Algebra worksheet — GCSE Higher

1.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

2.A student is asked to simplify (6x³ − 15x²)/(4x² − 10x) fully. Four attempts are shown below. Which one is correct?

3.A company's weekly profit, in £, is modelled by y = f(x), where x is the number of weeks since launch. The graph of y = f(x) has a maximum at (10, 45000). A rival company uses the same marketing strategy but starts trading 6 weeks later and has fixed costs £8000 higher every week, so its profit is modelled by y = f(x − 6) − 8000. In which week does the rival's maximum weekly profit occur, and what is it?

4.Work out the value of m² + 3m when m = −2

5.Work out the value of the discriminant b² − 4ac for the equation 2x² + 3x − 2 = 0.

6.A car accelerates uniformly from rest at 2.5 m/s² until it reaches a speed of 20 m/s, then travels at this constant speed for a further 30 seconds. Work out the total distance travelled.

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

8.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

9.The graph of y = f(x) passes through the point (0, 4). Work out the y-coordinate of the point where the graph of y = f(x) − 6 crosses the y-axis.

10.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.

11.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

12.By completing the square, find the turning point of the curve y = x² − 4x + 9.

13.The graph of y = f(x) passes through the point (2, 7). The graph of y = f(x) + a passes through the point (2, 3). Work out the value of a.

14.Solve 4(x − 3) = 2x + 6.

15.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.