Algebra worksheet — GCSE Foundation

1.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

2.Make c the subject of the formula k = 6c.

3.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

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.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.

6.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.

7.A cyclist's journey is shown on a distance–time graph. The graph is a straight line from (0 minutes, 0 km) to (40 minutes, 12 km). Work out her speed in kilometres per hour.

8.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

9.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

10.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

11.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

12.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

13.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

14.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.

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.