GCSE (9-1) Mathematics - GCSE Revisionmaths.st-chads.co.uk/images/zoo/uploads/GCSE 9-1 Maths...

GCSE (9-1) Mathematics

SPECIMEN PAPERS SET 1 Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics (1MA1)

Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics -Specimen Papers Set 1 - September 2015 © Pearson Education Limited 2015

ii

Contents

Introduction 1

General marking guidance 3

Paper 1F – specimen paper and mark scheme 7



Paper 1H – specimen paper and mark scheme 91



References to third party materials in these specimen papers are made in good faith.

Pearson does not endorse, approve or accept responsibility for the content of materials,

which may be subject to change, or any opinions expressed therein. (Material may include

textbooks, journals, magazines and other publications and websites.)

All information in this document is correct at time of publication.


iii


iv


11Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics -Specimen Papers Set 1 - September 2015 © Pearson Education Limited 2015

Introduction

These specimen papers have been produced to complement the sample assessment materials for Pearson Edexcel Level 1/ Level 2 GCSE (9-1) in Mathematics and are designed to provide extra practice for your students. The specimen papers are part of a suite of support materials offered by Pearson.

The specimen papers do not form part of the accredited materials for this qualification.


22 Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics -Specimen Papers Set 1 - September 2015 © Pearson Education Limited 2015



General marking guidance These notes offer general guidance, but the specific notes for examiners appertaining to individual questions take precedence. 1 All candidates must receive the same treatment. Examiners must mark the last

candidate in exactly the same way as they mark the first.

Where some judgement is required, mark schemes will provide the principles by which marks will be awarded; exemplification/indicative content will not be exhaustive.

2 All the marks on the mark scheme are designed to be awarded; mark schemes

should be applied positively. Examiners should also be prepared to award zero marks if the candidate’s response is not worthy of credit according to the mark scheme. If there is a wrong answer (or no answer) indicated on the answer line always check the working in the body of the script (and on any diagrams), and award any marks appropriate from the mark scheme.

Questions where working is not required: In general, the correct answer should be given full marks. Questions that specifically require working: In general, candidates who do not show working on this type of question will get no marks – full details will be given in the mark scheme for each individual question.

3 Crossed out work

This should be marked unless the candidate has replaced it with an alternative response.

4 Choice of method If there is a choice of methods shown, mark the method that leads to the answer given on the answer line.

If no answer appears on the answer line, mark both methods then award the lower number of marks.

5 Incorrect method

If it is clear from the working that the “correct” answer has been obtained from incorrect working, award 0 marks. Send the response to review for your Team Leader to check.

6 Follow through marks

Follow through marks which involve a single stage calculation can be awarded without working as you can check the answer, but if ambiguous do not award. Follow through marks which involve more than one stage of calculation can only be awarded on sight of the relevant working, even if it appears obvious that there is only one way you could get the answer given.



7 Ignoring subsequent work It is appropriate to ignore subsequent work when the additional work does not change the answer in a way that is inappropriate for the question or its context. (eg. an incorrectly cancelled fraction when the unsimplified fraction would gain full marks). It is not appropriate to ignore subsequent work when the additional work essentially makes the answer incorrect (eg. incorrect algebraic simplification).

8 Probability

Probability answers must be given as a fraction, percentage or decimal. If a candidate gives a decimal equivalent to a probability, this should be written to at least 2 decimal places (unless tenths). Incorrect notation should lose the accuracy marks, but be awarded any implied method marks. If a probability answer is given on the answer line using both incorrect and correct notation, award the marks. If a probability fraction is given then cancelled incorrectly, ignore the incorrectly cancelled answer.

9 Linear equations

Unless indicated otherwise in the mark scheme, full marks can be gained if the solution alone is given on the answer line, or otherwise unambiguously identified in working (without contradiction elsewhere). Where the correct solution only is shown substituted, but not identified as the solution, the accuracy mark is lost but any method marks can be awarded (embedded answers).

10 Range of answers

Unless otherwise stated, when an answer is given as a range (e.g 3.5 – 4.2) then this is inclusive of the end points (e.g 3.5, 4.2) and all numbers within the range.



Guidance on the use of abbreviations within this mark scheme

M method mark awarded for a correct method or partial method P process mark awarded for a correct process as part of a problem solving question A accuracy mark (awarded after a correct method or process; if no method or

process is seen then full marks for the question are implied but see individual mark schemes for more details)

C communication mark B unconditional accuracy mark (no method needed) oe or equivalent cao correct answer only ft follow through (when appropriate as per mark scheme) sc special case dep dependent (on a previous mark) indep independent awrt answer which rounds to isw ignore subsequent working



Centre Number Candidate Number

Write your name hereSurname Other names

Total Marks

Paper Reference

Turn over

S49815A©2015 Pearson Education Ltd.

6/6/6/

*S49815A0120*

MathematicsPaper 1 (Non-Calculator)

Foundation TierSpecimen Papers Set 1

Time: 1 hour 30 minutes 1MA1/1FYou must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser.

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 not be used.• Diagrams are NOT accurately drawn, unless otherwise indicated.• You must show all your working out.

Information

• The total mark for this paper is 80• The marks for each question are shown in brackets

– use this as a guide as to how much time to spend on each question.

Advice

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

Pearson EdexcelLevel 1/Level 2 GCSE (9 - 1)





Total Marks

Paper Reference

Turn over


6/6/6/

*S49815A0120*



Time: 1 hour 30 minutes 1MA1/1FYou must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser.

Instructions



Information



Advice





3

*S49815A0320* Turn over

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

5 Work out (–3)3

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

(Total for Question 5 is 1 mark)

6 Here are four cards. There is a number on each card.

4 5 2 1

(a) Write down the largest 4-digit even number that can be made using each card only once.

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

(b) Write down all the 2-digit numbers that can be made using these cards.

(2)

(Total for Question 6 is 4 marks)

2

*S49815A0220*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

Answer ALL questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

1 Change 530 centimetres into metres.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . metres


2 How many minutes are there in 314

hours?

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


3 Write 4.4354 correct to 2 decimal places.

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


4 Write 0.9 as a percentage.

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




3


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

5 Work out (–3)3

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


6 Here are four cards. There is a number on each card.

4 5 2 1

(a) Write down the largest 4-digit even number that can be made using each card only once.

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

(b) Write down all the 2-digit numbers that can be made using these cards.

(2)


2

*S49815A0220*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A




1 Change 530 centimetres into metres.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . metres


2 How many minutes are there in 314

hours?

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


3 Write 4.4354 correct to 2 decimal places.

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


4 Write 0.9 as a percentage.

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




5


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

8 Bernard says, “When you halve a whole number that ends in 8, you always get a number that ends in 4”

(a) Write down an example to show that Bernard is wrong.

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

(1)

Alice says, “Because 7 and 17 are both prime numbers, all whole numbers that end in 7 are prime numbers.”

(b) Is Alice correct? You must give a reason with your answer.

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

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

(1)


9 Work out 247 × 63

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


4

*S49815A0420*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

7 The table shows information about the sports some students like best.

Hockey Tennis Football Golf

Boys 3 8 15 9

Girls 6 14 7 1

Draw a suitable diagram or chart for this information.




7


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

11 Complete the two-way table.

blue eyes brown eyes green eyes total

boys 5 4 12

girls 7

total 9 30


12 There are 28 red pens and 84 black pens in a bag.

Write down the ratio of the number of red pens to the number of black pens. Give your ratio in its simplest form.

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


6

*S49815A0620*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

10 An American airline has a maximum size for bags on its planes. The diagram shows the maximum dimensions.

height 22 inches

width 14 inches

depth 9 inches

Chris has a bag.

It has height 50 cm width 40 cm depth 20 cm

1 inch = 2.54 cm

Can Chris take this bag on the plane? You must show your working.




9


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

14 A unit of gas costs 4.2 pence.

On average Ria uses 50.1 units of gas a week. She pays for the gas she uses in 13 weeks.

(a) Work out an estimate for the amount Ria pays.

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

(b) Is your estimate to part (a) an underestimate or an overestimate? Give a reason for your answer.

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

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

(1)


8

*S49815A0820*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

13 Here is a sequence of patterns made with grey square tiles and white square tiles.

pattern number pattern number pattern number 1 2 3

(a) In the space below, draw pattern number 4

(1)

(b) Find the total number of tiles in pattern number 20

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

(c) Write an expression, in terms of n, for the number of grey tiles in pattern number n.

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




11


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

16

10 cm

2 cm

2 cm

8 cm

Work out the area of the shape.

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


17

x

y5

4

3

2

1

1 2 3 4 5O

–1

–2

–3

–4

–5

–4–5 –3 –2 –1

On the grid, rotate the triangle 90° clockwise about (0, 0).


10

*S49815A01020*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

15 This is a scale plan of a rectangular floor.

Diagram accurately drawn

Scale: 1 cm represents 2 m

Mrs Bridges is going to cover the floor with boards. Each board is rectangular in shape.

Each board is 1.2 m long and 1 m wide.

Mrs Bridges has 150 boards. Does she have enough boards? You must show how you get your answer.




13


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

19 A shop sells milk in 1 pint bottles and in 2 pint bottles.

Each 1 pint bottle of milk costs 52p. Each 2 pint bottle of milk costs 93p.

Martin has no milk.

He assumes that he uses, on average, 34

of a pint of milk each day.

Martin wants to buy enough milk to last for 7 days.

(a) Work out the smallest amount of money Martin needs to spend on milk. You must show all your working.

£.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3)

Martin actually uses more than 34


(b) Explain how this might affect the amount of money he needs to spend on milk.

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

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

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

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

(1)


12

*S49815A01220*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

18 There are 500 passengers on a train.

720

of the passengers are men.

40% of the passengers are women.

The rest of the passengers are children.

Work out the number of children on the train.

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




13


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

19 A shop sells milk in 1 pint bottles and in 2 pint bottles.

Each 1 pint bottle of milk costs 52p. Each 2 pint bottle of milk costs 93p.

Martin has no milk.

He assumes that he uses, on average, 34


Martin wants to buy enough milk to last for 7 days.

(a) Work out the smallest amount of money Martin needs to spend on milk. You must show all your working.

£.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3)

Martin actually uses more than 34


(b) Explain how this might affect the amount of money he needs to spend on milk.

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

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

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

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

(1)


12

*S49815A01220*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

18 There are 500 passengers on a train.

720

of the passengers are men.

40% of the passengers are women.

The rest of the passengers are children.

Work out the number of children on the train.

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




15


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

22 There are only red counters, blue counters, green counters and yellow counters in a bag.

The table shows the probabilities of picking at random a red counter and picking at random a yellow counter.

Colour red blue green yellow

Probability 0.24 0.32

The probability of picking a blue counter is the same as the probability of picking a green counter.

Complete the table.


23 A pattern is made using identical rectangular tiles.

7 cm

11 cm

Find the total area of the pattern.

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


14

*S49815A01420*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

20 The diagram shows a right-angled triangle.

7x 5x + 18

All the angles are in degrees.

Work out the size of the smallest angle of the triangle.

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


21 A box exerts a force of 140 newtons on a table. The pressure on the table is 35 newtons/m2.

Calculate the area of the box that is in contact with the table.p F

A=

p = pressureF = forceA = area

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




15


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A






Complete the table.



7 cm

11 cm


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


14

*S49815A01420*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A


7x 5x + 18



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




A=


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




17


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

25 Four friends each throw a biased coin a number of times. The table shows the number of heads and the number of tails each friend got.

Ben Helen Paul Sharif

heads 34 66 80 120

tails 8 12 40 40

The coin is to be thrown one more time.

(a) Which of the four friends’ results will give the best estimate for the probability that the coin will land heads?

Justify your answer.

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

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

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

(1)

Paul says,“With this coin you are twice as likely to get heads as to get tails.”

(b) Is Paul correct? Justify your answer.

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

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

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

(2)

The coin is to be thrown twice.

(c) Use all the results in the table to work out an estimate for the probability that the coin will land heads both times.

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


16

*S49815A01620*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

24 The diagram shows a sand pit. The sand pit is in the shape of a cuboid.

Sally wants to fill the sand pit with sand. A bag of sand costs £2.50 There are 8 litres of sand in each bag.

100 cm60 cm

40 cm

Sally says,“The sand will cost less than £70”

Show that Sally is wrong.




17


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A



heads 34 66 80 120

tails 8 12 40 40




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

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

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

(1)



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

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

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

(2)



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


16

*S49815A01620*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A



100 cm60 cm

40 cm






19

*S49815A01920*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

28 Factorise x2 – 16

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


29 Solve the simultaneous equations

4x + y = 25x – 3y = 16

x = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , y = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


TOTAL FOR PAPER IS 80 MARKS

18

*S49815A01820*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

26 (a) Write down the exact value of cos30°

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

(b)

x cm12 cm

30°

Given that sin30° = 0.5, work out the value of x.

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


27 Expand and simplify (x + 3)(x – 1)

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




19

*S49815A01920*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

28 Factorise x2 – 16

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


29 Solve the simultaneous equations

4x + y = 25x – 3y = 16

x = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , y = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



18

*S49815A01820*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A


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

(b)

x cm12 cm

30°


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


27 Expand and simplify (x + 3)(x – 1)

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




20

*S49815A02020*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

BLANK PAGE



20

*S49815A02020*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

BLANK PAGE

Pape

r 1M

A1:

1F

Que

stio

nW

orki

ngA

nsw

erN

otes

15.

3(0)

B1

cao

219

5B

1ca

o

34.

44B

1ca

o

490

B1

cao

5−27

B1

cao

6(a

)54

12B

2(B

1 fo

r any

4-d

igit

even

num

ber u

sing

4,5

,1,2

or

5421

)(b

)45

, 54,

41,

14

, 42,

24,

51

, 15,

52,

25

,12,

21

P1St

arts

to li

st sy

stem

atic

ally

; at l

east

6 c

orre

ct se

en (i

gnor

e re

peat

s)

A1

List

s all

12 n

umbe

rs (c

ondo

ne in

clus

ion

of a

llre

peat

s 44,

55

etc)

7ch

art

C1

for k

ey o

r sui

tabl

e la

bels

to id

entif

y bo

ys a

nd g

irls

C1

for 4

corr

ect s

port

labe

ls o

r a li

near

scal

eC

1fo

r dia

gram

or c

hart

(com

bine

d or

sepa

rate

), co

rrec

tly sh

owin

g da

ta fo

r at

leas

t 3 sp

orts

C1

for f

ully

cor

rect

dia

gram

or c

hart

with

axe

s cor

rect

ly sc

aled

and

labe

lled

8(a

)ex

ampl

eC

1fo

r app

ropr

iate

exa

mpl

e sh

own

(b)

exam

ple

C1

conc

lusi

on



Pape

r 1M

A1:

1F

Que

stio

nW

orki

ngA

nsw

erN

otes

915

561

M1

for c

ompl

ete

met

hod

with

rela

tive

plac

e va

lue

corr

ect (

addi

tion

not

nece

ssar

y)M

1fo

r add

ition

of a

ll ap

prop

riate

ele

men

tsA

1ca

o

10N

oP1

star

ts th

e pr

oces

s by

conv

ertin

g on

e di

men

sion

(sup

porte

d)A

1co

nver

ts a

t lea

st o

ne m

easu

rem

ent

C1

conc

lusi

on e

g N

o, si

nce

the

40 c

m >

14

inch

es

11(5

) 3

(4)

(12)

tabl

eC

1fo

r at l

east

2 c

orre

ct n

umbe

rs6

(7)

518

C1

for a

t lea

st 4

cor

rect

num

bers

11

10(9

) (3

0)C

1fo

r com

plet

ed ta

ble

121

: 3M

1fo

r sta

ting

a ra

tio e

g 28

: 84

or 1

: 3

inco

rrec

tly st

ated

or 3

:1A

1ca

o

13(a

)dr

awin

gC

1dr

awin

g of

pat

tern

num

ber 4

(b)

42C

1sh

ows a

proc

ess o

f wor

king

tow

ards

pat

tern

num

ber 2

0C

1ca

o

(c)

n+

2C

1be

gins

pro

cess

of s

tatin

g al

gebr

aic

expr

essi

on e

g n

C1

n+

2 o

e



Pape

r 1M

A1:

