Number worksheet — GCSE Higher

1.Work out the reciprocal of (2 + 3)

2.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.

3.Work out 3.7 × 24.

4.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

5.Work out (−6) + (−4) × 3

6.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.

7.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?

8.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?

9.Work out ((−3) + 5) × (−4) − (−6) ÷ 2

10.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.

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

12.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.

13.£60 is shared between Amir, Bo and Chen in the ratio 1:2:3. Work out the fraction of the £60 that Amir and Bo receive together.

14.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.

15.Write 7/12 as a decimal, showing clearly which digit is recurring.