Algebra worksheet — GCSE Foundation

1.Work out the gradient of the straight line with equation 2x + y = 8.

2.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

3.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

4.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

5.A cyclist's journey is shown on a distance–time graph. The graph is a straight line from (0 minutes, 0 km) to (40 minutes, 12 km). Work out her speed in kilometres per hour.

6.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

7.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

8.Write down the expression that means the same as (x + 7) ÷ 4.

9.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

10.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.

11.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.

12.Solve 3(2x − 1) = 27

13.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.

14.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

15.Solve x² + 3x − 10 = 0.