Number worksheet — GCSE Foundation

1.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

2.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

3.4ˣ = 64. Work out the value of x.

4.In a car park the ratio of vans to cars is 2 : 7. Work out the number of vans as a fraction of the number of cars.

5.Amelia eats 5/8 of a bar of chocolate and Oliver eats 3/4 of an identical bar. Write both amounts as eighths and write down the greater of the two fractions.

6.A block of butter has a mass of 250 g, correct to the nearest 10 g. Using m for the mass of the block in grams, write down the error interval for m.

7.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.

8.Work out the lowest common multiple of 9 and 15.

9.Work out the total cost of 3 pens at 45p each and one notebook at £2.35. Give your answer in pounds.

10.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

11.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

12.A laptop costs £720. A carrying case for it costs 1/9 of the price of the laptop. Work out the cost of the carrying case.

13.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

14.A tin of soup has a mass of 450 g. A bag of potatoes has a mass of 2.6 kg. Work out the total mass, in kilograms.

15.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?