Number worksheet — GCSE Higher

1.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

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

3.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.

4.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.

5.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

6.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.

7.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

8.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.

9.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.

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

11.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.

12.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

13.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

14.Write 90 as a product of its prime factors.

15.Work out how many factors 100 has.