Algebra worksheet — GCSE Foundation

1.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

2.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

3.A box contains 6 chocolates. Write down an expression for the total number of chocolates in c boxes.

4.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

5.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

6.Solve x² − x − 12 = 0.

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

8.Simplify 2a + 3b − a + 2b − b

9.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.

10.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

11.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.

12.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

13.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

14.Solve 3x − 5 = 4.

15.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.