Algebra worksheet — GCSE Foundation

1.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?

2.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

3.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

4.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.

5.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

6.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.

7.Solve x² + 7x = 0.

8.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

9.Solve x² = 81.

10.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

11.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

12.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

13.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

14.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

15.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.