Algebra worksheet — GCSE Foundation

1.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

2.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.

3.Expand 2(x − 13)

4.Which of these is a factor of 15x + 20?

5.Which of these points lies in the first quadrant?

6.Which expression is equivalent to 2(x + 6)?

7.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

8.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

9.Write down the expression that means the same as w ÷ 6.

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

11.Solve 4x − (2x − 6) = 18

12.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

13.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

14.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

15.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.