Algebra worksheet — GCSE Foundation

1.A student says 4(2x − 3) is equivalent to 8x − 3. Which statement gives the correct verdict and reason?

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

3.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

4.Which of these is an equation, rather than an expression, a formula or an identity?

5.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

6.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.

7.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

8.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

9.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

10.Which of these equations is equivalent to 5x − 2 = 3x + 8?

11.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

12.Write down the expression that means the same as p + p + p + q.

13.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

14.Which expression means the same as a × a × a?

15.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?