Algebra worksheet — GCSE Foundation

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

2.Simplify 5a/6 − a/3

3.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.

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.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.

6.Which of these statements is an equation with exactly one solution?

7.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

8.The point B has coordinates (−2, −2). In which quadrant is B?

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

10.Solve 6x − 5 = 3x + 13.

11.Solve 2x + 7 = x + 13

12.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

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

14.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

15.Solve the inequality 3x − 1 ≤ 11.