Algebra worksheet — GCSE Foundation

1.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.

2.Which of these is a factor of 15x + 20?

3.How many turning points does the graph of y = x² − 7x + 10 have?

4.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

5.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

6.Work out the value of 3x² − 4x when x = −2.

7.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

8.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

9.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

10.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.

11.A number machine adds 5 to its input. Work out the output when the input is 0.

12.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.

13.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.

14.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

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.