Algebra worksheet — GCSE Foundation

1.Work out the value of n² − n when n = −3

2.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.

3.Which of these quadratic graphs does NOT cross the x-axis at all?

4.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

5.Which expression is equivalent to 5x − (x + 3)?

6.Expand 4(2x − 3).

7.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

8.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.

9.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

10.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

11.a = 2 and b = 5. Work out the value of a²b.

12.Simplify (5x² + 3x − 2) − (2x² − x + 5)

13.The point A lies on the x-axis. Which statement about A must be true?

14.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

15.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.