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.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

3.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

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

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

6.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.

7.Work out the reciprocal of (2 + 3)

8.Work out the value of (√5)⁴

9.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

10.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

11.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

12.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

13.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.

14.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.

15.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.