Algebra worksheet — GCSE Foundation

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

2.Solve 6x + 4 = 28

3.Simplify 2b − 1 + 2b − 4 + 2b

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

5.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

6.Work out the coordinates of the reflection of (6, −3) in the y-axis.

7.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

8.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

9.Which of these values of x is a solution of x² + 2x − 15 = 0?

10.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

11.Four sequences are shown below. Sequence P: 4, 8, 16, 32, ... Sequence Q: 4, 8, 12, 16, ... Sequence R: 4, 7, 12, 19, ... Sequence S: 4, 9, 16, 25, ... Work out which of the sequences P, Q, R and S is geometric.

12.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

13.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

14.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

15.Solve x² + 7x = 0.