Algebra worksheet — GCSE Foundation

1.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

2.Simplify (5x² + 3x − 2) − (2x² − x + 5)

3.Which of these quadratic graphs does NOT cross the x-axis at all?

4.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

5.Make x the subject of the formula y = 3(x + 2).

6.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

7.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

8.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

9.Which of these is a formula?

10.Which expression means 'triple c, then add double d'?

11.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

12.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?

13.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

14.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

15.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.