Number worksheet — GCSE Higher

1.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

2.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

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

4.Which one of these statements is true?

5.A number is multiplied by 4, then 8 is added, giving the result 40. Work out the number.

6.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

7.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

8.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

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

10.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

11.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³

12.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

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

14.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.

15.Simplify √8 + √18, giving your answer in the form k√2.