Algebra worksheet — GCSE Higher

1.Solve (2x + 1)/3 = 5

2.Which of these is an identity?

3.The first four terms of a sequence are 2, 2√3, 6, 6√3, ... Work out the next term.

4.The tangent to a curve at the point (5, 2) is the line y = mx + c. This tangent crosses the y-axis at (0, −8). Work out the gradient, m, of the tangent.

5.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

6.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

7.The first five terms of a sequence are 7, 9, 13, 19, 27. By finding the second difference, work out the coefficient of n² in the nth term.

8.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

9.A train's distance-time graph shows it travelling 100 km at a steady speed in the first 1.5 hours, waiting at a signal for 0.25 hours, then travelling a further 47 km in 0.75 hours. Work out the average speed for the whole journey, correct to 1 decimal place.

10.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

11.For 0 ≤ x ≤ 360, the equation sin x = 0.5 has two solutions. What are they?

12.Solve x² − 100 = 0.

13.The mass of a chemical sample decays by 15% every hour. It starts at 500 g. Work out the mass remaining after 3 hours, correct to 1 decimal place.

14.Write down the first four terms of the sequence with nth term 6n − 5.

15.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.