,

6)(4

, 4)

(6

, 2)

2

M1

lists

as

orde

red

pair

s or

in a

tab

le w

ith

at le

ast

2 en

trie

s A1

all

3 co

rrec

t en

trie

s

(b

)

1664

M1

lists

the

sam

ple

spac

e (a

t le

ast

4 pa

irs)

A1

ful

ly c

orre

ct

M1

iden

tifi

es c

ases

whe

re A

li w

ins

A1 c

ao

Tota

l for

Que

stio

n: 6

mar

ks

13.

FE(a

)

2 co

rrec

t co

mbi

nati

ons

2 B1

Sin

gle

burg

er a

nd r

egul

ar c

ola

oe

B1 R

egul

ar f

ries

and

reg

ular

col

a oe

–1

for

eac

h ex

tra

inco

rrec

t

(b

) Be

st is

Cos

t

3.49

+ 1

.70

= 5.

19

Chan

ge =

10.

00 –

5.1

9

£4.8

1 3

M1

2 co

rrec

t in

divi

dual

cos

ts f

ound

M

1 su

m a

nd s

ubtr

act

from

£10

A1

cao

SC

B2

5.24

(B

1 2

× 1

.70

+ 0.

99 +

0.8

5 =

(5.2

4))

Tota

l for

Que

stio

n: 5

mar

ks

14. FE

(a)

48 +

37

+ 78

+ 2

1 =

184

184

× 40

= 7

360

4 ×

12 =

48

73.6

0 +

48

£121

.60

4 M

1 fi

nd t

he t

otal

mile

s M

1 to

tal m

iles

× 40

or

×0.

4(0)

M1

mile

age

expe

nses

+ 4

× 1

2 or

+ 5

× 1

2 A1

cao

(b

) 20

00 ÷

50

= 40

40

00 ÷

40

= 10

0 O

R20

00 ÷

0.4

= 5

0000

50

000

–50

= 1

00

OR

0.4

× 50

= 2

0 20

00 ÷

20

= 10

0

100

3 M

1 fo

r si

ght

of 2

000

, or

50,

or

2000

0

M1

dep

for

an a

ttem

pt t

o fi

nd c

ost

per

wee

k or

mile

age

per

year

A1

100

O

RM

1 si

ght

of 2

000,

or

50

M1

dep

0.4

× 50

and

200

0 ÷

’20’

A1

100

Tota

l for

Que

stio

n: 7

mar

ks


39

1MA

0/1F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e

15.

QW

Cii,

iii

8241 ;

8421 So

83 is

hal

f w

ay

OR

use

of 0

.5 a

nd 0

.25

to g

et

0.37

5 an

d co

mpa

re t

o 0.

33

OR 21

–31

= 61

and

31–

41 =

121 f

ollo

wed

by

conc

lusi

on

OR

use

of 0

.5 a

nd 0

.25

and

diff

eren

ces

of 0

.5 –

0.3

3(3,

…)

and

0.33

(3…

) –

0.25

Cohe

rent

and

w

ell

stru

ctur

edar

gum

ent

wit

hap

prop

riat

e re

ason

3 M

1 to

cha

nge

both

fra

ctio

ns t

o eq

uiva

lent

fra

ctio

ns

M 1

(dep

on

at le

ast

one

corr

ect

equi

vale

nt f

ract

ion)

to

find

mid

poin

t

C1 c

oncl

usio

n fo

llow

ing

corr

ect

wor

k by

sta

ting

tha

t 83

is n

ot e

qual

to

31Q

WC:

Dec

isio

n sh

ould

be

stat

ed w

ith

supp

orti

ng r

easo

n gi

ven

OR

M1

use

of 0

.5 a

nd 0

.25

M1

(dep

on

at le

ast

corr

ect

deci

mal

one

fin

d m

idpo

int)

C1

con

clus

ion

follo

win

g co

rrec

t w

ork

and

sigh

t of

0.3

7(5)

and

0.3

3(3.

.)

QW

C: D

ecis

ion

shou

ld b

e st

ated

wit

h su

ppor

ting

rea

son

give

n O

RM

1 fo

r w

orki

ng o

ut d

iffe

renc

es

M1

For

a co

rrec

t m

etho

d of

cal

cula

ting

dif

fere

nces

of

frac

tion

s us

ing

equi

vale

nt f

ract

ions

C1 c

oncl

usio

n fo

llow

ing

from

61 a

nd 121

QW

C: D

ecis

ion

shou

ld b

e st

ated

wit

h su

ppor

ting

rea

son

give

n O

RM

1 fo

r w

orki

ng o

ut d

iffe

renc

es

M1

for

a co

rrec

t m

etho

d of

cal

cula

ting

dif

fere

nces

of

frac

tion

s us

ing

equi

vale

nt f

ract

ions

C1 c

oncl

usio

n fo

llow

ing

from

61 a

nd 121

QW

C: D

ecis

ion

shou

ld b

e st

ated

wit

h su

ppor

ting

rea

son

give

nO

RM

1 us

e of

0.5

and

0.2

5 M

1(de

p on

at

leas

t on

e co

rrec

t de

cim

al)

for

wor

king

out

dif

fere

nces

C1

for

con

clus

ion

base

d on

0.1

7(or

bet

ter)

and

0.0

8(23

…)

QW

C: D

ecis

ion

shou

ld b

e st

ated

wit

h su

ppor

ting

rea

son

give

n

Tota

l for

Que

stio

n: 3

mar

ks


40

1MA

0/1F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 16

.

(a)

5p =

20

4 2

M1

add

16 t

o bo

th s

ides

A1

cao

(b

) –

4 –

5 =

5q –

2q

–3

2 M

1 fo

r co

rrec

t m

etho

d is

olat

e ±

3qA1

cao

(c

) 6x

– 3

− 1

0 –

6x =

–13

2 M

1 at

leas

t on

e ex

pans

ion

corr

ect

A1 c

ao

Tota

l for

Que

stio

n: 6

mar

ks


41

1MA

0/1F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 17

.1

214x

x

215x

,101

x

OR

Choo

se a

sui

tabl

e nu

mbe

r of

ba

lls (

say

10)

5

will

be

red

The

othe

r 5

need

to

be

shar

ed o

ut in

the

rat

io 1

:4,

henc

e 1

yello

w a

nd 4

blu

e

1043

M1

x +

4x +

21 =

1

A1x

= 101

A1104

oe

Tota

l for

Que

stio

n: 3

mar

ks

18.

Rota

tes

shap

e ab

out

(3,0

) by

18

0° t

o gi

ve U

Rota

tesU

abo

ut (

6, 0

) to

giv

e V (s

ee g

raph

at

end)

Tran

slat

ion

by

063

B3 T

rans

lati

on b

y 06

(B2

tran

slat

ion

by 6

to

the

righ

t or

jus

t06

on it

s ow

n )

(B1

tran

slat

ion

or m

ove

to t

he r

ight

6)

If n

o m

arks

ear

ned

from

a d

escr

ipti

on t

hen

B1U

cor

rect

ly p

lace

d B1V

cor

rect

ly p

lace

d

Tota

l for

Que

stio

n: 3

mar

ks


42

1MA

0/1F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 19

.

Num

ber

of p

rize

s sh

ould

buy

is83

100

0

= 37

5

OR

Each

tri

angl

e sh

ould

win

10

00 ÷

8 t

imes

(=1

25)

So 3

× 1

25 =

375

(376

) an

d ju

stif

icat

ion

that

mat

ches

an

swer

3 M

1 es

tim

ate

of p

roba

bilit

y

A1 f

or a

nsw

er >

83 o

f 10

00

C1 f

or j

usti

fica

tion

tha

t m

atch

es a

nsw

er

Num

ber

of p

rize

s be

twee

n 37

6 an

d 50

0

OR

M1

1000

÷ 8

A1 f

or a

nsw

er >

83 o

f 10

00

C1 f

or j

usti

fica

tion

tha

t m

atch

es a

nsw

er

Num

ber

of p

rize

s be

twee

n 37

6 an

d 50

0

Tota

l for

Que

stio

n: 3

mar

ks

20.

(a)

5(

x –

2y)

1 B1

cao

(b)

3p(q

– 4

p)2

B2 3

p(q

– 4p

)(B

1 co

rrec

t pa

rtia

l fac

tori

sati

on,

for

exam

ple,

p(3

q –

12p)

,

12p(

41q

– p)

,p(a

q +

bp) w

here

a a

nd b

are

num

bers

Tota

l for

Que

stio

n: 3

mar

ks


43

1MA

0/1F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 21 FE

Ar

ea o

f th

e ro

om

= 4

× 8

+ 4

× 6

= 5

6 Ar

ea o

f a

tile

=

0.5

× 0.

