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.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.

3.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

4.Work out ∛(−27) + ∛8

5.Simplify ⁴√(16a⁸b¹²)

6.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.

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

8.√700 lies between which two consecutive integers?

9.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

10.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.

11.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.

12.Write 0.36 as a fraction in its simplest form.

13.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

14.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.

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