Algebra worksheet — GCSE Foundation

1.Which of these is a formula, rather than an expression, an equation, or an identity?

2.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.

3.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

4.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.

5.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

6.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

7.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

8.Which expression is equivalent to 5x − (x + 3)?

9.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

10.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

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

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

13.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.

14.y = x + 4. Work out the value of y when x = 3.

15.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.