Algebra worksheet — GCSE Foundation

1.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

2.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

3.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

4.Which of these values of x is a solution of x² + 2x − 15 = 0?

5.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

6.Write down the expression that means the same as m² × m × 3.

7.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

8.a = 3 and b = 5. Work out the value of a²b.

9.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.

10.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.

11.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

12.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.

13.Simplify k + k + k + k + k.

14.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.

15.A wall is tiled in rows, and every row uses the same number of tiles. One row uses 10 tiles, two rows use 20 tiles and three rows use 30 tiles. Work out how many tiles are needed for 7 rows.