Number worksheet — GCSE Higher

1.A weather app records the temperature at three points in one day: 6 °C at noon, −2 °C at midnight, and −7 °C just before dawn. Work out the difference between the highest and lowest of these three temperatures.

2.Write 200 as a product of its prime factors, using index notation.

3.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

4.Work out 35% of 180.

5.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

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

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.Work out (2/3)² + (1/2)². Give your answer as a fraction.

9.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.

10.A jug holds 1.8 litres of juice. Priya pours out 3/4 of a litre to fill a glass. Work out how much juice is left in the jug, in millilitres.

11.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

12.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.

13.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

14.Given that 2⁵ = 32, work out 2⁶.

15.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.