Number worksheet — GCSE Higher

2.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.

3.At a book fair the ratio of fiction books to non-fiction books is 4 : 5. Of the non-fiction books, 3/5 are about history. Work out the fraction of all the books at the fair that are history books.

4.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

5.Simplify √45.

6.Work out the exact value of √(2² + 3²)

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

8.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.

9.A length, L cm, has the error interval 24.5 ≤ L < 25.5. Write down the degree of accuracy to which the length was measured.

10.Work out the value of (√5)⁴

11.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.

12.Work out how many factors 100 has.

13.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

14.A measuring jug shows a volume of 340 ml, correct to the nearest 20 ml. Work out the smallest possible volume in the jug.

15.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.