Number worksheet — GCSE Higher

1.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

2.Work out the value of (√5)⁴

3.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².

4.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

5.Write 7/12 as a decimal, showing clearly which digit is recurring.

6.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

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

8.Work out (−6) + (−4) × 3

9.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

10.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.

11.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

12.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

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

14.Which of these statements about −0.7 and −0.25 is true?

15.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.