Algebra worksheet — GCSE Foundation

1.Make c the subject of the formula k = 6c.

2.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.

3.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

4.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

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

6.Make p the subject of the formula n = p/3.

7.Work out the value of 2(x + 2) when x = −5

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

9.Write down the expression that means the same as (x + 7) ÷ 4.

10.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.

11.Work out the value of 5y + 9 when y = 0

12.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.

13.Solve (2x + 1)/3 = 5

14.Solve 3x − 5 = 4.

15.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.