Algebra worksheet — GCSE Foundation

1.Make p the subject of the formula n = p/3.

2.Solve 4(x − 3) = 2x + 6.

3.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.

4.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

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

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

7.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.

8.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.

9.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

10.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

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 graph of y = (x − 2)(x + 5) crosses the x-axis at two points. Work out the x-coordinates of these two points.

13.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

14.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

15.Write down the gradient of the line with equation y = 6 + 4x.