Number worksheet — GCSE Higher

1.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

2.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

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

4.Work out the value of (1/3)⁻²

5.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.

6.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?

7.√700 lies between which two consecutive integers?

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

9.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.

10.Round 0.006852 to 2 significant figures.

11.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.

12.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20

13.Simplify (y³)⁴, giving your answer as a single power of y.

14.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

15.A vending machine sells 4 types of crisps, 5 types of chocolate bar and 2 types of drink. Work out how many different combinations of one crisp packet, one chocolate bar and one drink can be bought.