Algebra worksheet — GCSE Foundation

1.Solve x/4 + 1 = 3

2.Solve the inequality x + 5 < 12.

3.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

4.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

5.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

6.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

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

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

9.Make m the subject of the formula w = m − 8.

10.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.

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

12.Which of these is an inequality?

13.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

14.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

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.