Algebra worksheet — GCSE Foundation

1.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

2.Factorise fully 56x − 24

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

4.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

5.Expand and simplify (x − 3)²

6.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.

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

8.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

9.Simplify k + k + k + k + k.

10.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

11.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.

12.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

13.Solve x/4 + 1 = 3

14.The formula for the energy stored in a stretched spring is E = (1/2)kx², where E is in joules, k is the spring constant in N/m and x is the extension in m. A spring with a spring constant of 40 N/m is stretched so that its extension is 0.3 m. Work out the energy stored in the spring.

15.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.