Algebra worksheet — GCSE Higher

1.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.

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 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.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

5.A train's distance-time graph shows it travelling 100 km at a steady speed in the first 1.5 hours, waiting at a signal for 0.25 hours, then travelling a further 47 km in 0.75 hours. Work out the average speed for the whole journey, correct to 1 decimal place.

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

7.f(x) = 2x − 1. Work out ff(x).

8.Line L has equation y = 3x − 2. Work out the gradient of a line perpendicular to L.

9.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.

10.A circle has centre (0, 0) and equation x² + y² = 50. Work out the length of the diameter of the circle, correct to 1 decimal place.

11.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

12.The discriminant of a quadratic equation is greater than zero. Which statement about the solutions of that equation is correct?

13.Solve (2x + 1)/3 = 5

14.The first five terms of a sequence are 7, 9, 13, 19, 27. By finding the second difference, work out the coefficient of n² in the nth term.

15.The graph of y = f(x) has x-intercepts at x = −2 and x = 6 and crosses the y-axis at (0, −12). Work out the x-intercepts and the y-intercept of y = −f(x).