Number worksheet — GCSE Higher

1.Write 5,000,000 in standard form.

2.A café buys 18 boxes of teabags at £3.45 each, and sells all the teabags for £108 in total. Work out the café's profit.

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

4.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.

5.Write 200 as a product of its prime factors, using index notation.

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

7.Which of these statements about −0.7 and −0.25 is true?

8.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

9.Work out (3 × 10²) × (2 × 10⁵). Give your answer in standard form.

10.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.

11.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?

12.In a youth club the number of girls is 2/3 of the number of boys. What fraction of the members of the club are girls?

13.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?

14.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.

15.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.