Algebra worksheet — GCSE Foundation

1.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

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

3.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

4.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

5.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

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

7.y = 5x − 1. Work out the value of y when x = 3.

8.Which of these is a term, rather than a whole expression, an equation, or a formula?

9.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

10.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.

11.The point A lies on the x-axis. Which statement about A must be true?

12.Make x the subject of the formula y = 4x − 3.

13.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

14.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

15.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.