Algebra worksheet — GCSE Foundation

1.Solve 4x² − 9 = 0.

2.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

3.The graph of P = 480 ÷ V shows how the pressure, P pascals, of a gas depends on its volume, V cm³, at constant temperature. Use the relationship to work out the volume when the pressure is 32 pascals, and then work out by how much the volume increases when the pressure drops to 24 pascals.

4.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.

5.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

6.Write down the number of terms in the expression 4x² − 7x + 3.

7.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

8.Solve 5x + 2 = 17.

9.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

10.Which expression is equivalent to 3(2x − 5) + 4x?

11.Which of these equations describes a vertical line?

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

13.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.

15.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?