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

3.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

4.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

5.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.

6.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.

7.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.

8.Simplify √45.

9.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

10.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?

11.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.

12.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

13.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

14.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

15.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.