Algebra worksheet — GCSE Foundation

1.n = 3. Work out the value of (2n)².

2.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

3.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

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

5.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

6.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

7.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

8.Solve x² − x − 12 = 0.

9.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.

10.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

11.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

12.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

13.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

14.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

15.The formula for the area of a trapezium is A = (a + b)h / 2, where a and b are the parallel side lengths and h is the height. Make h the subject of the formula.