1. Let's start by understanding the Kenya Certificate of Secondary Education (KCSE) Mathematics syllabus, which covers topics like Algebra, Geometry, Trigonometry, Statistics, and Calculus. 2. A key formula often used in Algebra is the quadratic formula: $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ which solves equations of the form $$ax^2+bx+c=0$$. 3. Important rules include the order of operations (PEMDAS), properties of exponents, and factorization techniques. 4. For Geometry, formulas for area and volume of shapes are crucial, e.g., area of a triangle $$A=\frac{1}{2}bh$$. 5. Trigonometry involves ratios like sine, cosine, and tangent, with formulas such as $$\sin^2\theta + \cos^2\theta = 1$$. 6. Statistics covers mean, median, mode, and standard deviation, essential for data analysis. 7. Calculus basics include differentiation and integration, for example, $$\frac{d}{dx}x^n = nx^{n-1}$$. 8. Predicting KCSE 2026 questions, expect problems on quadratic equations, simultaneous equations, trigonometric identities, coordinate geometry, and data interpretation. 9. Practice solving quadratic equations using the quadratic formula, simplifying expressions, and applying trigonometric identities. 10. Example question: Solve $$2x^2 - 4x - 6 = 0$$ using the quadratic formula. Step-by-step solution: 1. Identify coefficients: $$a=2$$, $$b=-4$$, $$c=-6$$. 2. Substitute into formula: $$x=\frac{-(-4)\pm\sqrt{(-4)^2 - 4\times 2 \times (-6)}}{2\times 2}$$. 3. Simplify inside the square root: $$\sqrt{16 + 48} = \sqrt{64} = 8$$. 4. Calculate numerator: $$4 \pm 8$$. 5. Calculate two solutions: $$x=\frac{4+8}{4} = 3$$ and $$x=\frac{4-8}{4} = -1$$. Final answer: $$x=3$$ or $$x=-1$$.