Number worksheet — GCSE Higher

1.Write 0.005 in standard form.

2.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

3.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.

4.A charity trek covers 830 miles over roughly 19 days. By rounding each number to 1 significant figure, work out an estimate for the number of miles walked per day.

5.Work out (4 × 10³) × (3 × 10¹). Give your answer in standard form.

6.Simplify ⁴√(16a⁸b¹²)

7.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?

8.Simplify (3a²)² × (2a)³

9.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

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

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

12.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.

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

14.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

15.Simplify x⁷ × x⁴, giving your answer as a single power of x.