Number worksheet — GCSE Higher

1.Work out ∛(−27) + ∛8

2.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

3.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.

4.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.

5.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

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

7.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.

8.Write 90 as a product of its prime factors.

9.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.

10.A driving instructor is working out how many current-style UK number plates are possible. The format is 2 letters, then 2 digits, then a space, then 3 letters (for example AB12 CDE). The letters I, O and Q are never used in any letter position, leaving 23 allowed letters, but every letter and every digit may repeat anywhere on the plate. Work out how many different number plates are possible, giving your answer in standard form to 2 significant figures.

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

12.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

13.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

14.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

15.A restaurant offers a lunch deal of one starter from 5 options, one main from 6 options and one dessert from 3 options. Work out how many different lunch deals are possible.