Number worksheet — GCSE Higher

1.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.

2.A plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.

3.Work out ⁴√81

4.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

5.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

6.A train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.

7.Bella's electricity supplier charges 28.5p per unit (kWh). Last month she used 340 units. Work out the total cost, giving your answer in pounds.

8.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

9.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

10.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.

11.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.

12.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

13.A washing machine costs £320 before VAT. VAT is charged at 20%. Work out the total price including VAT.

14.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.

15.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.