Number worksheet — GCSE Higher

1.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

2.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.

3.A photography studio offers 4 backdrops and 3 outfits for a portrait session. The plain grey backdrop, one of the 4 backdrops, cannot be used with the formal suit outfit, one of the 3 outfits. Work out how many different backdrop-and-outfit combinations are possible.

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

5.Write 90 as a product of its prime factors.

6.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.

7.A washing machine costs £320 before VAT. VAT is charged at 20%. Work out the total price including VAT.

8.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.

9.A country has an area of 25,000,000 hectares. Write this area in standard form.

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

11.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.

12.Four locations each record a temperature one winter morning. Which of these temperatures is the coldest?

13.Work out √144 − 2 × 3 + √25

14.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.

15.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.