Algebra worksheet — GCSE Foundation

1.y = x + 4. Work out the value of y when x = 3.

2.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

3.Make c the subject of the formula k = 6c.

4.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.

5.Solve 4(x − 3) = 2x + 6.

6.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.

7.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

8.Solve x² − 100 = 0.

9.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

10.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.

11.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

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

13.Work out the equation of the straight line through the points (−2, 1) and (0, 7).

14.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.

15.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.