Algebra worksheet — GCSE Foundation

1.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

2.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

3.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

4.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.

5.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

6.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

7.Work out the gradient of the straight line with equation y = (2x/5) − 3.

8.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

9.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

10.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

11.Solve x² = 81.

12.Which of these values of x is a solution of x² + 2x − 15 = 0?

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

14.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

15.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.