5 =

0.25

N

umbe

r of

tile

s

= 56

0.25

= 2

24

Cost

= 4

× 2

24

OR

No

of t

iles

arou

nd r

oom

=

2 ×

leng

ths

of r

oom

= 8

, 16

, 16

, 12

To

tal n

umbe

r of

tile

s =

8 ×

16

+ 8

× 12

= 2

24

Cost

= 4

× 2

24

£ 89

6 6

M1

for

full

met

hod

for

find

ing

the

area

of

the

room

A1

at

leas

t on

e ar

ea c

orre

ct

B1 f

or a

rea

of t

ile =

0.2

5m2 o

r 25

00 c

m2 o

r 4

tile

s =

1m2

M1

for

area

of

room

a

rea

of a

tile

M

1 fo

r 4

× nu

mbe

r of

tile

s A1

cao

OR

M1

for

doub

ling

each

leng

th t

o sh

ow n

umbe

r of

tile

s fo

r ea

ch s

ide

B1 f

or 8

, 16

, 16

and

12

M1

for

a fu

ll m

etho

d of

fin

ding

the

num

ber

of t

iles

(12

16+8

4)A1

for

at

leas

t on

e ‘s

ecti

on’

corr

ect

M1

for

4 ‘

224’

A1

cao

Tota

l for

Que

stio

n: 6

mar

ks


44

9 (c

)


45

18.

12345 -1 -2 -3 -4 -5

12

34

56

78

910

-1-2

0x

y

T

U

V


46


47



Total Marks

Paper Reference

*S37709A0127*

Edexcel GCSE

Mathematics APaper 1 (Non-Calculator)

Higher Tier


You must have:

Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser. Tracing paper may be used.

1MA0/1H

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 must not be used.

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 – you should take particular care on these questions with your spelling, punctuation


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.


2/2/2/2/3/3/2/2/

Turn over


48


Formulae – Higher Tier


Volume of a prism = area of cross section × length Area of trapezium = (a + b)h

Volume of sphere = r3 Volume of cone = r2h

Surface area of sphere = 4 r2 Curved surface area of cone = rl

In any triangle ABC The Quadratic Equation The solutions of ax2+ bx + c = 0 where a 0, are given by

Sine Rule

Cosine Rule a2= b2+ c2– 2bc cos A

Area of triangle = ab sin C

length

crosssection

rh

r

l

C

ab

c BA

13

a b csin A sin B sin C

xb b ac

a=

− ± −( )2 42

43

12

b

a

h

12


49




1 (i) Simplify 13x – 24y + 17x + 14y

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

(ii) Solve 6(1 – 2x) – 3(x + 1) = 0

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



50

*2 Jennie’s council has a target of 51 for households to recycle their waste.

In January, Jennie recycled 110

of her household waste.

In February, she recycled 15 kg of her 120 kg of household waste.

Her result for March was 13 % recycled out of 112 kg of household waste.

Has Jennie met the council’s target? Which was her best month for recycling? Show clearly how you got your answers.



51

3

The diagram is a plan of the floor of Nikola’s room. All the angles are right angles. Nikola is going to lay carpet tiles to cover all the floor. Each tile is a square 50 cm by 50 cm. Each tile costs £4

Work out the total cost of the carpet tiles needed to cover all the floor.

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



6 m

8 m

4 m

8 m


52

4 (a) Solve 5p – 16 = 4(2)

p = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b) Solve 2q – 4 = 5q + 5(2)

q = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

)35(2)12(3 xxy +−−=

(c) Show that y will always be the same value.(2)



53

5 The nth term of a sequence is 2n2

(i) Find the 4th term of the sequence.

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

(ii) Is the number 400 a term of the sequence?

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

Give reasons for your answer.



54

6 Last year Sasha was paid £15400 after deductions from her gross salary. She was paid 70% of her gross salary. This year Sasha’s gross salary increased by 2%.

Work out the increase in Sasha’s gross salary. Give your answer in pounds.

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



55

7 (a) Express 66 as a product of its prime factors.(2)

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

(b) Express 1322 as a product of its prime factors.(2)

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



56

8 A bag contains only red, yellow and blue discs.

The probability of drawing a red disc at random is 21

The probability of drawing a yellow disc at random is x The probability of drawing a blue disc at random is 4x

One disc is to be selected at random.

Work out the probability that it will be a blue disc. Give your answer as a numerical value.

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



57

9 (a) Simplify

(i) 35 aa ÷(3)

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

(ii) 2x2 × 3x2y2

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

(b) Expand and simplify (x + 3)(x + 7)(2)

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

(c) Factorise fully 3pq – 12p2

(2)

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

(d) (i) Factorise 3 10 32y y− +(4)

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

Hence, or otherwise

(ii) Factorise 3 2 10 2 32( ) ( )x x+ − + +

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



58

10

The diagram represents 100 cards. Each card has a whole number from 1 to 100 on it. No cards have the same number.

Bill puts a red dot on every card which has a multiple of 6 on it. Parul puts a green dot on every card which has a multiple of 9 on it.

All the cards are placed in a bag. Vicki selects a card is selected at random.

What is the probability that the card has both a red and a green dot on it?

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


2 31 1009998


59

11

CEAY and BDAX are straight lines. XY, ED and CB are parallel. AE = 5 cm. AX = 9 cm. AD = 4 cm. BC = 4 cm. BD = 2 cm.

CE = x cm. XY = y cm.

Find the value of x and the value of y.

x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

y = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


2 cm

4 cm

5 cmx cm A

D

E

B

C Y

9 cm

y cm

4 cm


X


60

12 Here are two fair 4-sided spinners. One is a Blue spinner and one is a Red spinner.

Blue spinner Red spinner

Each spinner has four sections numbered 2, 4, 6 and 8

Each spinner is to be spun once.

Total score = Blue spinner score + Red spinner score

(a) Find the probability that the total score will be 10(3)

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

2

4

6

8

2

4

6

8


61

Ali and Shazia play a game.

In each round of the game, Ali spins the Blue spinner once and Shazia spins the Red spinner once.

Ali wins when the Blue spinner score is greater than the Red spinner score.

Ali and Shazia play 80 rounds.

(b) Work out an estimate of the number of rounds that Ali will win.(3)

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



62

13 The population of Algeria is 34 million.

(a) Write 34 million in standard form.(1)

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

The total land area of Algeria is 2.4 × 1012 m2. 5% of the total land area is used to grow crops.

(b) Work out the area of land in Algeria which is used to grow crops. Write your answer in standard form, in km2.

(2)

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



63

14

ABCD is a rectangle. X is the midpoint of AB. Y is the midpoint of BC. Z is the midpoint of CD.

What fraction of the total area of ABCD is shaded?

Show clearly how you get your answer.

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


CD Z


XA B

Y


64

15

In the diagram,

OAC, OBX and BQC are all straight lines

AC = 2OA and BQ: QC = 1:3

(a) Find, in terms of a and b, the vectors which represent(4)

(i)

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

(ii)

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

Given that

(b) Show that AQX is a straight line. (3)


Diagram NOTaccurately drawn C

AQ

O B X

= 4a = 4bOA OBand

BC

AQ

BX = 8b


65

16 There are 10 students in a class. 6 of the students are boys and 4 of the students are girls.

Three students are picked at random from the class to form a team.

Work out the probability that the team consists of 1 girl and 2 boys.

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



66

17 Simplify 3 16 359 25

2

2

x xx− −

−

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



67

18 k33 =

(a) Write down the value of k(1)

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

(b) Expand and simplify (2 + √3)(1 + √3)

Give your answer in the form a + b √3

where a and b are integers(2)

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



68

19 (a) On the grid draw the graph of )3( −= xxy(2)

–4

–3

–2

–1

0

1

1 2 3 4 5 6 x

2

3

4

5

6

7

8

9

10

y


69

(b) Using your result for (a), or otherwise, solve the simultaneous equations

y = x(x – 3)

x2 + y2 = 9(3)



70

*20 Prove that the difference between the squares of consecutive odd numbers is a multiple of 8



71

BLANK PAGE


72

21 Mr Walton is responsible for maintaining fish stocks in a river. The table gives some information about the lengths, in centimetres, of a type of fish caught from the river.

Length (L) cm Frequency

0 < L 10 40

10 < L 20 60

20 < L 40 90

40 < L 80 60

L > 80 0

He wants to study the effect of returning to the river fish less than 50 cm in length that are caught.

Mr Walton suggests that fish which are less than 50 cm in length are returned to the river.

Draw a suitable statistical diagram for the information in the table.

Use it to find an estimate of the percentage of fish returned to the river.


73

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %




74


75


76

1MA

0/1H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 3. FE

N

o of

tile

s ar

ound

roo

m

= 2

× le

ngth

s of

roo

m =

8,

16,

16,

12

Tota

l num

ber

of t

iles

= 8

× 16

+ 8

× 1

2 =

224

Cost

= 4

× 2

24

OR

Area

of

the

room

=

4 ×

8 +

4 ×

6 =

56

Area

of

a ti

le

= 0.

5 ×

0.5

= 0.

25

Num

ber

of t

iles

= 56

0.25

=

224

Cost

= 4

× 2

24

£ 89

6 6

M1

for

doub

ling

each

leng

th t

o sh

ow n

umbe

r of

tile

s fo

r ea

ch s

ide

B1 f

or 8

, 16

, 16

and

12

M1

for

a fu

ll m

etho

d of

fin

ding

the

num

ber

of t

iles

(12

16

+ 8

4)

A1 f

or a

t le

ast

one

‘sec

tion

’ co

rrec

t M

1 fo

r 4

‘22

4’

A1 c

ao

OR

M1

for

full

met

hod

for

find

ing

the

area

of

the

room

A1

at

leas

t on

e ar

ea c

orre

ct

B1 f

or a

rea

of t

ile =

0.2

5m2 o

r 25

00 c

m2 o

r 4

tile

s =

1 m

2

M1

for

area

of

room

a

rea

of a

tile

M

1 fo

r 4

× nu

mbe

r of

tile

s A1

cao

Tota

l for

Que

stio

n: 6

mar

ks

4.

