Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 2(x + 6)?

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

3.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.

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

5.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

6.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

7.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.

8.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

9.Solve 6x − 5 = 3x + 13.

10.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?

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

12.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

13.A quadratic curve has a minimum turning point at (3, −4). Which of these statements about the curve must be true?

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

15.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.