Algebra worksheet — GCSE Foundation

1.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.

2.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

3.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

4.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

5.Write down the expression that means the same as m² × m × 3.

6.Two expressions are 6(x − 1) and 6x − 6. A student says these are equivalent for every value of x. Is the student correct?

7.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

8.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?

9.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.

10.Factorise x² − 64.

11.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

12.Make x the subject of the formula y = 4x − 3.

13.y = x + 10. Work out the value of y when x = 0.

14.Solve the inequality 6x ≥ 18.

15.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.