Algebra worksheet — GCSE Foundation

1.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

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

3.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

4.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?

5.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

6.Solve the inequality x + 5 < 12.

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

8.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

9.Write down the coefficient of p in the expression 7 − 4p + 9q.

10.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

11.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

12.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.

13.Work out the value of 2x² when x = −3

14.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

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