Algebra worksheet — GCSE Foundation

1.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

2.Solve 3x + 14 = 8x − 6

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

4.Which of these statements is an equation with exactly one solution?

5.Solve the inequality 5 − x ≤ 2.

6.Solve 4x − (2x − 6) = 18

7.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

8.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

9.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.

10.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

11.Solve the inequality 2(3x − 1) ≥ 4x + 8.

12.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.

13.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.

14.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

15.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.