Number worksheet — GCSE Higher

1.Write 60 as a product of its prime factors, using index notation.

2.Write 0.06 as a fraction in its simplest form.

3.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.

4.Work out 36 ÷ (2 × 3)

5.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

6.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

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

8.Work out the value of (1/3)⁻²

9.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

10.The two shorter sides of a right-angled triangle are √12 cm and √24 cm. Work out the exact length of the hypotenuse.

11.Round 0.006482 to 2 significant figures.

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.A charity trek covers 830 miles over roughly 19 days. By rounding each number to 1 significant figure, work out an estimate for the number of miles walked per day.

14.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

15.Write down the symbol that makes this statement true: −2/3 ___ −5/6