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