Algebra worksheet — GCSE Foundation

1.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

2.Solve the inequality 2(x − 1) ≤ 8.

3.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

4.Which expression means the same as a × a × a?

5.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.

6.Make x the subject of the formula y = 3(x + 2).

7.The graph of y = x² + 2x − 15 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

8.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

9.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

10.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

11.Make p the subject of the formula n = p/3.

12.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

13.Work out the value of (x − 4)/2 + 3 when x = 10

14.Expand 2(x − 13)

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.