Number worksheet — GCSE Higher

1.Work out √144 − 2 × 3 + √25

2.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.

3.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.

4.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.

5.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.

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

7.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.

8.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

9.Work out 4368 ÷ 12.

10.Write 60 as a product of its prime factors, using index notation.

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

12.A flight departs at 21:35 and lands at 06:10 the following morning. Work out the total flight time.

13.Expand and simplify √3(2 + √12).

14.Insert one pair of brackets into 2 + 3 × 5 − 1 so that the calculation is equal to 24. Which calculation is correct?

15.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.