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.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

3.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.

4.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

5.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.

6.A speed camera measures a car's speed as 34 mph, correct to the nearest mph. Work out the smallest possible actual speed of the car, in mph.

7.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.

8.Given that 2⁵ = 32, work out 2⁶.

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

10.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

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

12.A car travels 100 km, correct to the nearest km, in a time of 2 hours, correct to the nearest 0.1 hour. Work out the average speed, in km/h, to the greatest degree of accuracy the bounds can guarantee.

13.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.

14.The radius of a circular pond is given as 3.2 m, correct to 1 decimal place. Calculate the upper bound for the area of the pond, giving your answer correct to 3 significant figures.

15.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.