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.Which of these statements is an identity?

3.Expand and simplify (x − 3)²

4.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

5.Which of these rules generates the sequence 6, 11, 16, 21, …?

6.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.

7.A graph has equation y = −2x² + 5. Which statement about its shape is correct?

8.Write down the expression that means the same as m² × m × 3.

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

10.Which expression is equivalent to 2(x + 6)?

11.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

12.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

13.Solve x² − 5x + 6 = 0 by factorising.

14.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

15.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.