Algebra worksheet — GCSE Foundation

1.Which of these is a formula, rather than an expression, an equation, or an identity?

2.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

3.In which quadrant does the point (−3, 0.5) lie?

4.Make p the subject of the formula n = p/3.

5.Work out the value of 3x² − 4x when x = −2.

6.A market stall's cost of hiring n tables is modelled by two formulas: Formula A: C = 3(2n + 5); Formula B: C = 6n + 15, where C is in pounds. A stallholder says the two formulas always give the same cost. Work out the cost given by each formula when n = 4, and use your results to decide whether the stallholder is correct.

7.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

8.Write down the expression that means the same as (x + 7) ÷ 4.

9.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

10.The graph of y = x² − 2x − 8 crosses the x-axis at x = −2 and x = 4. Work out the x-coordinate of the turning point of the curve, using the symmetry of the graph.

11.Solve 2(x + 3) = 10

12.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

13.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.

14.Which of these is an equation, rather than an expression, a formula or an identity?

15.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.