Algebra worksheet — GCSE Foundation

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

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

3.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

4.Work out the value of 2x² when x = −3

5.Make x the subject of the formula y = 4(x − 6).

6.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.

7.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

8.The point B has coordinates (−2, −2). In which quadrant is B?

9.For the equation 2x + 3 = 11, and the inequality 2x + 3 > 11, which statement correctly compares their solutions?

10.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.

11.Simplify (5x² + 3x − 2) − (2x² − x + 5)

12.Which of these is a term, rather than a whole expression, an equation, or a formula?

13.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

14.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

15.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.