Number worksheet — GCSE Higher

1.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?

2.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

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

4.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

5.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.

6.Work out 6² − 4².

7.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.

8.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

9.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.

10.Work out 4368 ÷ 12.

11.Work out (−36) ÷ (−6) × 2

12.A country has an area of 25,000,000 hectares. Write this area in standard form.

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

14.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.

15.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.