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INTERNATIONAL GCSEMathematics (Specifi cation A) (9-1)SAMPLE ASSESSMENT MATERIALSPearson Edexcel International GCSE in Mathematics (Specifi cation A) (4MA1)

For fi rst teaching September 2016First examination June 2018Issue 2

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Acknowledgements References to third party material made in the sample assessment materials 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 the sample assessment materials is correct at time of going to publication. ISBN 978 1 446 95560 4 All the material in this publication is copyright © Pearson Education Limited 2017

Summary of Pearson Edexcel International GCSE in Mathematics A SAMs Issue 2 changes

Summary of changes made between previous issue and this current issue

Page number/s

Paper codes 4MA1/3H changed to 4MA1/1H Contents page, 67, 87,

Paper codes 4MA1/4H changed to 4MA1/2H Contents page, 99, 123

Earlier issues show previous changes.

If you need further information on these changes or what they mean, contact us via our website at: qualifications.pearson.com/en/support/contact-us.html.

Contents

Introduction 1

General marking guidance 3

Foundation Tier: Paper 1F – sample question paper 5

Foundation Tier: Paper 1F – sample mark scheme 25

Foundation Tier: Paper 2F – sample question paper 35

Foundation Tier: Paper 2F – sample mark scheme 59

Higher Tier: Paper 1H – sample question paper 67

Higher Tier: Paper 1H – sample mark scheme 87

Higher Tier: Paper 2H – sample question paper 99

Higher Tier: Paper 2H – sample mark scheme 123

Introduction

The Pearson Edexcel International GCSE in Mathematics (Specification A) is designed for use in schools and colleges. It is part of a suite of International GCSE qualifications offered by Pearson. These sample assessment materials have been developed to support this qualification and will be used as the benchmark to develop the assessment students will take.

1Pearson Edexcel International GCSE in Mathematics (Specification A) – Sample Assessment Materials (SAMs) Issue 2 – November 2017 © Pearson Education Limited 2017

2 Pearson Edexcel International GCSE in Mathematics (Specification A) – Sample Assessment Materials (SAMs) Issue 2 – November 2017 © Pearson Education Limited 2017

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

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

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

Examiners should mark according to the mark scheme not according to their perception of where the grade boundaries may lie.

There is no ceiling on achievement. All marks on the mark scheme should be used appropriately.

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

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

When examiners are in doubt regarding the application of the mark scheme to a

candidate’s response, the team leader must be consulted. Crossed out work should be marked UNLESS the candidate has replaced it with an

alternative response.


Centre Number Candidate Number

Write your name hereSurname Other names

Total Marks

Paper Reference

Turn over

S51830A©2016 Pearson Education Ltd.

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Mathematics ALevel 1/2Paper 1F

Foundation TierSample assessment material for first teaching September 2016

Time: 2 hours

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

Instructions

• Use black ink or ball-point pen.• Fill in the boxes at the top of this page with your name, centre number and candidate number.• Answer all questions.• Without sufficient working, correct answers may be awarded no marks.• Answer the questions in the spaces provided – there may be more space than you need.• Calculators may be used.• You must NOT write anything on the formulae page. Anything you write on the formulae page will gain NO credit.

Information

• The total mark for this paper is 100. • The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.

Advice

• Read each question carefully before you start to answer it.• Check your answers if you have time at the end.

4MA1/1F

Pearson Edexcel International GCSE




Total Marks

Paper Reference

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1/1/

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Time: 2 hours


Instructions


Information


Advice


4MA1/1F



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International GCSE MathematicsFormulae sheet – Foundation Tier

Area of trapezium = 12

(a + b)h

b

a

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Volume of prism = area of cross section × length

cross section

length

Volume of cylinder = πr2h

Curved surface area of cylinder = 2πrh

r

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Answer ALL TWENTY FIVE questions.

Write your answers in the spaces provided.

You must write down all stages in your working.

1 Here is a list of numbers.

2 8 15 24 31 36 40 64

From this list, write down

(a) an odd number

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

(1)

(b) a multiple of 6

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

(1)

(c) a square number

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

(1)

(d) a prime number

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

(1)

(Total for Question 1 is 4 marks)

2 (a) Write 64% as a fraction.

Give your fraction in its simplest form.

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

(2)

(b) Write 9% as a decimal.

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

(1)

(c) Work out 16

of 84 kg.

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



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(a + b)h

b

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cross section

length



r

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1 Here is a list of numbers.

2 8 15 24 31 36 40 64

From this list, write down

(a) an odd number

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

(1)

(b) a multiple of 6

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

(1)

(c) a square number

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

(1)

(d) a prime number

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

(1)


2 (a) Write 64% as a fraction.

Give your fraction in its simplest form.

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

(2)

(b) Write 9% as a decimal.

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

(1)

(c) Work out 16

of 84 kg.

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



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3 The pictogram shows some information about the number of calculators sold in a shop on each of five days.

Monday

Tuesday

Wednesday

Thursday

Friday

(a) On which day did the shop sell the greatest number of calculators?

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

(1)

The shop sold 24 calculators on Wednesday.

(b) Find the number of calculators sold on Thursday.

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

(2)

(c) Find the ratio of the number of calculators sold on Tuesday to the number of calculators sold on Friday.

Give your ratio in its simplest form.

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

(2)


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4 Here are the first five terms of a number sequence.

2 6 10 14 18

(a) Write down the next two terms of the sequence.

.. . . . . . . . . . . . . . . . . . . . . . . . . . ., . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) Explain how you worked out your answer.

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

(1)

(c) Find the 11th term of the sequence.

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

(1)

(d) Explain why 95 cannot be a term of the sequence.

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

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(1)



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3 The pictogram shows some information about the number of calculators sold in a shop on each of five days.

Monday

Tuesday

Wednesday

Thursday

Friday

(a) On which day did the shop sell the greatest number of calculators?

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

(1)

The shop sold 24 calculators on Wednesday.

(b) Find the number of calculators sold on Thursday.

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

(2)

(c) Find the ratio of the number of calculators sold on Tuesday to the number of calculators sold on Friday.

Give your ratio in its simplest form.

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

(2)


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4 Here are the first five terms of a number sequence.

2 6 10 14 18

(a) Write down the next two terms of the sequence.

.. . . . . . . . . . . . . . . . . . . . . . . . . . ., . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) Explain how you worked out your answer.

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

(1)

(c) Find the 11th term of the sequence.

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

(1)

(d) Explain why 95 cannot be a term of the sequence.

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

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(1)



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5 The diagram shows a shaded shape drawn on a centimetre grid and a line AB.

A

B

(a) Write down the order of rotational symmetry of the shape.

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

(1)

(b) Work out the perimeter of the shape.

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

(c) Work out the area of the shape.

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

(1)

(d) Reflect the shape in the line AB.(2)


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6 Rhianna has £25 to spend on plants. Each plant costs £3.95 She buys as many plants as she can.

How much change should Rhianna receive from £25?

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


7 (a) Simplify 8c + 7m – 5c + 2m

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

(2)

(b) Solve 5x – 9 = 4

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

(2)



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5 The diagram shows a shaded shape drawn on a centimetre grid and a line AB.

A

B

(a) Write down the order of rotational symmetry of the shape.

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

(1)

(b) Work out the perimeter of the shape.

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

(c) Work out the area of the shape.

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

(1)

(d) Reflect the shape in the line AB.(2)


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6 Rhianna has £25 to spend on plants. Each plant costs £3.95 She buys as many plants as she can.

How much change should Rhianna receive from £25?

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


7 (a) Simplify 8c + 7m – 5c + 2m

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

(2)

(b) Solve 5x – 9 = 4

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

(2)



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8 This rule can be used to work out the shortest distance from the screen a viewer should sit to watch TV.

Multiply the width of the screen by 3

Greg is going to watch his TV. The width of the screen is 65 cm.

(a) Work out the shortest distance from the screen he should sit.

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

Rashida is going to watch her TV. The shortest distance from the screen she should sit is 249 cm.

(b) Work out the width of the screen.

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

The width of a TV screen is w cm. The shortest distance from the screen a viewer should sit to watch this TV is d cm.

(c) Write down a formula for d in terms of w.

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

(2)


9


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9 ABC is an isosceles triangle.

A

BCD

132°

Diagram NOT accurately drawn

DCB is a straight line. AC = AB. Angle DCA = 132°

Work out the size of angle CAB. Give a reason for each stage in your working.

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



8

*S51830A0820*

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8 This rule can be used to work out the shortest distance from the screen a viewer should sit to watch TV.

Multiply the width of the screen by 3

Greg is going to watch his TV. The width of the screen is 65 cm.

(a) Work out the shortest distance from the screen he should sit.

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

Rashida is going to watch her TV. The shortest distance from the screen she should sit is 249 cm.

(b) Work out the width of the screen.

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

The width of a TV screen is w cm. The shortest distance from the screen a viewer should sit to watch this TV is d cm.

(c) Write down a formula for d in terms of w.

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

(2)


9


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9 ABC is an isosceles triangle.

A

BCD

132°


DCB is a straight line. AC = AB. Angle DCA = 132°

Work out the size of angle CAB. Give a reason for each stage in your working.

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



10

*S51830A01020*

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10

0.8 m

depth


0.3m

A fish tank is in the shape of a cuboid. The length of the fish tank is 0.8 m and the width is 0.3 m. The volume of water in the fish tank is 108 litres.

1 m3 = 1000 litres.

Work out the depth of the water in the fish tank.

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


11 (a) Work out the value of 51 7 2 89 3. .×+

Write down all the figures on your calculator display.

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

(2)

(b) Give your answer to part (a) correct to 3 significant figures.

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

(1)


11


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12 On the grid, draw the graph of y = 3x – 4 for values of x from −2 to 3

x

y

4

5

6

3

2

1

1 2 3O

–1

–2

–3

–4

–5

–6

–7

–8

–9

–10

–11

–12

–2 –1



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10

0.8 m

depth


0.3m

A fish tank is in the shape of a cuboid. The length of the fish tank is 0.8 m and the width is 0.3 m. The volume of water in the fish tank is 108 litres.

1 m3 = 1000 litres.

Work out the depth of the water in the fish tank.

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


11 (a) Work out the value of 51 7 2 89 3. .×+

Write down all the figures on your calculator display.

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

(2)

(b) Give your answer to part (a) correct to 3 significant figures.

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

(1)


11


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12 On the grid, draw the graph of y = 3x – 4 for values of x from −2 to 3

x

y

4

5

6

3

2

1

1 2 3O

–1

–2

–3

–4

–5

–6

–7

–8

–9

–10

–11

–12

–2 –1



12

*S51830A01220*

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13 A box contains four different kinds of sweets. Debbie takes at random a sweet from the box. The table shows the probabilities that Debbie takes an orange sweet or a cola sweet or a

lemon sweet.

Sweet Probability

orange 0.15

cola 0.40

lemon 0.35

strawberry

(a) Work out the probability that Debbie takes a strawberry sweet.

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

(2)

There are 40 sweets in the box.

(b) How many of the sweets in the box are lemon?

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

(2)


14 (a) Expand 5(2g + 7)

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

(1)

x is an integer.

(b) Write down all the values of x that satisfy −3 < x 2

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

(2)


13


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15 Anil lives in England. He does a search on the internet and sees the same type of camera on sale in Spain and in

America.

In Spain, the camera costs 149 euros. In America, the camera costs $164.78

Anil finds out these exchange rates.

Exchange rates

1 euro = £0.76

£1 = $1.54

How much cheaper is the camera in America than in Spain? Give your answer in pounds (£).

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



12

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13 A box contains four different kinds of sweets. Debbie takes at random a sweet from the box. The table shows the probabilities that Debbie takes an orange sweet or a cola sweet or a

lemon sweet.

Sweet Probability

orange 0.15

cola 0.40

lemon 0.35

strawberry

(a) Work out the probability that Debbie takes a strawberry sweet.

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

(2)

There are 40 sweets in the box.

(b) How many of the sweets in the box are lemon?

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

(2)


14 (a) Expand 5(2g + 7)

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

(1)

x is an integer.

(b) Write down all the values of x that satisfy −3 < x 2

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

(2)


13


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15 Anil lives in England. He does a search on the internet and sees the same type of camera on sale in Spain and in

America.

In Spain, the camera costs 149 euros. In America, the camera costs $164.78

Anil finds out these exchange rates.

Exchange rates

1 euro = £0.76

£1 = $1.54

How much cheaper is the camera in America than in Spain? Give your answer in pounds (£).

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



14

*S51830A01420*

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16 Yoko flew on a plane from Tokyo to Sydney. The plane flew a distance of 7800 km. The flight time was 9 hours 45 minutes.

Work out the average speed of the plane in kilometres per hour.

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


17 Penny, Amjit and James share some money in the ratio 3 : 6 : 4 Amjit gets $28 more than James.

Work out the amount of money that Penny gets.

$.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


15


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18 A factory has 60 workers.

The table shows information about the distances, in km, the workers travel to the factory each day.

Distance (d km) Frequency

0 < d 5 12

5 < d 10 6

10 < d 15 4

15 < d 20 6

20 < d 25 14

25 < d 30 18

(a) Write down the modal class.

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

(1)

(b) Work out an estimate for the mean distance travelled to the factory each day.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .km(4)

One of these workers is chosen at random.

(c) Write down the probability that this worker travels more than 20 km to the factory each day.

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

(2)



14

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


17 Penny, Amjit and James share some money in the ratio 3 : 6 : 4 Amjit gets $28 more than James.


$.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


15


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0 < d 5 12

5 < d 10 6

10 < d 15 4

15 < d 20 6

20 < d 25 14

25 < d 30 18


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

(1)


.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .km(4)



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

(2)



16

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19 Nigel bought 12 boxes of melons. He paid $15 for each box. There were 12 melons in each box.

Nigel sold 34

of the melons for $1.60 each.

He sold all the other melons at a reduced price.

He made an overall profit of 15%

Work out how much Nigel sold each reduced price melon for.

$.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


17


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20 Use ruler and compasses to construct the bisector of angle ABC. You must show all your construction lines.

