Number worksheet — GCSE Higher

1.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.

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

3.A board game has 5 different character pieces and 4 different colour tokens. The dragon piece can only be used with the gold token. Work out how many different combinations of one character piece and one colour token are possible.

4.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

5.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

6.A car is hired from 10:00 on Monday until 16:00 on Thursday. Work out the total length of the hire, in hours.

7.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

8.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.

9.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

10.Work out ⁴√16

11.Round 592.5 to the nearest 10.

12.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.

13.Work out 3.7 × 24.

14.Work out 3³ + 2⁴.

15.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.