Algebra worksheet — GCSE Foundation

1.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.

2.Solve 7x − 5 = 3x + 11

3.Write down the coefficient of p in the expression 7 − 4p + 9q.

4.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

5.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

6.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

7.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

8.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

9.Which of these values of x is a solution of x² + 2x − 15 = 0?

10.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

11.Make c the subject of the formula k = 6c.

12.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

13.Work out the value of 3b − 4 when b = 6

14.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.

15.n = 3. Work out the value of (2n)².