Algebra worksheet — GCSE Foundation

1.Solve 4(x − 3) = 2x + 6.

2.y = 5x − 1. Work out the value of y when x = 3.

3.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

4.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

5.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

6.Make c the subject of the formula k = 6c.

7.Work out the value of 5a + 2 when a = 3

8.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

9.Factorise fully 12x² + 18x.

10.The graph of y = x² + 2x − 15 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

11.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

12.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

13.A number machine adds 6 to its input. Work out the output when the input is −4.

14.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

15.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.