Algebra worksheet — GCSE Higher

1.Simplify (2x² + 7x + 3) ÷ (x² − 9), giving your answer as a single fraction.

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

3.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

4.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.

5.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

6.The nth term of a sequence is 3n² + 2n − 1. Work out the 10th term.

7.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

8.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

9.Factorise 3x² + 10x − 8.

10.The formula for the area of a trapezium is A = (a + b)h / 2, where a and b are the parallel side lengths and h is the height. Make h the subject of the formula.

11.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.

12.A car accelerates uniformly from rest at 2.5 m/s² until it reaches a speed of 20 m/s, then travels at this constant speed for a further 30 seconds. Work out the total distance travelled.

13.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

14.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

15.Solve (3x + 2)/5 = (x + 4)/3