Algebra worksheet — GCSE Foundation

1.Solve 3x − 5 = 4.

2.A number machine multiplies its input by 5. Work out the output when the input is −1.

3.The point A lies on the x-axis. Which statement about A must be true?

4.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

5.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

6.Which of these is a formula?

7.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

8.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

9.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

10.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

11.Solve the inequality x − 10 < −3.

12.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

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

14.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

15.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.