Algebra worksheet — GCSE Foundation

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

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

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

4.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.

5.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

6.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

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

8.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?

9.Work out the value of 3n − 2 when n = 1

10.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.

11.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

12.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

13.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?

14.Solve the inequality 4x + 1 > 2x + 9.

15.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.