Algebra worksheet — GCSE Foundation

1.Work out the coordinates of the reflection of (6, −3) in the y-axis.

2.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

3.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

4.The point A is at (5, −3). In which quadrant does A lie?

5.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

6.Write down the y-intercept of the line with equation y = 3x + 8.

7.The graph of y = x² + 2x − 15 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

8.Solve 5x − 9 = 16

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

10.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

11.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.

12.Which of these rules generates the sequence 6, 11, 16, 21, …?

13.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

14.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

15.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?