Question 1: Factorise the quadratic expression x² + 5x + 6.

Answer: (x + 2)(x + 3)

Question 2: Solve for x: x² - 3x - 10 = 0.

Answer: x = 5 or x = -2

Question 3: Factorise: x² - 4x - 5.

Answer: (x - 5)(x + 1)

Question 4: Construct a quadratic expression that factors to (x + 4)(x - 1).

Answer: x² + 3x - 4

Question 5: What are the roots of x² + 7x + 12 = 0?

Answer: x = -3 or x = -4

Question 6: Factorise: x² + 2x - 15.

Answer: (x + 5)(x - 3)

Question 7: Solve for x: x² + 6x + 9 = 0.

Answer: x = -3

Question 8: Factorise: 2x² + 8x.

Answer: 2x(x + 4)

Question 9: Plot the graph of y = x² - 4x + 3 on the grid.

Answer: Student plots parabola with roots at x=1 and x=3, vertex at (2,-1).

Question 10: Solve the quadratic: x² + 2x - 8 = 0 by factorising.

Answer: x = -4 or x = 2

Question 11: A rectangle's length is modeled by x + 2, and its width by x - 1. If the area is represented by the quadratic x² + x - 2, find the value of x.

Answer: x = 1 or x = -2

Question 12: The quadratic x² + 3x - 4 is factored as (x + 4)(x - 1). Identify and explain the mistake if students try to factor it as (x + 2)(x - 2).

Answer: The factorisation (x + 2)(x - 2) expands to x² - 4, which does not match x² + 3x - 4. The correct factors are (x + 4)(x - 1).