Algebra worksheet — GCSE Foundation

1.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.

2.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

3.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

4.Work out the distance of the point (−6, 4) from the x-axis.

5.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

6.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.

7.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.

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

9.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.

10.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.

11.In which quadrant does the point (−3, 0.5) lie?

12.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

13.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

14.Solve 2x + 7 = x + 13

15.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.