Number worksheet — GCSE Higher

1.Work out ∛64.

2.Work out 5⁰ + 5¹ + 5²

3.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

4.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

5.Write 0.325 as a fraction in its simplest form.

6.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

7.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.

8.Work out √25 + 4² − 12 ÷ 3

9.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.

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

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

12.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

13.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

14.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

15.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.