Number worksheet — GCSE Higher

1.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

2.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

3.Work out −4.5 + 2.8.

4.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

5.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.

6.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

7.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.

8.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.

9.Work out 3³ + 2⁴.

10.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

11.A school orders 187 packed lunches for a trip. Each packed lunch costs £4.85. The school has £900 to spend. By rounding each number to 1 significant figure, work out an estimate for the total cost and decide whether £900 is enough.

12.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

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

14.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.

15.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.