Algebra worksheet — GCSE Foundation

1.Solve the inequality 5x − 3 > 2x + 9.

2.Simplify k + k + k + k + k.

3.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.

4.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

5.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

6.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

7.Solve the inequality x − 10 < −3.

8.Solve (3x + 2)/5 = (x + 4)/3

9.Simplify 2a + 3b − a + 2b − b

10.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

11.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

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

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

14.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.

15.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.