Algebra worksheet — GCSE Foundation

1.Explain why the equation 4x + 3 = 4x + 10 has no solution for x.

2.Simplify 5a/6 − a/3

3.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.

4.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

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

6.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.

7.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

8.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

9.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

10.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

11.Work out the gradient of the straight line with equation 2x + y = 8.

12.Solve 5(x + 3) = 40

13.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

14.Solve the inequality 3x − 1 ≤ 11.

15.Solve 5x² − 15x = 0.