Number worksheet — GCSE Higher

1.A rectangular garden has a length of 12.4 m and a width of 7.5 m, each measured correct to 1 decimal place. Calculate the upper bound for the area of the garden.

2.Work out √144 − 2 × 3 + √25

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

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

5.A market trader buys 8 melons at £1.35 each. He sells all of them for a total of £15.60. Work out his profit.

6.√700 lies between which two consecutive integers?

7.Four locations each record a temperature one winter morning. Which of these temperatures is the coldest?

8.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.

9.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

10.Work out (−6) + (−4) × 3

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

12.A photography studio offers 4 backdrops and 3 outfits for a portrait session. The plain grey backdrop, one of the 4 backdrops, cannot be used with the formal suit outfit, one of the 3 outfits. Work out how many different backdrop-and-outfit combinations are possible.

13.At a book fair the ratio of fiction books to non-fiction books is 4 : 5. Of the non-fiction books, 3/5 are about history. Work out the fraction of all the books at the fair that are history books.

14.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.

15.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.