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 20 typed pages and 1 blank page.
Set A
Page 1
1. Work out
4.7 ÷ 102
[1]
2. Find the least common multiple of 36 and 14
[1]
3. Insert brackets to make the calculation correct
8 + 6 × 5 + 3 = 112
[1]
4. Draw a line perpendicular to line BG.
G
B
[1]
Page 2
5. (a) Write 417.96 correct to one decimal place
[1]
(b) Work out.
3.12 × 1.5
√900
Express your answer correct to two decimal places
[2]
6. Write an algebraic expression for:
Seven fewer than eight times a number, n.
[1]
7. Aziza changes 400 dollars into Indian rupee.
A currency exchanger converts 1 dollar to 82.68 rupees
Work out how many rupees she receives.
rupees [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
703 982
[1]
10. (a) Write 70% as a decimal
[1]
(b) Shade 70%of the grid.
[1]
Page 4
11. (a) Circle the formula that correctly calculates the number of days in any given
number of weeks.
w = 7d
w=d÷7
d = 7w
d=w÷7
w = 4d
d=w÷4
[1]
(b) Calculate the number of days in 15 weeks.
days [1]
12. Show the solution for x - 3 > -1 on the number line.
[1]
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.
Page 5
[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.
+
(a) Find the output when the input is
7-35
5
[1]
(b) Find the input when the output is 70
[1]
Page 6
15. Alissa would like to show that 23 117 is not divisible by 9 without actually dividing it.
Write down how Alissa would show that 23 117 is not divisible by 9.
[1]
16. (a) Complete the table of values for the equation y = 3x
[1]
(b) On the grid, draw the graph of y = 3x
[1]
Page 7
17. This graph shows some input and output values for a number machine.
[1]
b) Find the output when the input is -3
[1]
18. The graph shows the cost of gold in dollars.
Page 8
Use the graph to find a formula for the cost in dollars, C, of G grams of gold.
C=
[2]
19. The nth term of a sequence is 100 − 𝑛.
Find the largest number in this sequence.
[1]
Page 9
20. Find the measurements of angles x,y and z from the diagram below:
x=
o
[1]
y=
o
[1]
z=
o
[1]
21. These are the first four terms of a sequence.
-22
-17
-12
-7
…
(a) Write down the next two terms
[1]
(b) Write down the term-to-term rule for continuing this sequence
[1]
22. Simplify.
−23𝑥 + 19𝑦 − 12𝑥 + 8𝑦
[1]
Page 10
23. You can buy a new calculator for £1.25.
In 1979 the same type of calculator cost 22 times as much as it costs now.
How much did the same type of calculator cost in 1979?
Show your working.
£
[2]
24. The table shows a recipe for a fruit drink.
1
I want to make 1 2 litres of the same drink.
Complete the table below to show how much of each type of juice to use. Show your
working.
[3]
Page 11
25. A company sells books using the internet.
The graph shows their delivery charges.
For every extra book you buy, how much more must you pay for delivery?
£
26. Calculate the area
[1]
Page 12
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]
28. The diagram below shows a regular hexagon.
Page 13
Write down the order of rotational symmetry of the hexagon.
[1]
29. Draw the top, front, and side view of the diagram below:
TOP VIEW
FRONT VIEW
SIDE VIEW
[3]
Page 14
30. Two lines AB and CD are parallel.
Line EF cut the two lines and formed angles.
a) Calculate the value of x.
b) Write the measurements of angles y and z.
x=
[1]
y=
O
[1]
z=
O
[1]
Page 15
31. The scatter graph shows the average body length and average foot length of
different species of rodents.
a) What does the scatter graph tell you about the type of correlation between the
body length and foot length for these rodents?
[1]
b) If body length increased by 50mm, by approximately how many millimetres would
you expect foot length to increase?
Ring the correct value below.
2
7
15
50
275
[1]
Page 16
32. I have two fair 4-sided dice.
I throw both dice and add the scores.
What is the probability that the total is even?
[2]
33. Kyra has a faulty thermometer.
It always shows the temperature as 2 °C higher than the actual temperature.
The temperature on the thermometer is T°C.
Write an expression, in terms of T, for the actual temperature
°C [1]
34. The diagram below shows the nets of a solid.
a) Tick (✓) all the nets that would fold into the same 3D shape on the left.
[1]
b) Name the 3D shape shown by the nets.
(1)
35. Rearrange the equation to make t, the subject.
5(2 + t ) = w
Page 17
[2]
36.
𝑚3 × 𝑚𝑛 = 𝑚12
Find the value of n
n=
[1]
37. Rotate the trapezium T 270o anticlockwise about the origin.
Label the new trapezium T’.
[1]
38. Iqrah buys a box of different size plasters. Assume each plaster is equally likely to
be the top plaster inside the box.
Page 18
Altogether there are 35 plasters.
Iqrah takes the top plaster from inside the box.
a) What is the probability that the plaster is of
size D?
[1]
b) What is the probability that the plaster is of
size A?
[1]
c) What is the probability that the plaster is not
of size A?
[1]
39. A teacher asked her pupils if they recycled newspapers and glass. The pie chart
shows the results.
a) 5 pupils answered ‘Neither’. How many pupils answered ‘Newspapers only’?
_______________________pupils_[1]
Page 19
b) The teacher asked a different class if they recycled newspapers and glass.
There were 24 pupils in the class. 9 pupils answered ‘Newspapers only’.
On a pie chart, what would the angle be for the sector ‘Newspapers only’?
o
[1]
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.
Page 20
[1]
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]
b) In another set of dolls, the height of the tallest doll is 9cm.
What are the heights of the other dolls? Write your answers to 1 decimal place.
[2]
Page 21
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.
[2]
43. The table shows the preferred brand of mobile phone users.
Brand
Frequency
A
112
S
98
H
76
V
81
N
67
Which average would be most useful to show the tendency of the users’ choice?
[1]
44. On the grid, enlarge the shape with a scale factor of 2 from the centre C.
Page 22
C
[2]
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