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Curriculum Units (4 Modules):
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1

Quadratic Equations & Roots

2 Questions • 8 Marks

Discriminant root analysis, sign properties of trinomials, Vieta's relations, and common root conditions.

Comprehensive Unit Scope:

Discriminant root analysis, sign properties of trinomials, Vieta's relations, and common root conditions.

Sub-Topics & Theorems (4):
Discriminant & Nature of Roots (Real, Distinct, Complex)
Vieta's Formulas for Higher Degree Polynomials
Location of Roots with Geometric Boundary Constraints
Common Roots Between Two Quadratic Equations
Core Formula Benchmark:
x=−b±b2−4ac2a,α+β=−ba,αβ=cax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, \quad \alpha + \beta = -\frac{b}{a}, \quad \alpha\beta = \frac{c}{a}
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2

Conic Sections: Parabolas, Ellipses & Hyperbolas

3-4 Questions • 12-16 Marks

Focal parameters, equation of tangents with slope m, normal chords, and director circles.

3

Definite Integrals & Properties

2-3 Questions • 8-12 Marks

King's property (f(a+b-x)), Leibniz derivative rule for integral bounds, and area bounded by curves.

4

Limits, Continuity & Differentiability

2 Questions • 8 Marks

Indeterminate forms 0/0 and ∞/∞, standard limits, Squeeze Theorem, and differentiability criteria.