Algebra worksheet — GCSE Foundation

1.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

2.Solve 2(x + 3) = 10

3.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

4.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

5.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

6.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

7.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

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

9.Solve 5x² − 15x = 0.

10.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

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

12.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

13.Expand 2(x + 12)

14.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

15.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?