Algebra worksheet — GCSE Higher

1.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.

2.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.

3.The graph of y = x³ − 5x is reflected in the y-axis. Work out the equation of the image.

4.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

5.Which of these values of x is a solution of x² + 2x − 15 = 0?

6.The first four terms of a sequence are 2, 2√3, 6, 6√3, ... Work out the next term.

7.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

8.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

9.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

10.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

11.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

12.Which of these equations is equivalent to 5x − 2 = 3x + 8?

13.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

14.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

15.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.