Algebra worksheet — GCSE Foundation

1.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

2.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.

3.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

4.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.

5.Solve 5x + 2 = 17.

6.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

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

8.Which of these is an expression?

9.Solve 2x² − 32 = 0.

10.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

11.Factorise x² − 3x − 10.

12.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.

13.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

14.Work out the value of 3x² − 4x when x = −2.

15.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.