1F

Que

stio

nW

orki

ngA

nsw

erN

otes

915

561

M1

for c

ompl

ete

met

hod

with

rela

tive

plac

e va

lue

corr

ect (

addi

tion

not

nece

ssar

y)M

1fo

r add

ition

of a

ll ap

prop

riate

ele

men

tsA

1ca

o

10N

oP1

star

ts th

e pr

oces

s by

conv

ertin

g on

e di

men

sion

(sup

porte

d)A

1co

nver

ts a

t lea

st o

ne m

easu

rem

ent

C1

conc

lusi

on e

g N

o, si

nce

the

40 c

m >

14

inch

es

11(5

) 3

(4)

(12)

tabl

eC

1fo

r at l

east

2 c

orre

ct n

umbe

rs6

(7)

518

C1

for a

t lea

st 4

cor

rect

num

bers

11

10(9

) (3

0)C

1fo

r com

plet

ed ta

ble

121

: 3M

1fo

r sta

ting

a ra

tio e

g 28

: 84

or 1

: 3

inco

rrec

tly st

ated

or 3

:1A

1ca

o

13(a

)dr

awin

gC

1dr

awin

g of

pat

tern

num

ber 4

(b)

42C

1sh

ows a

proc

ess o

f wor

king

tow

ards

pat

tern

num

ber 2

0C

1ca

o

(c)

n+

2C

1be

gins

pro

cess

of s

tatin

g al

gebr

aic

expr

essi

on e

g n

C1

n+

2 o

e

Pape

r 1M

A1:

1F

Que

stio

nW

orki

ngA

nsw

erN

otes

14(a

)20

00p-

2600

pP1

Evid

ence

of e

stim

ate

eg. 4

or 5

0 us

ed in

cal

cula

tion

P1co

mpl

ete

proc

ess t

o so

lve

prob

lem

A1

2000

p-26

00p

or £

20-£

26

(b)

unde

rC

1un

dere

stim

ate

as v

alue

s hav

e be

en ro

unde

d do

wn

15no with

P1in

terp

rets

the

info

rmat

ion

and

the

scal

e eg

in c

alcu

latio

ns o

r sho

wn

as p

art

of a

dia

gram

eg

8m x

24m

(=19

2) o

r 8 x

20

(=16

0)ev

iden

ceP1

a co

rrec

t pro

cess

to fi

t boa

rds i

nto

the

spac

e in

a lo

gica

l way

or 1

50×1

×1.2

(=

180)

C1

“no”

with

supp

ortiv

e ev

iden

ce e

g sh

owin

g 16

0 ne

eded

or 1

80<1

92

1632

M1

form

etho

d to

find

area

of a

ny o

ne re

ctan

gle

A1

cao

17ro

tatio

nM

1fo

r tria

ngle

in c

orre

ct o

rient

atio

n or

rota

tion

90° a

ntic

lock

wis

eA

1ca

o

1812

5P1

for p

roce

ss to

find

7/2

0 of

500

(=17

5) o

r 7/2

0 +

4/10

(=3/

4)P1

for p

roce

ss to

find

40%

of 5

00 (=

200)

or ¼

× 5

00A

1ca

o



Pape

r 1M

A1:

1F

Que

stio

nW

orki

ngA

nsw

erN

otes

19(a

)P1

begi

ns to

wor

k w

ith fi

gure

s eg

findi

ng 7

× ¾

(=5.

25)

P1w

orks

with

inte

gers

eg

5.25

as 6

pin

ts a

nd 3

× 2

pin

ts2.

79A

1ca

o

(b)

pay

mor

eC

1de

duce

s he

may

hav

e to

pay

mor

e [if

he

uses

mor

e th

an 0

.857

pin

ts a

day

]

2042

P1pr

oces

s to

star

t pro

blem

solv

ing

eg fo

rms a

n ap

prop

riate

equ

atio

nP1

com

plet

e pr

oces

s to

solv

e eq

uatio

nA

1ca

o

214

m2

C1

subs

titut

ion

into

form

ula

eg

140

35A

=

A1

4 (o

e) st

ated

C1

(inde

p) u

nits

stat

ed e

g m

2

220.

22P1

begi

ns p

roce

ss o

f sub

tract

ion

of p

roba

bilit

ies f

rom

1A

1oe

2348

P1be

gins

to w

ork

with

rect

angl

e di

men

sion

s eg

l+w

=7or

2×l

+w(=

11)

C1

show

s a re

sult

for a

dim

ensi

on e

g us

ing

l=4

or w

=3P1

begi

ns p

roce

ss o

f fin

ding

tota

l are

a eg

4 ×

“3”

× “

4”A

1ca

o



Pape

r 1M

A1:

1F

Que

stio

nW

orki

ngA

nsw

erN

otes

19(a

)P1

begi

ns to

wor

k w

ith fi

gure

s eg

findi

ng 7

× ¾

(=5.

25)

P1w

orks

with

inte

gers

eg

5.25

as 6

pin

ts a

nd 3

× 2

pin

ts2.

79A

1ca

o

(b)

pay

mor

eC

1de

duce

s he

may

hav

e to

pay

mor

e [if

he

uses

mor

e th

an 0

.857

pin

ts a

day

]

2042

P1pr

oces

s to

star

t pro

blem

solv

ing

eg fo

rms a

n ap

prop

riate

equ

atio

nP1

com

plet

e pr

oces

s to

solv

e eq

uatio

nA

1ca

o

214

m2

C1

subs

titut

ion

into

form

ula

eg

140

35A

=

A1

4 (o

e) st

ated

C1

(inde

p) u

nits

stat

ed e

g m

2

220.

22P1

begi

ns p

roce

ss o

f sub

tract

ion

of p

roba

bilit

ies f

rom

1A

1oe

2348

P1be

gins

to w

ork

with

rect

angl

e di

men

sion

s eg

l+w

=7or

2×l

+w(=

11)

C1

show

s a re

sult

for a

dim

ensi

on e

g us

ing

l=4

or w

=3P1

begi

ns p

roce

ss o

f fin

ding

tota

l are

a eg

4 ×

“3”

× “

4”A

1ca

o

Pape

r 1M

A1:

1F

Que

stio

nW

orki

ngA

nsw

erN

otes

24ex

plan

atio

nM

1w

orks

with

vol

ume

eg 2

4000

0be

gins

wor

king

bac

k eg

70÷

2.50

M1

uses

con

vers

ion

1 lit

re =

100

0 cm

3us

es c

onve

rsio

n 1

litre

= 1

000

cm3

M1

uses

800

0 eg

vol

÷ 8

000

(=30

)us

es 8

000

eg “

28”×

800

0 (=

2240

00)

M1

uses

“30

” eg

“30

” ×

2.50

wor

ks w

ith v

ol. e

g 22

4000

C1

for e

xpla

natio

n an

d 75

stat

edfo

r exp

lana

tion

with

240

000

and

2240

00

25(a

)Sh

arif

B1

Shar

if w

ith m

entio

n of

gre

ates

t tot

al th

row

s(b

)D

ecis

ion

P1st

arts

wor

king

with

pro

porti

ons

(sup

porte

d)A

1C

oncl

usio

n: c

orre

ct fo

r Pau

l, bu

t not

for t

he re

st; o

r ref

to ju

st P

aul’s

resu

lts(c

)To

t: H

300

T 1

009 16

P1se

lect

s Sha

rif o

r ove

rall

and

mul

tiplie

s P(h

eads

)×P(

head

s) e

g ¾

× ¾

A1

oe

26(a

)3 2

B1

(b)

6M

1st

arts

pro

cess

eg

sin3

012x

=

A1

answ

er g

iven

27x2 +2

x−3

M1

star

ts e

xpan

sion

: at l

east

3 te

rms c

orre

ct w

ith si

gns,

or fo

ur te

rms c

orre

ct

igno

ring

sign

sA

1fo

r x2 +2

x−3





Total Marks

Paper Reference

Turn over


6/6/6/

*S49817A0124*

MathematicsPaper 2 (Calculator)


Time: 1 hour 30 minutes 1MA1/2FYou must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator.

Instructions


– 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.• Diagrams are NOT accurately drawn, unless otherwise indicated.• You must show all your working out.

Information



Advice



Pape

r 1M

A1:

1F

Que

stio

nW

orki

ngA

nsw

erN

otes

28(x

+4)(

x−4)

B1

for (

x+4)

(x−4)

29x=

7, y=−3

M1

for c

orre

ct p

roce

ss to

elim

inat

e on

e va

riabl

e (c

ondo

ne o

ne a

rithm

etic

err

or)

M1

(dep

) for

subs

titut

ing

foun

d va

lue

in o

ne o

f the

equ

atio

ns o

r app

ropr

iate

m

etho

d af

ter s

tarti

ng a

gain

(con

done

one

arit

hmet

ic e

rror

)A

1fo

r bot

h co

rrec

t sol

utio

ns





Total Marks

Paper Reference

Turn over


6/6/6/

*S49817A0124*




Instructions




Information



Advice



Pape

r 1M

A1:

1F

Que

stio

nW

orki

ngA

nsw

erN

otes

28(x

+4)(

x−4)

B1

for (

x+4)

(x−4)

29x=

7, y=−3

M1

for c

orre

ct p

roce

ss to

elim

inat

e on

e va

riabl

e (c

ondo

ne o

ne a

rithm

etic

err

or)

M1

(dep

) for

subs

titut

ing

foun

d va

lue

in o

ne o

f the

equ

atio

ns o

r app

ropr

iate

m

etho

d af

ter s

tarti

ng a

gain

(con

done

one

arit

hmet

ic e

rror

)A

1fo

r bot

h co

rrec

t sol

utio

ns



3


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

5 A shop sells pens at different prices. The cheapest pens in the shop cost 27p each.

Lottie buys 18 pens from the shop. She pays with a £10 note.

(a) If Lottie buys 18 of the cheapest pens, how much change should Lottie get?

£.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)

Instead of buying the cheapest pens, Lottie buys 18 of the more expensive pens. She still pays with a £10 note.

(b) How does this affect the amount of change she should get?

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

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

(1)


2

*S49817A0224*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A




1 Write down the value of the 3 in 16.35

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


2 Here is a list of six numbers.

1 3 6 9 12 24

Which number in the list is not a factor of 24?

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


3 Write 0.21 as a fraction.

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


4 (a) Simplify 5f – f + 2f

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

(b) Simplify 2 × m × n × 8

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

(c) Simplify t2 + t2

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

(1)




5


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

9 What percentage of this shape is shaded?

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


4

*S49817A0424*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

6 Michelle and Wayne have saved a total of £458 for their holiday. Wayne saved £72 more than Michelle.

How much did Wayne save?

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


7 Work out 70% of £90

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


8 Here are four fractions.

12

1724

34

512

Write these fractions in order of size. Start with the smallest fraction.

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




7


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

11 In a shop, the normal price of a coat is £65 The shop has a sale.

In week 1 of the sale, the price of the coat is reduced by 20% In week 2 of the sale, the price of the coat is reduced by a further £10

Maria has £40

Does Maria have enough money to buy the coat in week 2 of the sale? You must show how you get your answer.


6

*S49817A0624*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

10 The manager of a clothes shop recorded the size of each dress sold one morning.

10 10 12 12 14 14 14 14 14 14 16 16 16 16 18 18 18 20 20 20

The sizes of dresses are always even numbers. The mean size of the dresses sold that morning is 15.3

The manager says,“The mean size of the dresses is not a very useful average.”

(i) Explain why the manager is right.

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

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

(ii) Which is the more useful average for the manager to know, the median or the mode? You must give a reason for your answer.

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

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

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




9


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

13 Here are the heights, in centimetres, of 15 children.

123 147 135 150 147

129 148 149 125 137

133 138 133 130 151

(a) Show this information in a stem and leaf diagram.

(3)

One of the children is chosen at random.

(b) What is the probability that this child has a height greater than 140 cm?

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


8

*S49817A0824*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

12 The length of a car is 3.6 metres.

Karl makes a scale model of the car. He uses a scale of 1 cm to 30 cm.

Work out the length of the scale model of the car. Give your answer in centimetres.

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




11


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

15 (a) Work out 45

of 210 cm.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cm(1)

(b) Work out (6 – 2.5)2 + 9 34 2 58. .−

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


10

*S49817A01024*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

14

(a) Write down the coordinates of point C.

(. . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . .)(1)

ABCD is a square.

(b) On the grid, mark with a cross (X) the point D so that ABCD is a square.(1)

(c) Write down the coordinates of the midpoint of the line segment BC.

(. . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . .)(1)


y4

3

2

1

O

–1

–2

–3

–4

–4 –3 –2 –1 1 2 3 4 x

B

A

C



13


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

17 ABC is a right-angled triangle.

C B

A

P

Q

22°

P is a point on AB. Q is a point on AC. AP = AQ.

Work out the size of angle AQP. You must give a reason for each stage of your working.


12

*S49817A01224*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

16 (a) Solve 4c + 5 = 11

c = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

(b) Solve 5(e + 7) = 20

e = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

(c) Simplify (m3)2

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

(1)




15


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

19 Lethna worked out 25

12

+

She wrote:

25

12

210

110

310

+ = + =

The answer of 310

is wrong.

(a) Describe one mistake that Lethna made.

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

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

(1)

Dave worked out 112

× 5 13

He wrote:

1 × 5 = 5 and 12

× 13 = 16

so 1 12

× 5 13 = 5 1

6

The answer of 516

is wrong.

(b) Describe one mistake that Dave made.

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

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

(1)


14

*S49817A01424*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

18 Here is a list of ingredients for making 16 mince pies.

Ingredients for 16 mince pies

240 g of butter350 g of flour100 g of sugar280 g of mincemeat

Elaine wants to make 72 mince pies.

How much of each ingredient will Elaine need?

butter .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . g

flour .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . g

sugar .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . g

mincemeat .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . g




17


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

22 The time-series graph gives some information about the number of pairs of shoes sold in a shoe shop in the first six months of 2014

The sales target for the first six months of 2014 was to sell a mean of 96 pairs of shoes per month.

Did the shoe shop meet this sales target? You must show how you get your answer.


140

120

100

80

60January February March April May June

Months

Number of pairs of shoes sold

16

*S49817A01624*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

20 Make t the subject of the formula w = 3t + 11

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


21 Three companies sell the same type of furniture.

The price of the furniture from Pooles of London is £1480 The price of the furniture from Jardins of Paris is €1980 The price of the furniture from Outways of New York is $2250

The exchange rates are

£1 = €1.34

£1 = $1.52

Which company sells this furniture at the lowest price? You must show how you get your answer.




17


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A





140

120

100

80


Months


16

*S49817A01624*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A


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





£1 = €1.34

£1 = $1.52





19


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

24 At 9 am, Bradley began a journey on his bicycle.

From 9 am to 9.36 am, he cycled at an average speed of 15 km/h. From 9.36 am to 10.45 am, he cycled a further 8 km.

(a) Draw a travel graph to show Bradley’s journey.

(3)

From 10.45 am to 11 am, Bradley cycled at an average speed of 18 km/h.

(b) Work out the distance Bradley cycled from 10.45 am to 11 am.

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


20

15

10

5

09 am

Time of day

Distance in km

9.30 am 10 am 11am10.30 am

18

*S49817A01824*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

23 The grouped frequency table gives information about the heights of 30 students.

Height (h cm) Frequency

130 < h 140 1

140 < h 150 7

150 < h 160 8

160 < h 170 10

170 < h 180 4

(a) Write down the modal class interval.

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

(1)

This incorrect frequency polygon has been drawn for the information in the table.

(b) Write down two things wrong with this incorrect frequency polygon.

1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)


12

10

8

6

4

2

0120 130 140 150 160 170 180 190

Height (h cm)

Frequency



19


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A




(3)



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


20

15

10

5

09 am

Time of day

Distance in km

9.30 am 10 am 11am10.30 am

18

*S49817A01824*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A



130 < h 140 1

140 < h 150 7

150 < h 160 8

160 < h 170 10

170 < h 180 4


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

(1)



1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)


12

10

8

6

4

2

0120 130 140 150 160 170 180 190

Height (h cm)

Frequency



21


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

27 Here is a diagram showing a rectangle, ABCD, and a circle.

A B

D C

19cm

19cm

16cm

BC is a diameter of the circle.

