Algebra worksheet — GCSE Foundation

1.The first five terms of a sequence are 2, 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

2.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

3.Which of these equations gives a straight-line graph when plotted?

4.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

5.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?

6.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

7.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

8.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

9.Which of these is a term, rather than a whole expression, an equation, or a formula?

10.Solve 3(2x − 1) = 27

11.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

12.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.

13.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

14.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

15.Solve 2x² = 18.