Algebra worksheet — GCSE Higher

1.The graph of y = x² + 2x − 15 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

2.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

3.Solve (3x + 2)/5 = (x + 4)/3

4.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

5.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

6.A garden path runs along the line 4x + y = 12. A drainage pipe must be laid perpendicular to the path, passing through the point (3, 1) where a sprinkler sits. Work out the equation of the pipe's line, giving your answer in the form y = mx + c.

7.Simplify 5a/6 − a/3

8.Make x the subject of the formula y = 4(x − 6).

9.Points A(8, 15) and B(−8, 15) both lie on the circle x² + y² = 289, which has centre (0, 0). Work out the length of the chord AB.

10.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

11.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

12.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

13.The graph of y = f(x) has a minimum point at (4, −1). Write down the coordinates of the corresponding turning point on the graph of y = −f(x).

14.A circle has centre (0, 0) and radius 9. Work out the equation of the circle.

15.Simplify (x² − 9) ÷ (x² + 5x + 6).