Algebra worksheet — GCSE Higher

1.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

2.Solve 2x² − 32 = 0.

3.Which of these statements is an identity?

4.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

5.Describe a sequence of two transformations that maps the graph of y = cos x onto the graph of y = cos(x + 90°) − 2.

6.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

7.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

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

9.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

10.Work out the gradient of the straight line with equation y = (2x/5) − 3.

11.A proof that (n + 3)² − (n − 3)² is always a multiple of a certain number begins: Line 1: (n + 3)² − (n − 3)² = (n² + 6n + 9) − (n² − 6n + 9). Which expression correctly completes Line 2?

12.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?

13.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

14.A circle has centre (0, 0) and equation x² + y² = 64. Write down the radius of the circle.

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