Year 9 Sample Maths Paper

Page 1

Kingswood School Entrance Assessment

MATHEMATICS

(ENTRY TO YEAR 9) Standard Paper

Time Allowed: 1 hour

 Calculators are not allowed

 Write all your answers and working on the test paper – do not use any rough paper

 Try to answer all questions

 Check your work carefully

Please note: mobile devices (phones/tablets etc.) may not be taken into the examination room under any circumstances.

Write your full name here:

Write the name of your current school here: ……………………………………………………

Write your date of birth here: ……………………………………………………………………………

Mark = ________ out of 89

= ________ %

2a) b) c)

Find 20% of £5.50 Find of 6.24 metres Express your answer in centimetres Express 45% as a fraction in its lowest terms

Marks)

Page 2 of 12 1a)
(2) (2) (2) (6 Marks)
b) c) (2) (2) (1) (2) (7
8.45 + 2.57 8.43 – 2.55 10.36 ÷ 7
d)

3) Arrange the following numbers in order of size, starting with the smallest.

4)

a)

Write down the next two numbers in each of the following sequences:

3, 10, 17, 24, …

b)

1, 4, 16, 64, …

c)

15, …

Page 3 of 12
(3)
(3 Marks)
0, 3, 8,
(2) (2) (2)
(6 Marks)

5a)

Express the number 550 as a product of prime factors, using indices (powers).

b)

Use your answer to part (a) to find a common factor of 75 and 550.

(4 Marks)

6)

When answering the following questions, use the conversion rate given below:

a)

2.54 centimetres = 1 inch 12 inches = 1 foot Express 3 inches in centimetres.

b)

Jane hired some skis. Jane finds that her skis are 8 feet long.

What is this length in metres, rounded to the nearest centimetre?

(6 Marks)

Page 4 of 12
(3) (1)
(1) (5)

7) During a sudden cold spell, the temperature fell from 14˚C to -3˚C. By how many degrees did the temperature fall?

8)

A person with an overdraft (shown as a negative balance) owes the bank money. The following table shows the bank balance of Mr. Spender at the end of each of six months.

a)

In which month did Mr. Spender have the smallest overdraft?

b)

In which month did Mr Spender owe the most money?

c)

What was the greatest monthly increase in bank balance?

Page 5 of 12
(2)
(2 Marks)
(1) (1) (2)
(4 Marks)

9)

a)

You are told that 55lb = 25kg

b)

On the grid below, using a sensible scale, draw a graph to convert pounds to kilograms. Using the graph, express 25lb in kilograms.

Page 6 of 12
(3) (2) (5 Marks)

10)

Show all of the lines of symmetry of the following shapes:

a)

b)

Page 7 of 12
(2) (2) (4 Marks)

11a)

Adam, Brenda and Charles share a sum of money in proportion to their ages.

Adam is 10 years old and receives 60p.

If Brenda is 12 years old and Charles is 15 years old, what is the total sum of money shared out between the three children?

b)

The sizes of the angles of a quadrilateral are in the ratio 3:4:5:6.

Calculate the size of each angle.

Page 8 of 12
(3) (4) (7 Marks)

Solve these equations: (

Simplify: 2a + 4a 5a x 4a (2a)

Page 9 of 12
a) b) c) d)
(1) (2) (3) (1) (7 Marks)
a) b) c)
3 (1) (2) (2) (5 Marks)
12)
)
13)
Page 10 of 12 14) a) b) c) If p = -2, q = 7 and r = 3, find the values of pq + 6r q2 - pr
(2) (2)
(3) (7 Marks)

A coin and four sided die (with faces numbered 1 – 4) are thrown. Complete the table showing the possible equally likely outcomes.

Complete the table showing the possible likely outcomes.

Write down the probability that the outcome is a tail (T) and a 2

Write down the probability that the outcome is a head (H) and an even number.

What is the probability that the outcome is a tail (T) and a prime number?

Page 11 of 12
15) a) b) c) d)
(2) (2) (2)
(2)
(8 Marks)

d)

In an examination (out of 40) the following marks were recorded for a class of ten children.

24 26 37 19 28 36 27 35 29 33

Calculate the total number of marks scored by the class.

e)

Calculate the mean mark for the class.

Complete the distribution table for marks achieved by the class.

From your distribution table, select the modal mark range.

Write down an estimate for the probability that a pupil chosen at random from the class scored at least 30 marks.

Page 12 of 12
16) a) b) c)
(1) (2) (3) (1) (1)
END
(8 Marks)
OF EXAMINATION

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