Calculate the percentage of the area of the rectangle that is shaded. Give your answer correct to 1 decimal place.

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


20

*S49817A02024*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

25 Toby invested £7500 for 2 years in a savings account. He was paid 4% per annum compound interest.

How much money did Toby have in his savings account at the end of 2 years?

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


26 Becky has some marbles. Chris has two times as many marbles as Becky. Dan has seven more marbles than Chris.

They have a total of 57 marbles.

Dan says, “If I give some marbles to Becky, each of us will have the same number of marbles.”

Is Dan correct? You must show how you get your answer.




21


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A


A B

D C

19cm

19cm

16cm



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


20

*S49817A02024*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A



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









23

*S49817A02324*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

BLANK PAGE

22

*S49817A02224*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

DO

NO

T W

RIT

E I

N T

HIS

AR

EA

D

O N

OT

WR

ITE

IN

TH

IS A

RE

A

28 ABCD is a trapezium.

A

B

D

C7cm

5cm

9cm

A square has the same perimeter as this trapezium.

Work out the area of the square. Give your answer correct to 3 significant figures.

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





24

*S49817A02424*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

BLANK PAGE



24

*S49817A02424*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

BLANK PAGE

Pape

r 1M

A1:

2F

Que

stio

nW

orki

ngA

nsw

erN

otes

13

tent

hs o

r 3 10

B1

29

B1

321 10

0B

1

4a b c

6f16

mn

2t2

B1

B1

B1

cao

5a b

27 ×

18

= 48

65.

14

"les

s cha

nge"

M1

A1

C1

for 1

000

–"2

7 ×

18"

cao

for "

less

cha

nge"

oe

645

8–

72 =

386

386

÷ 2

= 19

326

5P1 A

1

for s

tart

to th

e pr

oces

s, eg

. 458

–72

or 4

58 ÷

2

(= 2

29) a

nd 7

2 ÷

2 (=

36)

763

M1

A1

for a

met

hod

to fi

nd p

erce

ntag

e of

a q

uant

ity



Pape

r 1M

A1:

2F

Que

stio

nW

orki

ngA

nsw

erN

otes

85 12

,1 2,17 24

,3 4M

1

A1

for a

met

hod

to c

onve

rt ea

ch to

a fo

rm th

at c

an

be e

asily

use

d fo

r com

parin

g, e

g. 5 12

= 10 24

for c

orre

ct o

rder

962

.5M

1fo

r 12.

5 sq

uare

s or u

se o

f 1 sq

= 5

%

M1

for 1

2.5÷

20×1

00 o

eA

1or

62½

10i ii

C1

C1

for c

orre

ct c

ritic

ism

of u

se o

f mea

n, e

g. "t

here

is

no d

ress

size

of 1

5.3"

Mod

e (=

14) i

s mos

t use

ful s

ince

it sh

ows t

he

mos

t pop

ular

size

11fo

r 'no

' with

su

ppor

ting

evid

ence

P1 P1 C1

for c

orre

ct p

roce

ss to

find

pric

ein

Wee

k 1,

eg

. 65

× 0.

8 (=

52)

for p

roce

ss to

find

the

pric

ein

wee

k 2,

eg

. "52

"–10

(=

42)

for '

no' w

ith su

ppor

ting

evid

ence

1212

P1 A1

for c

ompl

ete

proc

ess i

nclu

ding

uni

t con

vers

ion,

eg

. 3.6

× 1

00 ÷

30

cao



Pape

r 1M

A1:

2F

Que

stio

nW

orki

ngA

nsw

erN

otes

85 12

,1 2,17 24

,3 4M

1

A1

for a

met

hod

to c

onve

rt ea

ch to

a fo

rm th

at c

an

be e

asily

use

d fo

r com

parin

g, e

g. 5 12

= 10 24

for c

orre

ct o

rder

962

.5M

1fo

r 12.

5 sq

uare

s or u

se o

f 1 sq

= 5

%

M1

for 1

2.5÷

20×1

00 o

eA

1or

62½

10i ii

C1

C1

for c

orre

ct c

ritic

ism

of u

se o

f mea

n, e

g. "t

here

is

no d

ress

size

of 1

5.3"

Mod

e (=

14) i

s mos

t use

ful s

ince

it sh

ows t

he

mos

t pop

ular

size

11fo

r 'no

' with

su

ppor

ting

evid

ence

P1 P1 C1

for c

orre

ct p

roce

ss to

find

pric

ein

Wee

k 1,

eg

. 65

× 0.

8 (=

52)

for p

roce

ss to

find

the

pric

ein

wee

k 2,

eg

. "52

"–10

(=

42)

for '

no' w

ith su

ppor

ting

evid

ence

1212

P1 A1

for c

ompl

ete

proc

ess i

nclu

ding

uni

t con

vers

ion,

eg

. 3.6

× 1

00 ÷

30

cao

Pape

r 1M

A1:

2F

Que

stio

nW

orki

ngA

nsw

erN

otes

13a b

12|3

5 9

13| 0

3 3

5 7

814

| 7 7

8 9

15| 0

1K

ey: 1

2|3

repr

esen

ts 1

23

6 15oe

C1

C1

C1

M1

A1

for a

n un

orde

red

diag

ram

with

just

one

err

or o

r fo

r an

orde

red

diag

ram

with

no

mor

e th

an tw

o er

rors

for a

fully

cor

rect

dia

gram

fora

cor

rect

key

(uni

ts m

ay b

e om

itted

but

mus

t be

cor

rect

if in

clud

ed)

for c

orre

ct in

terp

reta

tion

from

thei

r dia

gram

(or

from

orig

inal

info

rmat

ion)

of t

he n

umbe

r (6)

out

of

15

over

140

for

6 15oe

or f

t the

ir di

agra

m

14a b c

(0, –

1)

× m

arke

d at

(3, 0

)

(–0.

5, 0

.5)

B1

B1

B1

15a b

168

14.8

5

B1

M1

A1

for 1

2.25

or 2

.6



Pape

r 1M

A1:

2F

Que

stio

nW

orki

ngA

nsw

erN

otes

16a b

1.5

oe

–3

M1

A1

M1

for r

earr

angi

ng, e

g 11

–5

= 4c

for a

firs

t ste

p of

eith

er d

ivid

ing

both

side

s by

5,

eg. 5

(𝑒𝑒+7)

5=

20 5or

for e

xpan

ding

the

brac

ket,

eg.

5×e

+ 5×

7 =

20

cm

6

A1

B1

cao

1756

ow

ith re

ason

sM

1

M1

C1

C1

for a

met

hod

lead

ing

to th

e ev

alua

tion

of a

noth

er

angl

e, e

g. a

ngle

A=1

80 –

90–

22 (=

68)

for c

orre

ctly

usi

ng th

e is

osce

les p

rope

rty in

id

entif

ying

two

equa

l ang

les,

eg (1

80 –

"68"

)÷2

(= 5

6)fo

r at l

east

one

cor

rect

reas

on g

iven

link

ed to

cl

ear w

orki

ng.

For a

ll co

rrec

t rea

sons

incl

uded

Rea

sons

as a

ppro

pria

te fr

om:

sum

of a

ngle

s in

a tri

angl

e=

180o

base

ang

leso

f iso

scel

estri

angl

e ar

e eq

ual

sum

of a

ngle

son

a st

raig

ht li

ne=

180o

sum

of a

ngle

sin

a qu

adril

ater

al=

360o



Pape

r 1M

A1:

2F

Que

stio

nW

orki

ngA

nsw

erN

otes

16a b

1.5

oe

–3

M1

A1

M1

for r

earr

angi

ng, e

g 11

–5

= 4c

for a

firs

t ste

p of

eith

er d

ivid

ing

both

side

s by

5,

eg. 5

(𝑒𝑒+7)

5=

20 5or

for e

xpan

ding

the

brac

ket,

eg.

5×e

+ 5×

7 =

20

cm

6

A1

B1

cao

1756

ow

ith re

ason

sM

1

M1

C1

C1

for a

met

hod

lead

ing

to th

e ev

alua

tion

of a

noth

er

angl

e, e

g. a

ngle

A=1

80 –

90–

22 (=

68)

for c

orre

ctly

usi

ng th

e is

osce

les p

rope

rty in

id

entif

ying

two

equa

l ang

les,

eg (1

80 –

"68"

)÷2

(= 5

6)fo

r at l

east

one

cor

rect

reas

on g

iven

link

ed to

cl

ear w

orki

ng.

For a

ll co

rrec

t rea

sons

incl

uded

Rea

sons

as a

ppro

pria

te fr

om:

sum

of a

ngle

sin

a tri

angl

e=

180o

base

ang

leso

f iso

scel

estri

angl

e ar

e eq

ual

sum

of a

ngle

son

a st

raig

ht li

ne=

180o

sum

of a

ngle

sin

a qu

adril

ater

al=

360o

Pape

r 1M

A1:

2F

Que

stio

nW

orki

ngA

nsw

erN

otes

18bu

tter =

108

0flo

ur =

157

5su

gar =

450

min

cem

eat =

12

60

M1

M1

A1

for c

orre

ct u

se o

f a c

orre

ct sc

ale

fact

or, 7

2 ÷

16

(= 4

.5) o

n at

leas

t one

ingr

edie

ntfo

r com

plet

e m

etho

d ap

plie

d to

all

ingr

edie

nts

corr

ect a

mou

nts c

orre

ctly

con

verte

d to

kg

19a b

C1

C1

for a

cor

rect

eva

luat

ion

of th

e m

etho

d sh

own

by

givi

ng a

t lea

st o

ne c

orre

ct e

rror

mad

e, e

g. "

didn

't m

ultip

ly th

e 1

by 5

"

for a

cor

rect

eva

luat

ion

of th

e m

etho

d sh

own

by

givi

ng a

t lea

st o

ne c

orre

ct e

rror

mad

e, e

g. "

can'

t sp

lit a

mix

ed n

umbe

r" o

r "sh

ould

con

vert

to

impr

oper

(oe)

frac

tions

firs

t"

20𝑡𝑡

=𝑤𝑤−

113

M1

for 3

t=w

–11

or 𝑤𝑤3

=3𝑡𝑡 3

+11 3

A1

for 𝑡𝑡

=𝑤𝑤−11 3

oe21

Jard

ins o

f Par

isP1 P1 C

1

corr

ect p

roce

ss to

con

vert

one

pric

e to

ano

ther

cu

rrec

ncy,

eg

1980

÷ 1

.34

for a

com

plet

e pr

oces

s lea

ding

to 3

pric

es in

the

sam

e cu

rren

cyfo

r 3 c

orre

ct a

nd c

onsi

sten

t res

ults

and

a c

orre

ct

com

paris

on m

ade.



Pape

r 1M

A1:

2F

Que

stio

nW

orki

ngA

nsw

erN

otes

22M

ean

of 9

6or

net

de

viat

ion

of 0

so ta

rget

met

M1

M1

C1

for c

orre

ct in

terp

reta

tion

of th

e gr

aph,

with

at

leas

t one

cor

rect

read

ing

or a

line

dra

wn

thro

ugh

96 w

ith a

t lea

st o

ne c

orre

ct d

evia

tion

com

plet

e m

etho

d to

find

mea

n of

six

mon

ths

sale

s, eg

. (11

0+84

+78+

94+9

0+12

0)÷6

(= 9

6) o

r th

e m

ean

of si

x de

viat

ions

, eg

. (14

–12–

16–2

–6+2

4)÷6

(= 0

)fo

r a c

orre

ct a

nsw

er o

f 96

or 0

with

cor

rect

co

nclu

sion

23a b

160

< h

≤ 17

0

1. P

oint

s sho

uld

be p

lotte

d at

mid

-in

terv

al v

alue

s2.

The

pol

ygon

sh

ould

not

be

clos

ed

B1

C1

C1

for i

dent

ifyin

g th

e co

rrec

t cla

ss in

terv

al

for a

cor

rect

err

or id

entif

ied

for a

cor

rect

err

or id

entif

ied



Pape

r 1M

A1:

2F

Que

stio

nW

orki

ngA

nsw

erN

otes

22M

ean

of 9

6or

net

de

viat

ion

of 0

so ta

rget

met

M1

M1

C1

for c

orre

ct in

terp

reta

tion

of th

e gr

aph,

with

at

leas

t one

cor

rect

read

ing

or a

line

dra

wn

thro

ugh

96 w

ith a

t lea

st o

ne c

orre

ct d

evia

tion

com

plet

e m

etho

d to

find

mea

n of

six

mon

ths

sale

s, eg

. (11

0+84

+78+

94+9

0+12

0)÷6

(= 9

6) o

r th

e m

ean

of si

x de

viat

ions

, eg

. (14

–12–

16–2

–6+2

4)÷6

(= 0

)fo

r a c

orre

ct a

nsw

er o

f 96

or 0

with

cor

rect

co

nclu

sion

23a b

160

< h

≤ 17

0

1. P

oint

s sho

uld

be p

lotte

d at

mid

-in

terv

al v

alue

s2.

The

pol

ygon

sh

ould

not

be

clos

ed

B1

C1

C1

for i

dent

ifyin

g th

e co

rrec

t cla

ss in

terv

al

for a

cor

rect

err

or id

entif

ied

for a

cor

rect

err

or id

entif

ied

Pape

r 1M

A1:

2F

Que

stio

nW

orki

ngA

nsw

erN

otes

24a

grap

hM

1

C1

C1

for m

etho

d to

star

t to

find

dist

ance

cyc

led

in 3

6 m

ins,

eg. l

ine

draw

n of

cor

rect

gra

dien

t or

15×

36 60fo

r cor

rect

gra

ph fr

om 9

.00

am to

9.3

6 am

for g

raph

dra

wn

from

"(9

.36,

9)"

to

(10.

45, "

9" +

8)

b4.

5M

1A

1fo

r 18

× 0.

25ca

o

2581

12M

1A

1fo

r co

mpl

ete

met

hod,

eg.

750

0 ×

1.04

2

cao

26N

o w

ith

supp

ortin

g ev

iden

ce

P1 P1 C1

for t

he st

art o

f a c

orre

ct p

roce

ss, e

g. tw

o of

x, 2

xan

d 2x

+7 o

e or

a fu

lly c

orre

ct tr

ial,

eg. 5

+ 1

0 +

17 =

32

for s

ettin

g up

an

equa

tion

in x

.eg.

x+

2x+

2x+

7 =

57 o

r a c

orre

ct tr

ial t

otal

ling

57, e

g. 1

0 +

20

+ 27

= 5

7(d

epon

P2)

for a

t lea

st o

ne c

orre

ct re

sult

and

for

a co

rrec

t ded

uctio

n fr

om th

eir a

nsw

ers f

ound

, eg.

C

hris

has

20

so it

is im

poss

ible

for a

ll to

hav

e 20

si

nce

60 m

arbl

es w

ould

be

need

ed.





Total Marks

Paper Reference

Turn over


6/6/6/

*S49819A0120*




Instructions




Information



Advice


Pearson Edexcel Level 1/Level 2 GCSE (9 - 1)

Pape

r 1M

A1:

2F

Que

stio

nW

orki

ngA

nsw

erN

otes

2766

.9P1 P1 P1 A

1

for p

roce

ss to

find

the

area

of o

ne sh

ape,

eg.

19

×16

(= 3

04) o

r 𝜋𝜋×

82(=

201

.06.

..)fo

r pro

cess

to fi

nd th

e sh

aded

are

a, e

g. "3

04" –

"201

.06"

÷2

(= 2

03.4

6...)

for a

com

plet

e pr

oces

s to

find

requ

ired

perc

enta

ge, e

g. "2

03.46"

304

×10

0

for a

nsw

er in

rang

e 66

to 6

8

2843

.5P1 P1 P1 P1 A

1

For p

roce

ss to

est

ablis

h a

right

-ang

led

trian

gle

with

two

side

s of 5

cm

and

9 –

7 =

2 cm

For c

orre

ct a

pplic

atio

n of

Pyt

hago

ras,

eg. 5

2+"

2"2

for a

com

plet

e pr

oces

s to

find

perim

eter

, eg.

