Number worksheet — GCSE Higher

1.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

2.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?

3.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.

4.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.

5.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

6.Work out √225 ÷ 3.

7.During one night on a mountain, four hikers each recorded the temperature they felt: Ben −6 °C, Priya −2 °C, Sam −9 °C, Alex 1 °C. Work out the difference between the coldest and the warmest of these four temperatures.

8.Work out ∛(−27) + ∛8

9.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

10.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.

11.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

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

13.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.

14.Work out 3 × (−2)² − 5

15.Write 5/6 as a decimal, showing clearly which digit recurs.