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

3.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

4.Solve 2(x + 3) = 10

5.Work out the value of n² − n when n = −3

6.Write down the expression that means the same as w ÷ 6.

7.Solve 5x² − 15x = 0.

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

9.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.

10.Work out the coordinates of the reflection of (6, −3) in the y-axis.

11.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

12.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

13.Solve x² − 6x = 0.

14.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.

15.Factorise fully 56x − 24