Algebra worksheet — GCSE Foundation

1.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

2.Work out the gradient of the straight line with equation 3y = 12 − 6x.

3.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?

4.y = 5 − 2x. Work out the value of x when y = 11.

5.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

6.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

7.Work out the value of 3a − 2b when a = 5 and b = 4

8.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

9.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.

10.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

11.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

12.Work out the y-intercept of the graph of y = x² + 3x − 10.

13.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

14.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

15.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?