Algebra worksheet — GCSE Foundation

1.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

2.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

3.Solve the inequality x − 10 < −3.

4.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

5.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.

6.Which expression is equivalent to 0.5(4x + 6) − x?

7.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

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

9.Solve x² − 6x = 0.

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

11.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

12.Make c the subject of the formula k = 6c.

13.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

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

15.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.