Algebra worksheet — GCSE Foundation

1.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

2.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.

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

4.A student says that 5(x + 2) is equivalent to 5x + 2. Which statement explains why the student is wrong?

5.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

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

7.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

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

9.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

10.A number machine adds 5 to its input. Work out the output when the input is 0.

11.Solve x² − 100 = 0.

12.Which expression is equivalent to 7x − 3(2x − 6)?

13.How many turning points does the graph of y = x² − 7x + 10 have?

14.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?

15.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?