Number worksheet — GCSE Foundation

1.Simplify x⁶ ÷ x²

2.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

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

4.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.

5.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.

6.Write 45,000 in standard form.

7.Work out the lowest common multiple of 4 and 6.

8.Write the fraction 47/50 as a decimal.

9.Work out √144

10.Work out 6² − 4².

11.A newspaper reports that 48,000 people attended a festival. The figure is correct to the nearest thousand. Which statement about the number of people who attended must be true?

12.A tin of paint has a mass of 5.672 kg. Round this mass to 1 decimal place.

13.Sara has a red T-shirt, a blue T-shirt and a green T-shirt. She has black shorts and grey shorts. By listing the combinations systematically, work out how many different outfits of one T-shirt and one pair of shorts she can make.

14.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.

15.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.