Algebra worksheet — GCSE Foundation

1.Which of these is an identity?

2.A park is drawn on a grid in which 1 unit represents 1 km. The car park is at the point (0, 0) and the lake is at the point (3, 5). Work out the direct distance, in km, from the car park to the lake, giving your answer to 1 decimal place.

3.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.

4.Solve x² − 2x − 24 = 0.

5.The formula for the profit, £P, made on an item is P = S − C, where S is the selling price and C is the cost price. Make S the subject of the formula.

6.Solve 2x² = 18.

7.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

8.Solve x² − 6x = 0.

9.Make x the subject of the formula y = 2x − 9.

10.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

11.Factorise fully 56x − 24

12.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

13.y = x + 4. Work out the value of y when x = 3.

14.Expand 2(x − 13)

15.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.