Number worksheet — GCSE Higher

1.Work out 3.7 × 24.

2.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

3.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.

4.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

5.A length, L cm, has the error interval 24.5 ≤ L < 25.5. Write down the degree of accuracy to which the length was measured.

6.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?

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

8.Work out how many factors 100 has.

9.Write 0.06 as a fraction in its simplest form.

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

11.Work out ∛64.

12.Simplify x⁷ × x⁴, giving your answer as a single power of x.

13.Find the missing number: 17 × ▢ = 391

14.Postage on a parcel is calculated as £4.60, correct to the nearest 20p. Which of these could not be the actual cost of the postage?

15.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.