Algebra worksheet — GCSE Foundation

1.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

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.Simplify (5x² + 3x − 2) − (2x² − x + 5)

4.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

5.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

6.Which of these is an inequality?

7.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

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

9.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

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

11.Which expression is equivalent to 3(2x − 5) + 4x?

12.n = 3. Work out the value of (2n)².

13.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

14.Work out the value of 5y + 9 when y = 0

15.Simplify 2a + 3b − a + 2b − b