Number worksheet — GCSE Higher

1.A charity bake sale sells 187 cakes at £2.95 each. By rounding each number to 1 significant figure, work out an estimate for the total amount raised.

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

3.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.

4.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

5.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.

6.Find the missing number: 17 × ▢ = 391

7.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

8.Work out (2/3)² + (1/2)². Give your answer as a fraction.

9.Write 60 as a product of its prime factors, using index notation.

10.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

11.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

12.A cake recipe needs 3/4 of a kilogram of sugar. Aisha wants to make half the recipe. Work out how much sugar she needs, giving your answer as a fraction of a kilogram in its simplest form.

13.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?

14.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

15.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.