11+ MATHEMATICS

EXAMPLE

ENTRANCE EXAMINATION PAPER

NAME ___________________________________Entrance Number _____

Time allowed: 60 minutes

Answer as many questions as you can. You are not expected to answer every question. Do not spend too long on one question. If you cannot do a question, miss it out. Show the stages of your working clearly. You are not allowed to use a calculator. The total mark for this paper is 100.

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Q1.

Work out

1048 + 208 = ..................

1 mark

4828 – 480 = ...................

1 mark

Q2.

(a) Write the answers.

(4 + 2) × 3 = ................... 1 mark

4 + (2 × 3) = ...................

1 mark

504 ÷ 8 = 1 mark

(b) Put brackets in the calculation to make the answer 50

4 + 5 + 1 × 5

1 mark

(c) Now put brackets in the calculation to make the answer 34

4 + 5 + 1 × 5

1 mark

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Q3.

Work out the missing numbers. In each part, you can use the first line to

help you.

(a)

16 × 15 = 240

16 × …........ = 480

1 mark

(b)

46 × 44 = 2024

46 × 22 = …...

1 mark

(c)

600 ÷ 24 = 25

600 ÷ ........... = 50

1 mark

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Q4.

Add three to the number on each number line. The first one is done for

you.

2 marks

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Q5.

(a) The number chain below is part of a doubling number chain.

Fill in the two missing numbers.

1 mark

(b) Find two different prime numbers so that when added together the

answer is 32 and when multiplied the answer is 247.

1 mark

(c) How many mm are there in 2.01 m? 1 mark

(d) Write down two prime numbers smaller than 100, but bigger than 90.

1 mark

(e) Write down all factors of 30.

2 marks

(f) Now write down all the prime factors of 30 1 mark

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Q6.

The diagram shows some shapes on a 10 by 6 square grid.

(a) Which two shapes have the same area as shape A?

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

1 mark

(b) Which two shapes have the same perimeter as shape A?

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

1 mark

(c) How many of shape C would you need to cover a 10 by 6 square

grid?

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

1 mark

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Q7.

1 cm

1 cm

(a) (i) Find the area of the shaded shape.

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

(ii) Find the perimeter of the shaded shape.

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

2 marks

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Q8.

Here is a solid prism made from centimeter cubes.

1 cm3

Find the volume of the solid prism.

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

1 mark

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Q9.

100 cm 20 cm

20 cm

100 cm

Diagrams accurately drawn

NOT

200 cm

50 cm

A carton measures 200 cm by 100 cm by 100 cm.

The carton is to be completely filled with boxes.

Each box measures 50 cm by 20cm by 20 cm.

Work out the number of boxes which can completely fill the carton.

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

3 marks

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Q10.

.

This diagram shows the floor plan of a room.

Work out the area of the floor.

Give the units with your answer.

.................... …………. 2 marks

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Q11.

Write down the special mathematical name of each of these two 3-D shapes.

(i) (ii)

(i) ………………………… (ii)……………………………………

2 marks

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Q12.

a) Write down the fraction of this shape that is shaded.

…………………

1 mark

(b) .altogether shaded is shape theof 4

3 that so shadingenough Add

1 mark

(c) Write down the percentage of the shape that is now unshaded.

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

1 mark

(d) Shade 10% of this grid.

1 mark

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Q13.

(a) Which of these fractions is smaller than2

1? Circle the correct

one.

6

4,

16

7,

12

6,

20

11 1 mark

(b) List five consecutive whole numbers which add up to 100.

2 marks

Q14.

A meal in a restaurant costs the same for each person.

For 11 people the total cost is £253

What is the total cost for 12 people?

£

2 marks

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Q15.

(a) 9 × 28

2 marks

(b) What is 27 × 28?

You can use part (a) to help you.

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

1 mark

Q16. Give the answer to each of the following as a fraction in its simplest

form:

+ =

2 marks

– =

2 marks

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Q17.

(a) Write the missing numbers.

