Algebra worksheet — GCSE Foundation

1.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

2.Make x the subject of the formula y = (x − 4)/5.

3.Solve x² − 100 = 0.

4.A square has sides of length y cm. Write down an expression for the perimeter of the square.

5.Write down the expression that means the same as m × m × m × n.

6.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

7.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.

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

9.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

10.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

11.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

12.Make m the subject of the formula w = m − 8.

13.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

14.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.

15.Solve the inequality x − 10 < −3.