Mathematics
Grade 5
2023
End-of-Year Examination
Name:
Class:
Date:
120 minutes
Additional materials: Geometrical instruments
Tracing paper (optional)
INSTRUCTIONS
● Answer all questions.
● Write your answer clearly to each question in the space provided.
● You should show all your working on the question paper.
● Use a pencil for drawing or graphing and black or dark blue pen for all others.
● Do not use an erasable pen or correction fluid.
● You are not allowed to use a calculator.
INFORMATION
● The total mark for this paper is 80.
● The number of marks for each question or part question is shown in brackets [ ].
● The paper consists of 21 typed pages and 1 blank page.
Set B
Page 1
1. Work out
3
12.7 ÷ 10
[1]
2. Find the least common multiple of 45 and 63
[1]
3. Insert brackets to make the calculation correct
8 + 6 × 5 + 3 = 56
[1]
4. Draw a line perpendicular to line BG.
B
G
[1]
Page 2
5. (a) Write 500.05 correct to one decimal place
[1]
(b) Work out.
2
1.5 × 3.1
√400
Express your answer correct to two decimal places
[2]
6. Write an algebraic expression for:
Nine more than five times a number, n.
[1]
7. Ava changes 432 US dollars into Euros.
A currency exchanger converts 1 Euro to 1.08 US dollars
Work out how many US dollars she receives.
dollars [1]
Page 3
8. Write these numbers in order, starting with the smallest
5
6
148%
0.71
3
8
<
<
<
[2]
9. Write the value of the underlined digit
912 075
[1]
10. (a) Write 45% as a decimal
[1]
(b) Shade 45%of the grid.
[1]
Page 4
11. (a) Circle the formula that correctly calculates the number of weeks (w) in any given
number of years (y).
y = 52w
y = w ÷ 52
w = 52y
w = y ÷ 52
w = 4y
w=y÷4
[1]
(b) Calculate the number of weeks in 5 years.
weeks [1]
12. Show the solution for x +5 > -1 on the number line.
[1]
Page 5
13. The perimeter of a shape is the sum of all its sides.
a) Given the rectangle below, write an expression for its perimeter, P.
[1]
b) Find the value of x
x=
[1]
P=
units [1]
c) Work out the perimeter of the given rectangle
14. Here is a function machine.
6
7
(a) Find the output when the input is -34
[1]
(b) Find the input when the output is 70
Page 6
[1]
15. Greg would like to show that 23 217 is divisible by 3 without actually dividing it.
Write down how Greg would show that 23 217 is divisible by 3.
[1]
16. (a) Complete the table of values for the equation y = 5x
5
5
[1]
(b) On the grid, draw the graph of y = 5x
Page 7
[1]
17. A sports centre has two different clubs.
a) 22 children go to the gym club. Complete the pictogram
[1]
b) 10 more girls than boys go to the swimming club. Complete the key.
Page 8
[1]
18. 2 tins balance 1 bottle.
1 tin and 1 bottle balance 1 box.
a) How many bottles do 6 tins balance?
bottles [1]
Page 9
b) How many boxes do 6 tins balance?
boxes [1]
19. The nth term of a sequence is 99 + (1 − 𝑛).
Find the largest number in this sequence.
[1]
20. Look at the diagram.
l
m
l
AB is a straight line.
Work out the size of angle k, l, m.
k=
o
[1]
l=
o
[1]
m=
o
[1]
Page 10
21. Look at the sequence below.
To get the next term in the sequence, subtract 90 from the term before.
500
410
320 …
Write the first two terms of the sequence that are less than zero.
,
[2]
22. Simplify.
79𝑥 − 14𝑦 − 52𝑥 + 26𝑦
[1]
23. You can buy a new calculator for £2.25.
In 1979 the same type of calculator cost 20 times as much as it costs now.
How much did the same type of calculator cost in 1979?
Show your working.
£
24. The table below helps to change centimetres into inches.
[2]
Page 11
a) About how many inches are there in 14 centimetres?
[1]
b) About how many inches in 1 centimetres?
[1]
c) There are 30 centimetres in one straight ruler,
How many inches is that?
[1]
25. A company sells books using the internet.
The graph shows their delivery charges.
Page 12
For every extra book you buy, how much more must you pay for delivery?
£
[1]
26. Calculate the area
cm2 [2]
27. You can make only four different cuboids with 16 cubes.
a) Which of the cuboids A and D has the larger surface area?
Tick (✓) the correct answer below.
● Cuboid A
● Cuboid D
● All the same
[1]
b) Which cuboid has the largest volume?
Tick (✓) the correct answer below.
● Cuboid A
● Cuboid B
● Cuboid C
● Cuboid D
● All the same
[1]
Page 13
28. The diagram below shows a regular octagon .
Write down the order of rotational symmetry of the octagon.
[1]
29. Draw the front view, side view and top view of this shape.
[3]
Page 14
30. Two lines are parallel.
A line cuts the two lines and forms angles.
Calculate the value of x and y
x=
[1]
y=
[1]
Page 15
31. Complete this diagram so that the three numbers in each line add to 8.
[3]
32. Jerry has a bag of counters. Inside his bag are 2 blue, 4 green, 5 red, and 9 yellow
counters.
Jerry is going to take a counter at random from his bag.
Write the correct colours to complete these sentences.
[2]
Page 16
33. The table shows information about a pentagonal prism
a) Complete the table to show information about a triangular prism.
[1]
b) Complete the table.
[3]
Page 17
34. Rearrange the equation to make t, the subject.
5t( r + s ) = w
[2]
35.
𝑚
−5
𝑛
×𝑚 =𝑚
15
Find the value of n
n=
[1]
36. Rotate the trapezium T 90o anticlockwise about the origin.
Label the new trapezium T’.
[1]
Page 18
37. The graph shows information about 13 different types of eel that live in the sea.
a) One type of eel is called a goldentail moray.
The longest it can grow is 70cm.
The deepest it can swim is 60m.
Put a ring around the point on the graph that
represents this eel.
[1]
b) How many of these different types of eel can
swim deeper than 100m?
[1]
Page 19
38. The pie chart shows how pupils in class 9A travelled to school one morning.
5 pupils in class 9A walked to school.
Work out how many pupils in class 9A travelled by bus.
pupils [2]
39. a) Every day a machine makes 500 000 drawing pins and puts them into boxes.
The machine needs 150 drawing pins to fill a box.
How many boxes can be filled with the 500 000 drawing pins?
boxes [1]
b) Each drawing pin is made from 0.23g of metal.
How many drawing pins can be made from 1kg of metal?
drawing pins [2]
Page 20
40. The square grid below shows a quadrilateral that has four right angles.
a) Draw a quadrilateral that has exactly two right angles.
[1]
b) Draw a quadrilateral that has exactly one right angle.
[1]
Page 21
41. The heights of Russian dolls are in the ratio 4:6:7
a) In a set of dolls, the height of the middle doll is 9cm. What are the heights of the
other dolls?
[2]
42. Altogether, I have 10 bags of sweets.
The mean number of sweets in the all 10 bags is 41
The table shows how many sweets there are in 9 of the bags…
Calculate how many sweets there are in the 10th bag.
Page 22
[2]
43. On the grid, enlarge the shape with a scale factor of 2 from the centre C.
C
[1]
Page 23
BLANK PAGE