Algebra worksheet — GCSE Foundation

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

2.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.

3.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?

4.Solve 3x − 5 = 4.

5.A point lies on the y-axis. What can be said about the x-coordinate of that point?

6.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

7.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.

8.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

9.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?

10.Make x the subject of the formula y = (x − 4)/5.

11.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

12.Write down the coefficient of p in the expression 7 − 4p + 9q.

13.A straight line has equation y = 5x. Work out the value of y when x = 3.

14.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

15.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.