Algebra worksheet — GCSE Foundation

1.Make x the subject of the formula y = x + 7.

2.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?

3.Which expression is equivalent to 6x − (2x − 5)?

4.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.

5.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

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

7.Make x the subject of the formula y = 4x − 3.

8.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.

9.The point A lies on the x-axis. Which statement about A must be true?

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

11.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.

12.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

13.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

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

15.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.