Number worksheet — GCSE Higher

1.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

2.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

3.Robert is converting 0.999... (with the 9s recurring forever) into a fraction. He lets x = 0.999... . Multiplying by 10 gives 10x = 9.999... . Subtracting x from 10x gives 9x = 9, so x = 1. Which statement correctly explains this result?

4.Work out 36 ÷ (2 × 3)

5.A restaurant offers a lunch deal of one starter from 5 options, one main from 6 options and one dessert from 3 options. Work out how many different lunch deals are possible.

6.Work out 100 − 4 × 5²

7.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.

8.Work out 35% of 180.

9.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.

10.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

11.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

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

13.To estimate the cost of buying 38.7 m of rope at £21.40 per metre, both numbers are first rounded to 1 significant figure. Work out the estimate.

14.A recipe for one cake needs 2/3 of a cup of sugar. Priya has 3 1/2 cups of sugar. Work out how many complete cakes she can make.

15.A courier's van has a weight limit of 850 kg for its parcels. The driver's display shows the total mass of the parcels loaded as 850 kg, correct to the nearest 5 kg. Decide whether the parcels are definitely within the weight limit.