Algebra worksheet — GCSE Foundation

1.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.

2.Work out the value of 5y + 9 when y = 0

3.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

4.Solve x² + 7x = 0.

5.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

6.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

7.Two expressions are 6(x − 1) and 6x − 6. A student says these are equivalent for every value of x. Is the student correct?

8.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

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

10.Make p the subject of the formula n = p/3.

11.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

12.Simplify k + k + k + k + k.

13.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

14.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

15.Given that (x + 2)(x − 7) = 0, write down the two solutions of x.