Algebra worksheet — GCSE Foundation

1.Make x the subject of the formula y = x/2 − 5.

2.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

3.A number machine adds 6 to its input. Work out the output when the input is −4.

4.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?

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

6.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

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

8.Factorise x² − 64.

9.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

10.Work out the gradient of the straight line with equation 3y = 12 − 6x.

11.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

12.Solve the inequality 2(x − 1) ≤ 8.

13.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.

14.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

15.Solve x − 4 = −9