A

B

C


21 (a) Factorise fully 18e3f + 45e2f 4

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

(2)

(b) Solve x2 – 4x – 12 = 0 Show clear algebraic working.

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

(3)



16

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Nigel sold 34

of the melons for $1.60 each.




$.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


17


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A

B

C



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

(2)


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

(3)



18

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22

QR

P

35°


17.6 cm

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

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


23 In a sale, all normal prices are reduced by 15% The normal price of a mixer is reduced by 22.50 dollars.

Work out the normal price of the mixer.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .dollars


19


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24 The table shows the diameters, in kilometres, of five planets.

Planet Diameter (km)

Venus 1.2 × 104

Jupiter 1.4 × 105

Neptune 5.0 × 104

Mars 6.8 × 103

Saturn 1.2 × 105

(a) Write 1.4 × 105 as an ordinary number.

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

(1)

(b) Which of these planets has the smallest diameter?

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

(1)

(c) Calculate the difference, in kilometres, between the diameter of Saturn and the diameter of Neptune.

Give your answer in standard form.

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



18

*S51830A01820*

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

QR

P

35°


17.6 cm


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




.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .dollars


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

24 The table shows the diameters, in kilometres, of five planets.


Venus 1.2 × 104

Jupiter 1.4 × 105

Neptune 5.0 × 104

Mars 6.8 × 103

Saturn 1.2 × 105


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

(1)


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

(1)



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



20

*S51830A02020*

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

25

BA

CDiagram NOT accurately drawn

9.5 cm

7.6 cm

The diagram shows a shape made from triangle ABC and a semicircle with diameter BC. Triangle ABC is right-angled at B.

AB = 7.6 cm and AC = 9.5 cm.

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

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


TOTAL FOR PAPER IS 100 MARKS


20

*S51830A02020*

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

25

BA

CDiagram NOT accurately drawn

9.5 cm

7.6 cm


AB = 7.6 cm and AC = 9.5 cm.


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



Inte

rnat

iona

l GC

SE in

Mat

hem

atic

s A -

Pape

r 1F

mar

k sc

hem

e

Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

1 a

15

or 3

1 4

AO

1 B

1 fo

r 15

or 3

1 or

bot

h

b

24

or 3

6

AO

1 B

1 fo

r 24

or 3

6 or

bot

h

c

36

or 6

4

AO

1 B

1 fo

r 36

or 6

4 or

bot

h

d

2

or 3

1

AO

1 B

1 fo

r 2 o

r 31

or b

oth

2 a

64 100

A

O1

M1

any

frac

tion

equi

vale

nt to

64 10

0

16 25

2

A

1

b

0.

09

1 A

O1

B1

c

14

1

AO

1 B

1

3 a

Th

ursd

ay

1 A

O3

B1

b

24 ÷

3 ×

5

AO

3 M

1 fo

r 24

÷ 3

(=8)

40

2

A

1

c

2 : 3

.25

oe

or

2×’

8’ :

3.25

×’8

’

A

O1

M1

any

corr

ect r

atio

ft fr

om ‘8

’ in

(b)

8:

13

2

A1

acce

pt 1

: 13 8

oe

4 a

22

, 26

1 A

O1

B1

b

ad

d 4

1 A

O1

B1

c

42

1

AO

1 B

1

d

re

ason

1

AO

1 B

1 e.

g. n

o nu

mbe

rs in

sequ

ence

are

odd

num

bers

; 4n﹣

2 =

95

give

s n =

24.

25 w

hich

is n

ot a

n in

tege

r;


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

5 a

2

1 A

O2

B1

b

20

1

AO

2 B

1

c

16

1

AO

2 B

1

d

co

rrec

t ref

lect

ion

2 A

O2

B2

B1

for r

efle

ctio

n in

a d

iffer

ent v

ertic

al li

ne

6

25 ÷

3.9

5 (=

6.32

…)

AO

1 M

1 ac

cept

repe

ated

add

ition

or r

epea

ted

subt

ract

ion

from

25

25 –

‘6’ ×

3.9

5

M1

1.

3(0)

3

A

1

7 a

A

O1

M1

for 3

c or

9m

3c

+ 9

m

2

A1

for 3

c +

9m o

r 3(c

+ 3

m)

b

5x =

4 +

9

AO

1 M

1

2.

6 oe

2

A

1

8 a

19

5 1

AO

1 B

1 ca

o

b

249

÷ 3

2

AO

1 M

1

83

A

1 ca

o

c

d

= 3w

2

AO

1 B

2 B

1 fo

r d =

line

ar e

xpre

ssio

n in

w

B1

for 3

w o

e

SC:

B1

for

3dw

oe


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

9

180

– 13

2 (=

48)

AO

2 M

1

180

– 2×

’48’

M1

A1

84

5

B

2 A

ngle

s in

a tri

angl

e su

m to

180

o , bas

e an

gles

of a

n is

osce

les

trian

gle

are

equa

l, an

gles

on

a st

raig

ht li

ne su

m to

180

o

(B1

for a

ny c

orre

ct re

ason

)

10

0.

8 ×

0.3

= 0.

24 o

r

108

÷ 10

00 (=

0.10

8)

AO

2 M

1

‘0.1

08’ ÷

‘0.2

4’

M

1 de

p

0.

45

3

A1

11

a

13.4

88(5

6…)

2 A

O1

B2

B1

for 1

44.7

6 o

r 10

.73…

b

13

.5

1 A

O1

B1

ft fr

om (a

) fro

m 4

or m

ore

sig

figs


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

12

x

−2

−1

0 1

2 3

y −1

0 −7

−4

−1

2

5

y =

3x –

4 d

raw

n fr

om

x =

−2

to

x =

3

A

O1

B4

For a

cor

rect

line

bet

wee

n x

= −2

and

x =

3

B3

For a

cor

rect

stra

ight

line

segm

ent t

hrou

gh a

t lea

st 3

of

(−2,

−10

) (−1

, −7)

(0, −

4) (1

, −1)

(2, 2

) (3,

5)

OR

for a

ll of

(−2,

−10

) (−1

, −7)

(0, −

4) (1

, −1)

(2, 2

) (3,

5)

plot

ted

but n

ot jo

ined

B2

For a

t lea

st 2

cor

rect

poi

nts p

lotte

d O

R

for a

line

dra

wn

with

a p

ositi

ve g

radi

ent t

hrou

gh (0

, −4)

and

cl

ear i

nten

tion

to u

se o

f a g

radi

ent o

f 3

(eg.

a li

ne th

roug

h (0

, -4)

and

(0.5

, −1)

4

B1

For a

t lea

st 2

cor

rect

poi

nts s

tate

d (m

ay b

e in

a ta

ble)

OR

for a

line

dra

wn

with

a p

ositi

ve g

radi

ent t

hrou

gh (0

, −4)

but

no

t a li

ne jo

inin

g (0

, −4)

and

(3, 0

) OR

a lin

e w

ith g

radi

ent 3


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

13

a 1

– (0

.15

+ 0.

4 +

0.35

) or

1 –

0.9

AO

3 M

1

0.

1 oe

2

A

1

b

0.35

× 4

0

A

O3

M1

14

2

A

1

14

a

10g

+ 35

1

AO

1 B

1

b

−2

, −1,

0, 1

, 2

2 A

O1

B2

B1

for

−3,

−2,

−1,

0, 1

, 2

o

r

−2,

−1,

0, 1

15

14

9 ×

0.76

(=11

3…)

or 1

13.2

4

A

O1

M1

M

1 fo

r 149

× 0

.76

× 1.

54

(=17

4…)

164.

78 ÷

1.5

4 (=

107)

M1

M

1 fo

r “17

4…”

– 16

4.78

(=

9.60

96)

"113

.24"

− "

107"

M1

dep

on a

t lea

st o

ne p

revi

ous

M m

ark

; acc

ept "

107"

–“1

13.2

4”

M1

for “

9.60

96”

÷ 1.

54

6.

24

4

A1

16

78

00 ÷

9.7

5 o

r 780

0 ÷

585

x 60

A

O2

M2

M1

for 7

800

÷ 9.

45 o

r 780

0 ÷

585

or 1

3.3.

...

80

0 3

A

1


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

17

28

÷ (6

− 4

) (=1

4)

AO

1 M

1 or

use

of c

ance

lled

ratio

s

(eg

3 : 6

: 4

= 0.

75 :

1.5

: 1)

"14"

× 3

(=42

)

M1

(dep

) 28

÷0.5

(=56

)

or c

ance

lled

ratio

s, (e

.g. 5

6 ×

0.75

)

or M

2 fo

r 28

÷ 2 3

oe

42

3

A

1

18

a

25 <

d ≤

30

1 A

O3

B1

B1

iden

tifie

s 25

→ 3

0 cl

ass

b

(12

× 2.

5) +

(6 ×

7.5

) + (4

× 1

2.5)

+

(6 ×

17.

5) +

(14

× 22

.5) +

( 18

×

27.5

) or

30

+ 45

+ 5

0 +

105

+ 31

5 +

495

or

1040

AO

3 M

2 M

1 fo

r fre

quen

cy ×

con

sist

ent v

alue

with

in in

terv

al

NB

. Pro

duct

s do

not n

eed

to b

e ad

ded

Con

done

one

err

or

‘104

0’ ÷

60

M

1

1

173

4

A

1 ac

cept

17.

3(33

…)

c

A

O3

M1

for

60a w

ith a

< 6

0 or

32 b w

ith b

> 3

2

32 60

oe

2

A1

Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

19

W

orki

ng w

ith a

ll 12

box

es

12 ×

15

(=18

0) o

r 12

× 1

2 (=

144)

AO

1 M

1

for c

orre

ct to

tal c

ost o

r cor

rect

tota

l num

ber o

f mel

ons

(eith

er m

ay a

ppea

r as p

art o

f ano

ther

cal

cula

tion)

312

121.

6oe

(17

2.8)

4

M

1

for r

even

ue fr

om a

ll fu

ll pr

ice

mel

ons

sold

1215

1.15

oe

(=20

7) o

r

180

× 0

.15

oe (=

27)

M

1

for t

otal

reve

nue

or to

tal p

rofit

'207

''1

72.8

'36

or 34

.2 36 o

r

'27'

('180

''1

72.8

')36

M

1

dep

on M

3

0.

95

5

A1

cao

Alte

rnat

ive

– w

orki

ng w

ith o

ne b

ox

15 ÷

12

(=1.

25) o

r 3

12(

9)4

M1

for p

rice

of 1

mel

on o

r nu

mbe

r of f

ull p

rice

mel

ons

312

1.6

oe(

14.4

)4

M

1

for r

even

ue fr

om a

ll fu

ll pr

ice

mel

ons s

old

151.

15

(=17

.25)

M1

for t

otal

reve

nue

from

one

box

"17.

25"

"14.

4"3

or 2.

85 3

M

1

dep

on M

3

0.

95

5

A1

cao


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

19

W

orki

ng w

ith a

ll 12

box

es

12 ×

15

(=18

0) o

r 12

× 1

2 (=

144)

AO

1 M

1

for c

orre

ct to

tal c

ost o

r cor

rect

tota

l num

ber o

f mel

ons

(eith

er m

ay a

ppea

r as p

art o

f ano

ther

cal

cula

tion)

312

121.

6oe

(17

2.8)

4

M

1

for r

even

ue fr

om a

ll fu

ll pr

ice

mel

ons

sold

1215

1.15

oe

(=20

7) o

r

180

× 0

.15

oe (=

27)

M

1

for t

otal

reve

nue

or to

tal p

rofit

'207

''1

72.8

'36

or 34

.2 36 o

r

'27'

('180

''1

72.8

')36

M

1

dep

on M

3

0.

95

5

A1

cao

Alte

rnat

ive

– w

orki

ng w

ith o

ne b

ox

15 ÷

12

(=1.

25) o

r 3

12(

9)4

M1

for p

rice

of 1

mel

on o

r nu

mbe

r of f

ull p

rice

mel

ons

312

1.6

oe(

14.4

)4

M

1

for r

even

ue fr

om a

ll fu

ll pr

ice

mel

ons s

old

151.

15

(=17

.25)

M1

for t

otal

reve

nue

from

one

box

"17.

25"

"14.

4"3

or 2.

85 3

M

1

dep

on M

3

0.

95

5

A1

cao


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

20

C

ircul

ar a

rc, c

entre

B, t

o in

ters

ect

both

line

s AB

and

BC

Equa

l len

gth

arcs

, fro

m in

ters

ectio

ns

on e

ach

line,

mee

ting

to g

ive

a po

int

on th

e bi

sect

or

AO

2 M

1

co

rrec

t bis

ecto

r 2

A

1 de

p on

M1.

Ful

l con

stru

ctio

n sh

own.

21

a

AO

1 M

1 A

ny c

orre

ct p

artia

lly fa

ctor

ised

exp

ress

ion

9e

2 f (2e

+ 5

f 3)

2

A1

b

(x ±

6)(

x ±

2)

AO

1 M

1 or

cor

rect

subs

titut

ion

into

qua

drat

ic fo

rmul

a (c

ondo

ne o

ne

sign

err

or)

(x –

6)(

x +

2)

M

1 or

464

2

6,

−2

3

A1

dep.

on

at le

ast M

1

22

co

s 35

= 17

.6PR

A

O2

M1

17.6

× c

os35

M1

14

.4

3

A1

14.4

~ 1

4.42

23

22

.50

÷ 15

(=1.

5) o

r 10

0 ÷

15

(=6.

6….)

AO

1 M

1

M2

for 2

2.5

÷ 0.

15

‘1.5

’ × 1

00 (=

150)

or

‘6.6

…’ ×

22

.5(0

)

M1

dep

15

0 3

A

1

Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

24

a

140

000

1 A

O1

B1

b

M

ars

1 A

O1

B1

c

1.2

× 10

5 – 5

× 1

04 or

1200

00 –

500

00 o

r 70

000

oe

AO

1 M

1

7

× 10

4 2

A

1

25

2

29.

57.

6

or

90.2

557

.76

o

r 32

.49

or

32.5

AO

2 M

1

(BC

= )

5.7

A

1

'7.5'6.7

21

o

r 21

.6(6

) or

21.7

M1

dep

on fi

rst M

1

or e

g.

