Algebra worksheet — GCSE Foundation

1.y = x + 10. Work out the value of y when x = 0.

2.A taxi company charges a £2.50 booking fee plus £1.80 per mile. A journey costs £15.10 in total. Work out the number of miles travelled.

3.Work out the gradient of the straight line with equation y = (2x/5) − 3.

4.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

5.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

6.Which of these numbers is a cube number?

7.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

8.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

9.Solve the inequality 2(x − 1) ≤ 8.

10.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

11.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

12.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

13.Solve 3x − 5 = 4.

14.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

15.How many turning points does the graph of y = x² − 7x + 10 have?