Number worksheet — GCSE Higher

1.Simplify √45.

2.Work out √3 × √12, giving your answer as an integer.

3.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

4.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

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

6.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.

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

8.Work out √225 ÷ 3.

9.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

10.Priya has 24 red beads and 36 blue beads. She makes identical bracelets, using every bead and with none left over. Work out the greatest number of bracelets she can make.

11.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.

12.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.

13.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

14.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.

15.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.