Number worksheet — GCSE Higher

1.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

2.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

3.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

4.Work out 3 × (−2)² − 5

5.Work out 5/6 × 2/9, giving your answer in its simplest form.

6.A board game has 5 different character pieces and 4 different colour tokens. The dragon piece can only be used with the gold token. Work out how many different combinations of one character piece and one colour token are possible.

7.Priya has 24 red beads and 36 blue beads. She makes identical bracelets, using every bead and with none left over. Work out the greatest number of bracelets she can make.

8.Write these numbers in order, starting with the smallest: −1.4, 5/4, −6/5, 1.3, 0

9.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

10.A crowd of 8,400 people is recorded correct to the nearest 100. Work out the smallest possible number of people in the crowd.

11.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.

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

13.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.

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

15.A recipe needs 0.485 kg of flour per cake. A bakery estimates its flour order by rounding this amount to 1 significant figure, then multiplying by the 60 cakes it plans to bake. Work out the bakery's estimate for the total flour needed, in kg.