Algebra worksheet — GCSE Foundation

1.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

2.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

3.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

4.Write down the expression that means the same as m × m × m × n.

5.a = 3 and b = 5. Work out the value of a²b.

6.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

7.Solve the inequality x − 10 < −3.

8.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

9.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

10.Solve the inequality x + 5 < 12.

11.Make m the subject of the formula w = m − 8.

12.Factorise x² − 3x − 10.

13.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

14.Which of these points lies in the first quadrant?

15.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?