Number worksheet — GCSE Higher

1.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

2.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.

3.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.

4.Work out the value of √49 + ∛27

5.Work out how many factors 100 has.

6.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.

7.Work out the value of 6² − 4³.

8.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

9.Which of these is written correctly in standard form?

10.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.

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

12.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.

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

14.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

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.