(a)

5p=

20

p=

4 2

M1

add

16 t

o bo

th s

ides

A1

cao

(b

) –9

= 3

q q

= −

32

M1

corr

ect

met

hod

to is

olat

e ±3

qA1

cao

(c

) 6x

– 3 −1

0 –

6x =

–1

3 2

M1

at le

ast

one

expa

nsio

n co

rrec

t A1

–13

or a

sta

tem

ent

that

the

ans

wer

is in

dep

of x

dep

endi

ng o

n co

rrec

t w

orki

ng

Tota

l for

Que

stio

n: 6

mar

ks


77


78

1MA

0/1H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 8.

121

4x

x

215

x,

101x

OR

Choo

ses

a su

itab

le n

umbe

r of

ba

lls (

say

10)

5 w

ill b

e re

d Th

e ot

her

5 ne

ed t

o be

sh

ared

out

in t

he r

atio

1:4

, H

ence

1 y

ello

w a

nd 4

blu

e

1043

M1

121

4x

x

A1101

x

A1104

oe

Tota

l for

Que

stio

n: 3

mar

ks


79

1MA

0/1H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 9.

(a

) (i

)

(ii)

a2

6x4 y3

3 B1

cao

B26x

4 y3

(B1

for

2 ou

t of

3 t

erm

s co

rrec

t in

a p

rodu

ct)

(b

) x2 +

3x

+ 7x

+ 2

1 x2 +

10x

+ 2

1 2

M1

3 or

4 t

erm

s ou

t of

4 c

orre

ct in

a 4

ter

m e

xpan

sion

A1

cao

(c

)

3p(q

− 4p

) 2

B2 c

ao

(B1

p(3q

− 12

p), 1

2p( 41

q−

p), p

(aq

+ bp

) whe

re a

and

b a

re n

umbe

rs)

(d

)(i)

(ii)

)32

(1

)2(3

xx

OR

320

1012

123

2x

xx

=5

23

2x

x

(3y–

1)(y

– 3

) )1)(5

3(x

x

4 B2

cao

(B

1 (3

y −

m)(y

− n

) whe

re m

n =

±3 o

r m

+ n

= ±

10

M1

use

of t

he f

acto

rise

d fo

rm w

ith

y re

plac

ed t

wic

e by

3x

+ 2

A1 c

ao

OR

B15

23

2x

xB1

cao

Tota

l for

Que

stio

n: 1

1 m

arks


80

1MA

0/1H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 10

.

Reds

6,

12,

18,

24,

30…

G

reen

s 9,

18,

27…

201

3 B1

list

of

red

and

gree

n m

ulti

ples

(bo

th t

o at

leas

t 18

) or

exp

licit

ly

stat

es ‘

LCM

’ B1

wor

ks o

ut h

ighe

st n

umbe

r (9

0 se

en)

B1201

(ac

cept

1005)

Tota

l for

Que

stio

n: 3

mar

ks

11.

425x

695

xy

or6

59

xy

x =

2.5

y =1

1.25

4M

1 a

corr

ect

expr

essi

on f

or x

invo

lvin

g ra

tios

of

side

s, e

.g.

425x

oe

A1 c

ao

M1

695

xy

or6

59

xy

oe

A1 c

ao

OR

495y A1

cao

Tota

l for

Que

stio

n: 4

mar

ks


81

1MA

0/1H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 12

.

(a)

4

6

8

10

6

8 1

0

12

8 1

0 1

2 1

4 10

12

14

16

OR 41

41

441

41

1643

M1

Atte

mpt

s to

list

all

outc

ome

pair

s A1

all

16 f

ound

A1

cao

OR

M2

441

41

(M1

2,1

4141

or 3

)

A1164

oe

(b

) Pr

ob A

li w

ins

= 166

Num

ber

of w

ins

= 80

166

30

3 B1

Pro

b Al

i win

s =

166 o

e

M1

80'

166'

A1 f

t

Tota

l for

Que

stio

n: 6

mar

ks


82

1MA

0/1H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 13

. (a

) 7

104.3

1 B1

cao

(b)

1005

104.2

12(

610

)5

102.1

2M

1 10

0510

4.212

oe (

610

)

A1 c

ao

Tota

l for

Que

stio

n: 3

mar

ks


83

1MA

0/1H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 14

.

Let

AB =

x,A

D =

yAr

ea o

f re

ctan

gle

=xy

Area

AXD

=

4xy

Area

CYZ

=8xy

Shad

ed a

rea

= 85xy

854

M1

a fu

ll m

etho

d to

fin

d th

e un

shad

ed a

rea

and

subt

ract

ing

from

1

B1 a

rea

of A

XD =

are

a of

ABC

D4

B1 a

rea

of C

YZ=

are

a of

ABC

D8

A1 c

ao

OR

Dia

gram

M1

for

divi

ding

left

into

2 c

ongr

uent

tri

angl

es

f

or d

ivid

ing

righ

t in

to 4

con

grue

nt t

rian

gles

B1

left

= 2

Aan

d 2A

or

sha

ded

= 21

of

21=

41 =

82

B1 r

ight

= 2

A an

d A

and

A or

shad

ed =

43of

21 =

83

A1 c

ao

Subs

titu

tion

M1

for

deci

ding

upo

n su

itab

le s

ide

leng

ths

for

ADan

d AB

and

cal

cula

ting

di

men

sion

s of

inte

rnal

sha

pes

B1 f

or a

rea

of D

ZXB1

for

are

a of

ZXB

YA1

cao

OR

M1

for

deci

ding

upo

n su

itab

le s

ide

leng

ths

for

ADan

d AB

and

cal

cula

ting

di

men

sion

s of

inte

rnal

sha

pes

B1 f

or a

rea

ADX

B1 f

or a

rea

ZCY

A1 c

ao

Tota

l for

Que

stio

n: 4

mar

ks


84

1MA

0/1H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 15

.

(a)

(i)

(ii)

BC =

O

BC

O

AQ =

BQ

OB

AO

= –

4a +

4b

+ 41

(12a

– 4b

)

12a

– 4b

3b–

a

4

M1

BC =

O

BC

OA1

cao

M1

–4a

+ 4b

+ 41

‘(12

a–

4b)’

A1 c

ao

(b

) O

X=

12b

, AX

=–4a

+ 1

2b=

4(–a

+ 3

b)

Corr

ect

reas

on,

wit

h co

rrec

t w

orki

ng

3B1

OX

= 12

b

B1AX

=–4a

+ 1

2bC1

con

vinc

ing

expl

anat

ion

Tota

l for

Que

stio

n: 7

mar

ks


85

1MA

0/1H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 16

.

8596

104 =

720

120

720

120

+

8495

106 +

8594

106

720

360

4M

1 fo

r 85

96104

A1 f

or 72

012

0 o

e

M1

720'

120

' +

2 c

orre

ct c

ases

(M

1 an

y 2

corr

ect

case

s)

or72

0'12

0'

X 3

A1 c

ao

SC w

ith

repl

acem

ent

M1

106106

104

M1

106106

104×3

Tota

l for

Que

stio

n: 4

mar

ks

17.

)53)(5

3()7

)(53(

xx

xx

53

7xx

3B1

)7)(5

3(x

xB1

)53)(5

3(x

x

B15

37

xx

Tota

l for

Que

stio

n: 3

mar

ks


86

1MA

0/1H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 18

. (a

)

211

B1

(b

) (2

+

3)

)31(

=9

33

22

33

52

M1

4 te

rm e

xpan

sion

wit

h 3,

4 t

erm

s co

rrec

t an

d si

ght

of 3

or

9A1

cao

Tota

l for

Que

stio

n: 3

mar

ks

19.

(a)

Sm

ooth

cu

rve

2 B1

cor

rect

plo

t of

the

ir v

alue

s B1

sm

ooth

cur

ve t

hrou

gh t

heir

poi

nts

(b

)

x =

3 y

= 0

3 M

1 at

tem

pts

to d

raw

cir

cle

at o

rigi

n M

1 us

es r

adiu

s 3

cm (

usin

g gr

aph

scal

e co

rrec

tly)

A1

cao

OR

B1 f

or s

ubst

itut

ing

a va

lue

of x

into

y =

x(x

– 3)

and

2

2r

yx

B1 f

or s

ubst

itut

ing

yin

tox

= 3

into

x(x

– 3

) and

2

2r

yx

B1 c

ao

Tota

l for

Que

stio

n: 5

mar

ks


87

1MA

0/1H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 20

.Q

WC

ii, ii

i

22

)12(

)12(

nn

=)1

44(

14

42

2n

nn

n

=8n

OR

22

)12(

)12(

nn

=))1

21

2()12(

)12(

nn

nn

=2

× 4n

= 8

n

Fully

alge

brai

c ar

gum

ent,

se

t ou

t in

a

logi

cal a

nd

cohe

rent

man

ner

6 B2

the

nth

term

for

con

secu

tive

odd

num

bers

is 2

n –

1 oe

(B

12n

+ k

,1

kor

n=

2n –

1 o

r 2x

−1B1

use

of

2n +

1 a

nd 2

n–

1 oe

M

1 2

2)1

2()1

2(n

nM

1)1

44(

14

42

2n

nn

n

C1 c

oncl

usio

n ba

sed

on c

orre

ct a

lgeb

ra Q

WC:

Con

clus

ion

shou

ld b

e st

ated

, w

ith

corr

ect

supp

orti

ng a

lgeb

ra.

