11-Plus-Maths.pdf

Page total:
1. Work out:
a) 2019 – 567
Answer: _______________________ [2]
b) 67 × 89
Answer: _______________________ [2]
c) 81.9 ÷ 6
Answer: _______________________ [2]
d) 17.4 + 8.78
Answer: _______________________ [2]

Page total:
2. Fill in the missing numbers in these sequences:
a) 15 , 22 , 29 , _____ , 43 , ______
[2]
b) 9 , 5 , 1 , _____ , ______
[2]
c) 96 , −48 , 24 , −12 , ____ , ______
[2]
3. Fill in the blanks to make the calculation correct.
a) 18 – 6 + 7 = ______
[1]
b) 21 – ( ____ × 3) = 9
[1]
c) 16 – (-3)2
= _____
[1]

Page total:
4. The perimeter of the rectangle below is 18 cm.
a) Find the width of the rectangle.
Answer: _______________________cm [1]
b) Find the area of the rectangle.
Answer: _______________________ cm2
[1]
c) A square with sides of length 3 cm is divided into three identically sized
rectangles. These are then arranged as shown. What is the perimeter of the
new shape?
Answer: _______________________ [2]
3 cm
3 cm

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5. The diagram below shows 4 triangular pieces of card.
The pieces can be put together to form geometric shapes. The cards can be
turned upside down or rotated if necessary. On the grid below the 4 pieces have
been put together to make a pentagon.
On each grid below draw a diagram to show how all 4 pieces of card could be put
together to form the named shape.
a) A rectangle
[1]
b) A parallelogram that is not
a rectangle
[2]

Page total:
6.
a) Round 649 to the nearest 100
Answer: _______________________ [1]
b) Round 832 to the nearest 10
Answer: _______________________ [1]
c) A number has been rounded to the nearest 10 to give 370. What is the
smallest whole number possible?
Answer: _______________________ [1]
7.
a) Calculate 0.4 +
1
4
+
27
100
Answer: _______________________ [2]
b) Write
51
60
as a decimal
Answer: _______________________ [2]

Page total:
8. Find:
a) One third of £120
Answer: £_______________________ [1]
b) 40% of £728
Answer: £_______________________ [2]
9. A sleeper train travels from London to Glasgow. The train departs at 11:28 pm
and arrives at 06:53 am.
a) How long does the journey take?
Answer: __________ hours____________minutes [2]
b) A different train travels from London to Edinburgh at constant speed.
The journey takes 3 hours and 30 minutes and the distance travelled is 420
miles. Calculate the speed of the train.
Answer: _______________________ mph [2]

Page total:
10.You are given the following five numbers: 34, 21, 35, 42, 28
a) Find the mean of these five numbers.
Answer: _______________________ [1]
b) Find the median for these five numbers.
Answer: _______________________ [1]
c) Find the range of these five numbers.
Answer: _______________________ [1]
d) A sixth number is added to the list and the mean changes to 33.
Find what this sixth number was.
Answer: _______________________ [2]

Page total:
11.The diagram shows a triangle and a line. The two angles marked 𝑦° are equal.
a) Work out the value of x
Answer: _______________________ [1]
b) Work out the value of y
Answer: _______________________ [2]
12.Draw the reflection of each shape in the mirror line as shown.
[1]
𝑦°
𝑦°
𝑥°
108°

Page total:
13.
a) Plot the point (4, -2) and label it B.
[1]
b) Plot the point that is midway between A and B and write down its
coordinates below.
Answer: (____________,___________) [2]
2
4
-2
-4
2 4
-2
-4 0 x
y
A

Page total:
c) Point D is the point midway between the points C and E. Find the
coordinates of the point E.
Answer: (____________,___________) [2]
2
4
-2
-4
2 4
-2
-4 0 x
y
C
D

Page total:
14.A set of solid towers are made by adding layers as shown below. The shape is
solid inside with no missing blocks.
a) How many cubes are needed to build tower number 2?
Answer: _______________________ [1]
b) How many cubes are needed to build tower number 3?
Answer: _______________________ [1]
c) Without drawing it, how many cubes would be needed to build tower
number 5?
Answer: _______________________ [2]
d) Which tower number would contain 120 cubes?
Answer: _______________________ [2]

