Algebra worksheet — GCSE Foundation

1.Write down the expression that means the same as p + p + p + q.

2.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.

3.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

4.Solve x² − 5x + 6 = 0 by factorising.

5.The graph of y = x² − 2x − 8 crosses the x-axis at x = −2 and x = 4. Work out the x-coordinate of the turning point of the curve, using the symmetry of the graph.

6.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

7.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.

8.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.

9.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

10.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

11.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

12.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

13.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

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

15.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).