Algebra worksheet — GCSE Foundation

1.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

2.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

3.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

4.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.

5.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.

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

7.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

8.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

9.y = 3x − 2. Work out the value of y when x = 4.

10.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

11.Solve 3(2x − 1) = 27

12.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

13.Solve the inequality 6x ≥ 18.

14.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

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