OR

B1 u

se o

f 2n

+ 1

and

2n

–1 o

e M

1 2

2)1

2()1

2(n

nM

1))1

21

2()12(

)12(

nn

nn

C1 c

oncl

usio

n ba

sed

on c

orre

ct a

lgeb

ra Q

WC:

Con

clus

ion

shou

ld b

e st

ated

, w

ith

corr

ect

supp

orti

ng a

lgeb

ra. To

tal f

or Q

uest

ion:

6 m

arks


88

1MA

0/1H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 21

.

L F

FD

CF

0–1

0 40

4

40

10–2

0 60

6

100

20–4

0 90

4.

5 19

0 40

–80

60

1.5

250

>80

0 0

250

His

togr

amO

RCu

mul

ativ

e Fr

eque

ncy

poly

gon

82%

6 B1

Sca

les

labe

lled

and

also

mar

ked

on t

he v

erti

cal a

xis

wit

h fr

eque

ncy

dens

ity

or w

ith

cum

ulat

ive

freq

uenc

y M

1 fr

eque

ncy

dens

itie

s ca

lcul

ated

, at

leas

t on

e no

n-tr

ivia

l one

cor

rect

. A1

all

corr

ectl

y pl

otte

d (M

1 cu

mul

ativ

e fr

eque

ncie

s co

rrec

t)

M1

Use

50

on t

he h

oriz

onta

l sca

le o

f CF

dia

gram

rea

d of

f ve

rtic

al a

xis

(200

-210

)or

Use

50

on t

he h

oriz

onta

l sca

le o

f a

hist

ogra

m a

nd c

over

t ar

ea t

o th

e le

ft t

o a

freq

uenc

y M

1 co

nver

t to

a p

erce

ntag

e A1

80

– 85

Tota

l for

Que

stio

n: 6

mar

ks


89

2.

Frac

tion

D

ecim

al

%

kg

Jan

1010.

110

%N

ot k

now

n

Feb

810.

125

12.5

% 15

kg

Mar

100

130.

13

13%

14.5

6 kg

14.

AB C

D

X

Y

Z

AB C

D

X

Y

Z


90


91



Total Marks

Paper Reference

*S37712A0129*

Edexcel GCSE

Mathematics APaper 2 (Calculator)

Foundation Tier


You must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

1MA0/2F

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 π button, take the value of π 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 – you should take particular care on these questions with your spelling, punctuation


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.


2/2/2/3/2/2

Turn over


92

GCSE Mathematics 2544

Formulae: Foundation Tier


Area of trapezium = (a + b)h

Volume of prism = area of cross section × length

b

a

h

length

crosssection

12



93




1 Susie has one pound and sixty pence.

Her friend, Katie, has two pounds and five pence.

They want to buy a pizza between them. The pizza costs £3.50 How much money will they have left?

Show your working here.



94

2 The pictogram shows the number of packets of toffees sold by a shop some days in one week.

Monday

Key

represents 20packets

Tuesday

Wednesday

Thursday

Friday

Saturday

(a) Write down the number of packets of toffees that were sold on (2)

(i) Tuesday,

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . packets

(ii) Thursday.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . packets

40 packets were sold on Friday.

30 packets were sold on Saturday.

(b) Use this information to complete the pictogram.(2)



95

3

(a) Write down the fraction of this shape that is shaded. Write your fraction in its simplest form.

(2)

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

(b) Shade 23

of this shape.(1)



96

4 Here is a dual bar chart showing the number of hours of TV that Helen and Robin watched each day last week.

9

8

7

6

5

4

3

2

1

0 Sunday Monday Tuesday Wednesday Thursday Friday Saturday

Helen

Robin

Num

ber o

f hou

rs

Day

(a) Write down the number of hours of TV that Helen watched on Monday.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . hours

(b) How many more hours of TV did Robin watch than Helen watch last week?(2)

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

(c) Find the median of the number of hours Robin watched TV last week.(2)

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

(d) On Saturday and Sunday Helen watched 7 programmes altogether.

Work out the average length of the programmes that she watched.(2)

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



97

5 (a) On the probability scale below, mark with a cross (×) the probability that it will snow in London in June.

(1)

0 112

(b) On the probability scale below, mark with a cross (×) the probability that it will rain in Manchester next year.

(1)

0 112

(c) What is the probability that you will get a head when you flip a fair coin?(1)

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



98

6

810

6

175

16

4

Using only the numbers in the cloud, write down

(i) an odd number

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

(ii) a multiple of 4

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

(iii) two numbers which have a sum which is a prime number

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

(iv) the value of 2³

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



99

7 Here is a sketch of triangle ABC.

A

B C8.5 cm

68° 35°


BC = 8.5 cm Angle B = 68° Angle C = 35°

Draw an accurate diagram of triangle ABC in the space below.



100

8 The graph shows the cost of using a mobile phone for one month for three different tariffs.

60

50

40

30

20

10

00 20 40 60 80 100 120

Cost (£)

Time used in minutes

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

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

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

The three tariffs are

Tariff A Rental £20 every minute costs 20p Tariff B Pay as you go every minute costs 50p Tariff C Rental £25 first 60 minutes free, then each minute costs 10p

(a) Label each line on the graph with the letter of the tariff it represents.(1)


101

Jim uses tariff A for 100 minutes in one month.

(b) Find the total cost.(1)

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

Fiona uses her mobile phone for about 60 minutes each month.

(c) Explain which tariff would be the cheapest for her to use. You must give the reasons for your answer.

(2)

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

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

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



102

9 Jason hired a van.

Fuel

98.9pper litre

Van Hire

£90 a day You pay for the fuel

Van Hire

£90 a day

You buy the fuel 6 miles

per litre

The company charges £90 per day plus the cost of the fuel used. The van can travel 6 miles for each litre of fuel used. Fuel costs 98.9p for 1 litre.

On Monday Jason hired the van and drove from London to Cardiff. On Tuesday Jason drove from Cardiff to Edinburgh. On Wednesday, Jason drove from Edinburgh back to London and returned the van.

Jason thought the total cost would be about £400.

Jason uses this table for information about distances between cities.

London

153 Cardiff

212 245 York

413 400 193 Edinburgh


103

Work out the total cost of hiring the van and the fuel used.

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



104

10 This formula is used to predict the adult height of a baby girl.

H = F M+ −12 5

2.

H = adult height of girl (cm)F = height of father (cm)M = height of mother (cm)

Karen and Keith have a baby girl.

They are interested in finding out how tall their baby girl is likely to grow.

Karen has a height of 156 cm. Keith has a height of 172 cm.

(a) Use the formula to predict the adult height of their baby girl. Show clearly how you get your answer.

(2)

Height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm


105

John and Jenny also have a baby girl. John and Jenny are the same height.

When they use the formula to predict the adult height of their baby girl they get an answer of 162 cm.

(b) Find an estimate of Jenny’s height. Give your answer to the nearest centimetre.

(3)

Height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm



106

11 Bill is planning the layout of a school playground. For safety reasons he has to mark part of the playground where children cannot play

games. He makes a plan of the playground drawn to a scale of 1 cm to 1 m.

A B

CD

Scale 1 cm represents 1 m

For Health and Safety reasons, children cannot play games

within 4 m of the corner D Or

within 3 m of the side BC.

(a) Complete the plan of the playground accurately to show where children cannot play games.

(4)


107

Children can play games on the rest of the playground. There has to be at least 1 m2 for each child.

*(b) Calculate the largest number of children that can play in the rest of the playground.(6)

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



108

12

Item Costs (£)

Motor oil 1l 2.50

Wiper blades 1 8.75

Brake Pads 1 14.85

Antifreeze 1l 3.99

Hydraulic Fluid 1l 5.99

Spark Plugs 1.75

Mr Smith had his car serviced. He had to pay for a 15 000 mile service, 3 litres of oil and 4 spark plugs. Complete his bill, and work out the total amount to pay.

Gary’s GarageItem Number

of itemsCost of one

item Total

15 000 mile Service (labour charge)

Motor oil 1l

Spark plugs

1 £75.50 £75.50

Total £ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

VAT at 17 12 % of Total £ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Total amount to pay £ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



109

13

68°

N

P Q

B

X

R


PQR is a straight line going East. B is on a bearing, 052° from P. B and Q are the same distance from P.

Find the bearing of X from B. You must show your working out clearly.

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



110

14 In the diagram all of the angles are in degrees. Find the size of angle CDE.


A

B

CD

E 2x

2x

2x + 20

3x – 30150 – x

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



111

15 Rain water is collected in a tank.The graph gives information about the depth of the water in the tank between 1000 and 1600.

