Number worksheet — GCSE Higher

1.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.

2.The rainfall in a town during April is recorded as 62.4 mm, correct to 1 decimal place. Write down the error interval for the actual rainfall, r mm.

3.A plane flies 2340 km at an average speed of 780 km/h. It departs at 08:20. Work out the arrival time, using the 24-hour clock.

4.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

5.A market trader buys 8 melons at £1.35 each. He sells all of them for a total of £15.60. Work out his profit.

6.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.

7.Find the missing number: ▢ ÷ 15 = 24

8.Write 200 as a product of its prime factors, using index notation.

9.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.

10.Priya has 24 red beads and 36 blue beads. She makes identical bracelets, using every bead and with none left over. Work out the greatest number of bracelets she can make.

11.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

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

13.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

14.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.

15.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.