© Oxford University Press 2015 Acknowledgements: www.oxfordsecondary.co.uk/acknowledgements Paper 1 – Non-calculator Paper

Mathematics

Higher 80 marks

1 hour

30 minutes

Ch 1 Set A Paper 1: Non-Calculator

Name ______________________________________ Class _________

______________________________________ Date ______________________

Test A

Materials For this paper you must have:

mathematical instruments You may not use a calculator. Instructions

Use black or blue ink or ball-point pen. Draw diagrams in pencil.

Answer all the questions.

Do all rough work in on this paper. Cross through any work that you do not want to be marked.

In all calculations, show clearly how you work out your answer.

Information

The maximum mark for this paper is 80.

The marks for each question are shown in brackets [ ]. - Use this as a guide as to how much time to spend

on each question. Advice

Read each question carefully before you start to answer it.

Keep an eye on the time.

Try to answer every question.

Check your answers if you have time at the end.

Question Mark

1

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Total

© Oxford University Press 2015 Acknowledgements: www.oxfordsecondary.co.uk/acknowledgements Paper 1 – Non-calculator Paper

1 What is the ratio 4 : 10 in the form 1 : n?

Circle your answer.

2 : 5 1 : 2.5 1: 0.4 2.5 : 1

[1 mark]

2 Circle the number that is square, even and a multiple of 6.

16 36 25 30

[1 mark]

3 The length of a swimming pool is 50 metres.

Jane swims 24 lengths of the pool.

How far does she swim? Give your answer in kilometres.

____________________

[2 marks]

4 Which of these is not a square number? Circle your answer.

9 × 106 9 × 10

5 16 × 10

2 16 × 10

4

[1 mark]

© Oxford University Press 2015 Acknowledgements: www.oxfordsecondary.co.uk/acknowledgements Paper 1 – Non-calculator Paper

5 Convert these areas to the units given.

a 300 mm2 to cm

2

____________________

b 5 m2 to cm

2

____________________

c 250 000 m2 to km

2

____________________

d 0.3 m2 to mm

2

____________________

[1 mark]

[1 mark]

[1 mark]

[1 mark]

© Oxford University Press 2015 Acknowledgements: www.oxfordsecondary.co.uk/acknowledgements Paper 1 – Non-calculator Paper

6 Complete these calculations.

a

b

[1 mark]

[1 mark]

7 Expand and simplify

2(2x + 4) + 4(3x + 2)

Circle the correct answer

16x + 12 12x + 16 16x + 10 16x + 6

[1 mark]

8 Ellie and Jaffar both worked out

Ellie

Jaffar

Comment on their work.

____________________________________________________________________

____________________________________________________________________

____________________________________________________________________

[2 marks]

© Oxford University Press 2015 Acknowledgements: www.oxfordsecondary.co.uk/acknowledgements Paper 1 – Non-calculator Paper

9 Investigators test three coins for bias.

They flip each coin several times and put

their results in this table.

List the coins in order of bias, with the

least biased first, giving a reason for each.

____________________________________________________________________

____________________________________________________________________

[4 marks]

10 For a scatter graph with a line of best fit explain the meaning of these terms and

comment on the reliability of each technique.

a Interpolation.

____________________________________________________________________

____________________________________________________________________

____________________________________________________________________

____________________________________________________________________

b Extrapolation.

____________________________________________________________________

____________________________________________________________________

____________________________________________________________________

____________________________________________________________________

[2 marks]

[2 marks]

© Oxford University Press 2015 Acknowledgements: www.oxfordsecondary.co.uk/acknowledgements Paper 1 – Non-calculator Paper

11 The nth term of a sequence is 4n – 3.

a Is 75 a term of this sequence? Give a reason for your answer.

__________________because____________________________________________

____________________________________________________________________

b Write an expression for the (n + 1)th term of this sequence.

____________________

c Write an expression for the sum of the nth and (n + 1)th terms

____________________

d The sum of two consecutive numbers in the sequence is 326.

Work out the smaller of these numbers.

____________________

[2 marks]

[1 mark]

[1 mark]

[2 marks]

© Oxford University Press 2015 Acknowledgements: www.oxfordsecondary.co.uk/acknowledgements Paper 1 – Non-calculator Paper

12 Two triangles are shown on the grid.

a Write down the column vector for the translation that moves triangle P to

triangle Q.

____________________

b Translate triangle Q using the vector ( ).

Label your new triangle R.

c Write down the vector for the single translation that moves triangle P to

triangle R.

____________________

d Show the connection between the vectors in parts a and b and your answer to

part c.

____________________________________________________________________

[1 mark]

[2 marks]

[1 mark]

[1 mark]

© Oxford University Press 2015 Acknowledgements: www.oxfordsecondary.co.uk/acknowledgements Paper 1 – Non-calculator Paper

13 When two ordinary coins are spun the only possible outcomes are two heads, two

tails or one head and one tail

a Explain why the probability of each outcome is not 1

3.

