Algebra worksheet — GCSE Foundation

1.Make x the subject of the formula y = 3(x + 2).

2.A quadratic graph has equation y = (x − 4)². A student says this graph crosses the x-axis at two different points. Explain why the student is wrong.

3.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

4.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

5.A number machine multiplies its input by 3. The output is 15. Work out the input.

6.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.

7.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

8.Write down the expression that means the same as m² × m × 3.

9.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

10.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.

11.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

12.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

13.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

14.Solve x² − x − 12 = 0.

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