Number worksheet — GCSE Higher

1.A photography studio offers 4 backdrops and 3 outfits for a portrait session. The plain grey backdrop, one of the 4 backdrops, cannot be used with the formal suit outfit, one of the 3 outfits. Work out how many different backdrop-and-outfit combinations are possible.

2.A rectangular garden has a length of 12.4 m and a width of 7.5 m, each measured correct to 1 decimal place. Calculate the upper bound for the area of the garden.

3.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

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 car is hired from 10:00 on Monday until 16:00 on Thursday. Work out the total length of the hire, in hours.

6.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.

7.Work out 35% of 180.

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

9.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

10.A jacket normally costs £65. In a sale it is reduced by 20%, and the shop then takes a further £5 off at the till. Work out the final price.

11.After a price increase of 10%, a laptop costs £330. Work out the original price.

12.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

13.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

14.Postage on a parcel is calculated as £4.60, correct to the nearest 20p. Which of these could not be the actual cost of the postage?

15.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.