Algebra worksheet — GCSE Foundation

1.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

2.Which expression means the same as a × a × a?

3.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

4.Solve 4(x − 3) = 2x + 6.

5.Solve 5x + 2 = 17.

6.Solve the inequality 6x ≥ 18.

7.Solve 3x + 14 = 8x − 6

8.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

9.Solve the inequality x + 5 < 12.

10.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.

11.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

12.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.

13.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.

14.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

15.A vertical line passes through the point (4, 7). Write down the equation of this line.