Algebra worksheet — GCSE Foundation

1.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.

2.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

3.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

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

5.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

6.Simplify x + x + 4

7.Write down the first four terms of the sequence with nth term 6n − 5.

8.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

9.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.

10.Which of these quadratic graphs does NOT cross the x-axis at all?

11.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

12.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.

13.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).

14.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

15.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.