1000 1200 1400 1600 18001100 1300 1500 1700 1900

6

5

4

3

2

1

0Time

Depth (m)

(a) Write down the depth of water at 1300.(1)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m

(b) Write down the time at which the depth was 2 metres.(1)

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

After 1600, the water is used for irrigating a field. The depth of water continues to fall at the same rate as it fell between 1500 and 1600.

(c) Find the time at which the depth of the water is zero.(1)

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



112

16 Use your calculator to work out

Give your answer as a decimal. Write down all the figures on your calculator display.

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


17 The equation x3 – 5x = 60 has a solution between 4 and 5

Find this solution and give your answer correct to 1 decimal place. You must show all your working.

x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


13 2 6 83 25 4 9

. .. .

−+


113

18 Alan and Bhavana are planning their fitness program. They plan to run on parts of a field. The diagram below shows a rectangular field 80 metres by 60 metres.

80 m

60 m

A

BC Diagram NOTaccurately drawn

Alan runs around the field from A to C (via B) at 5m/s.

Bhavana runs directly across the diagonal of the field from A to C at 3m/s.

If they both started at the same time, who would reach point C first?

You must explain your answer.

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

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


*


114

19 (a) Complete the table of values for y = x(x – 3) for values of x from 0 to 5(1)

x 0 1 2 3 4 5

y 0 −2 0 4

(b) On the grid draw the graph of y = x2 – 3x(2)

1 2 3 4 5 6

y

x

10

9

8

7

6

5

4

3

2

1

0

–1

–2

–3

–4


115

The length of a rectangle is 3m less than the width. The area of the rectangle is 7 m2

(c) Find an estimate for the width of the rectangle.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m



116

20 Harry and Sally want to keep free range hens.

They have a rectangular piece of land that they intend to use for a chicken run.

The length of the land is 30 m and the width is 10 m.

Harry and Sally will need to put a fence, with a gate, around the chicken run.

They are advised that the least area a free range hen needs is 0.8 m².

They want to have as many hens as they can.

Hens cost £7.50 each. Putting in the fence and gate will cost £9.85 per metre.

Work out the total cost of buying the hens and fencing the land.


117

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



118

21 Pablo is an artist. He wants to find estimates for the prices of some of the new pictures he has painted. The scatter graph, below, gives information about the area and the price of some of his old pictures.

1600

1400

1200

1000

800

600

400

200

0 500 1000 1500 2000 2500 3000 3500

Area (cm2)

Price (£)


119

The table shows the area and the price of another three of his old pictures.

Area (cm2) 2000 2900 3260

Price (£) 1150 1250 1500

(a) Find an estimate of the price of a new picture with an area of 2500 cm2.(3)

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

All Pablo’s pictures are rectangles. One of his pictures has a price of £1000 Its length is 48 cm.

(b) Find an estimate for the width of the picture.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm




120


121

Spec

ific

atio

n A

: Pa

per

2 Fo

unda

tion

Tie

r

1MA

0/2F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 1.

1.60

+ 2

.05

= 3.

65

15p

2 B1

£3.

65 o

e

B1 1

5p

Tota

l for

Que

stio

n: 2

mar

ks

2.

(a)(

i)

(ii)

60

50

2 B1

60

cao

B1 5

0 ca

o

(b)

2 fu

ll pa

cket

s 1.

5 fu

ll pa

cket

s 2

B1 2

ful

l pac

kets

cao

B1

1.5

ful

l pac

kets

Tota

l for

Que

stio

n: 4

mar

ks

3.

(a)

432

B243

cao

( B1

2418,

1612,

129,

86)

(b)

An

y 16

squ

ares

sh

aded

1 B1

Any

16

squa

res

shad

ed

Tota

l for

Que

stio

n: 3

mar

ks


122

1MA

0/2F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 4.

(a

)

2 1

B1 c

ao

(b)

7 +

4 +

3 +

5 +

2 +

4 +

5 =

30

6 +

2 +

1 +

5 +

3 +

3 +

8 =

28

OR

1 +

2 +

2 +

0 –

1 +

1 –

3 =

2

2 ho

urs

2 M

1 fi

nds

the

tota

ls o

f Ro

bin

and

Hel

en.

A1 c

ao

OR

M1

find

the

dif

fere

nces

of

Robi

n an

d H

elen

A1

cao

(c

) 2

3 4

4 5

5 7

4

hour

s 2

M1

orde

rs t

he v

alue

s A1

cao

(d)

(6 +

8)÷

7

2 2

M1

atte

mpt

s to

fin

d m

ean

A1

2 c

ao

Tota

l for

Que

stio

n: 7

mar

ks

5.

(a)

Co

rrec

t pl

ot

1 B1

Cro

ss p

lace

d w

ithi

n 0.

5 cm

to

righ

t of

0 in

clus

ive

(b

)

Corr

ect

plot

1

B1 C

ross

pla

ced

wit

hin

0.5

cm t

o le

ft o

f 1

incl

usiv

e

(c

)

211

B1 0

.5 o

e

Tota

l for

Que

stio

n: 3

mar

ks


123

1MA

0/2F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 6.

(i

)

(ii)

(iii)

(iv)

5

or 1

7

4, 8

, or

16

5 an

d 6

8

1 1 1 1

B1 5

or

17 o

r bo

th

B1 f

or o

ne,

two

or t

hree

of

4, 8

or

16

B1 5

and

6 o

e

B1 c

ao

Tota

l for

Que

stio

n: 4

mar

ks

7.

8.

5 cm

line

dra

wn

angl

es a

t B

and

C dr

awn

Corr

ect

Cons

truc

tion

of

tria

ngle

3 B1

8.5

cm

line

dra

wn

tole

ranc

e ±

0.2c

m

B1 a

ngle

s at

B a

nd C

dra

wn

tole

ranc

e ±

2°

B1 f

ully

cor

rect

wit

hin

tole

ranc

e

Tota

l for

Que

stio

n: 3

mar

ks

8.

(a)

B,

A,

C 1

B1 c

ao

(b

)

£40

1 B1

cao

(c

)

C +

reas

on

2 C2

cor

rect

+ c

ompa

riso

n w

ith

the

two

othe

r ta

riff

s (C

1 co

rrec

t +

com

pari

son

wit

h on

e ot

her

tari

ff o

r lin

e dr

awn

at 6

0 up

fr

om t

he t

ime

axis

to

inte

rsec

t at

leas

t on

e lin

e)

Tota

l for

Que

stio

n: 4

mar

ks

9.

153

+ 40

0 +

413

= 96

6 N

umbe

r of

litr

es u

sed

=

966

÷ 6

= 16

1 Co

st o

f fu

el 1

61 ×

98.

9p =

£1

59.2

3 D

ay c

ost

= 3

× 90

= 2

70

Tota

l = £

159.

23 +

£27

0

429.

23

8 B1

any

one

cor

rect

dis

tanc

e id

enti

fied

M

1 15

3 +

400

+ 41

3A1

966

M

1 ‘9

66’

÷6

M1

‘161

’ ×

98.9

M

1 3

× 90

M

1 ’1

59.2

3’ +

‘27

0’

A1 c

ao

Tota

l for

Que

stio

n: 8

mar

ks


124

1MA

0/2F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 10

. (a

)

25.

1217

415

615

7.75

2

M1

subs

titu

te c

orre

ctly

A1

157

.75

or 1

58

(b

) 16

22

5.12

jj

324

5.12

2j

25.

1232

4

168

3 M

1 16

22

5.12

jj

M1

corr

ect

met

hod

to is

olat

e j

A1 1

68 o

r be

tter

Tota

l for

Que

stio

n: 5

mar

ks

11.

(a

) co

mpl

ete

diag

ram

at

end

4

M1

quar

ter

circ

le c

entr

e D

rad

ius

4 cm

A1

cle

ar in

dica

tion

of

regi

on b

y sh

adin

g in

or

shad

ing

out

M1

stra

ight

line

par

alle

l to

BC 3

cm

aw

ay

A1 c

lear

indi

cati

on o

f th

e re

gion

by

shad

ing

in o

r sh

adin

g ou

t.

(b

) Q

WC

i, ii

Area

=

442

=12.

5663

7…

Area

= 3

× 8

= 2

4

43

6 M

1 2 4

M1

3 ×

8 A1

sig

ht o

f ei

ther

cor

rect

are

aA1

36.

5663

7…

M1

8 ×

10

– ’3

6.56

637.

.’ =

43.

4336

…C1

43

QW

C: D

ecis

ion

shou

ld b

e st

ated

, fo

llow

ing

on f

rom

wor

king

out

Tota

l for

Que

stio

n: 1

0 m

arks

12

.FE

3

2.5

= 7

.50

4 1

.75

= 7

75.5

0 +

7.50

+ 7

= 9

0

9 +

4.5

+ 2.

25 =

15.

75

105.

75

6 B1

3 a

nd 7

.50

B1 4

and

7

B1 9

0 ft

M

1 9

+ 4.

5 +

2.25

see

n A1

15.

75

A1 c

ao

Tota

l for

Que

stio

n: 6

mar

ks

13.

