Algebra worksheet — GCSE Foundation

1.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

2.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

3.Solve x² = 81.

4.Write down the coefficient of p in the expression 7 − 4p + 9q.

5.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

6.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.

7.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

8.Solve the inequality 5 − x ≤ 2.

9.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

10.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.

11.Solve 2x + 7 = x + 13

12.Which of these rules generates the sequence 6, 11, 16, 21, …?

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

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

15.Make a the subject of the formula b = 20 − a.