17.

6si

n(

53.1

...)

9.5

ACB

a

nd

19.

5'5

.7'

sin'

53.1

'2

2

21

2'7.5'

or

12.7

(587

...) o

r

12.8

M

1 de

p on

firs

t M1

34

.4

5

A1

for a

nsw

er ro

undi

ng to

34.

4

(π→

34.

4187

...

3.1

4→34

.412

3...)


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

24

a

140

000

1 A

O1

B1

b

M

ars

1 A

O1

B1

c

1.2

× 10

5 – 5

× 1

04 or

1200

00 –

500

00 o

r 70

000

oe

AO

1 M

1

7

× 10

4 2

A

1

25

2

29.

57.

6

or

90.2

557

.76

o

r 32

.49

or

32.5

AO

2 M

1

(BC

= )

5.7

A

1

'7.5'6.7

21

o

r 21

.6(6

) or

21.7

M1

dep

on fi

rst M

1

or e

g.

17.

6si

n(

53.1

...)

9.5

ACB

a

nd

19.

5'5

.7'

sin'

53.1

'2

2

21

2'7.5'

or

12.7

(587

...) o

r

12.8

M

1 de

p on

firs

t M1

34

.4

5

A1

for a

nsw

er ro

undi

ng to

34.

4

(π→

34.

4187

...

3.1

4→34

.412

3...)




Total Marks

Paper Reference

Turn over


1/1/2/

*S51831A0124*



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1/1/2/

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Answer ALL TWENTY SIX questions.



1 The table shows the distance from Delhi to each of six cities.

City Distance (km)

Bengaluru 2061

Chennai 2095

Hyderabad 1499

Kolkata 1461

Mumbai 1407

Pune 1417

(a) Which number in the table is the smallest number?

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

(1)

(b) Which number in the table is a multiple of 5?

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

(1)

(c) Write down the value of the 6 in the number 1461

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

(1)

(d) Write the number 1499 correct to the nearest thousand.

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

(1)



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Answer ALL TWENTY SIX questions.



1 The table shows the distance from Delhi to each of six cities.

City Distance (km)

Bengaluru 2061

Chennai 2095

Hyderabad 1499

Kolkata 1461

Mumbai 1407

Pune 1417

(a) Which number in the table is the smallest number?

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

(1)

(b) Which number in the table is a multiple of 5?

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(1)

(c) Write down the value of the 6 in the number 1461

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

(1)

(d) Write the number 1499 correct to the nearest thousand.

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

(1)



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2 On the probability scale, mark with a cross (×) the probability that

(a) a fair 6-sided dice will land on a number less than 7 Label this cross A.

(1)

(b) a fair 6-sided dice will show an even number when thrown. Label this cross B.

(1)

0 0.5 1


3 The table shows midday temperatures in five cities one day in winter.

City Midday temperature (°C)

Paris 2

Cardiff –5

London –3

Edinburgh –1

Berlin –8

(a) Which city had the lowest midday temperature?

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(1)

The midday temperature in Exeter is 6°C higher than the midday temperature in Cardiff.

(b) Work out the midday temperature in Exeter.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .°C(1)

By midnight, the temperature in London had fallen by 4°C.

(c) Work out the midnight temperature in London.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .°C(1)

The midday temperature in Glasgow is halfway between the midday temperature in Paris and the midday temperature in Berlin.

(d) Work out the midday temperature in Glasgow.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .°C(2)


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4 There are 30 counters in a bag. 1 of the counters is yellow. The rest of the counters are either blue or green.

Sharita takes a counter from the bag at random.

(a) Write down the probability that she will take

(i) a yellow counter

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

(1)

(ii) a red counter

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(1)

The probability that Sharita will take a blue counter from the bag is 310

(b) Find the probability that she will not take a blue counter.

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

(1)



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2 On the probability scale, mark with a cross (×) the probability that

(a) a fair 6-sided dice will land on a number less than 7 Label this cross A.

(1)

(b) a fair 6-sided dice will show an even number when thrown. Label this cross B.

(1)

0 0.5 1


3 The table shows midday temperatures in five cities one day in winter.

City Midday temperature (°C)

Paris 2

Cardiff –5

London –3

Edinburgh –1

Berlin –8

(a) Which city had the lowest midday temperature?

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

(1)

The midday temperature in Exeter is 6°C higher than the midday temperature in Cardiff.

(b) Work out the midday temperature in Exeter.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .°C(1)

By midnight, the temperature in London had fallen by 4°C.

(c) Work out the midnight temperature in London.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .°C(1)

The midday temperature in Glasgow is halfway between the midday temperature in Paris and the midday temperature in Berlin.

(d) Work out the midday temperature in Glasgow.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .°C(2)


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4 There are 30 counters in a bag. 1 of the counters is yellow. The rest of the counters are either blue or green.

Sharita takes a counter from the bag at random.

(a) Write down the probability that she will take

(i) a yellow counter

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

(1)

(ii) a red counter

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(1)

The probability that Sharita will take a blue counter from the bag is 310

(b) Find the probability that she will not take a blue counter.

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(1)



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5 Jason runs in a race. The graph shows his speed, in metres per second (m/s), during the first 10 seconds

of the race.

12

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8

6

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O 2

Speed (m/s)

Time (seconds)4 6 8 10

(a) Write down Jason’s speed at 2 seconds.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .m/s(1)

(b) Write down Jason’s greatest speed.

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(c) Write down the time at which Jason’s speed was 3 m/s.

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


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6 Here are seven triangles drawn on a square grid.

A

G

F

E

DC

B

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

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) One of the triangles is similar to triangle A. Write down the letter of this triangle.

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

(1)

(c) One of the triangles is isosceles. Write down the letter of this triangle.

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

(1)



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5 Jason runs in a race. The graph shows his speed, in metres per second (m/s), during the first 10 seconds

of the race.

12

10

8

6

4

2

O 2

Speed (m/s)

Time (seconds)4 6 8 10

(a) Write down Jason’s speed at 2 seconds.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .m/s(1)

(b) Write down Jason’s greatest speed.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .m/s(1)

(c) Write down the time at which Jason’s speed was 3 m/s.

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


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6 Here are seven triangles drawn on a square grid.

A

G

F

E

DC

B

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

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)

(b) One of the triangles is similar to triangle A. Write down the letter of this triangle.

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

(1)

(c) One of the triangles is isosceles. Write down the letter of this triangle.

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

(1)



8

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7 PQR is a triangle. PQ = 7 cm and QR = 7.5 cm. Angle QPR = 50°

Draw accurately the triangle PQR with PQ as its base.

P Q


8 (a) Find the value of 46 24.

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

(1)

(b) Find the value of 93

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

(1)

(c) Find the cube root of 19.683

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

(1)


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9 (a) Simplify 3m + 2m – m

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(1)

(b) Simplify 6k × 3p

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

(1)

(c) Solve 7e = 28

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

(1)

P = 4r – 3q

(d) Work out the value of P when r = −7 and q = 5

P = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

P = 4r – 3q

(e) Work out the value of r when P = 9 and q = 8

r = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(3)

(f) Factorise 5c + 30

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

(1)



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7 PQR is a triangle. PQ = 7 cm and QR = 7.5 cm. Angle QPR = 50°

Draw accurately the triangle PQR with PQ as its base.

P Q


8 (a) Find the value of 46 24.

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

(1)

(b) Find the value of 93

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

(1)

(c) Find the cube root of 19.683

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

(1)


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9 (a) Simplify 3m + 2m – m

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(1)

(b) Simplify 6k × 3p

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

(1)

(c) Solve 7e = 28

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

(1)

P = 4r – 3q

(d) Work out the value of P when r = −7 and q = 5

P = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

P = 4r – 3q

(e) Work out the value of r when P = 9 and q = 8

r = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(3)

(f) Factorise 5c + 30

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

(1)



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10 Umar buys 7 first-class tickets and 9 second-class tickets for the train journey from Colombo to Kandy.

The total cost is 4500 Sri Lankan rupees. The cost of each first-class ticket is 360 Sri Lankan rupees.

(a) Work out the cost of each second-class ticket.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Sri Lankan rupees(3)

The train left Colombo at 16:55 The train arrived in Kandy at 20:15

(b) How long did the train take to get from Colombo to Kandy?

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

(2)


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11 The pie chart shows information about Andrew’s spending last month.

30°

45°

75°

195°

entertainment

travelclothes

household bills

food and drink

15°

Andrew spent $80 on travel last month.

(a) Work out the amount Andrew spent on household bills last month.

$.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(3)

A second pie chart is to be drawn for Cathy’s spending. Cathy spent a total of $800 last month. She spent $120 on entertainment last month.

(b) Calculate the size of the angle for entertainment in the second pie chart.

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

(2)



10

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10 Umar buys 7 first-class tickets and 9 second-class tickets for the train journey from Colombo to Kandy.

The total cost is 4500 Sri Lankan rupees. The cost of each first-class ticket is 360 Sri Lankan rupees.

(a) Work out the cost of each second-class ticket.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Sri Lankan rupees(3)

The train left Colombo at 16:55 The train arrived in Kandy at 20:15

(b) How long did the train take to get from Colombo to Kandy?

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

(2)


11


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11 The pie chart shows information about Andrew’s spending last month.

30°

45°

75°

195°

entertainment

travelclothes

household bills

food and drink

15°

Andrew spent $80 on travel last month.

(a) Work out the amount Andrew spent on household bills last month.

$.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(3)

A second pie chart is to be drawn for Cathy’s spending. Cathy spent a total of $800 last month. She spent $120 on entertainment last month.

(b) Calculate the size of the angle for entertainment in the second pie chart.

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

(2)



12

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12 The diagram shows the floor plan of a room in Kate’s house.


11 m

7 m5 m

3 m

Kate is going to cover the floor with tiles. She is going to buy some packs of tiles.

The tiles in each pack of tiles cover 2 m2 of floor. Each pack of tiles costs £24.80

Work out how much it will cost Kate to buy the packs of tiles she needs.

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


13


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13 A ship has a length of 345 metres. A scale model is made of the ship. The scale of the model is 1:200

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

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


14 A has coordinates (3, 6) B has coordinates (−5, 8)

Work out the coordinates of the midpoint of AB.

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



12

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12 The diagram shows the floor plan of a room in Kate’s house.


11 m

7 m5 m

3 m

Kate is going to cover the floor with tiles. She is going to buy some packs of tiles.

The tiles in each pack of tiles cover 2 m2 of floor. Each pack of tiles costs £24.80

Work out how much it will cost Kate to buy the packs of tiles she needs.

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


13


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13 A ship has a length of 345 metres. A scale model is made of the ship. The scale of the model is 1:200

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

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


14 A has coordinates (3, 6) B has coordinates (−5, 8)

Work out the coordinates of the midpoint of AB.

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



14

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15 Here is a list of the ingredients needed to make leek and potato soup for 6 people.

Leek and Potato Soup

Ingredients for 6 people

900 ml

900 ml

750 g

350 g

350 g

chicken stock

water

leeks

potatoes

onions

Paul wants to make leek and potato soup for 15 people.

(a) Work out the amount of chicken stock he needs.

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

Mary makes leek and potato soup for a group of people. She uses 3 kg of leeks.

(b) Work out the number of people in the group.

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

(2)


15


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16 Find the lowest common multiple (LCM) of 20, 30 and 45

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


17 The first four terms of an arithmetic sequence are

2 9 16 23

Write down an expression, in terms of n, for the nth term.

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



14

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15 Here is a list of the ingredients needed to make leek and potato soup for 6 people.

Leek and Potato Soup

Ingredients for 6 people

900 ml

900 ml

750 g

350 g

350 g

chicken stock

water

leeks

potatoes

onions

Paul wants to make leek and potato soup for 15 people.

(a) Work out the amount of chicken stock he needs.

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

Mary makes leek and potato soup for a group of people. She uses 3 kg of leeks.

(b) Work out the number of people in the group.

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

(2)


15


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



2 9 16 23


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



16

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18


10 cm

6 cm

9 cm

14 cm

The diagram shows a solid prism. The cross section of the prism is a trapezium.

The prism is made from wood with density 0.7 g/cm3

Work out the mass of the prism.

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


17


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19 (a) Simplify p5 × p4

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

(1)

(b) Simplify (m4)−3

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

(1)

(c) Write down the value of c0

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

(1)

(d) Solve 5(x + 7) = 2x – 10 Show clear algebraic working.

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

(3)



16

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18


10 cm

6 cm

9 cm

14 cm




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


17


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

(1)


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

(1)


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

(1)

(d) Solve 5(x + 7) = 2x – 10 Show clear algebraic working.

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

(3)



18

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20 On 1 May 2012, the cost of 5 grams of gold was 14 000 rupees. The cost of gold decreased by 7.5% from 1 May 2012 to 1 May 2013

Work out the cost of 20 grams of gold on 1 May 2013

... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .rupees


19


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21

x

y

1

2

3

4

5

1 2 3 4 5 6O–1

–2

–3

–4

–7

–1–2–3–4–5–6

A

B

–5

–6

(a) On the grid, translate triangle A by the vector 5

2

(1)

(b) Describe fully the single transformation that maps triangle A onto triangle B.

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

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

(3)



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... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .rupees


19


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21

x

y

1

2

3

4

5

1 2 3 4 5 6O–1

–2

–3

–4

–7

–1–2–3–4–5–6

A

B

–5

–6


2

(1)


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

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(3)



20

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22 a, b, c and d are 4 integers written in order of size, starting with the smallest integer.

The mean of a, b, c and d is 15 The sum of a, b and c is 39

(a) Find the value of d.

d = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

Given also that the range of a, b, c and d is 10

(b) work out the median of a, b, c and d.

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

(2)


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23 Kwo invests HK$40 000 for 3 years at 2% per year compound interest. Work out the value of the investment at the end of 3 years.

HK$... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



20

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O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA




d = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)



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

(2)


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


HK$... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



22

*S51831A02224*

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 Solve the simultaneous equations

3x + y = 13x – 2y = 9

Show clear algebraic working.

