Number worksheet — GCSE Higher

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

2.A florist has 5 different flowers. Freya picks 3 of them to make a small bunch, and the order in which she picks them does not matter. Work out how many different bunches she could make.

3.Write ∛(x²) as a single power of x.

4.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

5.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.

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

7.A train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.

8.Simplify √45.

9.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

10.Work out the reciprocal of (2 + 3)

11.Ten players enter a chess tournament. Every player plays every other player exactly once. Work out how many games are played in the tournament.

12.Work out √(4 × 9)

13.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

14.Work out 35% of 180.

15.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.