Algebra worksheet — GCSE Foundation

1.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

2.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

3.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

4.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

5.A cyclist's journey is shown on a distance–time graph. The graph is a straight line from (0 minutes, 0 km) to (40 minutes, 12 km). Work out her speed in kilometres per hour.

6.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.

7.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

8.Write down the expression that means 5 more than half of n.

9.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

10.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

11.Solve 4x² − 9 = 0.

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

13.Which expression means the same as a × a × a?

14.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

15.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.