Algebra worksheet — GCSE Foundation

1.Make x the subject of the formula y = 5x + 3.

2.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

3.Which of these is an equation, rather than an expression, a formula or an identity?

4.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?

5.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

6.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

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

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

9.A straight line has equation y = 5x. Work out the value of y when x = 3.

10.Work out the value of a² − 2b when a = −3 and b = 4.

11.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

12.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

13.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.

14.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

15.Work out the value of (x − 4)/2 + 3 when x = 10