Algebra worksheet — GCSE Higher

1.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

2.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

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

4.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

5.Two students each use the trapezium rule to estimate the area under the same curve between x = 0 and x = 8. Student A uses 4 strips of width 2. Student B uses 8 strips of width 1. Which estimate is more likely to be closer to the true area, and why?

6.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

7.Which of these pairs of lines are perpendicular to each other?

8.y = 5 − 2x. Work out the value of x when y = 11.

9.A tram sets off from a stop. Its velocity-time graph rises in a straight line from 0 m/s to 12 m/s over the first 8 seconds, then stays constant at 12 m/s for a further 10 seconds. Work out the total distance the tram travels in these 18 seconds, using the area under the graph.

10.A circle has centre O(0, 0) and equation x² + y² = 169. The point Q has coordinates (10, 11). Work out which of these gives the correct position of Q together with correct working.

11.Work out the value of 3a − 2b when a = 5 and b = 4

12.The tangent to a curve at the point (5, 2) is the line y = mx + c. This tangent crosses the y-axis at (0, −8). Work out the gradient, m, of the tangent.

13.A circle has centre (0, 0) and equation x² + y² = 100. Work out which one of these points lies on the circle.

14.The numbers x and y satisfy x + y = 10 and xy = 21. Work out the pair of values.

15.Factorise 6x² − 7x − 3.