50% of 80 = ..............

5% of 80 = ...............

1% of 80 = ..............

3 marks

(b) Work out 56% of 80

You can use part (a) to help you.

............................ 1 mark

(c) Write down 5

4 as a percentage. 1 marks

Q18.

Simplify this expression.

5k + 7 + 3k =

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

1 mark

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Q19.

(a) When x = 5, work out the values of the expressions below.

2x + 13 = ......................

5x – 5 = ........................

2 marks

(b) When 2y + 11 = 17, work out the value of y

Show your working.

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

2 marks

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Q20.

(a) Write each expression in its simplest form.

b + 7 + 2b + 10

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

1 mark

(3d + 5) + (d – 2)

......................................... 1 mark

3m – (– m)

........................................... 1 mark

(b) I think of a number. When multiplied by 4, then 8 is subtracted from the answer

and then divided by 5 the answer is 4. What number did I think of?

2 marks

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Q21.

(a) Here are two equations.

k = a + b

a + b + k = 30

What is the value of k?

k = ......................... 2 marks

(b) Look at this information.

10 = c + d

c is one more than d

What is the value of c?

c = .......................... 2 marks

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Q22.

Kim is thinking of a number.

1 mark

Q23.

The price of a coat is £6

In a sale the price is reduced by 15%

What is the sale price of the coat?

£

2 marks

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Q24.

The diagram shows triangle PQR.

-

Work out the sizes of angles a, b and c

a = ……………°

b = …..………°

c = …….………°

3 marks

-

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Q25.

2 tins balance 1 bottle. 1 tin and 1 bottle balance 1 box.

(a) How many bottles do 6 tins balance?

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

1 mark

(b) How many boxes do 6 tins balance?

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

1 mark

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Q26.

A shop sells school uniform.

Two shirts and one jumper cost £29

One shirt and one jumper cost £21

How much does one jumper cost?

£

2 marks

Q27.

(a) Look at these three numbers.

Find the mean of the three numbers.

1 mark

Find the median of the three numbers.

1 mark

-

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Q28.

Write the missing numbers in these fraction sums.

1 mark

Q29.

(a) Put these values in order of size with the smallest first.

52 3

2 3

3 2

4

............ ............ ............ ............ smallest largest

2 marks

(b) Write down the next three terms in each of the following sequences:

i) 10, 7, 4, 1, 1 mark

ii) 2, 3, 5, 7, 11, 13, 17, 19, 1 mark

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Q30.

(a) A teacher asked her pupils if they recycled newspapers and glass.

The pie chart shows the results.

5 pupils answered ‘Neither’.

How many pupils answered ‘Newspapers only’?

Show your working.

……….…… pupils

2 marks

45˚ 90˚

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(b) The teacher asked a different class if they recycled newspapers and

glass.

There were 20 pupils in the class.

9 pupils answered ‘Newspapers only’.

On a pie chart, what would the angle be for the sector ‘Newspapers

only’? Do not draw the Pi chart.

Show your working.

...............................°

2 marks

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Q31.

Solve this equation.

7 + 5k = 8k + 1

k = ......................... 2 marks

Q32.

Find the values of t.

63

2 t

t = ......................... 1 mark

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Q33.

A rectangular field has a length which is three times as long as the width. If

the perimeter is 32 m, what is its area in m2?

Area = .. .. m2

2 marks

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Q34.

I have two bags of cubes.

Each bag contains more than 20 but fewer than 30 cubes.

(a) I can share the cubes in bag A

equally between 9 people.

How many cubes are in bag A?

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

1 mark

(b) I can share the cubes in bag B

equally between 4 people.

How many cubes could be in bag B?

There are two answers. Write them both.

................. or .....................

2 marks

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Q35.

a) If 4(5x -7) = 2, calculate the value of 15- 10x.

2 marks

b) Given that x ☼ y = 2x + y

And m ۞n = n

m2

Work out the answer to:

[(4 ☼ 8) ☼ 3] ۞ 7 = 2 marks