Algebra worksheet — GCSE Foundation

1.Which of these statements is an equation with exactly one solution?

2.Solve 3x + 14 = 8x − 6

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

4.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

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.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?

7.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.

8.Which expression means the same as 3 × a × b?

9.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

10.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.

11.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

12.A ferry's distance-time graph is a straight line from (0 minutes, 0 km) to (25 minutes, 15 km). Work out the ferry's speed in kilometres per hour.

13.Solve 2x + 7 = x + 13

14.Solve 5x² − 15x = 0.

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