Post-Learning
Assessment
Year 8 Module 1: Prime numbers, Factorisation and Calculating with Fractions
Name: ………………………………………………………………….
Class: ……………………………………………………………………
Teacher: ……………………………………………………………….
You need:
 A Pen
 A Pencil
 A Ruler
You DO NOT need:
 A Calculator
What have we learnt this half term?
Unit 1: Prime Numbers and Factorisation

In this unit you have been introduced to prime numbers and prime factorisation and can use this to determine HCF
and LCM of a pair or group of numbers. You have also used prime factorisation to find squares, square roots, cubes
and cube roots and can use indices to record repeated multiplication
Unit 2: Calculating with Fractions

This unit refreshed your Year 7 fractions knowledge and introduced addition and subtraction of fractions with both like
and unlike denominators. You can also add and subtract mixed numbers and improper fractions.
Pre-Learning Assessment Mark:
50
Teacher Comment:
Post-Learning Assessment Mark:
50
1) Farah says “13 is a prime number”. Explain why Farah is correct.
…………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………… (1)
2)
25, 15, 7, 60, 11, 8
From the numbers given above select:
a) A number that is a factor of 30
…………………… (1)
b) A square number
…………………… (1)
c) The square root of 64
………….……..… (1)
3) For each statement decide whether it is true or false. If it is false explain why.
a) The factors of a number are always smaller than the number.
............................................................................................................................... (1)
b) 21 is a factor of 7
.............................................................................................................................. (1)
c) 35 is a factor of 70
……………………………………………………………………………………………………………………………. (1)
4) Write 140 as a product of its prime factors
…………………………………………………………………………………..……………………….. (2)
5) Put a circle round each of the numbers below that can be written as a product of their
prime factors using only the numbers 2 and 5
120, 250, 625, 192, 40
(3)
6) State the highest common factor of 60 and 90
............................... (1)
7) Find the lowest common multiple of 20 and 35
............................... (2)
8) Look at these numbers.
a) Which is the largest?
…………………………………………. (1)
b) Which pair of cards are of equal value?
………………………….. and …………………….. (1)
c) Which two of the numbers below are square numbers?
...................... and ...................... (2)
9) The highest common factor and lowest common multiple of a pair of numbers are 12
and 420 respectively. If one of the numbers is 60, find the other number.
You may find the diagram below helpful.
……..……..... (2)
10) Give a fraction which is equivalent to each of these:
a)
b)
1
8
3
7
=
=
(2)
11)
a) Samir is six and one twelfth feet tall. Write his height in feet as an improper
fraction.
……………….. (2)
b) There are four cookies in a full packet. If a baker has 33 cookies state the number of
packets he can make as a mixed number.
..………………. (2)
12) Complete the following Calculations, simplifying your answers where possible.
a)
3
x
5
10
b)
13
4
5
÷3
(2)
13) Tom wrote the calculation:
1
3
+
1
3
=
2
6
Is he correct?
Yes
No
Explain your answer.
………………………………………………………………………………………………………………………………..…..
……………………………………………………………………………………………………………………………… (1)
14) Find the sums of the following groups of fractions. Simplify your answers where
possible:
3 2 1
a) , ,
9 9 9
…………………… (2)
b)
5
,
3
11 11
…………………… (2)
15)
Jonah had one fifth of a chocolate bar. Tara had one quarter of a chocolate bar. What
fraction of a chocolate bar did they have altogether?
…………………………..……..…….. (3)
16)
Find the sum of
2 1
+ =
3 5
2
1
and . You may shade the model to help you.
3
5
+
……..……..
=
……..……..
……..……..
(2)
5
1
6
4
17) Find the difference between and . You may shade the models to help you.
5
6
-
1
4
-
=
……..……..
=
……..……..
……..……..
(2)
18) Match each calculation with the correct fraction answer.
The first one is done for you.
3
5
5
8
1
5
3
8
2
3
+
−
+
+
−
1
19
5
20
1
4
8
5
3
1
4
2
1
1
4
6
1
5
2
8
(3)
1
19) In a four week period a restaurant disposed of 3 2 tonnes of food. In the first two weeks
1
they disposed of 2 5 tonnes. How much did they dispose of in the second two weeks?
………………. Tonnes (3)
1
20) In an employee satisfaction survey 2 of the people surveyed claimed to be happy in their
1
1
jobs, 4 claimed to be very happy, 5 claimed to be unhappy and the rest claimed to be
neutral (neither happy or unhappy). What fraction claimed to be neutral?
……………………. (3)
Finishing Task
Prime Factorisation can be a useful problem solving tool. We can use it to find ALL
the factors of a number, for example the number 140.
140 = 2 x 2 x 5 x 7
So 2, 5 and 7 must be factors of 140, but also the product of any combination of the
numbers above must also be a factor, for example (2 x 7), (2 x 2 x 5) and (5 x 7) are all
factors of 140.
Use Prime Factorisation to find all the factors of the numbers below (remember to
include 1 and the number itself).
1) 42
2) 75
3) 27

What is different about the three prime factorisations?

How does this affect the number of factors?

Use your findings to make a prediction about all prime factorisations with exactly
three numbers in them. Try to find more examples to support your prediction.