Algebra worksheet — GCSE Foundation

1.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

2.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

3.Which of these is a term, rather than a whole expression, an equation, or a formula?

4.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

5.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

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

7.A curve has equation y = x² − 9. Which statement about its graph is correct?

8.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.

9.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

10.Solve 2x + 7 = x + 13

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

12.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

13.Which of these is a formula?

14.Solve 6x − 5 = 3x + 13.

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