📘 Stage 8 Mathematics – Worksheet
Chapter 1: The Number System
1. Operations with Numbers
1.1 Simplify:
a) 245+687
b) 508-236
c) 72*34
d) 528/12
1.2 Solve:
a) (34+18)*5
b) 96/(12-4)
c) (15*6)-48
2. Index Notation and Laws
2.1 Write the following in index form:
a) 2*2*2*2
b) 7*7*7
c) 11*11
2.2 Simplify using index laws:
a) 2^4*2^3
b) 5^6/5^2
c) (3^2)^3
d) 10^0
3. Primes and Prime Factorisation
3.1 Write down all the prime numbers between 20 and 50.
3.2 Express the following numbers as a product of prime factors (using index form):
a) 72
b) 120
c) 98
3.3 Find the HCF (Highest Common Factor) of 84 and 126 using prime factorisation.
4. Common Factors and Common Multiples
4.1 Find the LCM (Lowest Common Multiple) of:
a) 12 and 18
b) 15 and 20
4.2 A bell rings every 6 minutes and another rings every 8 minutes. Both bells ring together at 12:00 noon. At what
time will they next ring together?
5. Squares, Square Roots, Cubes and Cube Roots
5.1 Work out:
a) 12^2
b) 15^2
c) 9^3
d) 5^3
5.2 Find:
a) √144
b) √225
c) 3√125
d) 3√512
5.3 Word problem:
A square garden has an area of 784 m². Find the length of one side of the garden.
6. Mixed Revision Questions
6.1 Simplify: (2^5/2^3)+(9^2-45)
6.2 Write 360 as a product of prime factors.
6.3 Find the LCM and HCF of 45 and 60.
6.4 A cube has a volume of 729 cm³. Find the length of one edge.
Challenge Question:
The product of two numbers is 144. One of them is 12. Using prime factorisation, find the other number and check if
it is prime or composite.