WOODHOUSE GROVE SCHOOL
ENTRANCE AND SCHOLARSHIP
EXAMINATION
13+ MATHEMATICS
TIME: 1 HOUR
SURNAME ______________________________________
KNOWN NAMES ______________________________________
READ THE FOLLOWING INSTRUCTIONS CAREFULLY BEFORE STARTING
THE EXAMINATION
1. DO NOT OPEN THE TEST UNTIL YOU ARE TOLD TO DO SO
2. CALCULATORS ARE NOT ALLOWED
3. WRITE YOUR ANSWERS ON THE LINES PROVIDED
4. THERE IS SPACE TO SHOW WORKING ON THE PAPER
YOU ARE STRONGLY ADVISED TO SHOW YOUR WORKING: YOU MAY
LOSE MARKS IF YOU DO NOT SHOW HOW YOU OBTAINED YOUR
ANSWER
1. Work Out
a) 37 + 18 = ........................................................... 1 mark
b) 73 – 68 = ........................................................... 1 mark
c) 7×7= ........................................................... 1 mark
d) 42 ÷ 7 = .......................................................... 1 mark
e) 249 + 1578 = .......................................................... 1 mark
f) 832 – 273 = ......................................................... 1 mark
g) What number should you subtract from 201 to make 140?
..................................................................... 1 mark
h) By what number should you multiply 53 to make 159?
.................................................................... 1 mark
2
2. Fill in the missing number or numbers to make the calculation correct.
M
a) 37 N + ..................... = 39 1 mark
b) 50 % of ........................ = 46 1 mark
M
c) P
of ........................... = 27 1 mark
d) ................ × ................ = 36 1 mark
e) ................ ÷ ................ = 36 1 mark
3
3. Calculate
a) 8.62 + 3.87 = ............................................................. 1 mark
b) 8.62 – 3.97 = ............................................................ 1 mark
c) 17.04 × 8 = ............................................................. 1 mark
d) 17.04 ÷ 8 = ............................................................. 1 mark
4
4. Calculate
a) 14 – 3 × 4 = .................................................................. 1 mark
b) 14 – (-12) = .................................................................. 1 mark
c) (2P )N = .................................................................. 1 mark
d) 2P + 3N = ................................................................... 1 mark
e) ³√27 = .................................................................... 1 mark
5
5.
a) 540 = 2V × 3W × 5X
540 is given a product of its prime factors
Find the values of the powers p, q and t. Working must be shown for this
question.
p = .......................... q = ............................ t = ............................ 5 marks
b) Write down the prime numbers between 99 and 104, inclusive
................................................. 2 marks
6
6.
a) Write 0.48 as a fraction in its lowest terms
................................................. 2 marks
\
b) Write ]^ as a decimal
.................................................. 2 marks
P
c) Calculate _
of £6.40
................................................... 2 marks
7
7.
a) A compact disc (CD) cost £4.99
What is the cost of 12 such CDs?
.......................................................... 2 marks
b) 4 litres of milk cost £3.60
M
What is the cost of N
litre of milk?
.......................................................... 3 marks
c) I buy socks for £6.80 and a tie for £12. I pay with a £20 note. How much change
should I get?
.......................................................... 3 marks
8
8.
X X X
X X
a) Complete: The ratio of the number of squares containing an X to the number of
blank squares
= ................................. : ................................... 2 marks
b) I have several such patterns containing a total of 57 squares (of either type).
How many blank squares are there?
................................................... 3 marks
9
9. Simplify
a)
i) 7a + 5a = ............................................ 1 mark
ii) 7a × 5a = ............................................ 2 marks
b) Remove the brackets and simplify.
4 (3b - 7c) + 8 (2b + c)
........................................................... 4 marks
c) Factorise
15p – 10q = ........................................... 3 marks
10
SHOW YOUR WORKING
10. Solve
a) x + 5 = 11
x = ...................................................... 1 mark
b) 3y – 2 = 7
y = ...................................................... 2 marks
M
c) p
z=8
z = ...................................................... 2 marks
d) 3 (w – 5) = w – 3
w = .................................................... 5 marks
11
11. When a = 3, b = 5, c = ‒ 4
Find the value of:
a) 3a + b =
............................................................... 2 marks
b) 𝑐P =
................................................................ 2 marks
c) ac + 2b =
............................................................... 2 marks
12
12.
Small Large
Loaf 38p 70p
Cake 42p 80p
a) Find the cost of 2 large loaves and 4 small cakes
.............................................................. 3 marks
b) The price of cakes is increased by 15%. How much does a large cake cost now?
.............................................................. 3 marks
c) The price of loaves is also increased by 10% (the cakes are still 15% more than
in the table).
By how much does the cost of one large loaf and one large cake increase?
.............................................................. 3 marks
13
13. The probability of a bird on my garden lawn being a wren is 0.16.
a) I observe 50 birds on the lawn. How many should I expect to be wrens?
............................................................ 2 marks
b) At another time I observed that 12 of the birds seen were starlings and I
calculated that the probability of a bird being a starling was 0.3. How many birds
did I see?
........................................................... 2 marks
14
14.
a°
b° 25°
120° c°
Find the angles marked a°, b°, c°,
Give reasons for your answers
a°= ........................................................ 1 mark
Reason: ..................................................................................................
b°= ........................................................ 2 marks
Reason: ..................................................................................................
c°= ....................................................... 2 marks
Reason: .................................................................................................
15
15.
a) Write down four numbers which have a mode of 4 and a range of 7
__________________ __________________ __________________ __________________
2 marks
b) 100 pupils were asked about the number of pets they own. Calculate the mean
number of pets.
Number of Pets Number of Pupils
0 24
1 47
2 9
3 5
4 12
5 2
20 1
....................................................... 3 marks
16
16.
Four cards A, B, C and D are shown
𝑥+𝑦 𝑥𝑦 𝑦 𝑥z
𝑥
A B C D
Which card will show the largest value when:
a) x = 2, y = 3?
............................................................. 1 mark
b) x = 2, y = 1?
.............................................................. 1 mark
c) x = 0.5 , y = 4?
............................................................. 1 mark
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