1. The problem is to provide sample Paper 3 math questions for BGCSE (Bahamas General Certificate of Secondary Education). 2. Paper 3 typically involves problem-solving and application questions in algebra, geometry, trigonometry, and statistics. 3. Example Question 1: Solve the quadratic equation $$2x^2 - 5x + 3 = 0$$. 4. Formula used: Quadratic formula $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=2$, $b=-5$, and $c=3$. 5. Calculate the discriminant: $$\Delta = (-5)^2 - 4 \times 2 \times 3 = 25 - 24 = 1$$. 6. Since $$\Delta > 0$$, there are two real roots. 7. Calculate roots: $$x = \frac{5 \pm \sqrt{1}}{4}$$ $$x_1 = \frac{5 + 1}{4} = \frac{6}{4} = 1.5$$ $$x_2 = \frac{5 - 1}{4} = \frac{4}{4} = 1$$. 8. Example Question 2: Find the area of a triangle with base 8 cm and height 5 cm. 9. Formula: Area $$= \frac{1}{2} \times \text{base} \times \text{height}$$. 10. Calculate area: $$= \frac{1}{2} \times 8 \times 5 = 20$$ cm$^2$. 11. Example Question 3: Simplify the expression $$\frac{3x^2 - 12}{6x}$$. 12. Factor numerator: $$3x^2 - 12 = 3(x^2 - 4) = 3(x-2)(x+2)$$. 13. Simplify expression: $$\frac{3(x-2)(x+2)}{6x} = \frac{3}{6} \times \frac{(x-2)(x+2)}{x} = \frac{1}{2} \times \frac{(x-2)(x+2)}{x} = \frac{(x-2)(x+2)}{2x}$$. 14. These sample questions cover algebra, geometry, and simplification relevant to BGCSE Paper 3. Final answers: 1) $$x=1.5, 1$$ 2) Area = 20 cm$^2$ 3) Simplified expression $$\frac{(x-2)(x+2)}{2x}$$