Algebra worksheet — GCSE Higher

1.Which of these equations represents the graph of y = 2ˣ translated by 3 units in the positive y-direction?

2.Factorise x² − 64.

3.Solve the inequality x² ≥ 16, giving your answer using set notation.

4.The nth term of a sequence is n² + 2n − 4. Work out the 7th term.

5.Which expression is equivalent to 6x − (2x − 5)?

6.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

7.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

8.Which of these statements is an identity?

9.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.

10.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

11.A student is proving that (n + 1)² − n² is always an odd number. Which of these correctly completes the first line of algebra?

12.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?

13.A car's journey is represented by a velocity-time graph. The total distance travelled, found from the area under the graph, is 350 metres, and the total time for the journey is 25 seconds. Work out the car's average speed for the whole journey, in m/s.

14.Work out the value of 3x² − 4x when x = −2.

15.Work out the value of 2(x + 2) when x = −5