Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 0.5(4x + 6) − x?

2.Work out the y-intercept of the graph of y = x² + 3x − 10.

3.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

4.Solve 5x² − 15x = 0.

5.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

6.Make x the subject of the formula y = 3(x + 2).

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

8.Which expression is equivalent to 6x − (2x − 5)?

9.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.

10.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.

11.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

12.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

13.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

14.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

15.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.