Number worksheet — GCSE Higher

1.Work out ∛64.

2.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.

3.A cube-shaped storage tank has a volume of 15,625 cubic centimetres. Work out the length of one edge of the tank.

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

5.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.

6.A measuring jug shows a volume of 340 ml, correct to the nearest 20 ml. Work out the smallest possible volume in the jug.

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

8.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

9.A country has an area of 25,000,000 hectares. Write this area in standard form.

10.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

11.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.

12.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

13.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

14.Work out 36 ÷ (2 × 3)

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