Algebra worksheet — GCSE Foundation

1.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.

2.Which of these values of x is a solution of x² + 2x − 15 = 0?

3.p = 4. Work out the value of 2p³.

4.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.

5.Solve the inequality 2(x − 1) ≤ 8.

6.Work out the value of 3b − 4 when b = 6

7.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

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

9.Expand and simplify (x − 3)²

10.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

11.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

12.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

13.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

14.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

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