Algebra worksheet — GCSE Foundation

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

2.Solve 5x² − 15x = 0.

3.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

4.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

5.Write down the expression that means 5 more than half of n.

6.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

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

8.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

9.Simplify 5x + 3y − 2x + y.

10.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

11.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

12.Solve the inequality 4x + 1 > 2x + 9.

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

14.Which expression means the same as a × a × a?

15.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?