Number worksheet — GCSE Higher

1.Work out −4.5 + 2.8.

2.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

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

4.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

5.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

6.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

7.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.

8.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.

9.Write 7/12 as a decimal, showing clearly which digit is recurring.

10.Write down the exact decimal value of the fraction 1/6.

11.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.

12.The decimal 0.2333... has one non-recurring digit (the 2) followed by a single recurring digit (the 3), so it can be written as 0.2 recurring 3. Let x = 0.2333... . Work out x as a fraction in its simplest form.

13.Simplify (x⁻²)³, giving your answer as a fraction.

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

15.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2