Page total:
15.Write all the square numbers between 1 and 100, inclusive, in the correct region
in the diagram below.
Circle A needs to contain factors of 360.
Circle B needs to contain multiples 4.
You will need to put some numbers outside of the two circles.
[4]

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16.The scatter plot shows the maths and science scores for 9 pupils.
a) Who had the highest score in maths?
Answer: _______________________ [1]
b) Who is good at science and poor at maths?
Answer: _______________________ [1]
c) The total of the two scores are added together. Who has the highest
total?
Answer: _______________________ [2]

Page total:
17.Some children in a class write down the first letter of their surname on a card;
these cards are shown below:
A card is chosen at random.
a) Which letter is most likely to be taken?
Answer: _______________________ [1]
b) Give two letters that have the same probability of being chosen as an E?
Answer: _______________________ [2]

Page total:
18. The diagram shows a design formed by drawing six lines in a regular hexagon.
The lines divide each edge of the hexagon into three equal parts. What fraction
of the hexagon is shaded?
Answer: _______________________ [3]
19.Whilst driving to work Alison noticed that there were nine lamp posts equally
spaced along a road. The distance from the first to the third is 60m. How far is it
from the first to the last?
Answer: _______________________ [2]

Page total:
20.The perimeter of this shape is 40 units. The sides labelled x are all the same
length. Find the length of one of these sides.
Answer: _______________________ [3]
x
x
x
x
x

Page total:
21.The instruction 𝑥 ∗ 𝑦 means subtract 𝑥 from 𝑦 and then multiply by 3.
For example 2 ∗ 6 = (6 − 2) × 3 = 12
a) Work out the value of 20 ∗ 27
Answer: _______________________ [1]
b) Work out the value of 10 ∗ 6
Answer: _______________________ [1]
c) Work out the value of 𝑎 if 3 ∗ 𝑎 = 6
Answer: _______________________ [1]
d) Work out the value of 𝑏 if 𝑏 ∗ 5 = 9
Answer: _______________________ [1]
e) Work out the value of 𝑐 if 𝑐 ∗ 5 = 4 ∗ 𝑐
Answer: _______________________ [1]

Page total:
22.Sarah has designed a tile for her new kitchen as shown below.
+ ⃝
↔
a) Complete the grid below to show the tile if it is rotated through a quarter turn
clockwise.
+
[1]
b) Sarah decides to reflect the tile in the dashed line shown below and then rotate
it through half a turn.
Draw the resulting tile on the grid below. You may complete the middle tile if
you wish.
+ ⃝ +
↔
[2]

Page total:
23.For each of the following questions you need to find a whole number between 0
and 100 that has all of the following properties.
a) When the number is divided by 5 the remainder is 4.
When the number is divided by 6 the remainder is 0.
What is the number?
Answer: _______________________ [2]
b) When the number is divided by 2 the remainder is 1.
What is the number?
Answer: _______________________ [2]

Page total:
24.In this subtraction, P, Q, R, S and T represent single digits.
Find the values of P, Q, R, S and T.
P: _____________ [1]
Q: _____________ [1]
R: _____________ [1]
S: _____________ [1]
T: _____________ [1]

Page total:
25.Anastasia thinks of a positive integer, which Barry then doubles. Next, Charlie
trebles Barry’s number. Finally, Damien multiplies Charlie’s number by six. Eve
notices that the sum of these four numbers is a perfect square. What is the
smallest number that Anastasia could have thought of?
Answer: _______________________ [3]

Page total:
26.
Calum and his friend cycle from A to C, passing through B.
During the trip he asks his friend how far they have cycled.
His friend replies “one third as far as it is from here to B”.
Ten miles later Calum asks him how far they still have to cycle to reach C.
His friend replies again “one third as far as it is from here to B”.
How far from A will Calum have cycled when he reaches C?
Answer: _______________________ [3]
End of the Examination
If you have time, go back and check your answers and
make sure that you have shown all of your working.
A C
B

11-Plus-Maths.pdf

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