Algebra worksheet — GCSE Foundation

1.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.

2.y = 5 − 2x. Work out the value of x when y = 11.

3.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

4.Work out the gradient of the straight line with equation 2x + y = 8.

5.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

6.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

7.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

8.Write down the gradient of the line with equation y = 7x − 2.

9.Solve 6x + 4 = 28

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

11.Simplify (5x² + 3x − 2) − (2x² − x + 5)

12.Simplify x + x + 4

13.Solve the inequality 2(3x − 1) ≥ 4x + 8.

14.Solve the inequality 3x + 6 ≤ 0.

15.Simplify 5x + 3y − 2x + y.