Algebra worksheet — GCSE Foundation

1.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.

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

3.The point B has coordinates (−2, −2). In which quadrant is B?

4.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

5.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.

6.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.

7.The point A lies on the x-axis. Which statement about A must be true?

8.Which of these points lies in the first quadrant?

9.Work out the coordinates of the reflection of (6, −3) in the y-axis.

10.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.

11.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

12.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

13.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.

14.Expand 2(x − 13)

15.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.