Number worksheet — GCSE Higher

1.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

2.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.

3.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

4.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

5.Work out √25 + 4² − 12 ÷ 3

6.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

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

8.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.

9.Write 12 as a product of its prime factors.

10.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.

11.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.

12.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

13.A car travels 180 km using 6 litres of fuel. Work out the car's fuel consumption in kilometres per litre, then work out how many kilometres it can travel on a full tank of 12 litres at this rate.

14.A measuring jug shows a volume of 340 ml, correct to the nearest 20 ml. Work out the smallest possible volume in the jug.

15.Write 0.06 as a fraction in its simplest form.