Algebra worksheet — GCSE Foundation

1.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

2.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

3.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

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

5.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?

6.Which of these equations describes a vertical line?

7.Solve x² = 81.

8.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

9.Which expression means 'add 3 to n, then multiply the result by 4'?

10.Simplify x + x + 4

12.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.

13.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

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

15.A wall is tiled in rows, and every row uses the same number of tiles. One row uses 10 tiles, two rows use 20 tiles and three rows use 30 tiles. Work out how many tiles are needed for 7 rows.