Algebra worksheet — GCSE Foundation

1.Write down the expression that means the same as 3 × y × y.

2.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

3.y = x + 4. Work out the value of y when x = 3.

4.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

5.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

6.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

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

8.Solve the inequality 6x ≥ 18.

9.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.

10.Solve x² = 81.

11.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

12.Work out the gradient of the straight line with equation 2x + y = 8.

13.Work out the value of 3b − 4 when b = 6

14.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.

15.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.