Algebra worksheet — GCSE Foundation

1.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.

2.Write down the expression that means the same as w ÷ 6.

3.In which quadrant does the point (−3, 0.5) lie?

4.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

5.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

6.Simplify 2b − 1 + 2b − 4 + 2b

7.Work out the coordinates of the reflection of (6, −3) in the y-axis.

8.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

9.a = 3 and b = 5. Work out the value of a²b.

10.y = x + 4. Work out the value of y when x = 3.

11.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

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

13.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.

14.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

15.A straight line has equation y = 4 − 3x. Work out the gradient of the line.