Algebra worksheet — GCSE Foundation

1.Simplify 2a + 3b − a + 2b − b

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

3.Which of these equations describes a vertical line?

4.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.

5.Solve x² + 3x − 10 = 0.

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

7.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?

8.Solve 5(x + 3) = 40

9.Solve the inequality x − 10 < −3.

10.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

11.Make x the subject of the formula y = x + 7.

12.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

13.Work out the coordinates of the reflection of (6, −3) in the y-axis.

14.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.

15.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.