Algebra worksheet — GCSE Higher

1.Work out the gradient of a line that is perpendicular to the line with equation 2x + 3y = 6.

2.A car's velocity–time graph is a straight line from (0 s, 4 m/s) rising to (6 s, V m/s), followed by a straight line falling from (6 s, V m/s) to (9 s, 0 m/s). The gradient of the second line is −8 m/s². Work out the total distance travelled between t = 0 and t = 9 seconds.

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

4.For the equation 2x + 3 = 11, and the inequality 2x + 3 > 11, which statement correctly compares their solutions?

5.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

6.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

7.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

8.A region S consists of every point that lies on or above the line y = 2, on or below the line y = x, and on or to the left of the line x = 6. Which of these is the system of inequalities that defines S?

9.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

10.x = 5. Work out the value of 3x² − 4.

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

12.Work out the period of the graph of y = cos x, in degrees.

13.The equation x² − 5x − 2 = 0 can be solved using the iterative formula xₙ₊₁ = √(5xₙ + 2). The starting value is x₀ = 2, so x₁ is the value after the formula has been used once. Work out x₃ correct to 3 decimal places.

14.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

15.Solve the inequality 5 − x ≤ 2.