Algebra worksheet — GCSE Higher

1.Work out the gradient of the straight line with equation 3y = 12 − 6x.

2.f(x) = (x + 1)/2. Find f⁻¹(x).

3.Write down the expression that means the same as m² × m × 3.

4.Solve x² − 5x + 6 = 0 by factorising.

5.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.

6.Solve 4x − (2x − 6) = 18

7.A geometric sequence has first term 3 and common ratio √3. Work out the position of the first term of the sequence that exceeds 30.

8.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.

9.Simplify (x² − 9) ÷ (x² + 5x + 6).

10.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.

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

12.Make x the subject of the formula y = 5x + 3.

13.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.

14.Two students each use the trapezium rule to estimate the area under the same curve between x = 0 and x = 8. Student A uses 4 strips of width 2. Student B uses 8 strips of width 1. Which estimate is more likely to be closer to the true area, and why?

15.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.