Algebra worksheet — GCSE Foundation

1.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.

2.Which of these equations describes a vertical line?

3.Four sequences are shown below. Sequence P: 4, 8, 16, 32, ... Sequence Q: 4, 8, 12, 16, ... Sequence R: 4, 7, 12, 19, ... Sequence S: 4, 9, 16, 25, ... Work out which of the sequences P, Q, R and S is geometric.

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

5.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

6.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

7.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

8.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.

9.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

10.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

11.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

12.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

13.Which expression is equivalent to 3(2x − 5) + 4x?

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

15.Work out the equation of the straight line through the points (−2, 1) and (0, 7).