Number worksheet — GCSE Higher

1.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

2.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

3.Which of these statements about −0.7 and −0.25 is true?

4.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.

5.A lift has a safe working load of 500 kg. Four people get in the lift and the lift's display records their total mass as 493 kg, correct to the nearest kg. Decide whether the four people are definitely within the safe working load.

6.Work out ((−3) + 5) × (−4) − (−6) ÷ 2

7.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

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

9.Work out 100 − 4 × 5²

10.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

11.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

12.Write ∛(x²) as a single power of x.

13.Which of these is written correctly in standard form?

14.Write down the exact decimal value of the fraction 1/6.

15.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.