Number worksheet — GCSE Higher

1.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

2.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.

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

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

5.Work out the value of √49 + ∛27

6.Simplify √8 + √18, giving your answer in the form k√2.

7.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.

8.Work out how many factors 36 has.

9.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

10.A flight departs at 21:35 and lands at 06:10 the following morning. Work out the total flight time.

11.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.

12.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

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

14.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

15.A driving instructor is working out how many current-style UK number plates are possible. The format is 2 letters, then 2 digits, then a space, then 3 letters (for example AB12 CDE). The letters I, O and Q are never used in any letter position, leaving 23 allowed letters, but every letter and every digit may repeat anywhere on the plate. Work out how many different number plates are possible, giving your answer in standard form to 2 significant figures.