Number worksheet — GCSE Higher

1.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.

2.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.

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

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

5.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

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

7.Work out 36 ÷ (2 × 3)

8.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

9.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.

10.Work out ((−3) + 5) × (−4) − (−6) ÷ 2

11.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.

12.Write 0.35 as a fraction in its lowest terms.

13.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

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

15.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.