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

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


23


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 (a) Show that 59

16

1318

+ =

(2)

(b) Show that 4 23

59

1 516

÷ 3 =

(3)



22

*S51831A02224*

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


3x + y = 13x – 2y = 9


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

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


23


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 (a) Show that 59

16

1318

+ =

(2)

(b) Show that 4 23

59

1 516

÷ 3 =

(3)



24

*S51831A02424*

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

26

86°

y° y°

123°

A

B C

D

EF

105°

140°Diagram NOT accurately drawn

ABCDEF is a hexagon.

Work out the value of y.

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




24

*S51831A02424*

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

26

86°

y° y°

123°

A

B C

D

EF

105°




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



Inte

rnat

iona

l GC

SE in

Mat

hem

atic

s A -

Pape

r 2F

mar

k sc

hem

e

Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

1 a

14

07

1 A

O1

B1

b

20

95

1 A

O1

B1

c

60

1

AO

1 B

1 ac

cept

tens

, six

ty

d

10

00

1 A

O1

B1

2 a

×

at 1

1

AO

3 B

1

b

×

at 0

.5

1 A

O3

B1

3 a

B

erlin

1

AO

1 B

1

b

1

1 A

O1

B1

c

-7

1

AO

1 B

1

d

(2 +

−8)

÷ 2

oe

AO

1 M

1 m

etho

d to

find

mid

poin

t

−3

2

A

1

4 ai

1 30 o

e 1

AO

3 B

1

ai

i

0 1

AO

3 B

1

b

7 10

oe

1 A

O3

B1

5 a

9

1 A

O1

B1

b

11

.8

1 A

O1

B1

c

0.

6 1

AO

1 B

1


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

6 a

B

, G

1 A

O2

B1

b

F

1 A

O2

B1

c

D

1

AO

2 B

1

7

Line

from

P a

t 50o to

bas

e or

a

rc fr

om Q

of l

engt

h 7.

5 cm

A

O2

M1

co

rrec

t tria

ngle

2

A

1

8 a

6.

8 1

AO

1 B

1

b

72

9 1

AO

1 B

1

c

2.

7 1

AO

1 B

1

9 a

4m

1

AO

1 B

1

b

18

kp

1 A

O1

B1

c

4

1 A

O1

B1

d

4×−7

−3×

5 or

−28

and

−15

A

O1

M1

−4

3 2

A

1

e

9 =

4r –

3×8

or

9 =

4r −

24

AO

1 M

1

9 +

24 =

4r

M

1 is

olat

e te

rm in

r

8.

25 o

e 3

A

1

f

5(

c +

6)

1 A

O1

B1

Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

10

a 36

0 ×

7 (=

2520

)

A

O1

M1

(450

0 –

‘252

0’)÷

9

M1

dep

22

0 3

A

1

b

A

O2

M1

clea

r evi

denc

e of

met

hod

to w

ork

out t

ime

inte

rval

3

hour

s 20

min

s 2

A

1 ac

cept

200

min

utes

11

a 80

÷ 3

0 (=

2.66

…)

AO

3 M

1

80 ÷

30

× 19

5

M1

52

0 3

A

1

b

120

360

800

oe

AO

3 M

1

54

2

A

1

12

5

× 3

(=15

) or

7 ×

(11

– 5)

(=42

) or

11 ×

7 (=

77) o

r 5×

(7-3

)(=2

0)

or 1

1×3(

=33)

or

(11-

5)×(

7-3)

(=24

)

AO

1,

AO

2

M1

met

hod

to fi

nd a

rea

of p

art o

f flo

or

5 ×

3 +

7 ×

(11

– 5)

(=57

) or

11 ×

7 −

5×(

7-3)

(=57

) or

11 ×

3 +

(11

-5)×

(7-3

)(=5

7)

M

1 co

mpl

ete

met

hod

to fi

nd a

rea

‘57’

÷ 2

(28.

5)

M

1 de

p on

at l

east

M1

‘29’

× 2

4.8

M

1

71

9.20

5

A

1


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

10

a 36

0 ×

7 (=

2520

)

A

O1

M1

(450

0 –

‘252

0’)÷

9

M1

dep

22

0 3

A

1

b

A

O2

M1

clea

r evi

denc

e of

met

hod

to w

ork

out t

ime

inte

rval

3

hour

s 20

min

s 2

A

1 ac

cept

200

min

utes

11

a 80

÷ 3

0 (=

2.66

…)

AO

3 M

1

80 ÷

30

× 19

5

M1

52

0 3

A

1

b

120

360

800

oe

AO

3 M

1

54

2

A

1

12

5

× 3

(=15

) or

7 ×

(11

– 5)

(=42

) or

11 ×

7 (=

77) o

r 5×

(7-3

)(=2

0)

or 1

1×3(

=33)

or

(11-

5)×(

7-3)

(=24

)

AO

1,

AO

2

M1

met

hod

to fi

nd a

rea

of p

art o

f flo

or

5 ×

3 +

7 ×

(11

– 5)

(=57

) or

11 ×

7 −

5×(

7-3)

(=57

) or

11 ×

3 +

(11

-5)×

(7-3

)(=5

7)

M

1 co

mpl

ete

met

hod

to fi

nd a

rea

‘57’

÷ 2

(28.

5)

M

1 de

p on

at l

east

M1

‘29’

× 2

4.8

M

1

71

9.20

5

A

1


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

13

34

5 ÷

200

(=1.

725)

or

345

× 10

0 (=

3450

0)

AO

2 M

1 D

ivis

ion

by 2

00 o

r con

vers

ion

of u

nits

‘1.7

25’ ×

100

or

‘345

00’ ÷

200

M1

Div

isio

n by

200

and

con

vers

ion

of u

nits

17

2.5

3

A1

14

(6

+ 8

) ÷ 2

(=7)

or

(−5

+ 3)

÷2

(= −

1)

AO

1 M

1

(−

1, 7

) 2

A

1

15

a 90

0 ÷

6 ×

15 o

e

A

O1

M1

22

50

2

A1

b

3 ×

1000

÷ 7

50 ×

6

AO

1 M

1

24

2

A

1

16

2

× 2

× 5

or 2

× 3

× 5

or 3

× 3

× 5

or tw

o of

20, 4

0, 6

0 …

30, 6

0, 9

0 …

45, 9

0, 1

05

AO

1 M

1 fo

r one

of 2

0, 3

0, 4

5 w

ritte

n as

pro

duct

of p

rime

fact

ors o

r

list o

f at l

east

3 m

ultip

les o

f any

two

of 2

0, 3

0, 4

5

2 ×

2 ×

5 an

d 2

× 3

× 5

and

3 ×

3 ×

5

or a

ll of

20, 4

0, 6

0 , 8

0 …

180

30, 6

0, 9

0 …

180

45, 9

0, 1

05 …

180

M1

18

0 3

A

1 fo

r 180

or 2

× 2

× 3

× 3

× 5

oe

Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

17

AO

1 M

1 fo

r 7n

+ k

(k m

ay b

e ze

ro)

7n

– 5

oe

2

A1

18

1

(10

14)

92

oe

(= 1

08)

AO

2 M

1 fo

r are

a of

cro

ss se

ctio

n

‘108

’ × 6

(=64

8)

M

1 (d

ep o

n pr

evio

us M

1) fo

r vol

ume

of p

rism

‘648

’ × 0

.7

M

1 (in

depe

nden

t)

45

3.6

4

A1

acce

pt 4

54

19

a

p9 1

AO

1 B

1

b

m

−12

1 A

O1

B1

c

1

1 A

O1

B1

d

5x +

35

= 2x

– 1

0 or

210

75

5x

x

AO

1 M

1 fo

r rem

ovin

g br

acke

t or d

ivid

ing

all t

erm

s by

5

eg. 5

x –

2x =

−10

– 3

5 or

102

75

5xx

M

1 fo

r iso

latin

g x

term

s in

a co

rrec

t equ

atio

n

−1

5 3

A

1 de

p on

M1


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

17

AO

1 M

1 fo

r 7n

+ k

(k m

ay b

e ze

ro)

7n

– 5

oe

2

A1

18

1

(10

14)

92

oe

(= 1

08)

AO

2 M

1 fo

r are

a of

cro

ss se

ctio

n

‘108

’ × 6

(=64

8)

M

1 (d

ep o

n pr

evio

us M

1) fo

r vol

ume

of p

rism

‘648

’ × 0

.7

M

1 (in

depe

nden

t)

45

3.6

4

A1

acce

pt 4

54

19

a

p9 1

AO

1 B

1

b

m

−12

1 A

O1

B1

c

1

1 A

O1

B1

d

5x +

35

= 2x

– 1

0 or

210

75

5x

x

AO

1 M

1 fo

r rem

ovin

g br

acke

t or d

ivid

ing

all t

erm

s by

5

eg. 5

x –

2x =

−10

– 3

5 or

102

75

5xx

M

1 fo

r iso

latin

g x

term

s in

a co

rrec

t equ

atio

n

−1

5 3

A

1 de

p on

M1


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

20

14

000

× 4

(=56

000)

A

O1

M1

NB

. mul

tiplic

atio

n by

4 m

ay o

ccur

bef

ore

or a

fter p

erce

ntag

e de

crea

se

0.07

5 ×

‘560

00’ (

=420

0) o

r

0.0

75 ×

140

00 (=

1050

)

M

1

M2

for 0

.925

×

‘560

00’o

r

0.92

5 ×

1400

0

‘560

00’ –

‘420

00’ o

r

1400

0 –

‘105

0’

M

1 (d

ep)

51

800

4

A

1

21

a

trian

gle

with

ve

rtice

s

(3, -

1) (3

, -4)

(5, -

4)

1 A

O2

B1

b

R

otat

ion

A

O2

B1

ce

ntre

(-3,

0)

B1

90

o ant

iclo

ckw

ise

3

B1

acce

pt +

900 , 2

70o c

lock

wis

e, −

270o

NB

. If m

ore

than

one

tran

sfor

mat

ion

then

no

mar

ks c

an b

e aw

arde

d


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

22

a 4

× 15

(=60

) or

154

ab

cd

or

4×15

– 3

9

2

AO

3 M

1

21

A

1

b

d −

a =

10

or a

= 1

1 or

a =

“21”

– 1

0 or

b +

c =

39

− 11

= 2

8

2

A

O3

M1

ft fr

om (a

)

(can

be

impl

ied

by 1

1, b

¸ c, 2

1 O

R

a, b

, c, d

with

b +

c =

28)

14

A

1 ca

o

23

0.

02 ×

40

000

(=80

0) o

r

1.02

× 4

0 00

0 (=

4080

0) o

r 24

00

AO

1 M

1

"408

00"×

0.02

(=81

6) a

nd

"416

16"×

0.02

(=83

2.32

) OR

2448

.32

M

1 (d

ep) m

etho

d to

find

inte

rest

for

year

2 a

nd y

ear 3

M

2 fo

r 40

000

× 1.

023

42

448.

32

3

A1

24

3x

+ y

= 1

3

or

6

x +

2y =

26

−

3x –

6y

= 27

+

x –

2y =

9

AO

1 M

1 m

ultip

licat

ion

of o

ne e

quat

ion

with

cor

rect

ope

ratio

n se

lect

ed

or re

arra

ngem

ent o

f one

equ

atio

n w

ith su

bstit

utio

n in

to

seco

nd

eg. 3

x –

2 =

13 o

r 15

+ y

= 1

3

M1

(dep

) cor

rect

met

hod

to fi

nd se

cond

var

iabl

e

5,

−2

3

A1

for b

oth

solu

tions

dep

ende

nt o

n co

rrec

t wor

king


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

25

a e.

g. 10

318

18

or

309

5454

AO

1 M

1 fo

r tw

o fr

actio

ns w

ith c

omm

on d

enom

inat

or w

ith a

t lea

st o

ne

num

erat

or c

orre

ct

an

swer

giv

en

2

A1

corr

ect a

nsw

er fr

om c

orre

ct w

orki

ng

b

1432

39

AO

1 M

1

149

332

o

r 12

696

2727

o

r 42

329

9

M1

an

swer

giv

en

3

A1

corr

ect a

nsw

er fr

om c

orre

ct w

orki

ng

26

(6

– 2

) × 1

80 (=

720)

A

O2

M1

com

plet

e m

etho

d to

find

sum

of i

nter

ior a

ngle

s

‘720

’ – (8

6 +

123

+ 14

0 +

105)

(=

266)

or

‘720

’ – 4

54 (=

266)

M1

dep

on 1

st m

etho

d m

ark

‘266

’ ÷ 2

M1

dep

on 1

st m

etho

d m

ark

13

3 4

A

1



Total Marks

Paper Reference

Turn over


1/2/1/

*S51832A0120*

Mathematics ALevel 1/2Paper 1H

Higher TierSample assessment material for first teaching September 2016

Time: 2 hours


Instructions


Information


Advice


4MA1/1H





Total Marks

Paper Reference

Turn over


1/2/1/

*S51832A0120*



Time: 2 hours


Instructions


Information


Advice


4MA1/1H



2

*S51832A0220*

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

International GCSE MathematicsFormulae sheet – Higher Tier

Arithmetic series

Sum to n terms, Sn = n2

[2a + (n – 1)d]Area of trapezium = 1

2(a + b)h

b

a

h

The quadratic equation

The solutions of ax2 + bx + c = 0 where a ¹ 0 are given by:

x b b aca

= − ± −24

2

Trigonometry

A B

C

b a

c

In any triangle ABC

Sine Rule aA

bB

cCsin sin sin

= =

Cosine Rule a2 = b2 + c2 – 2bccos A

Area of triangle = 1

2ab sin C

Volume of cone = 1

3πr2h

Curved surface area of cone = πrl

r

lh


cross section

length

Volume of cylinder = πr2h Curved surface area of cylinder = 2πrh

r

h

Volume of sphere = 4

3πr3

Surface area of sphere = 4πr2

r

3


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Answer ALL TWENTY THREE questions.