9 +

7

+ 5

+ "5

.39"

(= 2

6.38

5...)

for p

roce

ss to

find

are

a of

squa

re,

eg. (

26.3

85...

÷4)

2

for a

nsw

er in

rang

e 43

.5 to

43.

6





Total Marks

Paper Reference

Turn over


6/6/6/

*S49819A0120*




Instructions




Information



Advice



Pape

r 1M

A1:

2F

Que

stio

nW

orki

ngA

nsw

erN

otes

2766

.9P1 P1 P1 A

1

for p

roce

ss to

find

the

area

of o

ne sh

ape,

eg.

19

×16

(= 3

04) o

r 𝜋𝜋×

82(=

201

.06.

..)fo

r pro

cess

to fi

nd th

e sh

aded

are

a, e

g. "3

04" –

"201

.06"

÷2

(= 2

03.4

6...)

for a

com

plet

e pr

oces

s to

find

requ

ired

perc

enta

ge, e

g. "2

03.46"

304

×10

0

for a

nsw

er in

rang

e 66

to 6

8

2843

.5P1 P1 P1 P1 A

1

For p

roce

ss to

est

ablis

h a

right

-ang

led

trian

gle

with

two

side

s of 5

cm

and

9 –

7 =

2 cm

For c

orre

ct a

pplic

atio

n of

Pyt

hago

ras,

eg. 5

2+"

2"2

for a

com

plet

e pr

oces

s to

find

perim

eter

, eg.

9 +

7

+ 5

+ "5

.39"

(= 2

6.38

5...)

for p

roce

ss to

find

are

a of

squa

re,

eg. (

26.3

85...

÷4)

2

for a

nsw

er in

rang

e 43

.5 to

43.

6



3


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

5 There are 1.5 litres of water in a bottle.

There are 250 millilitres of water in another bottle.

Work out the total amount of water in the two bottles.

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


6 Here is a trapezium.

This diagram is accurately drawn.

P Qx

(a) Measure the length of the line PQ.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .cm

(1)

(b) Measure the size of the angle marked x.

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

(1)


2

*S49819A0220*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA




1 Write the number 5689 correct to the nearest thousand.

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


2 Work out 30 125 3

++

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


3 Work out the reciprocal of 0.125

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


4 Here is a list of numbers.

1 2 5 6 12

From the list, write down

(i) a multiple of 4

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

(ii) a prime number

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




5


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

9 The two numbers, A and B, are shown on a scale.

A

0

B

The difference between A and B is 48

Work out the value of A and the value of B.

A =... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B =... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


10 Complete this table of values.

n 3n + 2

12... . . . . . . . . . . . . . . . . . . . . . . . . .

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

47


4

*S49819A0420*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

7 (a) Solve f + 2f + f = 20

f =.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) Solve 18 – m = 6

m =. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(c) Simplify d 2 × d 3

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

(1)


8 Jayne writes down the following

3.4 × 5.3 = 180.2

Without doing the exact calculation, explain why Jayne’s answer cannot be correct.

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

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




7


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

13 Here are the first three terms of a sequence.

32 26 20

Find the first two terms in the sequence that are less than zero.

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


14 Here is a triangle ABC.

(a) Mark, with the letter y, the angle CBA.(1)

Here is a cuboid.

Some of the vertices are labelled.

(b) Shade in the face CDEG.(1)

(c) How many edges has a cuboid?

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

(1)


A

C B

A

F E

D

B C

G

6

*S49819A0620*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

11 The same number is missing from each box.

× × = 343

(a) Find the missing number.

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

(1)

(b) Work out 44

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

(1)


12 Here are two numbers.29 37

Nadia says both of these numbers can be written as the sum of two square numbers.

Is Nadia correct? You must show how you get your answer.




9


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

16 Give an example to show that when a piece is cut off a rectangle the perimeter of the new shape

(i) is less than the perimeter of the rectangle,

(ii) is the same as the perimeter of the rectangle,

(iii) is greater than the perimeter of the rectangle.


8

*S49819A0820*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

15 There are 5 grams of fibre in every 100 grams of bread.

A loaf of bread has a weight of 400 g. There are 10 slices of bread in a loaf.

Each slice of bread has the same weight.

Work out the weight of fibre in one slice of bread.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . g




11


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

18 In a breakfast cereal, 40% of the weight is fruit. The rest of the cereal is oats.

(a) Write down the ratio of the weight of fruit to the weight of oats. Give your answer in the form 1 : n.

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

(2)

A different breakfast cereal is made using only fruit and bran. The ratio of the weight of fruit to the weight of bran is 1 : 3

(b) What fraction of the weight of this cereal is bran?

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

(1)


10

*S49819A01020*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

17 ABC is an isosceles triangle. When angle A = 70°, there are 3 possible sizes of angle B.

(a) What are they?

.. . . . . . . . . . . . . . . . . . . . . . . . . . .° , . . . . . . . . . . . . . . . . . . . . . . . . . . . . ° , . . . . . . . . . . . . . . . . . . . . . . . . . . . . °(3)

When angle A = 120°, there is only one possible size of angle B.

(b) Explain why.

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

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

(1)




13


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

20 E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {multiples of 2} A ∩ B = {2, 6} A ∪ B = {1, 2, 3, 4, 6, 8, 9, 10}

Draw a Venn diagram for this information.


12

*S49819A01220*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

19 Boxes of chocolates cost £3.69 each. A shop has an offer.

Boxes of chocolates

3 for the price of 2

Ali has £50 He is going to get as many boxes of chocolates as possible.

How many boxes of chocolates can Ali get?

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




15


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

For all the other points

(b) (i) draw the line of best fit,

(ii) describe the correlation.

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

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

(2)

A different student revised for 9 hours.

(c) Estimate the mark this student got

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

(1)

The Spanish test was marked out of 100

Lucia says,

“I can see from the graph that had I revised for 18 hours I would have got full marks.”

(d) Comment on what Lucia says.

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

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

(1)


22 The length, L cm, of a line is measured as 13 cm correct to the nearest centimetre.

Complete the following statement to show the range of possible values of L

. . . . . . . . . . . . . . . . . . . . . . . . . . . L < . . . . . . . . . . . . . . . . . . . . . . . . . . . .


14

*S49819A01420*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

21 The scatter diagram shows information about 10 students.

For each student, it shows the number of hours spent revising and the mark the student achieved in a Spanish test.

One of the points is an outlier.

(a) Write down the coordinates of the outlier.

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

(1)

100

90

80

70

60

50

40

30

20

10

02 4 6 8 10 12 14 16 18

Mark

Hours spent revising

0



15


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA




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

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

(2)

A different student revised for 9 hours.

(c) Estimate the mark this student got

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

(1)


Lucia says,



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

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

(1)




. . . . . . . . . . . . . . . . . . . . . . . . . . . L < . . . . . . . . . . . . . . . . . . . . . . . . . . . .


14

*S49819A01420*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA


For each student, it shows the number of hours spent revising and the mark the student achieved in a Spanish test.



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

(1)

100

90

80

70

60

50

40

30

20

10

02 4 6 8 10 12 14 16 18

Mark


0



17


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

24 Jenny works in a shop that sells belts.

The table shows information about the waist sizes of 50 customers who bought belts from the shop in May.

Belt size Waist (w inches) Frequency

Small 28 < w 32 24

Medium 32 < w 36 12

Large 36 < w 40 8

Extra Large 40 < w 44 6

(a) Calculate an estimate for the mean waist size.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .inches(3)

Belts are made in sizes Small, Medium, Large and Extra Large.

Jenny needs to order more belts in June. The modal size of belts sold is Small.

Jenny is going to order 34

of the belts in size Small.

The manager of the shop tells Jenny she should not order so many Small belts.

(b) Who is correct, Jenny or the manager? You must give a reason for your answer.

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

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

(2)


16

*S49819A01620*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

23 Line L is drawn on the grid below.

Find an equation for the straight line L. Give your answer in the form y = mx + c

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


yL

–2 2

–2

–4

4O x

10

8

6

4

2



17


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA




Small 28 < w 32 24

Medium 32 < w 36 12

Large 36 < w 40 8



.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .inches(3)







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

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

(2)


16

*S49819A01620*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA


Find an equation for the straight line L. Give your answer in the form y = mx + c

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


yL

–2 2

–2

–4

4O x

10

8

6

4

2



19

*S49819A01920*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

Turn over

Karen is advised to buy 10% more tiles than she estimated. Buying 10% more tiles will affect the number of the tiles Karen needs to buy.

She assumes she will need to buy 10% more packs of tiles.

(b) Is Karen’s assumption correct? You must show your working.

(2)


26 Factorise x 2 + 3x – 4

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


18

*S49819A01820*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

25 The diagram shows part of a wall in the shape of a trapezium.

0.8 m

1.8 m

2.7 m

Karen is going to cover this part of the wall with tiles. Each rectangular tile is 15 cm by 7.5 cm

Tiles are sold in packs. There are 9 tiles in each pack.

Karen divides the area of the wall by the area of a tile to work out an estimate for the number of tiles she needs to buy.

(a) Use Karen’s method to work out an estimate for the number of packs of tiles she needs to buy.

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

(5)



19

*S49819A01920*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

Turn over




(2)



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


18

*S49819A01820*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

25 The diagram shows part of a wall in the shape of a trapezium.

0.8 m

1.8 m

2.7 m

Karen is going to cover this part of the wall with tiles. Each rectangular tile is 15 cm by 7.5 cm


Karen divides the area of the wall by the area of a tile to work out an estimate for the number of tiles she needs to buy.

(a) Use Karen’s method to work out an estimate for the number of packs of tiles she needs to buy.

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

(5)



20

*S49819A02020*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

27 Here are the equations of four straight lines.

Line A y = 2x + 4 Line B 2y = x + 4 Line C 2x + 2y = 4 Line D 2x – y = 4

Two of these lines are parallel. Write down the two parallel lines.

Line .. . . . . . . . . . . . . . . . . . . . . . . . . . . and line.. . . . . . . . . . . . . . . . . . . . . . . . . . .


28 The densities of two different liquids A and B are in the ratio 19 : 22

The mass of 1 cm3 of liquid B is 1.1 g.

5 cm3 of liquid A is mixed with 15 cm3 of liquid B to make 20 cm3 of liquid C.

Work out the density of liquid C.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .g/cm3





20

*S49819A02020*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA



Two of these lines are parallel. Write down the two parallel lines.

Line .. . . . . . . . . . . . . . . . . . . . . . . . . . . and line.. . . . . . . . . . . . . . . . . . . . . . . . . . .


28 The densities of two different liquids A and B are in the ratio 19 : 22

The mass of 1 cm3 of liquid B is 1.1 g.

5 cm3 of liquid A is mixed with 15 cm3 of liquid B to make 20 cm3 of liquid C.

Work out the density of liquid C.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .g/cm3



Pape

r 1M

A1:

3F

Que

stio

nW

orki

ngA

nsw

erN

otes

160

00B

1 ca

o

25.

25B

1 ca

o

38

B1

cao

4i ii

12 2 or

5

B1

cao

B1

51.

75lo

r 175

0 m

lB

1 fo

r kno

wle

dge

of 1

litre

is 1

000

mill

ilitre

sP1

for a

ddin

g th

eir t

wo

amou

nts

C1

for 1

.75l

or 1

750

ml(

mus

t inc

lude

uni

ts)

6(a)

6(b)

8 35

B1

8 ±2

mm

B1

35 ±

2˚

7(a)

7(b)

7(c)

5 12 𝑑𝑑5

B1

cao

B1

cao

B1

8St

atem

ent

C1

for a

full

expl

anat

ion

9−1

6, 3

2P1

for 4

8 ÷

6P1

for a

com

plet

e pr

oces

s to

find

eith

er A

or B

A1



Pape

r 1M

A1:

3F

Que

stio

nW

orki

ngA

nsw

erN

otes

1038 15

B1

cao

P1 (4

7-2)

÷3

A1

cao

11(a

)

11(b

)

7 256

B1

cao

B1

cao

12Y

es w

ith e

vide

nce

C1

for w

ritin

g do

wn

at le

ast t

wo

squa

res n

umbe

rsP1

for a

ddin

g sq

uare

num

bers

A

1 ca

o w

ith su

ppor

ting

evid

ence

13−

4 an

d −1

0M

1 fo

r rep

eate

d su

btra

ctio

n of

6oe

A

1 −

4A

1 −1

0

14(a

)

14(b

)

14(c

)

Ang

le m

arke

d

Face

shad

ed

12

B1

cao

B1

cao

B1

cao

152

P1 fo

r cor

rect

pro

cess

to fi

nd fi

bre

for 4

00g

P1 fo

r a c

ompl

ete

proc

ess t

o fin

d th

e fib

re p

er sl

ice

A1

cao

16(i) (ii

)

(iii)

3 op

tions

show

nC

1 D

iagr

am w

ith d

ecre

ased

per

imet

er d

raw

n

C1

Dia

gram

with

sam

e pe

rimet

er d

raw

n

C1

Dia

gram

with

incr

ease

d pe

rimet

er d

raw

n



Pape

r 1M

A1:

3F

Que

stio

nW

orki

ngA

nsw

erN

otes

1038 15

B1

cao

P1 (4

7-2)

÷3

A1

cao

11(a

)

11(b

)

7 256

B1

cao

B1

cao

12Y

es w

ith e

vide

nce

C1

for w

ritin

g do

wn

at le

ast t

wo

squa

res n

umbe

rsP1

for a

ddin

g sq

uare

num

bers

A

1 ca

o w

ith su

ppor

ting

evid

ence

13−

4 an

d −1

0M

1 fo

r rep

eate

d su

btra

ctio

n of

6oe

A

1 −

4A

1 −1

0

14(a

)

14(b

)

14(c

)

Ang

le m

arke

d

Face

shad

ed

12

B1

cao

B1

cao

B1

cao

152

P1 fo

r cor

rect

pro

cess

to fi

nd fi

bre

for 4

00g

P1 fo

r a c

ompl

ete

proc

ess t

o fin

d th

e fib

re p

er sl

ice

A1

cao

16(i) (ii

)

(iii)

3 op

tions

show

nC

1 D

iagr

am w

ith d

ecre

ased

per

imet

er d

raw

n

C1

Dia

gram

with

sam

e pe

rimet

er d

raw

n

C1

Dia

gram

with

incr

ease

d pe

rimet

er d

raw

n

Pape

r 1M

A1:

3F

Que

stio

nW

orki

ngA

nsw

erN

otes

17(a

)

17(b

)

70,4

0 an

d 55

Expl

anat

ion

P1 fo

r a m

etho

d to

find

one

of a

ngle

s eg

(180

-70

) ÷ 2

or 7

0 st

ated

as t

he e

qual

or 1

80 –

2×

70P1

for a

met

hod

to fi

nd a

ang

leA

1 fo

r 70,

40

and

55 (

any

orde

r)

C1

Expl

anat

ion

eg o

nly

one

optio

n on

ce a

n ob

tuse

ang

le g

iven

18(a

)

18(b

)

1:1.

5

3 4

M1

for 4

0:(1

00-4

0)

A1

cao

B1

193.

69×

2 =

7.38

19P1

for 7

.38

repe

ated

ly a

dded

at l

east

6 ti

mes

OR

50

÷ 7.

38P1

for 6

× 7

.38

+ 3.

