Number worksheet — GCSE Higher

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

2.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.

3.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.

4.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.

5.A triangle has a base of 8 cm and a perpendicular height of 5 cm, each correct to the nearest centimetre. Work out the upper bound of the area.

6.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.

7.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.

8.Work out 36 ÷ (2 × 3)

9.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.

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

11.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

12.Which of these decimals lies between 1/4 and 2/5?

13.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

14.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.

15.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.