Number worksheet — GCSE Higher

1.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

2.A bag of flour is labelled 1.5 kg, correct to the nearest 0.1 kg. The true mass of the flour is m kg. Which inequality gives all the possible values of m?

3.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.

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

5.Write 200 as a product of its prime factors, using index notation.

6.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.

7.A paint mix is made from white paint and blue paint in the ratio 5 : 3. Priya uses 1.2 litres of blue paint and the matching amount of white paint. Work out the total volume of the mix.

8.A café meal deal is one sandwich, one snack and one drink. There are 4 different sandwiches, 3 different snacks and 2 different drinks to choose from. Work out how many different meal deals are possible.

9.Work out (2/3)² + (1/2)². Give your answer as a fraction.

10.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

11.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56

12.Work out √225 ÷ 3.

13.Work out the value of (√5)⁴

15.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.