69

A1

19 b

oxes

20V

enn

diag

ram

M1

for t

wo

over

lapp

ing

and

labe

lled

oval

sM

1 fo

r 2 a

nd 6

in th

e in

ters

ectio

nM

1 fo

r 5 a

nd 7

in th

e un

iver

sal s

et o

nly

C1

for a

fully

cor

rect

Ven

n D

iagr

am



Pape

r 1M

A1:

3F

Que

stio

nW

orki

ngA

nsw

erN

otes

21(a

)

21(b

)(i)

(ii)

21(c

)

21(d

)

(4,1

0)

Line

dra

wn

Posi

tive

Val

ue b

etw

een

60

and

70

Stat

emen

t

B1

cao

B1

Stra

ight

line

dra

wn

pass

ing

bet

wee

n (2

,20)

and

(2,3

0) A

ND

(13,

86) a

nd (1

3,94

)

C1

posi

tive

C1

a co

rrec

t val

ue g

iven

C1

for r

efer

ring

to th

e da

nger

of e

xtra

pola

tion

outs

ide

the

give

n

rang

e or

for a

giv

en p

oint

Eg li

ne o

f bes

t fit

may

not

con

tinue

or f

ull m

arks

are

har

d to

ac

hiev

e no

mat

ter h

ow m

uch

revi

sion

is d

one

2212

.5≤

L<

13.5

B1

12.5

B1

13.5

23𝑦𝑦

=2𝑥𝑥

+1

M1

for a

met

hod

to fi

nd th

e gr

adie

ntM

1 fo

r a m

etho

d to

find

the

c in

y=

mx

+ c

A1 𝑦𝑦

=2𝑥𝑥

+1

oe in

this

form

at

24(a

)(7

20+4

08+3

04+2

52)÷

5033

.68

M1

for f

indi

ng4

prod

ucts

fwco

nsis

tent

ly w

ithin

inte

rval

(in

clud

ing

end

poin

ts)

M1

(dep

on

1st M

) for

'Ʃfw

'÷50

A1

cao

24(b

)M

anag

er w

ith

reas

ons

M1

for s

trate

gy to

com

pare

num

ber o

f sm

all s

ize

sold

to n

umbe

r or

dere

dC

1 cl

ear c

ompa

rison

that

smal

l siz

e is

not

¾ a

nd so

Jenn

y is

not

co

rrec

t or t

he m

anag

er is

cor

rect



Pape

r 1M

A1:

3F

Que

stio

nW

orki

ngA

nsw

erN

otes

21(a

)

21(b

)(i)

(ii)

21(c

)

21(d

)

(4,1

0)

Line

dra

wn

Posi

tive

Val

ue b

etw

een

60

and

70

Stat

emen

t

B1

cao

B1

Stra

ight

line

dra

wn

pass

ing

bet

wee

n (2

,20)

and

(2,3

0) A

ND

(13,

86) a

nd (1

3,94

)

C1

posi

tive

C1

a co

rrec

t val

ue g

iven

C1

for r

efer

ring

to th

e da

nger

of e

xtra

pola

tion

outs

ide

the

give

n

rang

e or

for a

giv

en p

oint

Eg li

ne o

f bes

t fit

may

not

con

tinue

or f

ull m

arks

are

har

d to

ac

hiev

e no

mat

ter h

ow m

uch

revi

sion

is d

one

2212

.5≤

L<

13.5

B1

12.5

B1

13.5

23𝑦𝑦

=2𝑥𝑥

+1

M1

for a

met

hod

to fi

nd th

e gr

adie

ntM

1 fo

r a m

etho

d to

find

the

c in

y=

mx

+ c

A1 𝑦𝑦

=2𝑥𝑥

+1

oe in

this

form

at

24(a

)(7

20+4

08+3

04+2

52)÷

5033

.68

M1

for f

indi

ng4

prod

ucts

fwco

nsis

tent

ly w

ithin

inte

rval

(in

clud

ing

end

poin

ts)

M1

(dep

on

1st M

) for

'Ʃfw

'÷50

A1

cao

24(b

)M

anag

er w

ith

reas

ons

M1

for s

trate

gy to

com

pare

num

ber o

f sm

all s

ize

sold

to n

umbe

r or

dere

dC

1 cl

ear c

ompa

rison

that

smal

l siz

e is

not

¾ a

nd so

Jenn

y is

not

co

rrec

t or t

he m

anag

er is

cor

rect

Pape

r 1M

A1:

3F

Que

stio

nW

orki

ngA

nsw

erN

otes

25(a

)

25(b

)

160

tiles

18 p

acks

176

tiles

20

pac

ks

18 Supp

orte

d st

atem

ent

M1

a fu

ll m

etho

d to

find

the

area

of t

he tr

apez

ium

M1

a fu

ll m

etho

d to

con

vert

all a

reas

to c

onsi

sten

t uni

tsM

1 fo

r the

are

a of

the

trape

zium

÷ar

ea o

f a ti

leM

1 fo

r com

mun

icat

ion

of th

e nu

mbe

r of w

hole

pac

ks re

quire

dA

1

P1 fi

ndin

g th

at 1

0% e

xtra

requ

ires t

wo

mor

e pa

cks o

r 10%

of 1

8C

1Sta

tem

ent e

g.in

crea

se in

pac

ks is

2 m

ore

whi

ch is

mor

e th

an

10%

26( 𝑥𝑥−

1)( 𝑥𝑥

+4)

M1

( 𝑥𝑥±

1)( 𝑥𝑥

±4)

A1

( 𝑥𝑥−

1)(𝑥𝑥

+4)

oe

27A

and

DC

1 in

any

ord

er

281.

0625

P1 fo

r a c

ompl

ete

proc

ess t

o fin

d th

e de

nsity

of l

iqui

d A

P1 fo

r a c

ompl

ete

proc

ess t

o fin

d th

e m

ass o

f liq

uid

CP1

for a

com

plet

e pr

oces

s to

find

the

dens

ity o

f liq

uid

C

A1

cao





Total Marks

Paper Reference

Turn over


6/6/6/

*S49816A0120*


Higher TierSpecimen Papers Set 1

Time: 1 hour 30 minutes 1MA1/1HYou must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser.

Instructions



Information

• The total mark for this paper is 80 • The marks for each question are shown in brackets


Advice







Total Marks

Paper Reference

Turn over


6/6/6/

*S49816A0120*



Time: 1 hour 30 minutes 1MA1/1HYou must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser.

Instructions



Information

• The total mark for this paper is 80 • The marks for each question are shown in brackets


Advice





3


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA






Complete the table.



7 cm

11 cm


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


2

*S49816A0220*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA





7x 5x + 18



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




A=


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




5


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA



heads 34 66 80 120

tails 8 12 40 40




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

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

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

(1)



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

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

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

(2)



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


4

*S49816A0420*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA



100 cm60 cm

40 cm






7


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

8 The mass of Jupiter is 1.899 × 1027 kg. The mass of Saturn is 0.3 times the mass of Jupiter.

(a) Work out an estimate for the mass of Saturn. Give your answer in standard form.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kg(3)

(b) Give evidence to show whether your answer to (a) is an underestimate or an overestimate.

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

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

(1)


9 Walkden Reds is a basketball team.

At the end of 11 games, their mean score was 33 points per game. At the end of 10 games, their mean score was 2 points higher.

Jordan says,“Walkden Reds must have scored 13 points in their 11th game.”

Is Jordan right? You must show how you get your answer.

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


6

*S49816A0620*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA


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

(b)

x cm12 cm

30°


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




9


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

12 Sean drives from Manchester to Gretna Green.

He drives at an average speed of 50 mph for the first 3 hours of his journey.

He then has 150 miles to drive to get to Gretna Green. Sean drives these 150 miles at an average speed of 30 mph.

Sean says,“My average speed from Manchester to Gretna Green was 40 mph.”

Is Sean right? You must show how you get your answer.


13 m = k 3 14+

Make k the subject of the formula.

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


8

*S49816A0820*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

10 There are some red counters and some yellow counters in a bag. There are 30 yellow counters in the bag. The ratio of the number of red counters to the number of yellow counters is 1:6

(a) Work out the number of red counters in the bag.

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

Riza puts some more red counters into the bag. The ratio of the number of red counters to the number of yellow counters is now 1:2

(b) How many red counters does Riza put into the bag?

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


11 Write down the value of 12523

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




11


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

16 These graphs show four different proportionality relationships between y and x.

y

O x

y

O x

Graph A Graph B

y

O x

y

O x

Graph C Graph D

Match each graph with a statement in the table below.

Proportionality relationship Graph letter

y is directly proportional to x

y is inversely proportional to x

y is proportional to the square of x

y is inversely proportional to the square of x


10

*S49816A01020*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

14 Solve xx

xx

+ + − =23

22

3

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


15 Show that 2 3 56 5

2

2x x

x x− −

+ + can be written in the form ax b

cx d++

where a, b, c and d are integers.




13


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

18 The diagram shows a solid hemisphere.

Volume of sphere = 43πr3

Surface area of sphere = 4πr2

r

The volume of the hemisphere is 2503

π

Work out the exact total surface area of the solid hemisphere. Giveyouranswerasamultipleofπ.

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


12

*S49816A01220*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

17P

Q

S T

R

PQ = PR. S is the midpoint of PQ. T is the midpoint of PR.

Prove triangle QTR is congruent to triangle RSQ.




15


D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

21 There are 10 pens in a box.

There are x red pens in the box. All the other pens are blue.

Jack takes at random two pens from the box.

Find an expression, in terms of x, for the probability that Jack takes one pen of each colour. Give your answer in its simplest form.

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


14

*S49816A01420*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

19 Simplify fully ( )( )6 5 6 531

− +

You must show your working.

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


20 Prove algebraically that the difference between the squares of any two consecutive integers is equal to the sum of these two integers.




17

*S49816A01720*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

23

B

y

xA

C (5, –1)

4

O–2

Find an equation of the line that passes through C and is perpendicular to AB.

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



16

*S49816A01620*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

22 B

Y

CA

5a – b

6b

3a

CAYB is a quadrilateral.

CA→

= 3a CB→

= 6b BY

→ = 5a – b

X is the point on AB such that AX : XB = 1 : 2

Prove that CX→

= 25

CY→




19

*S49816A01920*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

BLANK PAGE

18

*S49816A01820*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

D

O N

OT

WR

ITE

IN T

HIS

AR

EA

BLANK PAGE



20

*S49816A02020*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

BLANK PAGE



20

*S49816A02020*

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

D

O N

OT W

RIT

E IN

TH

IS AR

EA

BLANK PAGE

Pape

r 1M

A1:

1H

Que

stio

nW

orki

ngA

nsw

erN

otes

142

P1pr

oces

s to

star

t pro

blem

solv

ing

eg fo

rms a

n ap

prop

riate

equ

atio

nP1

com

plet

e pr

oces

s to

solv

e eq

uatio

nA

1ca

o

24

m2

B1

subs

titut

ion

into

form

ula

eg

121.

5A

=

A1

4(o

e) st

ated

C1

(inde

p) u

nits

stat

ed

30.

22P1

begi

ns p

roce

ss o

f sub

tract

ion

of p

roba

bilit

ies f

rom

1A

1oe

448

P1be

gins

to w

ork

with

rect

angl

e di

men

sion

s eg

l+w

=7 o

r 2×l

+w(=

11)

C1

show

s a re

sult

for a

dim

ensi

on e

g us

ing

l=4

or w

=3P1

begi

ns p

roce

ss o

f fin

ding

tota

l are

a eg

4 ×

“3”

× “

4”A

1ca

o

5ex

plan

atio

nM

1w

orks

with

vol

ume

eg 2

4000

0be

gins

wor

king

bac

k eg

70÷

2.50

M1

uses

con

vers

ion

1 lit

re =

100

0 cm

3us

es c

onve

rsio

n 1

litre

= 1

000

cm3

M1

uses

800

0 eg

vol

÷ 8

000

(=30

)us

es 8

000

eg “

28”×

800

0 (=

2240

00)

M1

uses

“30

” eg

“30

” ×

2.50

wor

ks w

ith v

ol. e

g 22

4000

C1

for e

xpla

natio

n an

d 75

stat

edfo

r exp

lana

tion

with

240

000

and

2240

00



Pape

r 1M

A1:

1H

Que

stio

nW

orki

ngA

nsw

erN

otes

6(a

)Sh

arif

B1

Shar

if w

ith m

entio

n of

gre

ates

t tot

al th

row

s(b

)N

oP1

star

ts w

orki

ng w

ith p

ropo

rtion

s(s

uppo

rted)

A1

Con

clus

ion:

cor

rect

for P

aul,

but n

ot fo

r the

rest

; or r

ef to

just

Pau

l’s re

sults

(c)

Tot:

H 3

00

T 10

09 16

P1se

lect

s Sha

rif o

r ove

rall

and

mul

tiplie

s P(h

eads

)×P(

head

s) e

g ¾

× ¾

A1

oe

7(a

)3 2

B1

(b)

6M

1st

arts

pro

cess

eg

sin3

012x

=

A1

answ

er g

iven

8(a

)5.

7×10

26to

B1

uses

est

imat

es e

g 1.

899

to 1

.9 o

r 26×

1026

M1

proc

ess o

f mul

tiplic

atio

n eg

0.5

7 ×

1027

A1

betw

een

5.7×

1026

and

6×10

26

(b)

expl

anat

ion

C1

eg u

nder

estim

ate

a nu

mbe

r isr

ound

ed u

p

9‘Y

es’ w

ith

corr

ect

P1be

gins

pro

cess

of w

orki

ng w

ith m

ean

eg 3

5×10

(=35

0) o

r 33×

11 (=

363)

or

10×(

35−3

3) (=

20) o

r 11×

(35−

33) (

=22)

wor

king

P1(d

ep) f

indi

ng th

e di

ffer

ence

eg

“363

”−“3

50”,

or 3

3 –

“20”

or 3

5 –

“22”

C1

‘Yes

’ with

13

from

cor

rect

wor

king



Pape

r 1M

A1:

1H

Que

stio

nW

orki

ngA

nsw

erN

otes

6(a

)Sh

arif

B1

Shar

if w

ith m

entio

n of

gre

ates

t tot

al th

row

s(b

)N

oP1

star

ts w

orki

ng w

ith p

ropo

rtion

s(s

uppo

rted)

A1

Con

clus

ion:

cor

rect

for P

aul,

but n

ot fo

r the

rest

; or r

ef to

just

Pau

l’s re

sults

(c)

Tot:

H 3

00

T 10

09 16

P1se

lect

s Sha

rif o

r ove

rall

and

mul

tiplie

s P(h

eads

)×P(

head

s) e

g ¾

× ¾

A1

oe

7(a

)3 2

B1

(b)

6M

1st

arts

pro

cess

eg

sin3

012x

=

A1

answ

er g

iven

8(a

)5.

7×10

26to

B1

uses

est

imat

es e

g 1.

