Algebra worksheet — GCSE Foundation

1.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

2.A number machine adds 6 to its input. Work out the output when the input is −4.

3.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

4.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

5.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.

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

7.Expand and simplify (x − 3)²

8.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

9.Solve 6x − 5 = 3x + 13.

10.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

11.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

12.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

13.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

14.Expand 2(x + 12)

15.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.