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


2 Penny, Amjit and James share some money in the ratios 3 : 6 : 4 Amjit gets $28 more than James.


$ .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



2

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Arithmetic series



2(a + b)h

b

a

h



x b b aca

= − ± −24

2

Trigonometry

A B

C

b a

c

In any triangle ABC

Sine Rule aA

bB

cCsin sin sin

= =



2ab sin C

Volume of cone = 1

3πr2h


r

lh


cross section

length


r

h

Volume of sphere = 4

3πr3


r

3


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Answer ALL TWENTY THREE questions.





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


2 Penny, Amjit and James share some money in the ratios 3 : 6 : 4 Amjit gets $28 more than James.


$ .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



4

*S51832A0420*

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0 < d 5 12

5 < d 10 6

10 < d 15 4

15 < d 20 6

20 < d 25 14

25 < d 30 18


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

(1)


.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .km(4)



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(2)


5


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Nigel sold 3

4 of the melons for $1.60 each.




$ .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



4

*S51832A0420*

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0 < d 5 12

5 < d 10 6

10 < d 15 4

15 < d 20 6

20 < d 25 14

25 < d 30 18


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

(1)


.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .km(4)



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(2)


5


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Nigel sold 3

4 of the melons for $1.60 each.




$ .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



6

*S51832A0620*

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A

B

C



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

(2)


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(3)


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7 P

R Q

17.6cm35°



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




.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .dollars



6

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A

B

C



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

(2)


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(3)


7


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7 P

R Q

17.6cm35°



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8

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9 The table shows the diameters, in kilometres, of five planets


Venus 1.2 × 104

Jupiter 1.4 × 105

Neptune 5.0 × 104

Mars 6.8 × 103

Saturn 1.2 × 105


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

(1)


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

(1)



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

The diameter of the Moon is 3.5 × 103 km. The diameter of the Sun is 1.4 × 106 km.

(d) Calculate the ratio of the diameter of the Moon to the diameter of the Sun. Give your ratio in the form 1 : n

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

(2)


9


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10

9.5cm

7.6cm

C

B


A


AB = 7.6 cm and AC = 9.5 cm.


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8

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9 The table shows the diameters, in kilometres, of five planets


Venus 1.2 × 104

Jupiter 1.4 × 105

Neptune 5.0 × 104

Mars 6.8 × 103

Saturn 1.2 × 105


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

(1)


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

(1)



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

The diameter of the Moon is 3.5 × 103 km. The diameter of the Sun is 1.4 × 106 km.

(d) Calculate the ratio of the diameter of the Moon to the diameter of the Sun. Give your ratio in the form 1 : n

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

(2)


9


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10

9.5cm

7.6cm

C

B


A


AB = 7.6 cm and AC = 9.5 cm.


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10

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11 Expand and simplify (x + 5) (x – 3) (x + 3)

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


12 Here are the points that Carmelo scored in his last 11 basketball games.

23 20 14 23 17 24 24 18 16 22 21

(a) Find the interquartile range of these points.

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

(3)

Kobe also plays basketball. The median number of points Kobe has scored in his last 11 games is 18.5 The interquartile range of Kobe’s points is 10

(b) Which of Carmelo or Kobe is the more consistent points scorer? Give a reason for your answer.

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

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

(1)


11


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13 (a) Findanequationofthelinethatpassesthroughthepoints(−3,5)and(1,2) Give your answer in the form ax + by = c where a, b and c are integers.

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(4)

Line L1 has equation y = 3x + 5 Line L2 has equation 6y + 2x = 1

(b) Show that L1 is perpendicular to L2

(2)



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11 Expand and simplify (x + 5) (x – 3) (x + 3)

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


12 Here are the points that Carmelo scored in his last 11 basketball games.

23 20 14 23 17 24 24 18 16 22 21

(a) Find the interquartile range of these points.

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

(3)

Kobe also plays basketball. The median number of points Kobe has scored in his last 11 games is 18.5 The interquartile range of Kobe’s points is 10

(b) Which of Carmelo or Kobe is the more consistent points scorer? Give a reason for your answer.

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

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

(1)


11


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13 (a) Findanequationofthelinethatpassesthroughthepoints(−3,5)and(1,2) Give your answer in the form ax + by = c where a, b and c are integers.

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

(4)

Line L1 has equation y = 3x + 5 Line L2 has equation 6y + 2x = 1

(b) Show that L1 is perpendicular to L2

(2)



12

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14 The histogram shows information about the heights of some tomato plants.

0 20 40 60 80

Height (cm)

Frequencydensity

26 plants have a height of less than 20 cm.

Work out the total number of plants.

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


13


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15 A rectangular lawn has a length of 3x metres and a width of 2x metres. The lawn has a path of width 1 metre on three of its sides as shown in the diagram.

1m

1m 1m

2x m

3x m

Lawn


The total area of the lawn and the path is 100 m2

(a) Show that 6x2 + 7x – 98 = 0

(2)

(b) Calculate the area of the lawn. Show clear algebraic working.

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

(5)



12

*S51832A01220*

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D

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IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

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TE IN

TH

IS A

REA

D

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TE IN

TH

IS A

REA

14 The histogram shows information about the heights of some tomato plants.

0 20 40 60 80

Height (cm)

Frequencydensity

26 plants have a height of less than 20 cm.

Work out the total number of plants.

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


13


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D

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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 rectangular lawn has a length of 3x metres and a width of 2x metres. The lawn has a path of width 1 metre on three of its sides as shown in the diagram.

1m

1m 1m

2x m

3x m

Lawn


The total area of the lawn and the path is 100 m2

(a) Show that 6x2 + 7x – 98 = 0

(2)

(b) Calculate the area of the lawn. Show clear algebraic working.

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

(5)



14

*S51832A01420*

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D

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IS AREA

D

O N

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WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

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TH

IS A

REA

16

CB

A

D

103°

39°P


A, B, C and D are points on a circle. PA is a tangent to the circle. Angle PAD = 39° Angle BCD = 103°

Calculate the size of angle ADB. Give a reason for each stage of your working.

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


15


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D

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IS AREA

D

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TE IN

TH

IS A

REA

D

O N

OT

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TE IN

TH

IS A

REA

D

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OT

WRI

TE IN

TH

IS A

REA

17 y ab c

=−

2

a = 42 correct to 2 significant figures. b = 24 correct to 2 significant figures. c = 14 correct to 2 significant figures.

Work out the lower bound for the value of y. Give your answer correct to 2 significant figures. Show your working clearly.

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


18 Show that 3 11

3 2

2

− − −+

+

( )x xx

ax b

a÷ can be written as where and bb are integers.



14

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TE IN

TH

IS A

REA

D

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TE IN

TH

IS A

REA

D

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TH

IS A

REA

16

CB

A

D

103°

39°P


A, B, C and D are points on a circle. PA is a tangent to the circle. Angle PAD = 39° Angle BCD = 103°

Calculate the size of angle ADB. Give a reason for each stage of your working.

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


15


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D

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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 y ab c

=−

2

a = 42 correct to 2 significant figures. b = 24 correct to 2 significant figures. c = 14 correct to 2 significant figures.

Work out the lower bound for the value of y. Give your answer correct to 2 significant figures. Show your working clearly.

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


18 Show that 3 11

3 2

2

− − −+

+

( )x xx

ax b

a÷ can be written as where and bb are integers.



16

*S51832A01620*

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D

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IS AREA

D

O N

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TH

IS A

REA

D

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TH

IS A

REA

D

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19

A B

O

VDiagram NOT accurately drawn

The diagram shows a solid cone. The base of the cone is a horizontal circle, centre O, with radius 4.5 cm. AB is a diameter of the base and OV is the vertical height of the cone. The curved surface area of the cone is 130 cm2

Calculate the size of the angle AVB. Give your answer correct to 1 decimal place.

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


17


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D

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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

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TE IN

TH

IS A

REA

20y

(3,5)

xO

The diagram shows part of the curve with equation y = f(x) The coordinates of the maximum point of the curve are (3, 5)

(a) Write down the coordinates of the maximum point of the curve with equation

(i) y = f(x + 3)

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

(ii) y = 2f(x)

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

(iii) y = f(3x)

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

The curve with equation y = f(x) is transformed to give the curve with equation y = f(x) – 4

(b) Describe the transformation.

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

(1)



16

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D

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IS AREA

D

O N

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WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

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REA

19

A B

O

VDiagram NOT accurately drawn

The diagram shows a solid cone. The base of the cone is a horizontal circle, centre O, with radius 4.5 cm. AB is a diameter of the base and OV is the vertical height of the cone. The curved surface area of the cone is 130 cm2

Calculate the size of the angle AVB. Give your answer correct to 1 decimal place.

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


17


D

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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

20y

(3,5)

xO

The diagram shows part of the curve with equation y = f(x) The coordinates of the maximum point of the curve are (3, 5)

(a) Write down the coordinates of the maximum point of the curve with equation

(i) y = f(x + 3)

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

(ii) y = 2f(x)

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

(iii) y = f(3x)

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

The curve with equation y = f(x) is transformed to give the curve with equation y = f(x) – 4

(b) Describe the transformation.

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

(1)



18

*S51832A01820*

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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

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TE IN

TH

IS A

REA

21 The curve with equation y xx

= +822 has one stationary point.

Find the co-ordinates of this stationary point. Show your working clearly.

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


19


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RITE IN TH

IS AREA

D

O N

OT W

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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

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TE IN

TH

IS A

REA

22

3b

A 12a B

18aD CE


ABCD is a trapezium. AB is parallel to DC.

AB→

= 12a

AD→

= 3b

DC→

= 18a

E is the point on the line DB such that DE : EB = 1 : 2

Show by a vector method that BC is parallel to AE.



18

*S51832A01820*

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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

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TE IN

TH

IS A

REA

21 The curve with equation y xx

= +822 has one stationary point.

Find the co-ordinates of this stationary point. Show your working clearly.

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


19


D

O N

OT W

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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

3b

A 12a B

18aD CE


ABCD is a trapezium. AB is parallel to DC.

AB→

= 12a

AD→

= 3b

DC→

= 18a

E is the point on the line DB such that DE : EB = 1 : 2

Show by a vector method that BC is parallel to AE.



20

*S51832A02020*

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23 The 4th term of an arithmetic series is 17 The 10th term of the same arithmetic series is 35

Find the sum of the first 50 terms of this arithmetic series.




20

*S51832A02020*

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23 The 4th term of an arithmetic series is 17 The 10th term of the same arithmetic series is 35

Find the sum of the first 50 terms of this arithmetic series.



Inte

rnat

iona

l GC

SE in

Mat

hem

atic

s A -

Pape

r 1H

mar

k sc

hem

e

Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

1

7800

÷ 9

.75

or 7

800

÷ 58

5 ×

60

AO

2 M

2 M

1 fo

r 780

0 ÷

9.45

or 7

800

÷ 58

5 or

13.

3....

80

0 3

A

1

2

28÷

(6 −

4) (

=14)

AO

1 M

1 or

use

of c

ance

lled

ratio

s

(e.g

. 3 :

6 : 4

= 0

.75

: 1.5

: 1)

‘14’

× 3

(=42

)

M1

(dep

) 28

÷0.5

(=56

)

or c

ance

lled

ratio

s, (e

.g. 5

6⨯0.

75)

or M

2 fo

r 28

÷ 2 3

oe

42

3

A

1

3 a

25

< d

≤ 3

0 1

AO

3 B

1 B

1 id

entif

ies 2

5 →

30

clas

s

b

(12

× 2.

5) +

(6 ×

7.5

) + (4

× 1

2.5)

+

(6 ×

17.

5) +

(14

× 22

.5) +

( 18

×

27.5

) or

30

+ 45

+ 5

0 +

105

+ 31

5 +

495

or

1040

AO

3 M

2 M

1 fo

r fre

quen

cy ×

con

sist

ent v

alue

with

in in

terv

al

NB

. Pro

duct

s do

not n

eed

to b

e ad

ded

Con

done

one

err

or

‘104

0’ ÷

60

M

1

1

173

4

A

1 ac

cept

17.

3(33

…)

c

A

O3

M1

for

60a w

ith a

< 6

0 or

32 b w

ith b

> 3

2

32 60

oe

2

A

1


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

4

Wor

king

with

all

12 b

oxes

12 ×

15

(=18

0) o

r 12

× 1

2 (=

144)

AO

1 M

1

for c

orre

ct to

tal c

ost o

r cor

rect

tota

l num

ber o

f mel

ons

(eith

er m

ay a

ppea

r as p

art o

f ano

ther

cal

cula

tion)

312

121.

6oe

(17

2.8)

4

M

1

for r

even

ue fr

om a

ll fu

ll pr

ice

mel

ons s

old

1215

1.15

oe

(=20

7) o

r

180

× 0

.15

oe (=

27)

M

1

for t

otal

reve

nue

or to

tal p

rofit

'207

''1

72.8

'36

or 34

.2 36 o

r

'27'

('180

''1

72.8

')36

M

1

dep

on M

3

0.

95

5

A1

cao

Alte

rnat

ive

– w

orki

ng w

ith o

ne b

ox

15 ÷

12

(=1.

25) o

r 3

12(

9)4

M1

for p

rice

of 1

mel

on o

r nu

mbe

r of f

ull p

rice

mel

ons

312

1.6

oe(

14.4

)4

M

1 fo

r rev

enue

from

all

full

pric

e m

elon

s sol

d

151.

15

(=17

.25)

M1

for t

otal

reve

nue

from

one

box

'17.

25'

'14.

4'3

or 2.

85 3

M

1 de

p on

M3

0.

95

5

A1

cao


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

5

Circ

ular

arc

, cen

tre B

, to

inte

rsec

t bo

th li

nes A

B a

nd B

C

Equa

l len

gth

arcs

, fro

m in

ters

ectio

ns

on e

ach

line,

mee

ting

to g

ive

a po

int

on th

e bi

sect

or

AO

2 M

1

co

rrec

t bis

ecto

r 2

A

1 de

p on

M1

Full

cons

truct

ion

show

n.

