Algebra worksheet — GCSE Foundation

1.The graph of y = x² + 2x − 15 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

2.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

3.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

4.Work out the value of (x − 4)/2 + 3 when x = 10

5.Write down the expression that means the same as p + p + p + q.

6.Simplify 2a + 3b − a + 2b − b

7.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

8.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

9.Simplify 5x + 3y − 2x + y.

10.A graph has equation y = x² − 6x + 5. A student says its turning point has x-coordinate 6, because that's the coefficient of x. Which statement corrects the student's mistake?

11.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.

12.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

13.A box contains 6 chocolates. Write down an expression for the total number of chocolates in c boxes.

14.A square tile has an area of 144 cm². Work out the side length of the tile.

15.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.