Number worksheet — GCSE Higher

1.Work out the value of 2⁻²

2.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

3.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

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

5.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.

6.The error interval for the mass of a suitcase, m kg, is given as 22.5 ≤ m < 23.5. Write down the mass of the suitcase, correct to the nearest whole number.

7.Work out (−2)³ + (−3)² − (−4)

8.Simplify x⁶ ÷ x²

9.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.

10.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.

11.A jacket normally costs £65. In a sale it is reduced by 20%, and the shop then takes a further £5 off at the till. Work out the final price.

12.A speed camera measures a car's speed as 34 mph, correct to the nearest mph. Work out the smallest possible actual speed of the car, in mph.

13.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

14.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

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