Algebra worksheet — GCSE Foundation

1.y = x + 4. Work out the value of y when x = 3.

2.Write down the gradient of the line with equation y = −x + 3.

3.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.

4.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.

5.Solve the inequality 2(3x − 1) ≥ 4x + 8.

6.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.

7.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.

8.A park is drawn on a grid in which 1 unit represents 1 km. The car park is at the point (0, 0) and the lake is at the point (3, 5). Work out the direct distance, in km, from the car park to the lake, giving your answer to 1 decimal place.

9.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

10.The point A is at (5, −3). In which quadrant does A lie?

11.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

12.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.

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

14.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

15.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.