Algebra worksheet — GCSE Foundation

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

2.Solve 4x + 3 = 19

3.Which of these is an inequality?

4.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

5.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

6.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

7.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

8.Solve x² − 2x − 24 = 0.

9.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

10.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

11.Simplify 2a + 3b − a + 2b − b

12.Solve 6x − 5 = 3x + 13.

13.Expand and simplify 2(a + 6) − 2(a − 7)

14.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

15.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.