Algebra worksheet — GCSE Foundation

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

2.The graph of y = x² − 2x − 8 crosses the x-axis at x = −2 and x = 4. Work out the x-coordinate of the turning point of the curve, using the symmetry of the graph.

3.Solve 4x + 3 = 19

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

5.Which of these rules generates the sequence 6, 11, 16, 21, …?

6.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

7.Factorise fully 12x² + 18x.

8.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

9.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

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.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

12.Solve the inequality 9 − 2x ≥ 1.

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

14.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

15.Write down the expression that means the same as 3 × y × y.