Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

2.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

3.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.

4.Expand 7(a + 8)

5.Solve 3(2x − 1) = 27

6.Expand and simplify (x − 3)²

7.The graph of a straight line has equation y = 4x − 5. Beth says the y-intercept is 4. Work out the correct y-intercept.

8.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

9.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

10.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.

11.A photo printing service has two adverts for its price. Advert A: cost in pounds = 3(2n + 4) for n photos. Advert B: cost in pounds = 6n + 12. A customer says the two adverts always charge the same amount. Is the customer correct?

12.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.

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

14.Which of these is an equation, rather than an expression, a formula or an identity?

15.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.