Number worksheet — GCSE Higher

1.Last year a company made a profit of £5,200,000. Write this amount in standard form.

2.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.

3.Work out 6² − 4².

4.Simplify x⁶ ÷ x²

5.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

6.Work out −4.5 + 2.8.

7.Petrol costs £1.48 per litre. Sam buys 35 litres and pays with three £20 notes. Work out his change.

8.A recipe for one cake needs 2/3 of a cup of sugar. Priya has 3 1/2 cups of sugar. Work out how many complete cakes she can make.

9.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?

10.Sam compares 0.6 and 5/8 by comparing the digit 6 with the digit 5, and says that 0.6 is the larger number. Convert 5/8 to a decimal to find the correct larger value.

11.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

12.Work out 36 ÷ (2 × 3)

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

14.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

15.A rectangular plywood panel measures 2.4 m by 0.75 m. Work out the area of the panel in square metres, giving your answer as a fraction in its simplest form.