Algebra worksheet — GCSE Foundation

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

2.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

3.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

4.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

5.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

6.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

7.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.

8.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

9.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

10.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

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

12.Write down 0.2x with its coefficient written as a fraction in its simplest form.

13.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

14.Solve x² − 5x + 6 = 0 by factorising.

15.Expand 2(x + 12)