Number worksheet — GCSE Higher

1.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.

2.Write down the exact decimal value of the fraction 1/6.

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

5.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

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

7.Work out ⁴√16

9.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.

10.Work out the exact value of √(2² + 3²)

11.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

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

13.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.

14.An allotment plot is divided into vegetables and flowers in the ratio 9 : 4. A third of the vegetable section is used for potatoes. What fraction of the whole plot is potatoes?

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.