Number worksheet — GCSE Higher

1.Write 90 as a product of its prime factors.

2.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.

3.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

4.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

5.Write 0.325 as a fraction in its simplest form.

6.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.

7.A market trader buys 8 melons at £1.35 each. He sells all of them for a total of £15.60. Work out his profit.

8.Simplify (3a²)² × (2a)³

9.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.

10.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.

11.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

12.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

13.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

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

15.Work out √225 ÷ 3.