Number worksheet — GCSE Higher

1.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

2.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

3.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

4.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

5.Work out the value of (√5)⁴

6.Simplify x⁷ × x⁴, giving your answer as a single power of x.

7.A charity raises 8 × 10⁶ pounds. This total is shared equally among 2 × 10² local projects. Work out how much each project receives, in standard form.

8.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

9.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

10.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

11.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.

12.Write down the reciprocal of 0.2

13.Simplify √45.

14.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.

15.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.