Algebra worksheet — GCSE Foundation

1.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

2.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

3.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

4.A point lies on the y-axis. What can be said about the x-coordinate of that point?

5.Work out the value of 3b − 4 when b = 6

6.Solve (3x + 2)/5 = (x + 4)/3

7.A student says 4(2x − 3) is equivalent to 8x − 3. Which statement gives the correct verdict and reason?

8.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

9.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

10.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

11.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

12.A ferry's distance-time graph is a straight line from (0 minutes, 0 km) to (25 minutes, 15 km). Work out the ferry's speed in kilometres per hour.

13.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).

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

15.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.