Number worksheet — GCSE Higher

1.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

2.A vending machine sells 4 types of crisps, 5 types of chocolate bar and 2 types of drink. Work out how many different combinations of one crisp packet, one chocolate bar and one drink can be bought.

3.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?

4.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

5.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

6.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56

7.Work out the value of (√5)⁴

8.Work out (5 + 2) × 3²

9.Work out the value of √(16 + 9)

10.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.

11.At a book fair the ratio of fiction books to non-fiction books is 4 : 5. Of the non-fiction books, 3/5 are about history. Work out the fraction of all the books at the fair that are history books.

12.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.

13.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

14.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

15.A grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.