Number worksheet — GCSE Higher

1.Work out 3.7 × 24.

2.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.

3.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

4.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

5.Work out the value of 6² − 4³.

6.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.

7.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

8.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.

9.A lift has a safe working load of 500 kg. Four people get in the lift and the lift's display records their total mass as 493 kg, correct to the nearest kg. Decide whether the four people are definitely within the safe working load.

10.4ˣ = 64. Work out the value of x.

11.Write 12 as a product of its prime factors.

12.Write 5,000,000 in standard form.

13.Simplify x⁶ ÷ x²

14.The recurring decimal 0.454545... can be written as 0.45 recurring, where both digits repeat forever. Let x = 0.45 recurring. Work out x as a fraction in its simplest form.

15.Write down the symbol that makes this statement true: −2/3 ___ −5/6