Algebra worksheet — GCSE Foundation

1.p = 4. Work out the value of 2p³.

2.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

3.Simplify p + p + p.

4.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

5.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

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

7.Work out the gradient of the straight line with equation 2x + y = 8.

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

9.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.

10.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

11.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.

12.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

13.x = 5. Work out the value of 3x² − 4.

14.The formula for the area of a trapezium is A = (a + b)h / 2, where a and b are the parallel side lengths and h is the height. Make h the subject of the formula.

15.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?