Algebra worksheet — GCSE Foundation

1.y = 5 − 2x. Work out the value of x when y = 11.

2.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

3.Which expression is equivalent to 4(x − 2) + 10?

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

5.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

6.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

7.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

8.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

9.Make x the subject of the formula y = (x − 4)/5.

10.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

11.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.

12.Solve 2x² − 32 = 0.

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

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

15.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.