899

to 1

.9 o

r 26×

1026

M1

proc

ess o

f mul

tiplic

atio

n eg

0.5

7 ×

1027

A1

betw

een

5.7×

1026

and

6×10

26

(b)

expl

anat

ion

C1

eg u

nder

estim

ate

a nu

mbe

r isr

ound

ed u

p

9‘Y

es’ w

ith

corr

ect

P1be

gins

pro

cess

of w

orki

ng w

ith m

ean

eg 3

5×10

(=35

0) o

r 33×

11 (=

363)

or

10×(

35−3

3) (=

20) o

r 11×

(35−

33) (

=22)

wor

king

P1(d

ep) f

indi

ng th

e di

ffer

ence

eg

“363

”−“3

50”,

or 3

3 –

“20”

or 3

5 –

“22”

C1

‘Yes

’ with

13

from

cor

rect

wor

king

Pape

r 1M

A1:

1H

Que

stio

nW

orki

ngA

nsw

erN

otes

10(a

)5

P1be

gins

to w

ork

with

scal

ing

fact

ors (

eg 5

) or ÷

6A

1ca

o(b

)10

P1w

orks

with

1:2

ratio

eg

no. r

ed c

ount

ers i

s 30÷

2 (=

15)

A1

ft

1125

B1

cao

1237

.5 m

phP1

show

s pro

cess

of f

indi

ng fi

rst d

ista

nce

eg 5

0 ×

3 (=

150)

P1sh

ows p

roce

ss o

f fin

ding

tim

e fo

r sec

ond

part

eg 1

50 ÷

30

(=5

h)P1

show

s pro

cess

of w

orki

ng w

ith a

v sp

. (di

st ÷

tim

e) (=

300

÷(3+

5) =

300

÷8 )

C1

conc

lusi

on w

ith su

ppor

ting

evid

ence

, cor

rect

not

atio

n an

d un

its e

g 37

.5 m

ph

133

24

1k

m=

−M

1cl

ear f

ract

ions

or r

emov

e sq

rt si

gn

or3

(21)

(21)

mm

+−

M1

(dep

) cle

ar fr

actio

ns a

nd re

mov

e sq

rt si

gnA

13

24

1k

m=

−or

3(2

1)(2

1)m

m+

−

142 13−

M1

mul

tiplie

s all

term

s by

2 or

3 to

reco

ncile

frac

tions

M1

com

plet

e pr

oces

s of e

xpan

ding

bra

cket

s and

isol

atin

g x

term

A1

cao

152

5 5x x− +

M1

fact

oris

ing

to g

ive

(2x

− 5)

(x+

1)

M1

fact

oris

ing

to g

ive

(x+

5)(x

+ 1)

A1

cao



Pape

r 1M

A1:

1H

Que

stio

nW

orki

ngA

nsw

erN

otes

16D

, A, B

, CB

1fo

r atl

east

2 c

orre

ctB

1fo

r all

corr

ect

17SA

SM

1lin

ks P

QR

and

PR

Q (e

g is

osce

les t

riang

le) w

ith fu

ll re

ason

sM

1lin

ks T

R a

nd S

Q w

ith fu

ll re

ason

sC

1gi

ves f

ull c

oncl

usio

n fo

r con

grue

ncy

eg S

AS

1875π

P1st

arts

pro

cess

by

usin

g 25

0 3π

and

31

42

3r

π×

to fi

nd ra

dius

as 5

P1st

arts

pro

cess

usi

ng ½

cur

ved

surf

ace

area

eg

(4 ×

π×

52) ÷

2P1

com

plet

e pr

oces

s sho

wn

eg (4

× π

× 52

) ÷ 2

+ ( π

× 52

)A

1fo

r 75π

19√3

1M

1ex

pand

s bra

cket

s eg

36

+ 6√

5 –

6√5

−√25

(=3

1)M

1ra

tiona

lises

the

deno

min

ator

eg

usin

g √3

1 w

ith n

umer

ator

& d

enom

inat

orA

1fo

r √31



Pape

r 1M

A1:

1H

Que

stio

nW

orki

ngA

nsw

erN

otes

16D

, A, B

, CB

1fo

r atl

east

2 c

orre

ctB

1fo

r all

corr

ect

17SA

SM

1lin

ks P

QR

and

PR

Q (e

g is

osce

les t

riang

le) w

ith fu

ll re

ason

sM

1lin

ks T

R a

nd S

Q w

ith fu

ll re

ason

sC

1gi

ves f

ull c

oncl

usio

n fo

r con

grue

ncy

eg S

AS

1875π

P1st

arts

pro

cess

by

usin

g 25

0 3π

and

31

42

3r

π×

to fi

nd ra

dius

as 5

P1st

arts

pro

cess

usi

ng ½

cur

ved

surf

ace

area

eg

(4 ×

π×

52) ÷

2P1

com

plet

e pr

oces

s sho

wn

eg (4

× π

× 52

) ÷ 2

+ ( π

× 52

)A

1fo

r 75π

19√3

1M

1ex

pand

s bra

cket

s eg

36

+ 6√

5 –

6√5

−√25

(=3

1)M

1ra

tiona

lises

the

deno

min

ator

eg

usin

g √3

1 w

ith n

umer

ator

& d

enom

inat

orA

1fo

r √31

Pape

r 1M

A1:

1H

Que

stio

nW

orki

ngA

nsw

erN

otes

20pr

oof

M1

for a

ny tw

o co

nsec

utiv

e in

tege

rs

expr

esse

d al

gebr

aica

lly e

g n

+ 1

and

n

for s

ight

of p

2–

q2=

(p–

q)(p

+q)

(sup

porte

d)M

1(d

ep) f

or th

e di

ffer

ence

bet

wee

n th

e sq

uare

s of “

two

cons

ecut

ive

inte

gers

” ex

pres

sed

alge

brai

cally

eg

(n+

1)2

− n2

for d

educ

tion

that

p–

q=

1

A1

for c

orre

ct e

xpan

sion

and

si

mpl

ifica

tion

of d

iffer

ence

of

squa

res e

g 2

n+

1

for l

inki

ng th

ese

two

stat

emen

ts e

g su

bstit

utio

n of

1 fo

r p−

q

C1

for s

how

ing

stat

emen

t is c

orre

ct

(with

supp

ortiv

e ev

iden

ce)

eg n

+n

+ 1

= 2n

+ 1

and

(n+

1)2

− n2

= 2n

+ 1

for f

ully

stat

ed p

roof

and

ded

uctio

n eg

p2

–q2

= 1

× (p

+q)

= p

+q

212

1045x

x−

P1fo

r10x

or 10

10x

−or

1

9x−or

109

x−

or 9x

or 9

9x

−se

en o

n di

agra

m o

r

in a

cal

cula

tion

P1fo

r 10x

×10

9x

−or

1010

x−

×9x

for

10x×

19x−

+10

10x

−×

99

x−

P1fo

r 10x

×10

9x

−+

1010

x−

×9x

for 1

–( 10x

×1

9x−+

1010

x−

×9

9x

−)

P1fo

r beg

inni

ng to

pro

cess

the

alge

bra

A1

210

45xx

−oe



Total Marks

Paper Reference

Turn over


6/6/6/

*S49818A0124*



Time: 1 hour 30 minutes 1MA1/2HYou must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator.

Instructions




Information



Advice





Pape

r 1M

A1:

1H

Que

stio

nW

orki

ngA

nsw

erN

otes

22M

1st

ates

AB

as 6

b–

3aM

1fo

rAX

= ⅓

ABor

⅓“(

6b–

3a)”

or ft

to 2

b–

aM

1fo

r C

Y

=CB

+BY

= 6b

+ 5a

–b

(=5b

+ 5a

)M

1fo

r C

X

= 3a

+ “

2b –

a” o

r C

X

= 6b

− ⅔

“(6b

–3a

)”

(= 2

a+

2b)

C1

for

22

55

CY=

(5a

+ 5b

) = 2

(a+

b) =

CX

231

32

2y

x=−

+

P1fo

r a p

roce

ss to

find

the

grad

ient

of t

he li

ne A

B

P1(d

ep) f

or a

pro

cess

to fi

nd th

e gr

adie

nt o

f a p

erpe

ndic

ular

line

eg

use

of −

1/m

P1(d

ep o

n P2

) for

subs

titut

ion

of x

=5, y

=−1

A1

equa

tion

stat

ed o

e



Total Marks

Paper Reference

Turn over


6/6/6/

*S49818A0124*




Instructions




Information



Advice





Pape

r 1M

A1:

1H

Que

stio

nW

orki

ngA

nsw

erN

otes

22M

1st

ates

AB

as 6

b–

3aM

1fo

rAX

= ⅓

ABor

⅓“(

6b–

3a)”

or ft

to 2

b–

aM

1fo

r C

Y

=CB

+BY

= 6b

+ 5a

–b

(=5b

+ 5a

)M

1fo

r C

X

= 3a

+ “

2b –

a” o

r C

X

= 6b

− ⅔

“(6b

–3a

)”

(= 2

a+

2b)

C1

for

22

55

CY=

(5a

+ 5b

) = 2

(a+

b) =

CX

231

32

2y

x=−

+

P1fo

r a p

roce

ss to

find

the

grad

ient

of t

he li

ne A

B

P1(d

ep) f

or a

pro

cess

to fi

nd th

e gr

adie

nt o

f a p

erpe

ndic

ular

line

eg

use

of −

1/m

P1(d

ep o

n P2

) for

subs

titut

ion

of x

=5, y

=−1

A1

equa

tion

stat

ed o

e



3


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA




£1 = €1.34

£1 = $1.52



2

*S49818A0224*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA





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




5


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA



130 < h 140 1

140 < h 150 7

150 < h 160 8

160 < h 170 10

170 < h 180 4


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

(1)



1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)


12

10

8

6

4

2

0120 130 140 150 160 170 180 190

Height (h cm)

Frequency

4

*S49818A0424*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA





140

120

100

80


Months




7


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA



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







6

*S49818A0624*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA




(3)



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


20

15

10

5

09 am

Time of day

Distance in km

9.30 am 10 am 11am10.30 am



9


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

9 The diagram shows the positions of three points, A, B and C, on a map.

N

N

N

A

C

B

50°

The bearing of B from A is 070°

Angle ABC is 50° AB = CB

Work out the bearing of C from A.

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


8

*S49818A0824*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA


A B

D C

19cm

19cm

16cm



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




11


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

11 Finlay plays two tennis matches.

The probability that he will win a match and the probability that he will lose a match are shown in the probability tree diagram.

First match Second match

win

lose

0.7

0.3

win

lose

0.7

0.3

win

lose

0.7

0.3

(a) Work out the probability that Finlay wins both matches.

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

(2)

(b) Work out the probability that Finlay loses at least one match.

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

(2)


10

*S49818A01024*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

10 The graph shows the depth, d cm, of water in a tank after t seconds.

(a) Find the gradient of this graph.

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

(2)

(b) Explain what this gradient represents.

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

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

(1)


240

180

120

60

0

Time (t seconds)

Depth (d cm)

0 20 40 60 80 100 120 140



13


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

14 ABC and ABD are two right-angled triangles.

Angle BAC = angle ADB = 90°

AB = 13 cm DB = 5 cm

Work out the length of CB.

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


A

13cm

5cm BDC

12

*S49818A01224*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

12 (a) Find the reciprocal of 2.5

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

(1)

(b) Work out 4.3 tan 3923.4 _ 6.06

× °3

Give your answer correct to 3 significant figures.

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

(2)


13 Show that

(3x – 1)(x + 5)(4x – 3) = 12x3 + 47x2 – 62x + 15

for all values of x.

(Total of Question 13 is 3 marks)



13


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

14 ABC and ABD are two right-angled triangles.

Angle BAC = angle ADB = 90°

AB = 13 cm DB = 5 cm

Work out the length of CB.

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


A

13cm

5cm BDC

12

*S49818A01224*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

12 (a) Find the reciprocal of 2.5

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

(1)

(b) Work out 4.3 tan 3923.4 _ 6.06

× °3

Give your answer correct to 3 significant figures.

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

(2)


13 Show that

(3x – 1)(x + 5)(4x – 3) = 12x3 + 47x2 – 62x + 15

for all values of x.




15


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

16 The histogram gives information about house prices in a village in 2015

20 houses in the village have a price between £300000 and £400000

Work out the number of houses in the village with a price under £200000

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


Price (£ thousands)

Frequency density

0 100 200 300 400 500 600 700 800 900 1000

14

*S49818A01424*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

15 A pendulum of length L cm has time period T seconds. T is directly proportional to the square root of L.

The length of the pendulum is increased by 40%.

Work out the percentage increase in the time period.

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




17


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

19 Here is a right-angled triangle.

x

x – 2

All measurements are in centimetres. The area of the triangle is 2.5 cm2.

Find the perimeter of the triangle. Give your answer correct to 3 significant figures. You must show all of your working.

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


16

*S49818A01624*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

17 Here are the first 5 terms of a quadratic sequence.

1 3 7 13 21

Find an expression, in terms of n, for the nth term of this quadratic sequence.

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


18 f(x) = 3x2 – 2x – 8

Express f(x + 2) in the form ax2 + bx

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




19


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

21 The number of bees in a beehive at the start of year n is Pn. The number of bees in the beehive at the start of the following year is given by

Pn + 1 = 1.05(Pn – 250)

At the start of 2015 there were 9500 bees in the beehive.

How many bees will there be in the beehive at the start of 2018?

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


18

*S49818A01824*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

20 The graph shows information about the velocity, v m/s, of a parachutist t seconds after leaving a plane.

(a) Work out an estimate for the acceleration of the parachutist at t = 6

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m/s2

(2)

(b) Work out an estimate for the distance fallen by the parachutist in the first 12 seconds after leaving the plane. Use 3 strips of equal width.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m(3)


40

30

20

10

O

Time (seconds)

Velocity (m/s)

2 4 6 8 10 12

50

60

t

v



21


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

23 Here is a circle, centre O, and the tangent to the circle at the point P(4, 3) on the circle.

y

5

O– 5 5 x

– 5

P(4, 3)

Find an equation of the tangent at the point P.

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


20

*S49818A02024*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

22 D = xy

x = 99.7 correct to 1 decimal place. y = 67 correct to 2 significant figures.

Work out an upper bound for D.

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




23

*S49818A02324*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

BLANK PAGE

22

*S49818A02224*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

24 A, B and C are points on the circumference of a circle centre O.

A

O

CB

Prove that angle BOC is twice the size of angle BAC.





24

*S49818A02424*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

BLANK PAGE



24

*S49818A02424*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

BLANK PAGE

Pape

r 1M

A1:

2H

Que

stio

nW

orki

ngA

nsw

erN

otes

1𝑡𝑡

=𝑤𝑤−

113

M1

For i

sola

ting

term

in t,

eg.

3t=

w–

11 o

r di

vidi

ng a

ll te

rms b

y 3,

eg.

𝑤𝑤 3=

3𝑡𝑡 3+

11 3A

1fo

r 𝑡𝑡=

𝑤𝑤−11 3

oe

2Ja

rdin

s of P

aris

P1 P1 C1

corr

ect p

roce

ss to

con

vert

one

pric

e to

ano

ther

cu

rrec

ncy,

eg

1980

÷ 1

.34

for a

com

plet

e pr

oces

s lea

ding

to 3

pric

es in

the

sam

e cu

rren

cyfo

r 3 c

orre

ct a

nd c

onsi

sten

t res

ults

and

a c

orre

ct

com

paris

on m

ade.

3M

ean

of 9

6 or

ne

t dev

iatio

n of

0

so ta

rget

met

M1

M1

C1

for c

orre

ct in

terp

reta

tion

of th

e gr

aph,

with

at

leas

t one

cor

rect

read

ing

or a

line

dra

wn

thro

ugh

96 w

ith a

t lea

st o

ne c

orre

ct d

evia

tion

com

plet

e m

etho

d to

find

mea

n of

six

mon

ths

sale

s, eg

. (11

0+84

+78+

94+9

0+12

0)÷6

(= 9

6) o

r th

e m

ean

of si

x de

viat

ions

, eg

. (14

–12–

16–2

–6+2

4)÷6

(= 0

)fo

r a c

orre

ct a

nsw

er o

f 96

or 0

with

cor

rect

co

nclu

sion



Pape

r 1M

A1:

2H

Que

stio

nW

orki

ngA

nsw

erN

otes

4a b

160

< h

≤ 17

0

1. P

oint

s sho

uld

be p

lotte

d at

m

id-in

terv

al

valu

es2.

The

pol

ygon

sh

ould

not

be

clos

ed

B1

C1

C1

for i

dent

ifyin

g th

e co

rrec

t cla

ss in

terv

al

for a

cor

rect

err

or id

entif

ied

for a

cor

rect

err

or id

entif

ied

5a

grap

hM

1

C1

C1

for m

etho

d to

star

t to

find

dist

ance

cyc

led

in 3

6 m

ins,

eg. l

ine

draw

n of

cor

rect

gra

dien

t or

15×

36 60fo

r cor

rect

gra

ph fr

om 9

.00

am to

9.3

6 am

for g

raph

dra

wn

from

"(9

.36,

9)"

to

(10.

45, "

9" +

8)

b4.

5M

1A

1fo

r 18

× 0.

25oe

cao

681

12M

1A

1fo

r co

mpl

ete

met

hod,

eg.

750

0 ×

1.04

2

cao



Pape

r 1M

A1:

2H

Que

stio

nW

orki

ngA

nsw

erN

otes

4a b

160

< h

≤ 17

0

1. P

oint

s sho

uld

be p

lotte

d at

m

id-in

terv

al

valu

es2.

