Number worksheet — GCSE Higher

1.A three-digit code is made using the digits 1, 2 and 3, and each digit may be used more than once. Work out how many different three-digit codes can be made.

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

3.Write ∛(x²) as a single power of x.

4.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.

5.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

6.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².

7.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.

8.A grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.

9.Insert one pair of brackets into 2 + 3 × 5 − 1 so that the calculation is equal to 24. Which calculation is correct?

10.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

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

12.Robert is converting 0.999... (with the 9s recurring forever) into a fraction. He lets x = 0.999... . Multiplying by 10 gives 10x = 9.999... . Subtracting x from 10x gives 9x = 9, so x = 1. Which statement correctly explains this result?

13.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

14.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

15.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.