Algebra worksheet — GCSE Foundation

1.n = 3. Work out the value of (2n)².

2.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.

3.Make c the subject of the formula k = 6c.

4.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

5.Which expression means 'triple c, then add double d'?

6.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

7.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

8.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.

9.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

10.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

11.Which of these is an identity?

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

13.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.

14.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.

15.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.