Algebra worksheet — GCSE Foundation

1.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?

2.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?

3.A vertical line passes through the point (4, 7). Write down the equation of this line.

4.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

5.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

6.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

7.The first five terms of a sequence are 2, 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

8.Write down the y-intercept of the line with equation y = 3x + 8.

9.Solve 7x − 5 = 3x + 11

10.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

11.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.

12.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.

13.Work out the value of n² − n when n = −3

14.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

15.Work out the equation of the straight line through the points (−2, 1) and (0, 7).