Algebra worksheet — GCSE Foundation

1.Write down the gradient of the line with equation y = 7x − 2.

2.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?

3.Solve the inequality x − 10 < −3.

4.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.

5.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

6.Solve x² − 6x = 0.

7.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.

8.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

9.x = 5. Work out the value of 3x² − 4.

10.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.

11.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

12.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

13.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

14.y = 5x − 1. Work out the value of y when x = 3.

15.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.