Algebra worksheet — GCSE Foundation

1.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.

2.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?

3.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

4.Solve 3x − 5 = 4.

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

6.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

7.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

8.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.

9.Which of these rules generates the sequence 6, 11, 16, 21, …?

10.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.

11.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

12.A straight line has equation y = 5x. Work out the value of y when x = 3.

13.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

14.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

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