Algebra worksheet — GCSE Foundation

1.Which of these statements is an equation with exactly one solution?

2.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

3.A number machine multiplies its input by 3. The output is 15. Work out the input.

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

5.Which of these is an equation, rather than an expression, a formula or an identity?

6.Which expression is equivalent to 6x − (2x − 5)?

7.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

8.Write down the number of terms in the expression 4x² − 7x + 3.

9.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

10.Work out the value of 3b − 4 when b = 6

11.Write down the expression that means the same as 3 × y × y.

12.Expand 4(2x − 3).

13.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

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

15.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.