The

pol

ygon

sh

ould

not

be

clos

ed

B1

C1

C1

for i

dent

ifyin

g th

e co

rrec

t cla

ss in

terv

al

for a

cor

rect

err

or id

entif

ied

for a

cor

rect

err

or id

entif

ied

5a

grap

hM

1

C1

C1

for m

etho

d to

star

t to

find

dist

ance

cyc

led

in 3

6 m

ins,

eg. l

ine

draw

n of

cor

rect

gra

dien

t or

15×

36 60fo

r cor

rect

gra

ph fr

om 9

.00

am to

9.3

6 am

for g

raph

dra

wn

from

"(9

.36,

9)"

to

(10.

45, "

9" +

8)

b4.

5M

1A

1fo

r 18

× 0.

25oe

cao

681

12M

1A

1fo

r co

mpl

ete

met

hod,

eg.

750

0 ×

1.04

2

cao

Pape

r 1M

A1:

2H

Que

stio

nW

orki

ngA

nsw

erN

otes

7N

o w

ith

supp

ortin

g ev

iden

ce

P1 P1 C1

for t

he st

art o

f a c

orre

ct p

roce

ss, e

g. tw

o of

x, 2

xan

d 2x

+7 o

e or

a fu

lly c

orre

ct tr

ial,

eg. 5

+ 1

0 +

17 =

32

for s

ettin

g up

an

equa

tion

in x

.eg.

x+

2x+

2x+

7 =

57 o

r a c

orre

ct tr

ial t

otal

ling

57, e

g. 1

0 +

20

+ 27

= 5

7(d

ep o

n P2

) for

at l

east

one

cor

rect

resu

lt an

d fo

r a

corr

ect d

educ

tion

from

thei

r ans

wer

s fou

nd, e

g.

Chr

is h

as 2

0 so

it is

impo

ssib

le fo

r all

to h

ave

20

sinc

e 60

mar

bles

wou

ld b

e ne

eded

.

866

.9P1 P1 P1 A

1

for p

roce

ss to

find

the

area

of o

ne sh

ape,

eg.

19

×16

(= 3

04) o

r 𝜋𝜋×

82(=

201

.06.

..)fo

r pro

cess

to fi

nd th

e sh

aded

are

a, e

g. "3

04" –

"201

.06"

÷2

(= 2

03.4

6...)

for a

com

plet

e pr

oces

s to

find

requ

ired

perc

enta

ge, e

g. "2

03.46"

304

×10

0

for a

nsw

er in

rang

e 66

to 6

8

913

5B

1

P1 A1

for i

dent

ifyin

g th

e an

gle

of 7

0o(o

n th

e di

agra

m),

show

ing

unde

rsta

ndin

g of

not

atio

nfo

r pro

cess

to fi

nd a

n an

gle

in tr

iang

le A

BC,e

g.

for p

roce

ss to

find

ang

le B

AC, e

g. (1

80 –

50) ÷

2

(= 6

5o )fo

r 135



Pape

r 1M

A1:

2H

Que

stio

nW

orki

ngA

nsw

erN

otes

10a b

–1.5

M1

A1

C1

for m

etho

d to

find

gra

dien

t, eg

. 210

÷ 1

40fo

r cor

rect

inte

rpre

tatio

n of

the

nega

tive

grad

ient

for e

xpla

natio

n, e

g. ra

te o

f cha

nge

of d

epth

of

wat

er in

tank

11a b

0.49

0.51

M1

A1

M1

A1

for 0

.7 ×

0.7

for 0

.49

oe

for a

cor

rect

pro

cess

, eg.

1 –

"0.4

9"

or 0

.7 ×

0.3

+ 0

.3×

0.7

+ 0.

3 ×

0.3

for 0

.51

oe

12a b

0.4

0.58

6

B1

B1

B1

For 0

.4 o

e

for 3

.482

07...

.. or

17.

34 o

r 0.2

0081

1...

for 0

.585

to 0

.586

13Fu

lly c

orre

ct

alge

bra

to sh

ow

give

n re

sult

M1

M1

A1

for m

etho

d to

find

the

prod

uct o

f any

two

linea

r ex

pres

sion

s; e

g. 3

cor

rect

term

s or 4

term

s ig

norin

g si

gns

for m

etho

d of

6 p

rodu

cts,

4 of

whi

ch a

re c

orre

ct

(ft t

heir

first

pro

duct

)fo

r ful

ly a

ccur

ate

wor

king

to g

ive

the

requ

ired

resu

lt



Pape

r 1M

A1:

2H

Que

stio

nW

orki

ngA

nsw

erN

otes

10a b

–1.5

M1

A1

C1

for m

etho

d to

find

gra

dien

t, eg

. 210

÷ 1

40fo

r cor

rect

inte

rpre

tatio

n of

the

nega

tive

grad

ient

for e

xpla

natio

n, e

g. ra

te o

f cha

nge

of d

epth

of

wat

er in

tank

11a b

0.49

0.51

M1

A1

M1

A1

for 0

.7 ×

0.7

for 0

.49

oe

for a

cor

rect

pro

cess

, eg.

1 –

"0.4

9"

or 0

.7 ×

0.3

+ 0

.3×

0.7

+ 0.

3 ×

0.3

for 0

.51

oe

12a b

0.4

0.58

6

B1

B1

B1

For 0

.4 o

e

for 3

.482

07...

.. or

17.

34 o

r 0.2

0081

1...

for 0

.585

to 0

.586

13Fu

lly c

orre

ct

alge

bra

to sh

ow

give

n re

sult

M1

M1

A1

for m

etho

d to

find

the

prod

uct o

f any

two

linea

r ex

pres

sion

s; e

g. 3

cor

rect

term

s or 4

term

s ig

norin

g si

gns

for m

etho

d of

6 p

rodu

cts,

4 of

whi

ch a

re c

orre

ct

(ft t

heir

first

pro

duct

)fo

r ful

ly a

ccur

ate

wor

king

to g

ive

the

requ

ired

resu

lt

Pape

r 1M

A1:

2H

Que

stio

nW

orki

ngA

nsw

erN

otes

1433

.8P1 P1 A

1

for r

ecog

nitio

n of

sim

ilar t

riang

les o

r equ

al ra

tio

of si

des

for p

roce

ss to

find

CB,

eg.

5 13=

13 𝐶𝐶𝐶𝐶

for 3

3.8

1518

.3P1 P1 A

1

for a

star

t to

the

proc

ess i

nter

pret

ing

the

info

rmat

ion

corr

ectly

, eg.

T=

k √𝐿𝐿

oefo

r nex

t sta

ge in

pro

cess

to fi

nd p

erce

ntag

e ch

ange

inT,

eg.

√1.

4fo

r 18.

3 to

18.

4

1684

M1

P1 A1

for c

orre

ct in

terp

reta

tion

of g

iven

info

rmat

ion

lead

ing

to a

met

hod

to fi

nd fd

, eg.

20

÷ 10

0 (th

ousa

nd)

for s

tart

of p

roce

ss to

find

requ

ired

freq

uenc

y,

eg. 0

.8 ×

50 (=

40)

or 0

.6 ×

50 (=

30)

or 0

.14

×10

0 (=

14)

for 8

4 ca

o

17n2

–n

+ 1

oeM

1

M1

A1

for c

orre

ct d

educ

tion

from

diff

eren

ces,

eg. 2

nd

diff

eren

ce o

f 2 im

plie

s 1n2

or si

ght o

f 12,

22 , 32 , .

.fo

r sig

ht o

f 12,

22 , 32 , .

. lin

ked

with

1, 2

, 3, .

..

for n

2 –

n+

1 oe



Pape

r 1M

A1:

2H

Que

stio

nW

orki

ngA

nsw

erN

otes

183x

2+

10x

M1

M1

A1

star

t a c

hain

of r

easo

ning

, eg

. 3(x

+2)2

–2(

x+2)

–8

cont

inue

cha

in b

y ex

pand

ing

brac

kets

cor

rect

ly,

eg. 3

x2+

12x

+12

–2x

–4

–8

for

3x2

+ 1

0x(a

= 3,

b=

10)

198.

63 to

8.6

5P1 P1 P1 P1 P1

A

1

for a

star

t of p

roce

ss, e

g. 0

.5𝑥𝑥(𝑥𝑥−

2)=

2.5

for r

earr

angi

ng to

giv

e a

quad

ratic

equ

atio

n,eg

x2

–2x

–5

= 0

oe.

for a

pro

cess

to so

lve

the

quad

ratic

equ

atio

n,

cond

onin

g on

e si

gn e

rror

in u

se o

f for

mul

a (x

=3.

449.

.. an

d x

=–1

.449

...)

for s

elec

ting

the

posi

tive

valu

e of

xan

d ap

plyi

ng

Pyth

agor

as to

find

the

hypo

tenu

se,

eg.√

(3.4

492

+ 1.

4492 )

(= 3

.74.

..)

for c

ompl

ete

proc

ess t

o fin

d pe

rimet

erfo

r ans

wer

in th

e ra

nge

8.63

to 8

.65



Pape

r 1M

A1:

2H

Que

stio

nW

orki

ngA

nsw

erN

otes

183x

2+

10x

M1

M1

A1

star

t a c

hain

of r

easo

ning

, eg

. 3(x

+2)2

–2(

x+2)

–8

cont

inue

cha

in b

y ex

pand

ing

brac

kets

cor

rect

ly,

eg. 3

x2+

12x

+12

–2x

–4

–8

for

3x2

+ 1

0x(a

= 3,

b=

10)

198.

63 to

8.6

5P1 P1 P1 P1 P1

A

1

for a

star

t of p

roce

ss, e

g. 0

.5𝑥𝑥(𝑥𝑥−

2)=

2.5

for r

earr

angi

ng to

giv

e a

quad

ratic

equ

atio

n,eg

x2

–2x

–5

= 0

oe.

for a

pro

cess

to so

lve

the

quad

ratic

equ

atio

n,

cond

onin

g on

e si

gn e

rror

in u

se o

f for

mul

a (x

=3.

449.

.. an

d x

=–1

.449

...)

for s

elec

ting

the

posi

tive

valu

e of

xan

d ap

plyi

ng

Pyth

agor

as to

find

the

hypo

tenu

se,

eg.√

(3.4

492

+ 1.

4492 )

(= 3

.74.

..)

for c

ompl

ete

proc

ess t

o fin

d pe

rimet

erfo

r ans

wer

in th

e ra

nge

8.63

to 8

.65

Pape

r 1M

A1:

2H

Que

stio

nW

orki

ngA

nsw

erN

otes

20a b

3 to

4

452

C1

B1

C1

M1

A1

for a

tang

ent d

raw

n at

t=

6fo

r ans

wer

in ra

nge

3 to

4

for s

plitt

ing

the

area

into

3 st

rips a

nd a

met

hod

of

findi

ng th

e ar

ea o

f one

shap

e un

der t

he g

raph

, eg

. 1 2×

4×

35(=

70)

for c

ompl

ete

proc

ess t

o fin

d th

e ar

ea u

nder

the

grap

h, e

g "7

0" +

1 2×

4×

(35

+51

)(=

172

) +

1 2×

4×

(51

+54

)(=

210

) [ =

452

]

for 4

52

2110

169

or 1

0170

P1 P1 C1

for c

orre

ct u

se o

f for

mul

a to

find

num

ber i

n 20

16, e

g. 1

.05(

9500

–25

0) (

= 97

12.5

)fo

r com

plet

e ite

rativ

e pr

oces

s, eg

. 201

7:

1.0

5(97

12.5

–25

0) (

= 99

35.6

25)

2018

: 1

.05(

9935

.625

–25

0)

for a

nsw

er o

f 101

69.9

0...

corr

ectly

roun

ded

or

trunc

ated

to n

eare

st w

hole

num

ber

221.

5B

1

M1

A1

for a

ny c

orre

ct b

ound

cle

arly

iden

tifie

d,

eg. 9

9.65

→x

→ 9

9.75

or

66.

5 →

y→

67.

5fo

r met

hod

to fi

nd U

B, e

g. "

99.7

5" ÷

"66.

5"fo

r 1.5





Total Marks

Paper Reference

Turn over


6/6/6/

*S49820A0120*




Instructions




Information



Advice



Pape

r 1M

A1:

2H

Que

stio

nW

orki

ngA

nsw

erN

otes

23y

= −

4 3x

+ 25 3

oe

M1

M1

A1

for m

etho

d to

find

gra

dien

t of t

ange

nt,

eg. −

1÷

3 4=−

4 3

for m

etho

d to

find

y-in

terc

ept u

sing

y =

"−

4 3"x

+ c

y =

−4 3

x +

25 3

oe

24Pr

oof

C1

C1

C1

C1

for j

oini

ng A

O(e

xten

ded

to D

) and

con

side

ring

angl

es in

two

trian

gles

(alg

ebra

ic n

otat

ion

may

be

use

d he

re)

for u

sing

isos

cele

s tria

ngle

pro

perti

es to

find

an

gle

BOD

(eg.

x+

x=

2x)o

rang

le C

OD

(eg.

y+

y=

2y)

for a

ngle

BO

C=

2x+

2y[=

2×a

ngle

BAO

+ 2×

angl

e C

AO]

for c

ompl

etio

n of

pro

of w

ith a

ll re

ason

s giv

en,

eg. b

ase

angl

esof

isos

cele

stria

ngle

are

equ

alan

d su

m o

f ang

lesa

t a p

oint

is 3

60o



3


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA




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

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

(2)

A different student studies for 9 hours.

(c) Estimate the mark gained by this student.

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

(1)


Lucia says,



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

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

(1)




. . . . . . . . . . . . . . . . . . . . . . . . . . . L < . . . . . . . . . . . . . . . . . . . . . . . . . . . .


2

*S49820A0220*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA





For each student, it shows the number of hours spent revising and the mark the student achieved in the Spanish test.



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

(1)

100

90

80

70

60

50

40

30

20

10

02 4 6 8 10 12 14 16 18

Mark


0



5


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA




Small 28 < w 32 24

Medium 32 < w 36 12

Large 36 < w 40 8



.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .inches(3)







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

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

(2)


4

*S49820A0420*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA


yL

–2 2

–2

–4

4O x

10

8

6

4

2

Find the equation for the straight line L. Give your answer in the form y = mx + c

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




7


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA




(2)


6

*S49820A0620*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

5 The diagram shows a wall in the shape of a trapezium.

Karen is going to cover this part of the wall with tiles. Each tile is rectangular, 15 cm by 7.5 cm


Karen divides the area of this wall by the area of a tile to work out an estimate for the number of tiles she needs to buy.

(a) Use Karen’s method to work out the estimate for the number of packs of tiles she needs to buy.

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

(5)

0.8 m

1.8 m

2.7 m



9


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

8 Ian invested an amount of money at 3% per annum compound interest. At the end of 2 years the value of the investment was £2652.25

(a) Work out the amount of money Ian invested.

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

(3)

Noah has an amount of money to invest for five years.

Saver Account

4% per annum compound interest.

Investment Account

21% interest paid at the end of 5 years.

Noah wants to get the most interest possible.

(b) Which account is best? You must show how you got your answer.

(2)


8

*S49820A0820*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA


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




Two of these lines are parallel.

Write down the two parallel lines?

Line .. . . . . . . . . . . . . . . . . . . . . . . . . . . and line.. . . . . . . . . . . . . . . . . . . . . . . . . . .




11


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

10 On the grid, shade the region that satisfies all these inequalities.

x + y < 4 y > x – 1 y < 3x

Label the region R.


O

10

8

6

4

2

–2

–4

y

x–4 –2 2 4 6

10

*S49820A01020*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

9 The diagram shows two vertical posts, AB and CD, on horizontal ground.

AB = 1.7 m CD : AB = 1.5 : 1

The angle of elevation of C from A is 52°

Calculate the length of BD. Give your answer correct to 3 significant figures.

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


1.7 m

C

A

BD



13


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

12 The diagram shows a cuboid ABCDEFGH.

AB = 7 cm, AF = 5 cm and FC = 15 cm.

Calculate the volume of the cuboid. Give your answer correct to 3 significant figures.