154°

3

B1 f

or 3

8°

B1 f

or 6

4°

B1 c

ao

Tota

l for

Que

stio

n: 3

mar

ks

10 m

8 m


125

1MA

0/2F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 14

.2x

+ 2x

+ 40

+ 3

x–

30 +

150

–x

+ 2x

=540

8x

+ 14

0 =

540

x= 5

0

100°

4

M1

2x+

2x+

40 +

3x

– 30

+ 1

50 –

x+

2xM

1 co

llect

s te

rms

corr

ectl

y A1

x =

50

A1 c

ao

Tota

l for

Que

stio

n: 4

mar

ks

15.

(a)

5

m

1 B1

cao

(b

)

10:3

0 1

B1 1

0:25

– 1

0:35

(c

)

18:1

0 –

18:3

0 1

B1 1

8:10

– 1

8:30

Tota

l for

Que

stio

n: 3

mar

ks

16.

15.84.6

0.31

0407

62…

2 M

1 co

rrec

t or

der

of e

valu

atio

n as

evi

denc

ed b

y si

ght

of 6

.4 o

r 8.

15

A1 0

.310

40(7

62…

.)

Tota

l for

Que

stio

n:2

mar

ks


126

1MA

0/2F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 17

.

xf(

x) =

xx

53

4.00

44

.00

4.10

48

.42

4.20

53

.09

4.30

58

.01

4.40

63

.18

4.50

68

.62

or

68.6

3 4.

60

74.3

4 4.

70

80.3

2 4.

80

86.5

9 4.

90

93.1

5 5.

00

100.

00

4.35

60

.56

4.3

4 B2

for

tri

al b

etw

een

4.3

and

4.4

incl

usiv

e (B

1 fo

r tr

ial b

etw

een

4 an

d 5

incl

usiv

e)

B1 f

or d

iffe

rent

tri

al b

etw

een

4.33

and

4.3

7 in

clus

ive

B1 (

dep

on a

t le

ast

one

prev

ious

B1)

for

4.3

onl

y N

B tr

ials

whe

re x

has

1 d

.p s

houl

d be

rou

nded

or

trun

cate

d to

at

leas

t

2 SF

; tr

ials

whe

re x

has

2 d.

p. o

r m

ore

shou

ld b

e ro

unde

d or

tru

ncat

ed t

o at

leas

t 3

SF

Tota

l for

Que

stio

n: 4

mar

ks

18.

QW

Cii

Alan

60

+ 80

= 1

40

140

÷ 5

= 28

Bh

avan

a 60

2 + 8

02 = 1

0000

100

1000

010

0÷

3=33

.333

33…

..

Alan

, w

ith

stat

emen

t su

ppor

ting

expl

anat

ion

6 B1

Ala

n ru

ns 1

40

M1

‘140

’÷ 5

M

1 60

2 + 8

02

A1 1

00

A1 2

8 or

33.

3333

3… s

een

C1 A

lan

stat

ed w

ith

com

pari

son

of t

imes

and

tim

es a

ttri

bute

d to

cor

rect

pe

rson

QW

C: D

ecis

ion

stat

ed w

ith

stat

emen

t su

ppor

ting

exp

lana

tion

Tota

l for

Que

stio

n: 6

mar

ks


127

1MA

0/2F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 19

. (a

) 0,

–2,

–2,

0, 4

, 10

–2

, 10

1

B1,

B1 f

or e

ach

cao

(b)

Sm

ooth

cu

rve

2 B1

cor

rect

plo

t of

the

ir v

alue

s B1

sm

ooth

cur

ve t

hrou

gh t

heir

poi

nts

prov

idin

g at

leas

t 1

mar

k ea

rned

in

(a)

(c)

Dra

ws

y =

7

OR

T&I W

idth

Ar

ea

4 4

4.1

4.51

4.2

5.04

4.3

5.59

4.4

6.16

4.5

6.75

4.6

7.36

4.7

7.99

4.8

8.64

4.9

9.31

5 10

4.55

7.

0525

4.5

2

M1

draw

y =

7A1

4.5

— 4

.6 f

t fr

om g

raph

O

R

Use

s T&

I

B2 4

.5 w

ith

2 x—

3x

eval

uate

d co

rrec

tly

at 4

.5 a

nd 4

.6

(B1

Loca

tes

‘roo

t’ b

etw

een

4 an

d 5

at le

ast

2 ev

alua

tion

s or

ref

ers

to

tabl

e)

Tota

l for

Que

stio

n: 5

mar

ks


128

1MA

0/2F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 20

.FE

A

rea

of la

nd =

30

10

= 30

0 m

2

Peri

met

er o

f la

nd=

30 +

30

+ 10

+ 1

0 =

80 m

N

o. o

f he

ns

= 30

0 0

.8 =

375

Co

st o

f he

ns =

375

7

.5 =

£2

812.

50

Cost

of

fenc

ing

= 80

9

.85

=

£788

To

tal c

ost

= £2

812.

50 +

£78

8 =

£360

0.50

£360

0.50

9

M1

for

area

of

land

30

10

= 30

0m2

M1

for

peri

met

er o

f la

nd =

30

+ 30

+ 1

0 +

10 =

80m

M1

for

“300

”0.

8A1

(ft

) fo

r 37

5 he

ns

M1

for

“375

” 7

.5A1

(ft

) fo

r £2

812.

50M

1 fo

r “8

0”

9.8

5A1

(ft

) fo

r £7

88

A1 c

ao f

or t

otal

cos

t

Tota

l for

Que

stio

n: 9

mar

ks


129

1MA

0/2F

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 21

.FE

(a)

Plot

s fu

rthe

r da

ta

Dra

ws

line

of b

est

fit

Read

s of

f va

lue

from

250

0

£ 11

00—

1200

3

M1

plot

s fu

rthe

r fi

gure

s M

1 dr

aws

line

of b

est

fit

A1 1

100

— 1

200

(b

) D

raw

s y

= 10

00‘2

000’

÷ 4

8 42

2

M1

draw

s y

= 10

00 a

nd d

ivid

es b

y 48

A1

40

— 4

4

Tota

l for

Que

stio

n: 5

mar

ks


130

11.

Scal

e 1

cm r

epre

sent

s 1

m

B CDA


131

19

12345678910 -1 -2 -3 -4

12

34

56

0x

y


132

21.

200

400

600

800

1000

1200

1400

1600

500

1000

1500

2000

2500

3000

3500

0

y =

0.4x

+ 2

00


133



Total Marks

Paper Reference

*S37713A0125*

Edexcel GCSE

Mathematics APaper 2 (Calculator)

Higher Tier


You must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

1MA0/2H


2/2/2/2/3/2

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 π button, take the value of π 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 – you should take particular care on these questions with your spelling, punctuation


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.

Turn over


134

Formulae – Higher Tier


Volume of a prism = area of cross section × length Area of trapezium = (a + b)h

Volume of sphere = r3 Volume of cone = r2h

Surface area of sphere = 4 r2 Curved surface area of cone = rl

In any triangle ABC The Quadratic Equation The solutions of ax2+ bx + c = 0 where a 0, are given by

Sine Rule

Cosine Rule a2= b2+ c2– 2bc cos A

Area of triangle = ab sin C

length

crosssection

rh

r

l

C

ab

c BA

13

a b csin A sin B sin C

xb b ac

a=

− ± −( )2 42

43

12

b

a

h

12

GCSE Mathamatics 1MA0


135




1 Peter won £75 as a prize.

He gave45

of the prize money as a present to Roger and Bethan.

Roger and Bethan shared the present in the ratio 2:3

Work out how much they each got.

Roger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Bethan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



136

2 The equation x3 – 5x = 60 has a solution between 4 and 5

Find this solution and give your answer correct to 1 decimal place. You must show all your working.

x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



137

3


25 cm

7 cm

Calculate the area of this right-angled triangle.

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



138

4 Imran wants to work out how much tax he needs to pay.

Last year he earned £18 000

He does not pay Income tax on the first £6475 he earned. He pays tax of 20 pence for each pound he earned above £6475

He pays the tax in two equal half-yearly instalments.

*(a) How much Income tax does Imran have to pay in his first half-yearly instalment?(4)

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

Imran wants to know what percentage of his earnings he pays in tax.

(b) Calculate the Income tax Imran has to pay as a percentage of his earnings last year.(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %



139

5 Here is some information about the time, in minutes, it took the 21 teachers at a school to get to work on Monday.

13 18 20 35 45 34 44

23 33 12 46 21 22 17

22 31 23 8 15 22 10

(a) Draw an ordered stem and leaf diagram to show this information. (3)

Roadworks near the school meant that the time to travel to school by every teacher on Tuesday was increased by 5 minutes.

(b) What was the median of the times on Tuesday?(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . minutes

(c) State whether the interquartile range of the times on Tuesday would be less, greater or the same as the interquartile range of the times on Monday.

Give a reason for your answer.(1)

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

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



140

6 The graph can be used to convert between gallons and litres.

gallons

litres

10

8

6

4

2

10 20 30 40 50O

The diagram shows a central heating oil tank.

60 cm

180 cm

The oil tank is in the shape of a cylinder of length 180 cm and radius 60 cm.

The oil tank contains 200 gallons of oil.


141

*(a) Is the oil tank more or less than full?(5)

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

The oil has a density of 0.85 g/cm³.

