Question 1: Factorise the quadratic expression 6x² + 11x + 3.

Answer: (2x + 1)(3x + 3)

Question 2: Expand the expression (4x + 5)(x + 2) and write it in the form ax² + bx + c.

Answer: 4x² + 13x + 10

Question 3: Solve for x: 3x² + 5x - 2 = 0 using factorisation.

Answer: x = 0.4 or x = - 2/3

Question 4: Identify the mistake: Factorise 2x² + 7x + 3 as (2x + 1)(x + 3).

Answer: Incorrect. The correct factorisation is (2x + 1)(x + 3). The student correctly factorised it; no mistake.

Question 5: Express the quadratic 5x² + 14x + 8 as a product of two binomials.

Answer: (5x + 2)(x + 4)

Question 6: A rectangular garden has an area modeled by 3x² + 8x + 4. Find the dimensions by factorising the quadratic.

Answer: Dimensions are (3x + 2) and (x + 2).

Question 7: Construct a quadratic with roots at x= -1 and x= 2, and factorise it.

Answer: Right answer: x² - x - 2 = (x + 1)(x - 2)

Question 8: Plot the graph of y=2x² + 7x + 3 on the grid provided.

Answer: Students will draw the parabola; no specific answer.

Question 9: Solve 4x² + 12x + 9 = 0 by factorisation and verify the roots.

Answer: x = - 3/2 (repeated root)

Question 10: A ladder against a wall forms a right-angled triangle. Its length squared is modeled by 2x² + 9x + 4. Factorise to find the possible lengths.

Answer: Lengths: (√(2x + 1)(x + 4))

Question 11: Find the roots of the quadratic 6x² + 5x - 6 = 0 by factorisation.

Answer: x = 1 or x = - 1/3