Algebra worksheet — GCSE Foundation

1.Solve 2(x + 3) = 10

2.Solve the inequality 2(3x − 1) ≥ 4x + 8.

3.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

4.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

5.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

6.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

7.Solve the inequality 6.3x + 1.8 ≤ 40. Hence write down the greatest number with exactly one decimal place that satisfies the inequality.

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

9.Solve x² − 100 = 0.

10.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

11.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

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

13.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

14.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.

15.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.