Number worksheet — GCSE Higher

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

2.A number is multiplied by 4, then 8 is added, giving the result 40. Work out the number.

3.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.

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

5.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

6.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

7.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

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

9.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

10.Work out √25 + 4² − 12 ÷ 3

11.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.

12.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.

13.Simplify √45.

14.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

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