Algebra worksheet — GCSE Foundation

1.Write down the coefficient of p in the expression 7 − 4p + 9q.

2.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

3.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

4.Simplify 2b − 1 + 2b − 4 + 2b

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

6.Write down the number of terms in the expression 4x² − 7x + 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.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.

9.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

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

11.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?

12.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

13.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

14.Which of these rules generates the sequence 6, 11, 16, 21, …?

15.A ferry's distance-time graph is a straight line from (0 minutes, 0 km) to (25 minutes, 15 km). Work out the ferry's speed in kilometres per hour.