Number worksheet — GCSE Higher

1.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.

2.Work out the exact value of √(2² + 3²)

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

4.Write 90 as a product of its prime factors.

5.A 3-character PIN starts with one letter chosen from A, B, C, D and E, followed by two different digits chosen from 1 to 9 (no digit may be used twice in the same PIN). Work out how many different PINs are possible.

6.A number is multiplied by 4, then 8 is added, giving the result 40. Work out the number.

7.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

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

9.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.

10.Work out how many factors 36 has.

11.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

12.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.

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

14.2/3 of an amount of money is £30. Work out the amount.

15.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.