Number worksheet — GCSE Higher

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

2.Ten athletes run in a final. Gold, silver and bronze medals are awarded to the first three athletes to finish, and there are no ties. Work out how many different ways the three medals can be awarded.

3.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.

4.Work out how many factors 36 has.

5.Four locations each record a temperature one winter morning. Which of these temperatures is the coldest?

6.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.

7.Work out the value of 6² − 4³.

8.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

9.Work out √225 ÷ 3.

10.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.

11.Work out ∛(−27) + ∛8

12.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.

13.Work out (−2)³ + (−3)² − (−4)

14.Robert is converting 0.999... (with the 9s recurring forever) into a fraction. He lets x = 0.999... . Multiplying by 10 gives 10x = 9.999... . Subtracting x from 10x gives 9x = 9, so x = 1. Which statement correctly explains this result?

15.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.