Algebra worksheet — GCSE Higher

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

2.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

3.Work out the value of 2x² when x = −3

4.Write down the first four terms of the sequence with nth term 6n − 5.

5.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

6.Work out the value of 2(x + 2) when x = −5

7.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

8.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.

9.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

10.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

11.Work out the gradient of the straight line with equation 3y = 12 − 6x.

12.Solve 4x² − 9 = 0.

13.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

14.f(x) = (x + 1)/2. Find f⁻¹(x).

15.An exponential model has equation y = A × bˣ, where b > 1. Its graph passes through the points (1, 135) and (2, 405). Work out the value of A.