Algebra worksheet — GCSE Foundation

1.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

2.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?

3.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

4.Solve the inequality 6x ≥ 18.

5.Make x the subject of the formula y = 5x + 3.

6.Write down the expression that means the same as (x + 7) ÷ 4.

7.A plumber charges a call-out fee plus an hourly rate. The total cost, y in pounds, of a job lasting x hours is given by y = 45x + 60. Work out the total cost of a job that lasts 3 hours.

8.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

9.Solve 3(2x − 1) = 27

10.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.

11.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.

12.y = x + 4. Work out the value of y when x = 3.

13.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

14.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.

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