Algebra worksheet — GCSE Foundation

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

2.Work out the value of m² + 3m when m = −2

3.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.

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

5.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

6.A sequence begins at 7. Each term after the first is found by adding 6 to the term before it. Work out the 6th term of the sequence.

7.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

8.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

9.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.

10.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.

11.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.

12.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

13.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.

14.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.

15.Work out the value of 5y + 9 when y = 0