Algebra worksheet — GCSE Foundation

1.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.

2.Work out the gradient of the straight line with equation 3y = 12 − 6x.

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

4.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

5.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.

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

7.Which expression is equivalent to 4(x − 2) + 10?

8.x = 5. Work out the value of 3x² − 4.

9.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

10.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

11.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

12.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?

13.The diagram shows the graph of a function. Which equation could it represent?

14.Two expressions are 6(x − 1) and 6x − 6. A student says these are equivalent for every value of x. Is the student correct?

15.Solve 5x − 9 = 16