Number worksheet — GCSE Higher

1.Write 5,000,000 in standard form.

2.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56

3.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.

4.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

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

6.Work out 3 × (−2)² − 5

7.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

8.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

9.A photography studio offers 4 backdrops and 3 outfits for a portrait session. The plain grey backdrop, one of the 4 backdrops, cannot be used with the formal suit outfit, one of the 3 outfits. Work out how many different backdrop-and-outfit combinations are possible.

10.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

11.A shop buys boxes of pens for £4 each. It sells each box on to a school for £3 more than it paid, and charges an extra £2 delivery fee for the whole order. A school orders 5 boxes. Work out the total cost of the order.

12.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.

13.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.

14.Work out ⁴√16

15.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.