(b) Work out, in kg, the mass of the oil in the tank.(3)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kg


12


142

7 The table shows information about the number of hours that 120 children used a computer last week.

Number of hours Frequency

0 < h 2 10

2 < h 4 15

4 < h 6 30

6 < h 8 35

8 < h 10 25

10 < h 12 5

Work out an estimate for the mean number of hours that the children used a computer. Give your answer to 2 decimal places.

(4)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm



143

8 Fred and Jim pay Malcolm to do some gardening.

Fred has £x Jim has ten pounds less than Fred.

Fred pays one third of his money to Malcolm.

Jim pays half of his money to Malcolm.

(a) Show that the amount that Malcolm is paid is x x3

102

+ − .(1)

Malcolm is paid a total of £170

(b) Use algebra to show how much money Fred has left.(4)

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



144

*9 Kevin and Joe each manage a shop that sells CDs. Kevin’s shop is in the High Street and Joe’s is in the Retail Park.

They want to compare the sales of CDs in each of their shops for the first 100 days of the year.

Frequency

CDs sold

60

50

40

30

20

10

0 10 20 30 40 50 60

Kevin’s information about the number of CDs sold each day in the High Street shop is shown on the grid. Each class interval is 10 CDs wide.

Joe’s information about the number of CDs sold each day in the Retail Park shop is shown in the table.

Number of CDs sold each day Frequency

0 – 10 10

11 – 20 34

21 – 30 24

31 – 40 13

41 – 50 7

51 – 60 12

Compare the sales of CDs in the two shops.


145



146

10 (a) Simplify fully

( ) ( )x x312 2

14×

(3)

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

(b) Solve

(x – 1)(x + 2) = 18(4)

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

(c) Solve the simultaneous equations

y = x2 – 1y = 5 – x

(5)

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

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



147

11 The cumulative frequency diagram gives information about the time, in minutes, 80 people were kept waiting at a hospital casualty department.

Cumulative Frequency

Time (minutes)

90

80

70

60

50

40

30

20

10

0 10 20 30 40 50 60

(a) Write down the number of people who waited for 20 minutes or less.(1)

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

(b) Work out an estimate of the number of people who waited for between 26 minutes and 40 minutes.

(2)

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

The hospital has a target that no more than 15% of people are kept waiting for 40 minutes or more in the casualty department each day.

(c) Has the hospital achieved its target for the day? You must explain your answer.

(2)

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

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



148

*12

D

BA

C

8.5 cm

68°


The diagram represents a vertical pole ACD. AB is horizontal ground. BC is a wire of length 8.5 metres.

The height of the pole AD is 9 metres.

For the pole to be correctly installed, the length DC has to be at least 1 metre.

Show that the pole has been correctly installed.

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



149

13 The time, T seconds, for a hot sphere to cool is proportional to the square root of the surface area, A m2, of the sphere.

When A = 100, T = 40.

Find the value of T when A = 60.

Give your answer correct to 3 significant figures.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . seconds



150

14 The line y = 2x + 3 meets the line y = 4x + 2 at the point P.

Find an equation of the line which is perpendicular to the line y = 2x + 3 and which passes through the point P.

(5)

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



151

15 Here is a rectangle.

a

b


a = 8.3 cm correct to 1 decimal place. b = 3.6 cm correct to 1 decimal place.

(a) Calculate the upper bound of the area of this rectangle. Write down all the figures on your calculator.

(2)

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

(b) Find the area of this rectangle correct to an appropriate number of significant figures.(2)

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



152

16

2

x

x – 2


The diagram shows a cuboid. All the measurements are in cm.

The volume of the cuboid is 51 cm3.

(a) Show that 2x2 – 4x – 51 = 0 for x > 2(4)

(b) Solve the quadratic equation

2x2 – 4x – 51 = 0

Give your solutions correct to 3 significant figures. You must show your working.

(3)

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

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



153

17

A

B C220 m

47° 58°


Angle ABC = 47° Angle ACB = 58° BC = 220 m

Calculate the area of triangle ABC. Give your answer correct to 3 significant figures.

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



154

18 Here is a regular dodecahedron.

A dodecahedron is a solid with 12 faces.

Each face is a regular pentagon.

Calculate the total surface area of a regular dodecahedron with edges of length 10 cm.




155


156


157

1MA

0/2H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 5.

(a

) 0:

8

1: 0

2357

8 2:

012

2233

3:

134

5 4:

456

Key

4 I

6 m

eans

46

min

utes

Corr

ect

stem

an

d le

af3

B3 F

ully

cor

rect

(B

2 Al

l ent

ries

cor

rect

, no

key

) (B

1 co

rrec

t en

trie

s un

orde

red,

key

or

no k

ey)

OR

(B2

Thre

e ro

ws

corr

ect,

key

or

no k

ey)

(B1

Two

row

s co

rrec

t, k

ey o

r no

key

)

(b

) O

ld m

edia

n =

22

New

med

ian

= 22

+ 5

27

min

utes

2

M1

find

s m

edia

n co

rrec

tly

for

orig

inal

dat

a an

d ad

ds 5

A1

cao

O

RM

1 Re

does

tab

le (

ft)

wit

h ea

ch v

alue

incr

ease

d by

5 a

nd a

ttem

pts

to

find

med

ian

A1 c

ao

(c

)

The

sam

e +

reas

on1

C1 A

ll th

e va

lues

hav

e in

crea

sed

by 5

min

utes

so

whe

n yo

u su

btra

ct t

he

5 m

inut

es w

ill c

ance

l out

.

Tota

l for

Que

stio

n: 6

mar

ks


158

1MA

0/2H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 6. FE QW

Cii,

iii

(a)

1 ga

llon

= 4.

54 li

tres

,

200

gal

lons

= 9

08 li

tres

=

908

000

cm3

Vol

of

tank

60

2xπ

180

=

2035

752.

04..

cm3

9080

00<

1017

876.

02

OR

Vol o

f ta

nk

602

π 1

80 =

203

5752

.04.

.cm

3

Hal

f vo

l of

tank

=

1017

876.

02 c

m3

= 10

17.8

76…

litre

s

1017

.876

÷ 4

.54

= 22

4 ga

llons

224

> 20

0

No

5 Re

spon

se m

ay c

onve

rt in

to g

allo

ns,

litre

s, o

r cm

3

Calc

ulat

ions

may

be

perf

orm

ed in

dif

fere

nt o

rder

s

M1

Usi

ng f

orm

ulae

to

find

vol

ume

of t

ank

B1 C

onve

rts

betw

een

litre

s an

d cu

bic

cent

imet

res

M1

read

s of

f gr

aph

for

1l,

2l ,

4l,

5l o

r 10

litr

es w

ithi

n to

lera

nce

(4.4

—

4.6)

A1 A

nsw

er in

cm

3 , lit

res

or g

allo

ns

C1 D

ecis

ion

and

reas

on Q

WC:

Dec

isio

n sh

ould

be

stat

ed,

wit

h ap

prop

riat

e su

ppor

ting

sta

tem

ent

(b

) “

9080

00”

cm3 ×

0.8

5 g/

cm3

= 77

1800

g

771.

8 3

M1

“908

000”

× 0

.85

M

1(de

p) 7

7180

0÷10

00

A1 7

70 —

772

To

tal f

or Q

uest

ion:

8 m

arks

7.

120

5522

524

515

045

106.

08 h

ours

4

M1

for

mid

inte

rval

val

ues

M

1 fo

r m

ulti

plyi

ng f

requ

enci

es b

y m

id-i

nter

val v

alue

s M

1 fo

r ad

ding

(fr

eq

mid

-int

erva

l val

ues)

÷ 1

20

A1 c

ao

Tota

l for

Que

stio

n: 4

mar

ks


159

1MA

0/2H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 8.

(a

) Fr

ed p

ays

3x a

nd J

im

pays

210x

Mal

colm

get

s £1

70 f

or F

red

and

Jim

, so

Mal

colm

get

s

170

2103

xx

Clea

r an

d co

here

ntex

plan

atio

n

1 C1

a c

lear

and

coh

eren

t ex

plan

atio

n

(b

) Fr

ed h

as

32x

left

, so

sol

ving

for

xus

ing

170

2103

xx 2x

+ 3(

x –

10) =

170

6

5x

= 1

050

x

= 2

10O

R

6)

10(3

2210

3x

xx

x

170

630

5x

5

x =

105

0

21

0x

£140

4

M1

mul

tipl

y th

roug

h by

6 a

nd c

ance

ls f

ract

ions

M

1 (d

ep)e

xpan

d 3(

x−

10)

M1

(dep

)col

lect

ter

ms

on e

ach

side

cor

rect

ly

A1 c

ao

OR

M1

colle

cts

term

s ov

er 6

M

1(de

p) e

xpan

d 3(

x−

10)

M1(

dep)

mul

tipl

y th

roug

h by

6 a

nd c

olle

ct t

erm

s

A1 c

ao

Tota

l for

Que

stio

n: 5

mar

ks


160

1MA

0/2H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 9.