____________________________________________________________________

____________________________________________________________________

____________________________________________________________________

____________________________________________________________________

b What is the probability of getting two heads?

____________________

[2 marks]

[1 mark]

14 The graph shows the height in metres, h, of a ball thrown into the air against time, t,

seconds.

a What is the maximum height of the ball?

Circle your answer.

10m 2 m 12m 4 m

b For how long was the ball in the air?

Circle your answer.

12 seconds 3 seconds 5 seconds 4 seconds

[1 mark]

[1 mark]

© Oxford University Press 2015 Acknowledgements: www.oxfordsecondary.co.uk/acknowledgements Paper 1 – Non-calculator Paper

15 Zak wants to go from London to York and back in the same day. This journey is a

distance of 205 miles each way. He can hire a car or go by train. A small car costs

£38.56 per day and 10.2 p per mile. A large car costs £71.53 per day and 19.2p per

mile. A one-way train costs £67.50 and takes 2 hours 14 minutes. By car, his average

speed will be about 50 mph (including rests).

a Estimate how much more a large car will cost than a small car.

____________________

b Use the estimates you found in part a to compare the total costs of the three

possibilities and advise Zak on how to travel. Give a reason for your answer.

____________________________________________________________________

____________________________________________________________________

____________________________________________________________________

[3 marks]

[2 marks]

16 a A square has side length x.

Khalid says,

‘The area of my square has the same numerical value as its perimeter.’

List the side lengths of all the squares that fit this description.

____________________

b A cube has side length y.

Mia says,

’The volume of my cube has the same numerical value as its surface area.’

List the side lengths of all the cubes that fit this description.

____________________

[2 marks]

[2 marks]

© Oxford University Press 2015 Acknowledgements: www.oxfordsecondary.co.uk/acknowledgements Paper 1 – Non-calculator Paper

17 PQRS is a square and PQT is an equilateral triangle.

Not drawn accurately

Work out the size of angle STR.

You must show your working.

____________________

[6 marks]

18 a Factorise x2 – 49

____________________

b Given that 4095 = 84 – 1 write 4095 as a product of its prime factors.

____________________

[1 mark]

[3 marks]

© Oxford University Press 2015 Acknowledgements: www.oxfordsecondary.co.uk/acknowledgements Paper 1 – Non-calculator Paper

19 A line has gradient 3.

M and N are two points on this line.

M is (5, k) and N is (6, _____).

Circle the expression for the y-coordinate of N.

k - 3 k + 5 k + 3 k + 6

[1 mark]

20 A, B, C and D are four points on the circumference of a circle.

BC and AD are extended to meet at E.

Angle ABC = 85° and angle CED = 36°.

a Complete the statement.

ABCD is a ____________________ quadrilateral.

b Work out the value of x.

Give a reason for each step of your working.

____________________

[1 mark]

[4 marks]

© Oxford University Press 2015 Acknowledgements: www.oxfordsecondary.co.uk/acknowledgements Paper 1 – Non-calculator Paper

21 Solve

____________________

[2 marks]

22 Sphere A has a 5 cm radius and sphere B has a 10 cm radius.

a Surface area of a sphere = 4πr2

Calculate the surface area of sphere A, giving your answer in terms of π.

____________________

b Write the ratio

surface area of A : surface area of B

in its simplest terms.

____________________

[2 marks]

[2 marks]

© Oxford University Press 2015 Acknowledgements: www.oxfordsecondary.co.uk/acknowledgements Paper 1 – Non-calculator Paper

23 In triangle OAB, ⃗⃗⃗⃗ ⃗ = a and ⃗⃗⃗⃗ ⃗ = b.

a Express ⃗⃗⃗⃗ ⃗ in terms of a and b.

____________________

b M is the midpoint of AB.

Express ⃗⃗⃗⃗⃗⃗ in terms of a and b.

____________________

c N is the midpoint of OM.

Express ⃗⃗ ⃗⃗ ⃗ in terms of a and b.

____________________

[1 mark]

[1 mark]

[3 marks]

© Oxford University Press 2015 Acknowledgements: www.oxfordsecondary.co.uk/acknowledgements Paper 1 – Non-calculator Paper

24 The half-life of a drug is the time it takes for a dose to reduce to half its initial

amount. A doctor prescribes a 4 mg sleeping pill with a half-life of 24 hours.

a How many times does the dose halve to reduce to 0.25 mg?

____________________

b How many hours does it take for the dose to reduce to 0.125 mg?

____________________

c Write down a formula connecting the mass, m, of drug remaining with its

half -life, t.

____________________

[2 marks]

[2 marks]

[2 marks]

Total for paper is 80 marks