Algebra worksheet — GCSE Foundation

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

2.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

3.Solve x² − 6x = 0.

4.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

5.Solve 2x − 2 = 2

6.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

7.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

8.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

9.Solve x/4 + 1 = 3

10.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

11.The first five terms of a sequence are 2, 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

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

13.Work out the value of 3n − 2 when n = 1

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

15.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.