Algebra worksheet — GCSE Foundation

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

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

3.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.

4.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

5.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

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

7.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

8.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

9.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

10.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.

11.A straight line has equation y = 5x. Work out the value of y when x = 3.

12.Explain why the equation 4x + 3 = 4x + 10 has no solution for x.

13.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.

14.p = 4. Work out the value of 2p³.

15.a = 3 and b = 5. Work out the value of a²b.