Algebra worksheet — GCSE Foundation

1.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

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

3.Solve 5(x + 3) = 40

4.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

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

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

7.Make p the subject of the formula n = p/3.

8.The diagram shows the graph of a function. Which equation could it represent?

9.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.

10.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

11.Make b the subject of the formula a = 5b.

12.Make c the subject of the formula k = 6c.

13.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.

14.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.

15.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.