Algebra worksheet — GCSE Foundation

1.Solve 5x² − 15x = 0.

2.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

3.Make x the subject of the formula y = 4x − 3.

4.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

5.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

6.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?

7.Solve 2x − 2 = 2

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

9.n = 3. Work out the value of (2n)².

10.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

11.Solve the inequality 2(x − 1) ≤ 8.

12.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

13.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

14.Solve 7x − 5 = 3x + 11

15.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?