Algebra worksheet — GCSE Foundation

1.Solve 4(x − 3) = 2x + 6.

2.Simplify 2b − 1 + 2b − 4 + 2b

3.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.

4.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

5.Which of these equations is equivalent to 5x − 2 = 3x + 8?

6.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

7.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.

8.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.

9.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

10.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

11.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

12.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

13.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

14.Write down the gradient of the line with equation y = 7x − 2.

15.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.