SURNAME ............................................................................... FIRST NAME .............................................................................
JUNIOR SCHOOL ................................................................... SENIOR SCHOOL .....................................................................
COMMON ENTRANCE EXAMINATION AT 11+
MATHEMATICS
Monday 7 November 2016
Please read this information before the examination starts.
This examination is 60 minutes long.
•
Please try all the questions.
•
Write your answers on the dotted lines.
•
All working should be written on the paper.
•
Tracing paper may be used.
•
Calculators are not allowed.
•
Answers given as fractions should be reduced to their simplest form.
28116103
•
© Independent Schools Examinations Board
1. Write down the answers to these questions.
(You may work them out in your head.)
(i)743 1 37
Answer: ..................................... (1)
(ii) 100 3 35
Answer: ..................................... (1)
(iii) 1006 2 899
Answer: ..................................... (1)
(iv) Half of 870
Answer: ..................................... (1)
(v) 840 4 4
Answer: ..................................... (1)
(vi) 10% of £46.00
Answer: £ .................................. (1)
(vii) 3 3 108
Answer: ..................................... (1)
(viii) 542 2 112
Answer: ..................................... (1)
S.A. 281161032
2. Look at the price list.
(i) What is the total cost of 5 soaps?
Price list
Soap£2.25
Sponge£1.75
Shampoo£1.99
Hairbrush£3.40
Answer: £ .................................. (1)
(ii) Emma buys 2 bottles of shampoo and a hairbrush.
(a) How much should Emma pay?
Answer: £ .................................. (2)
Emma pays with a £10 note.
(b) How much change should she receive?
Answer: £ .................................. (1)
(iii) Jenny has a £20 note.
How many hairbrushes can she buy?
Answer: ..................................... (2)
3. Write down the value of each of these Roman numerals.
(i)XV
Answer: ..................................... (1)
(ii) LIV
Answer: ..................................... (1)
S.A. 281161033
Turn over
4. Here is a set of number cards:
1
2
3
5
7
8
Two cards are chosen to make a 2-digit number.
To make the smallest even number Sarah picks 1 and 2. Use two cards each time to make the following 2 digit numbers.
You may use each card for more than one part of the question.
(i) A multiple of 7
Answer: ..................................... (1)
(ii) A prime number between 20 and 30
Answer: ..................................... (1)
(iii) The largest possible square number
Answer: ..................................... (1)
(iv) 33
Answer: ..................................... (1)
S.A. 281161034
5. (a) A number machine has the rule multiply by 7, then subtract 13
LQSXW
RXWSXW
Fill in the missing numbers on the dotted lines below.
5
......
......
......
37
......
49
213
......
50
......
(3)
(b) John chooses a number.
He divides it by 6 and then adds 88.
What number did he start with?
The result is 99.
Answer: ..................................... (2)
(c) Freya designs a number machine which adds 15 to whole numbers and then
multiplies by 6.
She says that all her answers will be even numbers.
Give a reason for your answer.
Circle below whether or not Freya is correct.
Answer: Yes / No
reason: .......................................................................................................................
.................................................................................................................................... (2)
S.A. 281161035
Turn over
6. Look at the shapes below.
UHJXODU
SHQWDJRQ
$
%
&
'
(i) Write down the letter name of all the shapes shown above which have only one line
of symmetry.
Answer: ..................................... (1)
(ii) Write down the order of rotational symmetry of shape C.
Answer: ..................................... (1)
7. Use the number statement below to work out the answers to the calculations which
follow.
12 3 235 5 2820
(i)24 3 235 5
Answer: ..................................... (1)
(ii) 28 200 4 12 5
Answer: ..................................... (1)
(iii) 12 3 23.5 5
Answer: ..................................... (1)
S.A. 281161036
8. The points (2, 4), (5, 4) and (3, 1) have been plotted on the centimetre-squared grid
below.
\
[
(i) Plot the point (5, 1) then join the four points to form a quadrilateral.
Label the shape A.(2)
(ii) What is the mathematical name of quadrilateral A?
Answer: ..................................... (1)
(iii) Translate shape A 4 units right and 5 units up.
Label the new shape B.(2)
(iv) Reflect shape A in the dashed line.
Label the new shape C.(2)
(v) What is the area of shape A?
Answer: ............................... cm2(1)
S.A. 281161037
Turn over
9. Here are five lengths:
830 mm 3.8 m 308 cm 0.38 m 8.03 m
(i) Write these lengths in order, from the shortest to the longest.
Answer: ......................, ......................, ......................, ......................, ...................... (3)
(ii)What is the difference, in centimetres, between the shortest and the longest
length?
Answer: ................................ cm(2)
10. (a) A full glass of milk contains 150 millilitres.
How many litres are there in 28 full glasses?
Answer: ............................. litres(3)
(b) Toby, the cat, drinks the same amount of milk each day.
