Algebra worksheet — GCSE Foundation

1.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

2.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

3.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

4.Solve 6x − 5 = 3x + 13.

5.Solve 3x − 5 = 4.

6.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.

7.Expand 4(2x − 3).

8.The formula for the energy stored in a stretched spring is E = (1/2)kx², where E is in joules, k is the spring constant in N/m and x is the extension in m. A spring with a spring constant of 40 N/m is stretched so that its extension is 0.3 m. Work out the energy stored in the spring.

9.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.

10.A geometric sequence starts at 4, and each term after that is found by multiplying the term before it by 3. Write down the first four terms of the sequence.

11.The formula for the area of a trapezium is A = (a + b)h / 2, where a and b are the parallel side lengths and h is the height. Make h the subject of the formula.

12.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

13.Solve 5x² − 15x = 0.

14.Work out the value of 3b − 4 when b = 6

15.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.