Number worksheet — GCSE Higher

1.Given that 2⁵ = 32, work out 2⁶.

2.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.

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

4.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

5.Work out the value of (1/3)⁻²

6.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

7.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

8.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.

9.An allotment is divided into two plots in the ratio 2:3. The larger plot has an area of 18 m². Work out the fraction of the total area taken up by the smaller plot.

10.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.

11.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

12.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

13.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.

14.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.

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