Algebra worksheet — GCSE Foundation

1.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

2.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

3.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.

4.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.

5.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

6.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

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

8.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.

9.Factorise fully 5x + 5y − 5

10.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

11.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

12.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

13.Write down the expression that means the same as 3 × y × y.

14.The diagram shows the graph of a function. Which equation could it represent?

15.Expand 7(a + 8)