Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

2.Solve 4(x − 3) = 2x + 6.

3.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

4.Which expression is equivalent to 2(x + 6)?

5.A student says 4(2x − 3) is equivalent to 8x − 3. Which statement gives the correct verdict and reason?

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

7.For the equation 2x + 3 = 11, and the inequality 2x + 3 > 11, which statement correctly compares their solutions?

8.a = 2 and b = 5. Work out the value of ab².

9.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

10.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.

11.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

12.Make c the subject of the formula k = 6c.

13.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

14.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

15.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.