Toby drinks 900 millilitres in 12 days.
How much milk does Toby drink each day?
Answer: ................................. ml(2)
S.A. 281161038
(c) There is juice in the container shown below.
David wants to add more juice to fill it to the level of the arrow.
How many more millilitres of juice does David need to add?
²
²
OLWUHV ²
²
²
²
²
OLWUHV ²
²
²
²
²
Answer: ................................. ml(2)
11. (a) In a group of lambs, 4 out of every 7 are male.
There are 12 male lambs.
How many lambs are there in total?
Answer: ..................................... (2)
(b) Venus and Serena play tennis.
For every 3 points Venus wins, Serena wins 5.
How many more points does Serena win than Venus?
They play 40 points altogether.
Answer: ..................................... (2)
S.A. 281161039
Turn over
12. Work out the following, giving your answer as a mixed number where appropriate.
(i)
3
7
1
8
8
Answer: ..................................... (2)
(ii)
2
3 4
5
(You may use the diagrams to help you.)
Answer: ..................................... (2)
(iii)
2
4
3
3
5
Answer: ..................................... (1)
13. (a) What fraction, in its simplest form, is equivalent to 0.6?
Answer: ..................................... (1)
(b) What decimal is equivalent to two and three quarters?
Answer: ..................................... (1)
14. Work out 30% of 70
Answer: ..................................... (2)
S.A. 2811610310
15. Three children each ate part of a cake.
Rob ate
3
1
1
, Sarah ate
and Tom ate
5
10
10
(i) What fraction of the cake was left over?
Answer: ..................................... (2)
(ii) Tom’s share of the cake weighed 360 grams.
Work out the mass of the whole cake in kilograms.
Answer: ................................. kg (2)
16. A shop is having a sale.
6$/(
Complete the table below by working out the new prices.
old price
reduction
new price
£60.00
£10.00 off
£50.00
£128.00
now pay half price
£ .............
£75.00
reduced by
£84.00
25% off
S.A. 2811610311
1
3
£ .............
£ .............
(4)
Turn over
17. The bar chart below shows the number of children attending a drama club during one
week.
FKLOGUHQDWGUDPDFOXE
0RQGD\
7XHVGD\
:HGQHVGD\
7KXUVGD\
)ULGD\
(i) What is the total number of children attending for the week?
Answer: ..................................... (2)
(ii) What is the mean number of children attending each weekday?
Answer: ..................................... (2)
(iii) What fraction of the total attended on Thursday?
Write your answer in its simplest form.
Answer: ..................................... (2)
(iv) The club starts at 3.45 p.m. and lasts for 1 21 hours.
At what time does it end?
Answer: ..................................... (1)
S.A. 2811610312
18. Rosie keeps her rabbits and guinea pigs in separate pens.
QRWWRVFDOH
ZLGWK
PHWUHV
PHWUHV
PHWUHV
PHWUHV
UDEELWSHQ
JXLQHDSLJSHQ
(i) Work out the perimeter of the rabbit pen.
Answer: .................................. m(1)
(ii) Work out the area of the rabbit pen.
Answer: .................................m2(2)
The guinea pig pen has the same area as the rabbit pen.
(iii) Work out the perimeter of the guinea pig pen.
Answer: .................................. m(2)
S.A. 2811610313
Turn over
19. (a) In the diagram below, AB and CD are straight lines.
Work out the size of each of the angles marked a, b and c
'
D
$
s
F
E
QRWWRVFDOH
%
&
°
Answer: a 5 .................... °
Answer: b 5 .................... °
Answer: c 5 ..................... (4)
(b) The diagram below shows an isoceles triangle.
Work out the size of the angle marked d
G
QRWWRVFDOH
s
°
Answer: d 5 .................... (2)
S.A. 2811610314
20. Laura uses letters to represent numbers.
for example:
d 1 17 5 27
therefore:
d 5 10
Work out the value of each of the letters a, b and c below.
(i)a 2 17 5 31
Answer: a 5 ..................... (1)
(ii) b 1 14 1 b 5 68
Answer: b 5 ..................... (1)
(iii) 240 4 c 5 20
Answer: c 5 ...................... (1)
21. Danny writes the equation below where e and f are positive whole numbers.
3e 1 f 5 15
Danny says that e 5 1 and f 5 12
Find two more pairs of answers.
His sister says there are other pairs of answers.
Answer: e 5 ................... f 5 ..................... Answer: e 5 ................... f 5 ..................... (2)
PLEASE TURN OVER FOR QUESTION 22
S.A. 2811610315
Turn over
22. 7 is exactly halfway between 5 and 9
Find the number which is exactly halfway between
(i) 149 and 156
Answer: ..................................... (1)
(ii) 22 41 and 24 43
Answer: ..................................... (1)
3
7
(iii) 4 and 8
Answer: ..................................... (2)
(Total marks: 100)
S.A. 2811610316