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CSCA MathematicsChapter 1: Sets, Logic & InequalitiesIntermediate

Quadratic, Fractional Inequalities & AM-GM

一元二次不等式、分式不等式与基本不等式 · Node 1.2

Root-sign method for polynomials, fractional transformation $\frac{f(x)}{g(x)} > 0 \iff f(x)g(x) > 0$, and arithmetic-geometric mean inequality $a+b \ge 2\sqrt{ab}$.

Chapter Weight: 25% of official examination
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Core Mathematical Axiom

Formula Proof & Traps
ax2+bx+c>0,g(x)f(x)​≥0⟺{f(x)g(x)≥0g(x)=0​,a+b≥2ab​(a,b>0)
CSCA Exam Trap Alert

Multiplying both sides of an inequality by an algebraic denominator without knowing its sign.

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