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


F

C

H

E

DG

B

A

12

*S49820A01220*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

11 Write x 2 + 2x – 8 in the form (x + m ) 2 + n where m and n are integers.

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




15


D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

15 A virus on a computer is causing errors. An antivirus program is run to remove these errors.

An estimate for the number of errors at the end of t hours is 106 × 2−t

(a) Work out an estimate for the number of errors on the computer at the end of 8 hours.

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

(2)

(b) Explain whether the number of errors on this computer ever reaches zero.

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

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

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

(1)


16 The graph of y = f (x) is transformed to give the graph of y = −f (x + 3) The point A on the graph of y = f (x) is mapped to the point P on the graph of y = −f (x + 3)

The coordinates of point A are (9, 1) Find the coordinates of point P.

(. . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . .)


14

*S49820A01420*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

13 There are 14 boys and 12 girls in a class.

Work out the total number of ways that 1 boy and 1 girl can be chosen from the class.

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


14 Write

4 3 5 62

2

− +( ) + +−

x x x

x÷

as a single fraction in its simplest form. You must show your working.

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




17

*S49820A01720*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

Turn over

18 Thelma spins a biased coin twice. The probability that it will come down heads both times is 0.09

Calculate the probability that it will come down tails both times.

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


19 (a) Write 0.000 423 in standard form.

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

(1)

(b) Write 4.5 × 104 as an ordinary number.

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

(1)


16

*S49820A01620*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

17 The diagram shows a solid cone.

Volume of cone = 13

πr 2h

Curved surface area of cone = πrl

l

r

h

16 x

24 x

The diameter of the base of the cone is 24x cm. The height of the cone is 16x cm.

The curved surface area of the cone is 2160π cm2. The volume of the cone is Vπ cm3, where V is an integer.

Find the value of V.

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




19

*S49820A01920*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

Turn over

21 (a) Show that the equation 3x2 – x3 + 3 = 0 can be rearranged to give

xx

= +3 32

(2)

(b) Using

xxnn

+ = +1 23 3 with x0 = 3.2,

find the values of x1, x2 and x3

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

(3)

(c) Explain what the values of x1, x2 and x3 represent.

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

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

(1)


18

*S49820A01820*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

20 Mark has made a clay model. He will now make a clay statue that is mathematically similar to the clay model.

The model has a base area of 6cm2 The statue will have a base area of 253.5cm2

Mark used 2kg of clay to make the model.

Clay is sold in 10kg bags. Mark has to buy all the clay he needs to make the statue.

How many bags of clay will Mark need to buy?

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




20

*S49820A02020*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

22 Here are the first five terms of an arithmetic sequence.

7 13 19 25 31

Prove that the difference between the squares of any two terms of the sequence is always a multiple of 24





20

*S49820A02020*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

22 Here are the first five terms of an arithmetic sequence.

7 13 19 25 31

Prove that the difference between the squares of any two terms of the sequence is always a multiple of 24



Pape

r 1M

A1:

3H

Que

stio

nW

orki

ngA

nsw

erN

otes

1(a)

1(b)

(i)

1(b)

(ii)

1(c)

1(d)

(4,1

0)

Line

dra

wn

Posi

tive

Val

ue b

etw

een

60

and7

0

Stat

emen

t

B1

cao

B1

Stra

ight

line

dra

wn

pass

ing

bet

wee

n (2

,20)

and

(2,3

0) A

ND

(13,

86) a

nd (1

3,94

)

C1

posi

tive

C1

a co

rrec

t val

ue g

iven

C1

for r

efer

ring

to th

e da

nger

of e

xtra

pola

tion

outs

ide

the

give

n

rang

e or

for a

giv

en p

oint

Eg li

ne o

f bes

t fit

may

not

con

tinue

or f

ull m

arks

are

har

d to

ac

hiev

e no

mat

ter h

ow m

uch

revi

sion

is d

one

212

.5≤

L<

13.5

B1

12.5

B1

13.5

3𝑦𝑦

=2𝑥𝑥

+1

M1

for a

met

hod

to fi

nd th

e gr

adie

ntM

1 fo

r a m

etho

d to

find

the

c in

y=

mx

+ c

A1 𝑦𝑦

=2𝑥𝑥

+1

oe in

this

form

at

4(a)

(720

+408

+304

+252

)÷50

33.6

8M

1 fo

r fin

ding

4 pr

oduc

ts fw

cons

iste

ntly

with

in in

terv

al

(incl

udin

g en

d po

ints

)M

1 (d

ep o

n 1s

t M) f

or 'Ʃ

ftw÷5

0A

1 ca

o



Pape

r 1M

A1:

3H

Que

stio

nW

orki

ngA

nsw

erN

otes

4(b)

Man

ager

with

re

ason

sM

1 fo

r stra

tegy

to c

ompa

re n

umbe

r of s

mal

l siz

e so

ld to

num

ber

orde

red

C1

clea

r com

paris

on th

at sm

all s

ize

is n

ot ¾

and

so Je

nny

is n

ot

corr

ect o

r the

man

ager

is c

orre

ct

5(a)

5(b)

160

tiles

18 p

acks

176

tiles

20

pac

ks

18 Supp

orte

d st

atem

ent

M1

a fu

ll m

etho

d to

find

the

area

of t

he tr

apez

ium

M1

a fu

ll m

etho

d to

con

vert

all a

reas

to c

onsi

sten

t uni

tsM

1 fo

r the

are

a of

the

trape

zium

÷ar

ea o

f a ti

leM

1 fo

r com

mun

icat

ion

of th

e nu

mbe

r of w

hole

pac

ks re

quire

dA

1

P1 fi

ndin

g th

at 1

0% e

xtra

requ

ires t

wo

mor

e pa

cks o

r 10%

of 1

8C

1Sta

tem

ent e

g in

crea

se in

pac

ks is

2 m

ore

whi

ch is

mor

e th

an

10%

6( 𝑥𝑥−

1)( 𝑥𝑥

+4)

M1

( 𝑥𝑥±

1)( 𝑥𝑥

±4)

A1

( 𝑥𝑥−

1)(𝑥𝑥

+4)

oe

7A

and

DC

1 in

any

ord

er

8(a)

8(b)

2500

Save

r acc

ount

w

ith su

ppor

t

P1 fo

r use

of 1

.03

P1 fo

r a fu

ll m

etho

d eq

uiva

lent

to ÷

1.03

²A

1 25

00

P1 p

roce

ss to

find

a c

ompa

rabl

e to

tal i

nter

est f

igur

e A

1 fo

r con

clus

ion

with

supp

ortin

g st

atem

ent e

g 21

.(665

..)>2

1

90.

664(

09..)

P1 fo

r fin

ding

the

diff

eren

ce in

hei

ght b

y ra

tio o

r mul

tiplie

rP1

for u

se o

f tan

ratio

P1 (d

ep) f

or 0

.85÷

tan5

2 A

1 aw

rt0.

664



Pape

r 1M

A1:

3H

Que

stio

nW

orki

ngA

nsw

erN

otes

4(b)

Man

ager

with

re

ason

sM

1 fo

r stra

tegy

to c

ompa

re n

umbe

r of s

mal

l siz

e so

ld to

num

ber

orde

red

C1

clea

r com

paris

on th

at sm

all s

ize

is n

ot ¾

and

so Je

nny

is n

ot

corr

ect o

r the

man

ager

is c

orre

ct

5(a)

5(b)

160

tiles

18 p

acks

176

tiles

20

pac

ks

18 Supp

orte

d st

atem

ent

M1

a fu

ll m

etho

d to

find

the

area

of t

he tr

apez

ium

M1

a fu

ll m

etho

d to

con

vert

all a

reas

to c

onsi

sten

t uni

tsM

1 fo

r the

are

a of

the

trape

zium

÷ar

ea o

f a ti

leM

1 fo

r com

mun

icat

ion

of th

e nu

mbe

r of w

hole

pac

ks re

quire

dA

1

P1 fi

ndin

g th

at 1

0% e

xtra

requ

ires t

wo

mor

e pa

cks o

r 10%

of 1

8C

1Sta

tem

ent e

g in

crea

se in

pac

ks is

2 m

ore

whi

ch is

mor

e th

an

10%

6( 𝑥𝑥−

1)( 𝑥𝑥

+4)

M1

( 𝑥𝑥±

1)( 𝑥𝑥

±4)

A1

( 𝑥𝑥−

1)(𝑥𝑥

+4)

oe

7A

and

DC

1 in

any

ord

er

8(a)

8(b)

2500

Save

r acc

ount

w

ith su

ppor

t

P1 fo

r use

of 1

.03

P1 fo

r a fu

ll m

etho

d eq

uiva

lent

to ÷

1.03

²A

1 25

00

P1 p

roce

ss to

find

a c

ompa

rabl

e to

tal i

nter

est f

igur

e A

1 fo

r con

clus

ion

with

supp

ortin

g st

atem

ent e

g 21

.(665

..)>2

1

90.

664(

09..)

P1 fo

r fin

ding

the

diff

eren

ce in

hei

ght b

y ra

tio o

r mul

tiplie

rP1

for u

se o

f tan

ratio

P1 (d

ep) f

or 0

.85÷

tan5

2 A

1 aw

rt0.

664

Pape

r 1M

A1:

3H

Que

stio

nW

orki

ngA

nsw

erN

otes

10R

egio

n R

M1

for o

ne li

ne c

orre

ctly

dra

wn

M1

for t

wo

or m

ore

lines

cor

rect

ly d

raw

nA

1 fo

r a c

orre

ct re

gion

indi

cate

d be

twee

n tw

o co

rrec

t lin

esA

1 fu

lly c

orre

ct re

gion

indi

cate

d w

ith a

ll lin

es c

orre

ct

11(𝑥𝑥

+1)

²−9

M1

for (𝑥𝑥

+1)

²A

1 ca

o

1243

1B

1 fo

r use

of P

ytha

gora

s inv

olvi

ng th

e un

know

n le

ngth

P1

for s

ettin

g up

an

equa

tion

equi

vale

nt to

𝑥𝑥²

=15

²−5²−

7²P1

for f

indi

ng th

e vo

lum

e us

ing

thei

r “�

15²−

5²−

7²A

1aw

rt 43

0.5

1316

8M

1 pr

oduc

t of 1

4 an

d 12

A1

cao

143𝑥𝑥

+10

𝑥𝑥+

2B

1 fo

r fac

toris

ing

to g

et ( 𝑥𝑥

+3)

(𝑥𝑥+

2)M

1 fo

r dea

ling

with

the

divi

sion

of (𝑥𝑥

+3)

by 𝑥𝑥

²+5𝑥𝑥+6

𝑥𝑥−2

M1

for t

wo

corr

ect f

ract

ions

with

a c

omm

on d

enom

inat

or o

r a

corr

ect s

ingl

e fr

actio

nA

1 3𝑥𝑥+10

𝑥𝑥+2

15(a

)

15(b

)

3906

Dec

isio

n

P1 1

000

000

÷25

6A

1 39

06 o

r 390

7 or

390

0or

390

6.25

C1

Dec

isio

n an

d su

ppor

ting

stat

emen

tEg

no

neve

r zer

o or

yes

can

not h

ave

a pa

rt er

ror

Not

e ju

st y

es o

r no

will

scor

e ze

ro



Pape

r 1M

A1:

3H

Que

stio

nW

orki

ngA

nsw

erN

otes

16(6

, −1)

M1

for a

met

hod

show

ing

the

trans

latio

n of

a g

raph

or a

cor

rect

co

ordi

nate

A1

cao

17𝑙𝑙=

20𝑥𝑥

𝑥𝑥=

320

736

P1 fo

r a m

etho

d to

find

the

slan

t hei

ght o

f the

con

e eg

�

16𝑥𝑥²

+12𝑥𝑥²

or b

y si

mila

r tria

ngle

s and

Pyt

hago

rean

trip

les

P1 fo

r set

ting

up a

n eq

uatio

n fo

r the

cur

ved

surf

ace

area

in te

rms

of x

eg 2

160𝜋𝜋

=𝜋𝜋

×12𝑥𝑥

×20𝑥𝑥

P1 fo

r com

plet

e m

etho

d to

find

the

valu

e of

xP1

for a

met

hod

to fi

nd th

e vo

lum

eA

1 c

ao

180.

49P1

for √

0.09

P1 fo

r (1-

" √0.

09")

²A

1 ca

o

19(a

)

(b)

4.23

× 1

0-4

4500

0

B1

B1

2055

P1 fo

r 25

3.5

6(=

6.5)

P1 fo

r 2 ×

“6.

5”3

÷ 10

(=54

.925

)A

1 ca

o



Pape

r 1M

A1:

3H

Que

stio

nW

orki

ngA

nsw

erN

otes

16(6

, −1)

M1

for a

met

hod

show

ing

the

trans

latio

n of

a g

raph

or a

cor

rect

co

ordi

nate

A1

cao

17𝑙𝑙=

20𝑥𝑥

𝑥𝑥=

320

736

P1 fo

r a m

etho

d to

find

the

slan

t hei

ght o

f the

con

e eg

�

16𝑥𝑥²

+12𝑥𝑥²

or b

y si

mila

r tria

ngle

s and

Pyt

hago

rean

trip

les

P1 fo

r set

ting

up a

n eq

uatio

n fo

r the

cur

ved

surf

ace

area

in te

rms

of x

eg 2

160𝜋𝜋

=𝜋𝜋

×12𝑥𝑥

×20𝑥𝑥

P1 fo

r com

plet

e m

etho

d to

find

the

valu

e of

xP1

for a

met

hod

to fi

nd th

e vo

lum

eA

1 c

ao

180.

49P1

for √

0.09

P1 fo

r (1-

" √0.

09")

²A

1 ca

o

19(a

)

(b)

4.23

× 1

0-4

4500

0

B1

B1

2055

P1 fo

r 25

3.5

6(=

6.5)

P1 fo

r 2 ×

“6.

5”3

÷ 10

(=54

.925

)A

1 ca

o

Pape

r 1M

A1:

3H

Que

stio

nW

orki

ngA

nsw

erN

otes

21(a

)

21(b

)

21(c

)

𝑥𝑥 1=

3.29

2968

75𝑥𝑥 2

= 3.

2766

5978

6𝑥𝑥 3

= 3.

2794

2068

5

Re

arra

ngem

ent

3.28

Stat

emen

t

M1

for r

e ar

rang

ing

to 𝑥𝑥

3=

C1

a cl

ear s

tep

to sh

ow re

arr

ange

men

t

M1

for o

ne c

orre

ct it

erat

ion

M1

for 2

furth

er it

erat

ions

seen

A1

cao

C1

Stat

emen

t eg

itera

tion

is an

est

imat

ion

of th

e so

lutio

n

22Pr

oof

B1

stat

e th

e di

ffer

ence

of t

wo

squa

res i

n al

gebr

aic

nota

tion

eg

𝑝𝑝²−𝑞𝑞²

M1

for w

ritin

g do

wn

expr

essi

ons f

or th

e tw

o di

ffer

ent n

umbe

rs

eg 6𝑛𝑛

+1

and

6𝑚𝑚+

1M

1 fo

rexp

andi

ng o

ne b

rack

et to

obt

ain

4 te

rms w

ith a

ll 4

corr

ect w

ithou

t con

side

ring

sign

s or f

or 3

term

s out

of 4

cor

rect

w

ith c

orre

ct si

gns

A1

for 3

6(𝑚𝑚2−𝑛𝑛2

) +12

(𝑛𝑛−𝑚𝑚

)oe

M1

(dep

M2)

for e

xtra

ctin

g a

fact

or o

f 12

from

thei

r exp

ress

ion

C1

for f

ully

cor

rect

wor

king

with

stat

emen

t jus

tifyi

ng(𝑛𝑛−𝑚𝑚

)(3(𝑛𝑛

+𝑚𝑚

) +1)

as a

mul

tiple

of 2

egco

nsid

erin

g od

d an

d ev

en c

ombi

natio

ns

GCSE (9-1) Mathematics - GCSE Revisionmaths.st-chads.co.uk/images/zoo/uploads/GCSE 9-1 Maths...

Documents

Transcript of GCSE (9-1) Mathematics - GCSE Revisionmaths.st-chads.co.uk/images/zoo/uploads/GCSE 9-1 Maths...