Number worksheet — GCSE Higher

1.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.

2.Write 200 as a product of its prime factors, using index notation.

4.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

5.Simplify √45.

6.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

7.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

8.Tickets for a fairground ride are sold in packs of 6. Tokens for the dodgems are sold in packs of 10. Yusuf wants to buy the smallest number of packs of each so that he ends up with the same number of ride tickets as dodgem tokens. Work out how many ride tickets that is.

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

10.Write 5/6 as a decimal, showing clearly which digit recurs.

11.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

12.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.

13.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.

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

15.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20