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 3³ + 2⁴.

3.Write down the reciprocal of 0.2

4.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

5.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.

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

7.Write these numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09

8.Which one of these statements is true?

9.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.

10.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.

11.A triangle has a base of 8 cm and a perpendicular height of 5 cm, each correct to the nearest centimetre. Work out the upper bound of the area.

12.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.

13.Work out ∛64.

14.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

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