Number worksheet — GCSE Higher

1.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

2.A photography studio offers 4 backdrops and 3 outfits for a portrait session. The plain grey backdrop, one of the 4 backdrops, cannot be used with the formal suit outfit, one of the 3 outfits. Work out how many different backdrop-and-outfit combinations are possible.

3.A length, L cm, has the error interval 24.5 ≤ L < 25.5. Write down the degree of accuracy to which the length was measured.

4.Work out √144 − 2 × 3 + √25

5.Work out (−6) + (−4) × 3

6.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

7.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

8.Work out the value of (√5)⁴

9.Work out ((−3) + 5) × (−4) − (−6) ÷ 2

10.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

11.A cake recipe needs 3/4 of a kilogram of sugar. Aisha wants to make half the recipe. Work out how much sugar she needs, giving your answer as a fraction of a kilogram in its simplest form.

12.A train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.

13.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

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

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