6 a

A

O1

M1

Any

cor

rect

par

tially

fact

oris

ed e

xpre

ssio

n

9e

2 f (2e

+ 5

f 3)

2

A1

b

(x ±

6)(

x ±

2)

AO

1 M

1 or

cor

rect

subs

titut

ion

into

qua

drat

ic fo

rmul

a (c

ondo

ne o

ne

sign

err

or)

(x –

6)(

x +

2)

M

1 or

464

2

6,

−2

3

A1

dep.

on

at le

ast M

1

7

cos 3

5 =

17.6

PR

AO

2 M

1

17.6

× c

os35

M1

14

.4

3

A1

14.4

~ 1

4.42

8

22.5

0 ÷

15 (=

1.5)

or

100

÷ 15

(=

6.6…

.)

A

O1

M1

M2

for 2

2.5

÷ 0.

15

"1.5

" ×

100

(=15

0) o

r “6

.6…

” ×

22.5

(0)

M

1 de

p

15

0 3

A

1


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

9 a

14

0 00

0 1

AO

1 B

1

b

M

ars

1 A

O1

B1

c

1.2

× 10

5 – 5

× 1

04 or

1200

00 –

500

00 o

r 70

000

oe

AO

1 M

1

7

× 10

4 2

A

1

d

3.5

× 10

3 : 1.

4 ×

106

AO

1 M

1

1

: 400

2

A

1

10

2

29.

57.

6

or

90.2

557

.76

o

r 32

.49

or

32.5

AO

2 M

1

(BC

= )

5.7

A

1

"7.5"6.7

21

o

r 21

.6(6

) or

21.7

M1

dep

on fi

rst M

1

or e

.g.

17.

6si

n(

53.1

...)

9.5

ACB

a

nd

19.

5"5

.7"

sin"

53.1

"2

2

21

2"7.5"

or

12.7

(587

...) o

r

12.8

M

1 de

p on

firs

t M1

34

.4

5

A1

for a

nsw

er ro

undi

ng to

34.

4

(π→

34.

4187

...

3.1

4→34

.412

3...)


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

11

e.

g. (x

2 + 5

x –

3x –

15)

(x +

3) o

r

(x2 +

2x

– 15

)(x

+ 3)

or

(x –

5)(

x2 + 3

x –

3x –

9) o

r

(x –

5)(

x2 – 9

)

AO

1 M

1 ex

pans

ion

of a

ny tw

o of

the

thre

e b

rack

ets –

at l

east

3

corr

ect t

erm

s

E.g.

x3 +

3x2 +

2x2 +

6x

– 15

x –

45 o

r

x3 + 5

x2 –

9x −

45

M

1 (d

ep) f

t for

at l

east

3 c

orre

ct te

rms i

n se

cond

exp

ansi

on

x3 +

5x2

– 9x

− 4

5 3

A

1

12

a 1

4 1

6 1

7 1

8 2

0 2

1 2

2 2

3 2

3 2

4

24

AO

3 M

1

arra

nge

in o

rder

or

One

of 2

1(m

edia

n), 1

7(LQ

), 23

(UQ

) ide

ntifi

ed

( 14

16

17

18

20

21

22

23

23

24

24

)

(14

16

17

18

20)

and

(22

23

23

24

24

) 23

- 17

M

1

Iden

tify

any

two

of 2

1, 1

7 an

d 23

6

3

A1

cao

b

C

arm

elo

and

reas

on

usin

g IQ

R

1 A

O3

B1

ft fr

om (a

) Car

mel

o - h

e ha

s a lo

wer

IQR

oe

(IQR

mus

t be

part

of th

e st

atem

ent)


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

13

a m

=

52

31

or

3 4

oe

eg. 2

=

3 4

× 1

+ c

or

y –

2 =

3 4

(x –

1)

AO

1 M

1

M1

for g

radi

ent

for m

etho

d to

find

c

y =

3 4

x +

11 4

M

1 fo

und

valu

es o

f m a

nd c

subs

titut

ed in

y =

mx

+ c

3x

+ 4

y =

11

4

A1

b

12 6

xy

or

m =

1 3

o

e

A

O1

M1

sh

own

2

A1

for c

oncl

usio

n fr

om c

orre

ct g

radi

ents

14

26

÷20

(=1.

3) o

r

3.6×

10 o

r 3.3

×10

or 1

×30

or

36 o

r 33

or 3

0 or

26

113

05

AO

3 M

1 A

ny o

ne fr

eque

ncy

dens

ity (w

ithou

t con

tradi

ctio

n) o

r,

e.g.

1cm

2 = 5

or

clea

r ass

ocia

tion

of a

rea

with

freq

uenc

y

26 +

3.6

×10

+ 3.

3×10

+ 1

×30

or

26 +

36

+ 33

+ 3

0 or

1

625

5

or

1(1

3018

016

515

0)5

M

1 A

ny fu

lly c

orre

ct c

ompl

ete

met

hod;

cond

one

one

erro

r in

bar w

idth

or b

ar h

eigh

t

12

5 3

A

1

Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

15

a (3

x +

2)(2

x +

1) =

100

AO

1,

AO

2 M

1 or

(2x

× 3x

) + 2

(2x

+ 1)

+ 3

x =

100

oe

or (

2x ×

3x)

+ (2

× 2

x (×

1)) +

1) +

3x

+ 1

+ 1

= 10

0 oe

othe

r par

titio

ns a

re a

ccep

tabl

e bu

t par

titio

ning

mus

t go

on to

fo

rm a

cor

rect

equ

atio

n.

6x

2 + 7

x –

98 =

0 *

2

A

1 A

ccep

t 6x2 +

7x

+ 2

= 10

0 if

M1

awar

ded

* A

nsw

er g

iven

b

(3x

+ 14

)(2x

– 7

) (=

0)

AO

1 M

2 or

749

2352

12x

or

7

2401

12x

If n

ot M

2 th

en M

1 fo

r (3x

±14

)(2x

± 7

)

o

r

2

77

46

982

6x

x =

3.5

A

1 D

epen

dent

on

at le

ast M

1 Ig

nore

neg

ativ

e ro

ot

(Are

a =)

6 ×

‘3.5

’2 or (

3 ×

‘3.5

) × (2

× ‘3

.5’)

M

1 ft

Dep

ende

nt o

n at

leas

t M1

and

x >

0

73

.5

5

A1


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

15

a (3

x +

2)(2

x +

1) =

100

AO

1,

AO

2 M

1 or

(2x

× 3x

) + 2

(2x

+ 1)

+ 3

x =

100

oe

or (

2x ×

3x)

+ (2

× 2

x (×

1)) +

1) +

3x

+ 1

+ 1

= 10

0 oe

othe

r par

titio

ns a

re a

ccep

tabl

e bu

t par

titio

ning

mus

t go

on to

fo

rm a

cor

rect

equ

atio

n.

6x

2 + 7

x –

98 =

0 *

2

A

1 A

ccep

t 6x2 +

7x

+ 2

= 10

0 if

M1

awar

ded

* A

nsw

er g

iven

b

(3x

+ 14

)(2x

– 7

) (=

0)

AO

1 M

2 or

749

2352

12x

or

7

2401

12x

If n

ot M

2 th

en M

1 fo

r (3x

±14

)(2x

± 7

)

o

r

2

77

46

982

6x

x =

3.5

A

1 D

epen

dent

on

at le

ast M

1 Ig

nore

neg

ativ

e ro

ot

(Are

a =)

6 ×

‘3.5

’2 or (

3 ×

‘3.5

) × (2

× ‘3

.5’)

M

1 ft

Dep

ende

nt o

n at

leas

t M1

and

x >

0

73

.5

5

A1


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

16

18

0 −

77 −

39

or

77

BAD

and

39

ABD

or

64

""X

BA w

here

X is

on

PA

prod

uced

or

a fu

lly c

orre

ct m

etho

d to

find

ang

le

ADB

AO

2 M

2 al

so a

ccep

t 103

−39

M1

for

77

BAD

or

39

ABD

(ang

les m

ay b

e st

ated

or m

arke

d on

dia

gram

)

B1

Opp

osite

ang

les i

n a

cycl

ic q

uadr

ilate

ral a

dd u

p to

180

o

B1

Alte

rnat

e se

gmen

t the

orem

oe

64

5

A

1 ca

o

17

41

.5 o

r 42

.5 o

r 24

.5 o

r 23

.5 o

r 14

.5

or 1

3.5

AO

1 B

1

241

.5(

) 24.5

13.5

y

M1

7.

5 3

A

1 A

1 ac

cept

83 11 o

r 7.5

5 or

45.7 (

depe

ndin

g on

M1)

NB

. Ans

wer

mus

t com

e fr

om c

orre

ct w

orki

ng


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

18

3

2(

1)2

(1)

xx

x

A

O1

M1

corr

ect m

etho

d fo

r div

sion

(x +

1)(

x –

1)

M

1 co

rrec

t fac

toris

atio

n of

x2 −

1

eg3(

1)(3

2)(

1)x

xx

M1

corr

ect s

ingl

e fr

actio

n

1

1x

4

A

1

19

13

04.

5l

A

O2

M1

130

4.5

l

o

r l =

9.1

956

M

1 Fo

r exa

ct e

xpre

ssio

n or

ans

wer

whi

ch ro

unds

to 9

.2

sin

(AVO

) = 4

.5/”

9.20

” (=

0.4

89..)

M1

For a

cor

rect

exp

ress

ion

for s

in A

VO o

r cos

AV

B

cos (

AVB)

= (“

9.2”

2 +

“9.2

”2 – 9

2 )/(2

× “9

.2”

× “9

.2”)

(=

0.52

1...)

58

.6

4

A1

awrt

58.6

20

ai

(0

, 5)

1 A

O1

B1

ai

i

(3, 1

0)

1

B1

ai

ii

(1, 5

) 1

B

1

b

tra

nsla

tion

0 4

1

AO

1 B

1


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

21

2

d2

82

dyx

xx

A

O1

M2

(M1

for o

ne te

rm d

iffer

entia

ted

corr

ectly

)

22

82

0x

x

M1

dep

on M

1

31 8

x

or x

= 0

.5 o

e

M1

(0

.5, 6

) 5

A

1

22

AE

ADD

E

o

e

A

O2

M1

may

be

fully

or p

artia

lly in

term

s of a

and

/or b

eg.

DE

= 1 3

DB

or

BE =

2 3BD

M1

corr

ect u

se o

f rat

io

AE

2b +

4a

A

1

BCBA

ADD

C

(=3b

+ 6

a)

M

1 m

ay b

e fu

lly o

r par

tially

in te

rms o

f a a

nd/o

r b

eg

. AE

2(

b +

2a)

and

BC

3(b

+ 2a

)

5

A

1 N

B C

orre

ct e

xpre

ssio

ns fo

r BC

and

AE

mus

t be

give

n

Q

uest

ion

Wor

king

A

nsw

er

Mar

k A

O

N

otes

23

a

+ 3d

= 1

7 or

a +

9d

= 35

or

35 –

17

= 6d

AO

1 M

1

M1

for 1

7 =

4p +

q a

nd 3

5 =

10p

+ q

d =

3

A1

p

= 3

and

q =

5

a =

8

A1

ft fr

om d

= 3

u 1

= 8

and

u50

= 1

55

50(2

'8'

(50

1)'3

')2

oe

M

1

150

(815

5)2

40

75

5

A1


Q

uest

ion

Wor

king

A

nsw

er

Mar

k A

O

N

otes

23

a

+ 3d

= 1

7 or

a +

9d

= 35

or

35 –

17

= 6d

AO

1 M

1

M1

for 1

7 =

4p +

q a

nd 3

5 =

10p

+ q

d =

3

A1

p

= 3

and

q =

5

a =

8

A1

ft fr

om d

= 3

u 1

= 8

and

u50

= 1

55

50(2

'8'

(50

1)'3

')2

oe

M

1

150

(815

5)2

40

75

5

A1




Total Marks

Paper Reference

Turn over


1/2/1/1/1/

*S51833A0124*



Time: 2 hours


Instructions


Information


Advice


4MA1/2H





Total Marks

Paper Reference

Turn over


1/2/1/1/1/

*S51833A0124*



Time: 2 hours


Instructions


Information


Advice


4MA1/2H



2

*S51833A0224*

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


Arithmetic series



2(a + b)h

b

a

h



x b b aca

= − ± −2 42

Trigonometry

A B

C

b a

c

In any triangle ABC

Sine Rule aA

bB

cCsin sin sin

= =



ab sin C

Volume of cone = 13πr2h


r

lh


cross section

length


r

h

Volume of sphere = 43πr3


r

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 9 16 23


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



2

*S51833A0224*

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


Arithmetic series



2(a + b)h

b

a

h



x b b aca

= − ± −2 42

Trigonometry

A B

C

b a

c

In any triangle ABC

Sine Rule aA

bB

cCsin sin sin

= =



ab sin C

Volume of cone = 13πr2h


r

lh


cross section

length


r

h

Volume of sphere = 43πr3


r

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 9 16 23


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



4

*S51833A0424*

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


10 cm

6 cm

9 cm

14 cm




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


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


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

(1)


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

(1)


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

(1)

(d) Write 3 2 as a power of 2

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

(1)

(e) Solve 5(x + 7) = 2x – 10 Show clear algebraic working.

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

(3)



4

*S51833A0424*

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


10 cm

6 cm

9 cm

14 cm




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


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


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

(1)


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

(1)


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

(1)

(d) Write 3 2 as a power of 2

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

(1)

(e) Solve 5(x + 7) = 2x – 10 Show clear algebraic working.

