Algebra worksheet — GCSE Foundation

1.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

2.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

3.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.

4.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

5.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

6.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

7.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

8.Solve 4x + 3 = 19

9.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.

10.Simplify 2a + 3b − a + 2b − b

11.A student says that 5(x + 2) is equivalent to 5x + 2. Which statement explains why the student is wrong?

12.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

13.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

14.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

15.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.