QW

Ci,

iii

FE

M

akes

a c

ompa

riso

n of

the

sh

ape

of t

he d

istr

ibut

ion

by

draw

ing

M

akes

a c

ompa

riso

n of

the

m

odal

cla

sses

(31—

40,

11—

20)

Mak

es a

com

pari

son

of t

he

clas

s in

terv

als

that

con

tain

th

e m

edia

ns.(

31—

40,

21—

30)

Wor

ks o

ut a

n es

tim

ate

of t

he

tota

l sal

es o

f ea

ch s

hop(

2635

, 35

30)

Corr

ect

com

pari

sons

4

B1,

B1,

B1 f

or a

ny 4

of

the

follo

win

g do

ne c

orre

ctly

Plot

s fr

eque

ncy

poly

gon

or p

rodu

ces

tabl

e co

mpa

res

mod

es

com

pare

s m

edia

ns

com

pare

s to

tal s

ales

C1 f

or c

omm

ents

on

shap

e of

the

dis

trib

utio

ns

QW

C: D

ecis

ions

sho

uld

be s

tate

d, a

nd a

ll co

mm

ents

sho

uld

be c

lear

an

d fo

llow

thr

ough

fro

m a

ny w

orki

ng o

r di

agra

ms

Tota

l for

Que

stio

n: 4

mar

ks


161


162

1MA

0/2H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 11

. (a

)

28

1 B1

27

— 2

9

(b

) 68

– 4

2 26

2

M1

68 —

42

A1 2

6 —

30

(ne

ed 21

sq

tole

ranc

e on

eac

h)

FE(c

) 15

% of

80

= 12

Ye

s, w

ith

corr

ect

conc

lusi

on

2 M

1 lo

oks

up 6

8 or

40

min

on

cum

ulat

ive

freq

uenc

y A1

cor

rect

con

clus

ion

Tota

l for

Que

stio

n: 5

mar

ks

12.

QW

Cii,

iii

FE

sin

68o =

5.8AC

AC =

8.5

× s

in 6

8o = 7

.881

7.

881

+ 1

< 9

Reas

onsu

ppor

ted

byca

lcul

atio

n

4M

1 si

n 68

o =

5.8AC

M1

AC =

8.5

× s

in 6

8o

A1 7

.88(

1…

C1 8

.88(

1… +

con

clus

ion

QW

C: D

ecis

ion

shou

ld b

e st

ated

, su

ppor

ted

by

clea

rly

laid

out

wor

king

Not

e

90si

n5.868

sinAC

does

not

get

mar

ks u

ntil

in t

he f

orm

68si

n90

sin5.8

AC

Tota

l for

Que

stio

n: 4

mar

ks


163

1MA

0/2H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 13

.A

kT

; 40

=

100

kk

= 4

AT

460

4T

31.0

4

M1

Ak

TM

1 40

=

100

k

A1A

T4

A1 f

or 3

0.98

… o

r 31

(.0)

OR

M2

for

40T =

10

060

oe

M1

for

100

6040

T o

e

A1 f

or 3

0.98

… o

r 31

.0

Tota

l for

Que

stio

n: 4

mar

ks


164


165

1MA

0/2H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 16

. (a

) Vo

l =

2)

2(x

x=

51

Vol =

x

x4

22

– 51

=0

Der

ives

giv

en

answ

er a

nd

cond

itio

n

4M

1 Vo

l =

2)2

(xx

M1

expa

nds

brac

ket

corr

ectl

y A1

(E1

) se

ts e

qual

to

51

B12

x a

s th

e le

ngth

s of

the

cub

oid

have

to

be p

osit

ive.

(b

)

22

)51

(2

4)4

()4

(2

x

4424

4x

6.15

, -4

.15

both

to

3sf

3 M

1 co

rrec

t su

bsti

tuti

on (

allo

w s

ign

erro

rs in

a,

b an

d c)

into

qua

drat

ic

form

ula

M1

442

44

x

A1 6

.14(

7…, −

4.14

(7…

)

Tota

l for

Que

stio

n: 7

mar

ks

17.

An

gle

BAC

= 18

0º —

47º

— 5

8º

= 75

º

)58

sin

(75

sin22

047

sin

ABAC

AC

=75

sin

47si

n22

0 =

166

.57.

.

Area

=58

sin

'57.

166

'22

021

= 15

538

1550

0 m

2 5

B1 f

or 7

5º

M1

)58

sin

(75

sin22

047

sin

ABAC

M1

AC

=75

sin

47si

n22

0

M1

21 ×

220

× “

166.

57”

× si

n58

A1 1

5500

m2

Tota

l for

Que

stio

n: 5

mar

ks


166

1MA

0/2H

Q

uest

ion

Wor

king

Ans

wer

Mar

kA

ddit

iona

l Gui

danc

e 18

.

Pent

agon

= 5

equ

al is

os

tria

ngle

s

5360

=72º

Base

ang

les

= (1

80 –

72)

2

=

54º

for

find

ing

equa

l sid

es o

f is

osce

les

tria

ngle

;

72si

n1054

sin

x=

8.50

6508

084…

area

of

isos

cele

s tr

iang

le =

72si

n21

2x

= 34

.409

5480

1..

area

of

pent

agon

=

5 3

4.40

9548

01

= 1

72.0

4774

01

area

of

dode

cahe

dron

=

12

172.

0477

401

OR

Usi

ng r

ight

-ang

led

trig

onom

etry

; h

= 5t

an54

º

= 6.

8819

…

Area

of

isos

cele

s tr

iang

le =

21 1

0 h

= 34

.409

5480

1…ar

ea o

f pe

ntag

on

= 5

34.

4095

4801

=

172.

0477

401

area

of

dode

cahe

dron

=

12

172.

0477

401

2065

cm

2 9

B1 f

or

5360

= 72

º

B1 (

180

–72

) 2

= 5

4º

M1

for

find

ing

equa

l sid

es o

f is

osce

les

tria

ngle

; x

=72

sin10

54si

nx

A1 f

or x

= 8

.506

5080

84…

M1

for

find

ing

area

of

isos

cele

s tr

iang

le =

72

sin

212 x

A1 f

or 3

4.40

9548

01…

(ft)

B1

for

are

a of

pen

tago

n =

5 (

ft)

= 17

2.04

7740

1…(f

t)

B1 f

or a

rea

of d

odec

ahed

ron

= 12

(

ft)=

206

4.57

2881

… c

m2

A1 f

or 2

065

cm2

(oe)

OR

B1 f

or

5360

= 72

º

B1 (

180

– 72

) 2

= 5

4 º

M

1 fo

r us

ing

righ

t-an

gled

tri

gono

met

ry;

h =

5 ta

n54º

A1

for

6.8

819…

M

1 fo

r fi

ndin

g ar

ea o

f is

osce

les

tria

ngle

= 21

10

h

A1 f

or 3

4.40

9548

01…

(ft)

B1 f

or a

rea

of p

enta

gon

= 5

(ft

) =

172.

0477

401…

(ft)

B1

for

are

a of

dod

ecah

edro

n =

12

(ft

) =

2064

.572

881…

cm

2

A1 f

or 2

065

cm2

(oe)


167


168

9.

102030405060

1020

3040

5060

0C

Ds s

old

Freq

uenc

y


169

14.

2468

24

0x

y


170

April 2010

For more information on Edexcel and BTEC qualifications please visit our website: www.edexcel.org.uk

Edexcel Limited. Registered in England and Wales No. 4496750 Registered Office: One90 High Holborn, London WC1V 7BH. VAT Reg No 780 0898 07

Edexcel GCSE in Mathematics A - Linear (1MA0)

Issue oneGCSE Mathematics 2010 Your proven formula for successInside this Sample Assessment Materials pack you’ll find:

Accessible papers to help you and your students prepare for the assessment

Clear and concise mark schemes to let you know what the examiners are looking for.

One of our hallmarks is the clarity of our papers, and we are committed to ensuring that each paper has:

clearly written, topic-focused questions – Our questions test studentson their mathematical knowledge and not their levels of comprehension.Readability tests show that our papers are the clearest available

questions that are ramped – Our questions become more demandingas the paper progresses, building students’ confidence because they havethe chance to show what they can do

a clear layout – We take time to ensure that our questions are clearlyset out with diagrams where necessary. This avoids ambiguities andhelps to reduce mistakes.

Building upon our reputation as the awarding body of choice with themost reliable examination papers, GCSE Maths10 is your proven formulafor success.

Edexcel190 High Holborn,London WC1V 7BHTel: 0844 576 0027Fax: 020 7190 5700

www.edexcel.com

Publication code: UG022478

If you have any questions regarding our new GCSE Mathematics Specification A for 2010, or if there isanything you’re unsure of, please contact our mathematics team at [email protected]

For further information, please visit our GCSE Mathematics website – www.maths10.co.uk

Ed

excel GC

SE in

Ma

them

atics A

- Lin

ear (1M

A0)

About EdexcelEdexcel, a Pearson company, is the UK's largest awarding body offering academic and vocational qualifications and testing to schools, colleges,employers and other places of learning here and in over 85 countries worldwide.

Edexcel Limited. Registered in England and Wales No. 4496750Registered office: 190 High Holborn, London WC1V 7BH.BTEC is a registered trademark of Edexcel Ltd.

Sample Assessment Materials

Further copies of this publication are available to order from Edexcel publications.Please call 01623 467 467 quoting the relevant publication code.

Documents

2010 Maths Spec.indd