Algebra worksheet — GCSE Foundation

1.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

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

3.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.

4.A curve has equation y = x² − 9. Which statement about its graph is correct?

5.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.

6.Write down the gradient of the line with equation y = 6 + 4x.

7.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.

8.Work out the value of 3x² − 4x when x = −2.

9.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

10.How many turning points does the graph of y = x² − 7x + 10 have?

11.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

12.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?

13.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

14.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

15.Write down the y-intercept of the line with equation y = 3x + 8.