Number worksheet — GCSE Foundation

1.Which one of these statements is true?

2.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.

3.A student always writes the digits after the decimal point over a denominator of 100, whatever the number of decimal places. Using this wrong rule, they convert 0.9 to a fraction. Work out the correct fraction that 0.9 is equal to, giving your answer in its simplest form.

4.Work out 3 × (−2)² − 5

5.Work out −(−3)⁴ + (−3)³

6.A café buys 18 boxes of teabags at £3.45 each, and sells all the teabags for £108 in total. Work out the café's profit.

7.Round 0.006852 to 2 significant figures.

8.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.

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

10.Work out the value of ∛125.

11.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.

12.A bag of flour is labelled 1.5 kg, correct to the nearest 0.1 kg. The true mass of the flour is m kg. Which inequality gives all the possible values of m?

13.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.

14.Work out an estimate for 6.8 × 41, by rounding each number to 1 significant figure.

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