Algebra worksheet — GCSE Foundation

1.Write down the expression that means the same as 3 × y × y.

2.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

3.Work out the value of 2x² when x = −3

4.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.

5.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

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

7.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

8.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.

9.The graph of y = x² − 2x − 8 crosses the x-axis at x = −2 and x = 4. Work out the x-coordinate of the turning point of the curve, using the symmetry of the graph.

10.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

11.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

12.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

13.Solve x² + 7x = 0.

14.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.

15.Solve 3x − 1 = 8