Algebra worksheet — GCSE Foundation

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

2.Solve the inequality 5 − x ≤ 2.

3.Make b the subject of the formula a = 5b.

4.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?

5.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

6.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

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

8.Make x the subject of the formula y = x + 7.

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

10.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.

11.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

12.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?

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

14.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.

15.Make x the subject of the formula y = x/2 − 5.