Algebra worksheet — GCSE Foundation

1.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

2.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.

3.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

4.Make x the subject of the formula y = 5x + 3.

5.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.

6.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.

7.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

8.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.

9.Which of these is a term, rather than a whole expression, an equation, or a formula?

10.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

11.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

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

13.Which expression is equivalent to 4(x − 2) + 10?

14.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

15.The graph of y = x² − 2x − 8 crosses the x-axis at x = −2 and x = 4. Work out the x-coordinate of the turning point of the curve, using the symmetry of the graph.