Algebra worksheet — GCSE Foundation

1.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

2.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

3.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

4.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.

5.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

6.Expand and simplify 2(a + 6) − 2(a − 7)

7.n = 3. Work out the value of (2n)².

8.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

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

10.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

11.Solve the inequality 3x − 1 ≤ 11.

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

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

14.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

15.Simplify 2b − 1 + 2b − 4 + 2b