Algebra worksheet — GCSE Higher

1.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

2.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

3.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

4.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

5.The graph of y = f(x) has a root (an x-intercept) at x = 5. Work out the x-coordinate of the corresponding root on the graph of y = f(x + 2).

6.Simplify (5x² + 3x − 2) − (2x² − x + 5)

7.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.

8.A sequence is defined by aₙ = aₙ₋₁ + aₙ₋₂ for n ≥ 3. Given that a₃ = 11 and a₅ = 29, work out a₁.

9.The point (9, 40) lies on the circle x² + y² = 1681, which has centre (0, 0). Work out the equation of the tangent to the circle at (9, 40), giving your answer in the form ax + by = c.

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

11.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.

12.Which of these is a factor of 15x + 20?

13.Work out the equation of the straight line through the points (−2, 1) and (0, 7).

14.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?

15.A plumber charges a call-out fee plus an hourly rate. The total cost, y in pounds, of a job lasting x hours is given by y = 45x + 60. Work out the total cost of a job that lasts 3 hours.