Algebra worksheet — GCSE Foundation

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

2.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

3.Solve 6x − 5 = 3x + 13.

4.a = 2 and b = 5. Work out the value of ab².

5.Which of these equations describes a vertical line?

6.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

7.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

8.Work out the value of a² − 2b when a = −3 and b = 4.

9.Solve 3(2x − 1) = 27

10.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

11.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

12.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

13.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.

14.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

15.Make x the subject of the formula y = 4x − 3.