Number worksheet — GCSE Higher

1.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

2.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

3.A triangle has a base of 8 cm and a perpendicular height of 5 cm, each correct to the nearest centimetre. Work out the upper bound of the area.

4.Simplify x⁶ ÷ x²

5.A paint mix is made from white paint and blue paint in the ratio 5 : 3. Priya uses 1.2 litres of blue paint and the matching amount of white paint. Work out the total volume of the mix.

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.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

8.Petrol costs £1.48 per litre. Sam buys 35 litres and pays with three £20 notes. Work out his change.

9.The recurring decimal 0.454545... can be written as 0.45 recurring, where both digits repeat forever. Let x = 0.45 recurring. Work out x as a fraction in its simplest form.

10.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.

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

12.Write down the symbol that makes this statement true: −2/3 ___ −5/6

13.Write 0.875 as a fraction in its simplest form.

14.Work out the value of 6² − 4³.

15.In a youth club the number of girls is 2/3 of the number of boys. What fraction of the members of the club are girls?