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

(3)



6

*S51833A0624*

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



... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .rupees


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

x

y

1

2

3

4

5

1 2 3 4 5 6O–1

–2

–3

–4

–7

–1–2–3–4–5–6

A

B

–5

–6


(1)


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

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

(3)



6

*S51833A0624*

D

O N

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RITE IN TH

IS AREA

D

O N

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RITE IN TH

IS AREA

D

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IS AREA

D

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TH

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D

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TH

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TH

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... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .rupees


7


D

O N

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IS AREA

D

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IS AREA

D

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RITE IN TH

IS AREA

D

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TH

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TH

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D

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TH

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6

x

y

1

2

3

4

5

1 2 3 4 5 6O–1

–2

–3

–4

–7

–1–2–3–4–5–6

A

B

–5

–6


(1)


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

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

(3)



8

*S51833A0824*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

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RITE IN TH

IS AREA

D

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IS AREA

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TH

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d = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)



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

(2)


9


D

O N

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RITE IN TH

IS AREA

D

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IS AREA

D

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IS AREA

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TH

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TH

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HK$... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



8

*S51833A0824*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

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RITE IN TH

IS AREA

D

O N

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RITE IN TH

IS AREA

D

O N

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TH

IS A

REA

D

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TH

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D

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TH

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d = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)



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

(2)


9


D

O N

OT W

RITE IN TH

IS AREA

D

O N

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RITE IN TH

IS AREA

D

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IS AREA

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TH

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HK$... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



10

*S51833A01024*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

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RITE IN TH

IS AREA

D

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IS A

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D

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TH

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D

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TH

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3x + y = 13x – 2y = 9


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

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


10 Show that 4 23

59

1 516

÷ 3 =


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

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WRI

TE IN

TH

IS A

REA

D

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TE IN

TH

IS A

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D

O N

OT

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TE IN

TH

IS A

REA

11

86°

y° y°

123°

A

B C

D

EF

105°




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



10

*S51833A01024*

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


3x + y = 13x – 2y = 9


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

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


10 Show that 4 23

59

1 516

÷ 3 =


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

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OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

11

86°

y° y°

123°

A

B C

D

EF

105°




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



12

*S51833A01224*

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 table shows information about the amount of money that 120 people spent in a shop.

Amount of money (£m) Frequency

0 < m 10 8

10 < m 20 17

20 < m 30 25

30 < m 40 40

40 < m 50 22

50 < m 60 8

(a) Complete the cumulative frequency table.

Amount of money (£m) Cumulative frequency

0 < m 10

0 < m 20

0 < m 30

0 < m 40

0 < m 50

0 < m 60(1)

13


D

O N

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RITE IN TH

IS AREA

D

O N

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RITE IN TH

IS AREA

D

O N

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RITE IN TH

IS AREA

D

O N

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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

(b) On the grid, draw a cumulative frequency graph for your table.

O 10 20 30 40

Amount of money (£)

Cumulative frequency

50 60

120

100

80

60

40

20

(2)

(c) Use your graph to find an estimate for the median amount of money spent in the shop by these people.

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

(2)



12

*S51833A01224*

D

O N

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IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

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RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

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WRI

TE IN

TH

IS A

REA

D

O N

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WRI

TE IN

TH

IS A

REA

12 The table shows information about the amount of money that 120 people spent in a shop.

Amount of money (£m) Frequency

0 < m 10 8

10 < m 20 17

20 < m 30 25

30 < m 40 40

40 < m 50 22

50 < m 60 8

(a) Complete the cumulative frequency table.

Amount of money (£m) Cumulative frequency

0 < m 10

0 < m 20

0 < m 30

0 < m 40

0 < m 50

0 < m 60(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

(b) On the grid, draw a cumulative frequency graph for your table.

O 10 20 30 40

Amount of money (£)

Cumulative frequency

50 60

120

100

80

60

40

20

(2)

(c) Use your graph to find an estimate for the median amount of money spent in the shop by these people.

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

(2)



14

*S51833A01424*

D

O N

OT W

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IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

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RITE IN TH

IS AREA

D

O N

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WRI

TE IN

TH

IS A

REA

D

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WRI

TE IN

TH

IS A

REA

D

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TE IN

TH

IS A

REA

13 Make b the subject of P ab c= +12

2 where b is positive.

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


15


D

O N

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IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

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RITE IN TH

IS AREA

D

O N

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WRI

TE IN

TH

IS A

REA

D

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WRI

TE IN

TH

IS A

REA

D

O N

OT

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TE IN

TH

IS A

REA

14 The line with equation y = 2x is drawn on the grid.

(a) On the same grid, draw the line with equation 4x + 3y = 12(2)

x

y

2

4

6

2 4 6O

–2

–4

–6

–2–4–6

(b) Show, by shading on the grid, the region defined by all four inequalities

y 2x

4x + 3y 12

y −3

x 4(3)



14

*S51833A01424*

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

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RITE IN TH

IS AREA

D

O N

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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 Make b the subject of P ab c= +12

2 where b is positive.

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


15


D

O N

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IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

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RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

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TE IN

TH

IS A

REA

D

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TE IN

TH

IS A

REA

14 The line with equation y = 2x is drawn on the grid.

(a) On the same grid, draw the line with equation 4x + 3y = 12(2)

x

y

2

4

6

2 4 6O

–2

–4

–6

–2–4–6

(b) Show, by shading on the grid, the region defined by all four inequalities

y 2x

4x + 3y 12

y −3

x 4(3)



16

*S51833A01624*

D

O N

OT W

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IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

O N

OT W

RITE IN TH

IS AREA

D

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WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

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D

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TH

IS A

REA

15 There are 100 students in Year 11

All 100 students study at least one of art, drama and music.

7 of the students study art and drama and music. 23 of the students study art and drama. 35 of the students study art and music. 12 of the students study music and drama. 65 of the students study art. 52 of the students study music.

(a) Draw a Venn diagram to show this information.

(3)

One of the 100 students is selected at random.

(b) Find the probability that this student studies Drama but not Music.

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

(1)

Given that the student studies Drama,

(c) find the probability that this student also studies Art.

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

(1)


17


D

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IS AREA

D

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IS AREA

D

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RITE IN TH

IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

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WRI

TE IN

TH

IS A

REA

D

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16 M is inversely proportional to g3

M = 24 when g = 2.5

(a) Find a formula for M in terms of g

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

(3)

(b) Work out the value of g when M = 19

g = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)



16

*S51833A01624*

D

O N

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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

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WRI

TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

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D

O N

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IS A

REA

15 There are 100 students in Year 11

All 100 students study at least one of art, drama and music.

7 of the students study art and drama and music. 23 of the students study art and drama. 35 of the students study art and music. 12 of the students study music and drama. 65 of the students study art. 52 of the students study music.

(a) Draw a Venn diagram to show this information.

(3)

One of the 100 students is selected at random.

(b) Find the probability that this student studies Drama but not Music.

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

(1)

Given that the student studies Drama,

(c) find the probability that this student also studies Art.

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

(1)


17


D

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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

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TH

IS A

REA

16 M is inversely proportional to g3

M = 24 when g = 2.5

(a) Find a formula for M in terms of g

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

(3)

(b) Work out the value of g when M = 19

g = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)



18

*S51833A01824*

D

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IS AREA

D

O N

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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

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TH

IS A

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D

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17 The function f is such that f ( )xx

=−3

2 (a) Find f(1)

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

(1)

(b) State which value of x must be excluded from any domain of f

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

(1)

The function g is such that g(x) = x + 4

(c) Calculate fg(2)

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

(2)


18 Solid A and solid B are mathematically similar.

Solid A has surface area 384 cm2

Solid B has surface area 864 cm2

Solid B has a volume of 2457 cm3

Calculate the volume of solid A.

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


19


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IS A

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D

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19 Here are nine graphs.

Graph A

y

xO

Graph B

y

xO

Graph C

y

xO

Graph D

y

xO

Graph E

y

xO

Graph F

y

xO

Graph G

y

xO

Graph H

y

xO

Graph I

y

xO

Complete the table below with the letter of the graph that could represent each given equation.

Equation Graph

y = sin x

y = 2 – 3x

y = x2 + x – 6

y = x3 + 3x2 – 2



18

*S51833A01824*

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IS AREA

D

O N

OT

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TE IN

TH

IS A

REA

D

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TE IN

TH

IS A

REA

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TE IN

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REA

17 The function f is such that f ( )xx

=−3

2 (a) Find f(1)

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

(1)

(b) State which value of x must be excluded from any domain of f

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

(1)

The function g is such that g(x) = x + 4

(c) Calculate fg(2)

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

(2)


18 Solid A and solid B are mathematically similar.

Solid A has surface area 384 cm2

Solid B has surface area 864 cm2

Solid B has a volume of 2457 cm3

Calculate the volume of solid A.

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


19


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19 Here are nine graphs.

Graph A

y

xO

Graph B

y

xO

Graph C

y

xO

Graph D

y

xO

Graph E

y

xO

Graph F

y

xO

Graph G

y

xO

Graph H

y

xO

Graph I

y

xO

Complete the table below with the letter of the graph that could represent each given equation.

Equation Graph

y = sin x

y = 2 – 3x

y = x2 + x – 6

y = x3 + 3x2 – 2



20

*S51833A02024*

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IS AREA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

O N

OT

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TE IN

TH

IS A

REA

D

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TE IN

TH

IS A

REA

20 Gemma has 9 counters. Each counter has a number on it.

1 2 3 4 5 6 7 8 9

Gemma puts the 9 counters into a bag. She takes at random two counters from the bag.

(a) Work out the probability that the number on each counter is an even number.

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

(2)

(b) Work out the probability that the sum of the numbers on the two counters is an odd number. Show your working clearly.

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

(3)


21


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TE IN

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21 Here is triangle LMN, where angle LMN is an obtuse angle.

13.8 cm

L

M N47°

8.5 cm Diagram NOT accurately drawn

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

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



20

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TE IN

TH

IS A

REA

D

O N

OT

WRI

TE IN

TH

IS A

REA

D

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OT

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TE IN

TH

IS A

REA

20 Gemma has 9 counters. Each counter has a number on it.

1 2 3 4 5 6 7 8 9

Gemma puts the 9 counters into a bag. She takes at random two counters from the bag.

(a) Work out the probability that the number on each counter is an even number.

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

(2)

(b) Work out the probability that the sum of the numbers on the two counters is an odd number. Show your working clearly.

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

(3)


21


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D

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TE IN

TH

IS A

REA

D

O N

OT

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TE IN

TH

IS A

REA

D

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TE IN

TH

IS A

REA

21 Here is triangle LMN, where angle LMN is an obtuse angle.

13.8 cm

L

M N47°

8.5 cm Diagram NOT accurately drawn

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

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



22

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TE IN

TH

IS A

REA

D

O N

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TE IN

TH

IS A

REA

D

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TE IN

TH

IS A

REA

22 (a) Write 2x2 − 8x + 9 in the form a(x + b)2 + c

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

(3)

(b) Hence, or otherwise, explain why the graph of the curve with equation y = 2x2 − 8x + 9 = 0 does not intersect the x-axis.

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

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

(1)


23 ABCD is a parallelogram.

AB AC→

=

→=

23

94

Find the magnitude of BC→

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


23

*S51833A02324*

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OT W

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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 Show that 12 12 3

4 3 3−−

+ can be written as

Show your working clearly.


25 A particle moves along a straight line. The fixed point O lies on this line. The displacement of the particle from O at time t seconds, t 0, is s metres, where

s = t3 – 5t2 – 8t + 3

Find the value of t for which the particle is instantaneously at rest.

t = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .




22

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IS AREA

D

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OT W

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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 (a) Write 2x2 − 8x + 9 in the form a(x + b)2 + c

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

(3)

(b) Hence, or otherwise, explain why the graph of the curve with equation y = 2x2 − 8x + 9 = 0 does not intersect the x-axis.

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

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

(1)


23 ABCD is a parallelogram.

AB AC→

=

→=

23

94

Find the magnitude of BC→

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


23

*S51833A02324*

D

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IS AREA

D

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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 Show that 12 12 3

4 3 3−−

+ can be written as

Show your working clearly.


25 A particle moves along a straight line. The fixed point O lies on this line. The displacement of the particle from O at time t seconds, t 0, is s metres, where

s = t3 – 5t2 – 8t + 3

Find the value of t for which the particle is instantaneously at rest.

t = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .




24

*S51833A02424*

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D

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IS AREA

D

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IS AREA

BLANK PAGE

Inte

rnat

iona

l GC

SE in

Mat

hem

atic

s A -

Pape

r 2H

mar

k sc

hem

e

Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

1

2 ×

2 ×

5 or

2 ×

3 ×

5 o

r 3

× 3

× 5

or tw

o of

20, 4

0, 6

0 …

30, 6

0, 9

0 …

45, 9

0, 1

05

AO

1 M

1 fo

r one

of 2

0, 3

0, 4

5 w

ritte

n as

pro

duct

of p

rime

fact

ors o

r

list o

f at l

east

3 m

ultip

les o

f any

two

of 2

0, 3

0, 4

5

2 ×

2 ×

5 an

d 2

× 3

× 5

and

3 ×

3 ×

5

or a

ll of

20, 4

0, 6

0 , 8

0 …

180

30, 6

0, 9

0 …

180

45, 9

0, 1

05 …

180

M

1

18

0 3

A

1 fo

r 180

or 2

× 2

× 3

× 3

× 5

oe

2

A

O1

M1

for 7

n +

k (k

may

be

zero

)

7n

– 5

oe

2

A1

3

1(1

014

)9

2

oe

(= 1

08)

AO

2 M

1 fo

r are

a of

cro

ss se

ctio

n

‘108

’ × 6

(=64

8)

M

1 (d

ep o

n pr

evio

us M

1) fo

r vol

ume

of p

rism

‘648

’ × 0

.7

M

1 (in

depe

nden

t)

45

3.6

4

A1

acce

pt 4

54


24

*S51833A02424*

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

Inte

rnat

iona

l GC

SE in

Mat

hem

atic

s A -

Pape

r 2H

mar

k sc

hem

e

Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

1

2 ×

2 ×

5 or

2 ×

3 ×

5 o

r 3

× 3

× 5

or tw

o of

20, 4

0, 6

0 …

30, 6

0, 9

0 …

45, 9

0, 1

05

AO

1 M

1 fo

r one

of 2

0, 3

0, 4

5 w

ritte

n as

pro

duct

of p

rime

fact

ors o

r

list o

f at l

east

3 m

ultip

les o

f any

two

of 2

0, 3

0, 4

5

2 ×

2 ×

5 an

d 2

× 3

× 5

and

3 ×

3 ×

5

or a

ll of

20, 4

0, 6

0 , 8

0 …

180

30, 6

0, 9

0 …

180

45, 9

0, 1

05 …

180

M

1

18

0 3

A

1 fo

r 180

or 2

× 2

× 3

× 3

× 5

oe

2

A

O1

M1

for 7

n +

k (k

may

be

zero

)

