Algebra worksheet — GCSE Foundation

1.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.

2.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.

3.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

4.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

5.Solve 6x − 5 = 3x + 13.

6.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

7.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

8.Solve the inequality x + 5 < 12.

9.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.

10.Expand 2(x + 12)

11.Write down the first four terms of the sequence with nth term 6n − 5.

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

13.Expand and simplify (x − 3)²

14.The graph of a straight line has equation y = 4x − 5. Beth says the y-intercept is 4. Work out the correct y-intercept.

15.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.