Number worksheet — GCSE Higher

1.A tank contains 120 litres of water. Water is drained out at a rate of 8 litres per minute for 6 minutes, and then a hose adds 15 litres. Work out how much water is left in the tank.

2.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

3.Simplify (3a²)² × (2a)³

4.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

5.Find the missing number: 17 × ▢ = 391

6.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.

7.Work out (−6) + (−4) × 3

8.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?

9.Simplify (x⁻²)³, giving your answer as a fraction.

10.Write 0.36 as a fraction in its simplest form.

11.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

12.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

13.Work out (2/3)² + (1/2)². Give your answer as a fraction.

14.Write these numbers in order, starting with the smallest: −1.4, 5/4, −6/5, 1.3, 0

15.Write 200 as a product of its prime factors, using index notation.