Number worksheet — GCSE Higher

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

2.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

3.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

4.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

5.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.

6.The decimal 0.2333... has one non-recurring digit (the 2) followed by a single recurring digit (the 3), so it can be written as 0.2 recurring 3. Let x = 0.2333... . Work out x as a fraction in its simplest form.

7.Work out the value of 2⁻²

8.Write 7/12 as a decimal, showing clearly which digit is recurring.

9.Last year a company made a profit of £5,200,000. Write this amount in standard form.

10.Simplify ⁴√(16a⁸b¹²)

11.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.

12.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.

13.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20

14.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

15.A café meal deal is one sandwich, one snack and one drink. There are 4 different sandwiches, 3 different snacks and 2 different drinks to choose from. Work out how many different meal deals are possible.