Algebra worksheet — GCSE Foundation

1.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.

2.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

3.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

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.Solve x² + 7x = 0.

6.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.

7.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

8.Which of these is an identity?

9.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

10.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

11.Solve the inequality 2(x − 1) ≤ 8.

12.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.

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

14.The formula for the profit, £P, made on an item is P = S − C, where S is the selling price and C is the cost price. Make S the subject of the formula.

15.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.