7n

– 5

oe

2

A1

3

1(1

014

)9

2

oe

(= 1

08)

AO

2 M

1 fo

r are

a of

cro

ss se

ctio

n

‘108

’ × 6

(=64

8)

M

1 (d

ep o

n pr

evio

us M

1) fo

r vol

ume

of p

rism

‘648

’ × 0

.7

M

1 (in

depe

nden

t)

45

3.6

4

A1

acce

pt 4

54


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

4 a

p9

1 A

O1

B1

b

m

−12

1 A

O1

B1

c

1

1 A

O1

B1

d

1 3 2

1

AO

1 B

1

e

5x +

35

= 2x

– 1

0 or

210

75

5x

x

AO

1 M

1 fo

r rem

ovin

g br

acke

t or d

ivid

ing

all t

erm

s by

5

eg. 5

x –

2x =

−10

−35

or

102

75

5xx

M

1 fo

r iso

latin

g x

term

s in

a co

rrec

t equ

atio

n

−1

5 3

A

1 de

p on

M1

5

1400

0 ×

4 (=

5600

0)

AO

1 M

1 N

B. m

ultip

licat

ion

by 4

may

occ

ur b

efor

e or

afte

r per

cent

age

decr

ease

0.07

5 ×

‘560

00’ (

=420

0) o

r

0.0

75 ×

140

00 (=

1050

)

M

1

‘560

00’ –

‘420

00’ o

r

1400

0 –

‘105

0’

M

1 (d

ep)

51

800

4

A

1

Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

6 a

tri

angl

e w

ith

verti

ces

(3, -

1) (3

, -4)

(5, -

4)

1 A

O2

B1

b

R

otat

ion

A

O2

B1

ce

ntre

(-3,

0)

B1

90

o ant

iclo

ckw

ise

3

B1

acce

pt +

900 , 2

70o c

lock

wis

e, −

270o

NB

. If m

ore

than

one

tran

sfor

mat

ion

then

no

mar

ks c

an b

e aw

arde

d

7 a

4 ×

15 (=

60) o

r 15

4a

bc

d

or

4×15

– 3

9

AO

3 M

1

21

2

A

1

b

d −

a =

10

or a

= 1

1 or

a =

“21”

– 1

0 or

b +

c =

39

− 11

= 2

8

AO

3 M

1

ft fr

om (a

)

(can

be

impl

ied

by 1

1, b

¸ c, 2

1 O

R

a, b

, c, d

with

b +

c =

28)

14

2

A

1 ca

o

8

0.02

× 4

0 00

0 (=

800)

or

1.

02 ×

40

000

(=40

800)

or

2400

A

O1

M1

"408

00"×

0.02

(=81

6) a

nd

"416

16"×

0.02

(=83

2.32

) OR

2448

.32

M

1 (d

ep) m

etho

d to

find

inte

rest

for y

ear 2

and

yea

r 3

42

448.

32

3

A1


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

6 a

tri

angl

e w

ith

verti

ces

(3, -

1) (3

, -4)

(5, -

4)

1 A

O2

B1

b

R

otat

ion

A

O2

B1

ce

ntre

(-3,

0)

B1

90

o ant

iclo

ckw

ise

3

B1

acce

pt +

900 , 2

70o c

lock

wis

e, −

270o

NB

. If m

ore

than

one

tran

sfor

mat

ion

then

no

mar

ks c

an b

e aw

arde

d

7 a

4 ×

15 (=

60) o

r 15

4a

bc

d

or

4×15

– 3

9

AO

3 M

1

21

2

A

1

b

d −

a =

10

or a

= 1

1 or

a =

“21”

– 1

0 or

b +

c =

39

− 11

= 2

8

AO

3 M

1

ft fr

om (a

)

(can

be

impl

ied

by 1

1, b

¸ c, 2

1 O

R

a, b

, c, d

with

b +

c =

28)

14

2

A

1 ca

o

8

0.02

× 4

0 00

0 (=

800)

or

1.

02 ×

40

000

(=40

800)

or

2400

A

O1

M1

"408

00"×

0.02

(=81

6) a

nd

"416

16"×

0.02

(=83

2.32

) OR

2448

.32

M

1 (d

ep) m

etho

d to

find

inte

rest

for y

ear 2

and

yea

r 3

42

448.

32

3

A1


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

9

3x +

y =

13

o

r

6x

+ 2y

= 2

6

−

3x –

6y

= 27

+

x –

2y =

9

AO

1 M

1 m

ultip

licat

ion

of o

ne e

quat

ion

with

cor

rect

ope

ratio

n se

lect

ed o

r

rear

rang

emen

t of o

ne e

quat

ion

with

subs

titut

ion

into

seco

nd

eg. 3

x –

2 =

13 o

r 15

+ y

= 1

3

M1

(dep

) cor

rect

met

hod

to fi

nd se

cond

var

iabl

e

5,

−2

3

A1

for b

oth

solu

tions

dep

ende

nt o

n co

rrec

t wor

king

10

14

323

9

A

O1

M1

149

332

o

r 12

696

2727

o

r 42

329

9

M1

an

swer

giv

en

3

A1

corr

ect a

nsw

er fr

om c

orre

ct w

orki

ng

11

(6

– 2

) × 1

80 (=

720)

A

O2

M1

com

plet

e m

etho

d to

find

sum

of i

nter

ior a

ngle

s

‘720

’ – (8

6 +

123

+ 14

0 +

105)

(=

266)

or

‘720

’ – 4

54 (=

266)

M1

dep

on 1

st m

etho

d m

ark

‘266

’ ÷ 2

M1

dep

on 1

st m

etho

d m

ark

13

3 4

A

1


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

12

a

8, 2

5, 5

0, 9

0, 1

12,

120

1 A

O3

B1

cao

b

Plot

ting

poin

ts fr

om ta

ble

at e

nds o

f in

terv

al

AO

3 M

1 +

½ sq

ft fr

om se

nsib

le ta

ble

ie c

lear

atte

mpt

to a

dd fr

eque

ncie

s

Poin

ts jo

ined

with

cur

ve o

r lin

e se

gmen

ts

2

A

1 ft

from

poi

nts i

f 4 o

r 5 c

orre

ct o

r if a

ll po

ints

are

plo

tted

cons

iste

ntly

w

ithin

eac

h in

terv

al a

t the

cor

rect

hei

ghts

Acc

ept c

f gra

ph w

hich

is n

ot jo

ined

to th

e or

igin

NB

A b

ar c

hart,

unl

ess i

t has

a c

urve

goi

ng c

onsi

sten

tly th

roug

h a

poin

t in

each

bar

, sco

res n

o po

ints

.

c

60 (o

r 60.

5) in

dica

ted

on c

f gra

ph

or st

ated

AO

3 M

1 fo

r 60

(or 6

0.5)

indi

cate

d on

cf a

xis o

r sta

ted

ap

prox

33

2

A1

If M

1 sc

ored

, ft f

rom

cf g

raph

If no

indi

catio

n of

met

hod,

ft o

nly

from

cor

rect

cur

ve &

if a

nsw

er is

co

rrec

t (+

½ sq

tole

ranc

e) a

war

d M

1 A

1

13

1

22

Pc

ab

AO

1 M

1 Is

olat

e te

rm in

b

2()

2P

cb

a

M1

Isol

ate

b2

2(

)P

cb

a

3

A

1 oe

with

b a

s the

subj

ect


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

14

a 2

corr

ect p

oint

s plo

tted

eg

(0, 4

) and

(3, 0

)

A

O1

M1

4x +

3y

= 12

dra

wn

2

A1

b

3

AO

1 B

3 C

orre

ct re

gion

B2

for x

= 4

and

y =

−3

draw

n an

d co

nsis

tent

shad

ing

corr

ect f

or a

t le

ast t

wo

ineq

ualit

ies

B1

for x

= 4

and

y =

−3

draw

n

15

a

3 A

O1

B3

Cor

rect

dia

gram

B2

for 3

ove

r-la

ppin

g ci

rcle

s with

7 in

inte

rsec

tion

and

at le

ast 2

ot

her c

orre

ct n

umbe

rs

B1

for 3

ove

r-la

ppin

g ci

rcle

s with

7 in

inte

rsec

tion

b

34 10

0 o

e 1

AO

3 B

1 ft

from

dia

gram

c

23 46

oe

1 A

O3

B1

ft fr

om d

iagr

am

7

18

A M

D 5

12

28

14

16

0

Corr

ect

regi

on


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

16

a 3k

Mg

o

r 3k

Mg

AO

1 M

1

243

2.5k

o

e or

(k =

375

)

M1

impl

ies f

irst M

1

37

5 3M

g

3

A

1 ac

cept

3k

Mg

w

ith k

= 3

75 st

ated

els

ewhe

re in

que

stio

n

b

13

()

375

9g

o

e or

3 3375

A

O1

M1

15

2

A

1

17

a

−3

1 A

O1

B1

b

2

1 A

O1

B1

c

g(2)

= 6

A

O1

M1

0.

75 o

e 2

A

1

18

co

rrec

t len

gth

scal

e fa

ctor

eg

384

864

or

2 3 o

r 3 2

AO

2 M

1

32

2457

3

M1

for c

ompl

ete

met

hod

72

8 3

A

1


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

19

E, B

, D, A

3

AO

1 B

3 A

ll co

rrec

t

B

2 fo

r 3 c

orre

ct

B

1 fo

r 2 c

orre

ct

20

a 4

39

8

A

O3

M1

1 6

2

A

1 oe

, eg

Allo

w 0

.16(

666.

..) r

ound

ed o

r tru

ncat

ed to

at l

east

2dp

b

54

45

2020

or

98

98

7272

oe

or

43

54

19

89

8

o

r '1

'5

41

69

8

oe

5 9

A

O3

M2

M1

for

45

54

20 o

r o

r 9

89

872

oe

Acc

ept f

ract

ions

eva

luat

ed

200.

277

72

, 12

0.16

672

roun

ded

or tr

unca

ted

to a

t lea

st 2

dp

3

A1

oe, e

.g.

40 72or

20 36

Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

21

si

n47

sin

13.8

8.5MLN

AO

2 M

1 O

r met

hod

usin

g a

right

ang

led

trian

gle

to fi

nd le

ngth

MX

(MX

is

perp

endi

cula

r to

LN)

sin

478.

5M

X

sin4

78.

51

sin

13.8

MLN

M1

Or

8.5s

in47

1co

s13

.8

MLN

= 2

6.7(

73...

)

A1

LMX=

63.

232

LMN

= 1

80 −

47

– ‘2

6.7.

..’ o

r 10

6(.2

2606

22…

)

M1

LMN

= 6

3.23

2 +

(180

– (9

0+47

))…

or 1

06(.2

2606

22…

)

18.

513

.8si

n("1

06")

2

M1

56

.3

6

A1

Acc

ept a

n an

swer

that

roun

ds to

56.

3 or

56.

4 un

less

cle

arly

obt

aine

d fr

om in

corr

ect w

orki

ng.

22

a 2(

x2 − 4

x ) +

9 o

r

2(x2 −

4x

+ 9 2

)

AO

1 M

1

2((x

− 2

)2 – 2

2 ) + 9

or

2((x

− 2

)2 – 2

2 +

9 2)

M

1

2(

x −

2)2 +

1

3

A1

b

ex

plan

atio

n 1

AO

1 B

1 E.

g. B

ecau

se m

inim

um is

at (

2, 1

)


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

21

si

n47

sin

13.8

8.5MLN

AO

2 M

1 O

r met

hod

usin

g a

right

ang

led

trian

gle

to fi

nd le

ngth

MX

(MX

is

perp

endi

cula

r to

LN)

sin

478.

5M

X

sin4

78.

51

sin

13.8

MLN

M1

Or

8.5s

in47

1co

s13

.8

MLN

= 2

6.7(

73...

)

A1

LMX=

63.

232

LMN

= 1

80 −

47

– ‘2

6.7.

..’ o

r 10

6(.2

2606

22…

)

M1

LMN

= 6

3.23

2 +

(180

– (9

0+47

))…

or 1

06(.2

2606

22…

)

18.

513

.8si

n("1

06")

2

M1

56

.3

6

A1

Acc

ept a

n an

swer

that

roun

ds to

56.

3 or

56.

4 un

less

cle

arly

obt

aine

d fr

om in

corr

ect w

orki

ng.

22

a 2(

x2 − 4

x ) +

9 o

r

2(x2 −

4x

+ 9 2

)

AO

1 M

1

2((x

− 2

)2 – 2

2 ) + 9

or

2((x

− 2

)2 – 2

2 +

9 2)

M

1

2(

x −

2)2 +

1

3

A1

b

ex

plan

atio

n 1

AO

1 B

1 E.

g. B

ecau

se m

inim

um is

at (

2, 1

)


Que

stio

n W

orki

ng

Ans

wer

M

ark

AO

Not

es

23

BC

BAAC

or

29

34

o

r 7 1

AO

2 M

1

22

'7'

'1'

M

1 de

p

50

oe

3

A1

acce

pt 7

.07(

06…

)

24

12

12

3

23

23

A

O1

M1

met

hod

to ra

tiona

lise

212

212

33

43

M1

corr

ect e

xpan

sion

of b

rack

ets

122

3

B1

may

be

seen

bef

ore

expa

nsio

n

sh

own

4

A1

answ

er fr

om fu

lly c

orre

ct w

orki

ng w

ith a

ll st

eps s

een

25

(v

= )

3t 2 –

5×2

t − 8

A

O1

M1

for 2

out

of 3

term

s diff

eren

tiate

d co

rrec

tly

3t 2 –

10t

– 8

= 0

A1

corr

ect e

quat

ion

(3t

+ 2)

(t –

4) =

0

M

1 fo

r met

hod

to so

lve

quad

ratic

4

4

A1

t = 4

onl

y


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