Algebra worksheet — GCSE Foundation

1.Work out the distance of the point (−6, 4) from the x-axis.

2.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.

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

4.In which quadrant does the point (−3, 0.5) lie?

5.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

6.Which expression is equivalent to 0.5(4x + 6) − x?

7.Expand 2(x + 12)

8.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.

9.Which of these is an expression?

10.Make x the subject of the formula y = 4(x − 6).

11.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

12.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.

13.Solve the inequality 3x − 1 ≤ 11.

14.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?

15.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.