Number worksheet — GCSE Higher

1.A crowd of 8,400 people is recorded correct to the nearest 100. Work out the smallest possible number of people in the crowd.

2.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

3.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

4.Work out ⁴√81

5.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

6.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

7.The number of visitors to a museum on Saturday is given as 1,800, correct to the nearest 100. Which of these could not be the actual number of visitors?

8.The rainfall in a town during April is recorded as 62.4 mm, correct to 1 decimal place. Write down the error interval for the actual rainfall, r mm.

9.A plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.

10.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.

11.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?

12.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

13.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.

14.Work out (2/3)² + (1/2)². Give your answer as a fraction.

15.A lift has a safe working load of 500 kg. Four people get in the lift and the lift's display records their total mass as 493 kg, correct to the nearest kg. Decide whether the four people are definitely within the safe working load.