Number worksheet — GCSE Higher

1.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

2.A shop buys boxes of pens for £4 each. It sells each box on to a school for £3 more than it paid, and charges an extra £2 delivery fee for the whole order. A school orders 5 boxes. Work out the total cost of the order.

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

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

5.Work out (−2)³ + (−3)² − (−4)

6.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

7.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.

8.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

9.Work out 4368 ÷ 12.

10.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.

11.The rainfall in a town during April is recorded as 62.4 mm, correct to 1 decimal place. Write down the error interval for the actual rainfall, r mm.

12.Work out 10% of 30% of £200.

13.Work out 3 + 4 × (−2).

14.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?

15.Robert is converting 0.999... (with the 9s recurring forever) into a fraction. He lets x = 0.999... . Multiplying by 10 gives 10x = 9.999... . Subtracting x from 10x gives 9x = 9, so x = 1. Which statement correctly explains this result?