Algebra worksheet — GCSE Foundation

1.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

2.Solve the inequality 2(x − 1) ≤ 8.

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

4.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

5.Work out the distance of the point (−6, 4) from the x-axis.

6.Solve 5x² − 15x = 0.

7.A square has sides of length y cm. Write down an expression for the perimeter of the square.

8.In which quadrant does the point (−3, 0.5) lie?

9.Expand and simplify (x − 3)²

10.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

11.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.

12.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

13.Make x the subject of the formula y = 4x − 3.

14.The braking distance of a car, in metres, is estimated using the formula d = 0.4v² + 6, where v is the speed in mph. A car travelling at 35 mph brakes. Work out the estimated braking distance.

15.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.