Algebra worksheet — GCSE Foundation

1.Which of these equations describes a vertical line?

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

3.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

4.Solve the inequality 2(x − 1) ≤ 8.

5.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

6.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

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.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

9.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

10.Solve 2(x + 3) = 10

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

12.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.

13.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?

14.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

15.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).