Algebra worksheet — GCSE Foundation

1.Work out the value of (x − 4)/2 + 3 when x = 10

2.a = 2 and b = 5. Work out the value of a²b.

3.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

4.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

5.Work out the value of n² − n when n = −3

6.y = 5x − 1. Work out the value of y when x = 3.

7.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

8.Simplify (5x² + 3x − 2) − (2x² − x + 5)

9.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

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

11.Solve 5(x + 3) = 40

12.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.

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

14.Which of these is a factor of 15x + 20?

15.A curve has equation y = x² − 9. Which statement about its graph is correct?