Algebra worksheet — GCSE Higher

1.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

2.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

3.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.

4.Work out the coordinates of the reflection of (6, −3) in the y-axis.

5.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

6.A circle has centre (0, 0) and equation x² + y² = 36. Work out the coordinates of the two points where the circle crosses the y-axis.

7.Solve the inequality x² + 6x + 9 > 0.

8.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

9.The nth term of a sequence is n² + 2n − 4. Work out the 7th term.

10.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

11.Solve the inequality 2(x − 1) ≤ 8.

12.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.

13.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.

14.The graph of y = f(x) has a maximum turning point at (−1, 6). Write down the coordinates of the maximum turning point of the graph of y = f(x − 3).

15.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.