Algebra worksheet — GCSE Foundation

1.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

2.The diagram shows the graph of a quadratic function. Which equation could it represent?

3.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.

4.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.

5.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

6.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

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

8.Which of these equations is equivalent to 5x − 2 = 3x + 8?

9.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

10.Which expression means 'y squared, multiplied by 3'?

11.Which of these statements is an equation with exactly one solution?

12.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

13.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

14.Which expression is equivalent to 2(x + 6)?

15.A straight line has equation y = 4 − 3x. Work out the gradient of the line.