Unit 1 — Set, Logic & Functions
Set, Real Numbers & Logic
Set Theory, Real Number System, Intervals, Absolute Value, Logic Connectives, Laws of Logic
Functions & Their Types
Injective, Surjective, Bijective, Algebraic, Trigonometric, Exponential, Logarithmic; Inverse & Composite Functions
Unit 2 — Algebra
Matrices & Determinants
Types and Properties of Matrices, Determinants, Inverse of a Matrix, Cramer's Rule
Complex Numbers & Polynomial Equations
Complex Number Operations, Argand Plane, Modulus, Argument, Polynomial Equations
Sequence, Series, Permutation & Combination
Arithmetic, Geometric & Harmonic Progressions, nPr, nCr, Counting Principles
Binomial, Exponential & Logarithmic Series
Binomial Theorem, Pascal's Triangle, Exponential Series (ex), Logarithmic Series
Unit 3 — Trigonometry
Trigonometric Equations & General Values
Solving Trig Equations, General and Particular Solutions, Principal Values
Inverse Trigonometric Functions
arcsin, arccos, arctan — Domain, Range, Principal Values, Identities
Properties of Triangles & Solution
Sine Rule, Cosine Rule, In-centre, Ortho-centre, Circum-centre, Solution of Triangles
Unit 4 — Coordinate Geometry
Straight Lines & Pair of Lines
Equations of Lines, Slope, Distance Formulae, Angle Between Lines, Pair of Straight Lines
Circles — Equations, Tangent & Normal
Standard & General Equations of Circle, Tangent, Normal, Chord of Contact
Conic Sections — Parabola, Ellipse & Hyperbola
Standard Equations, Focus, Directrix, Eccentricity, Simple Properties
Coordinates in Space & Plane Equation
3D Coordinates, Distance in Space, Direction Cosines, Equation of a Plane
Unit 5 — Calculus
Limits, Continuity & L'Hôpital's Rule
Limits of Functions, Indeterminate Forms (0/0, ∞/∞), Continuity, L'Hôpital's Rule
Derivatives & Applications
Rules of Differentiation, Higher Order Derivatives, Tangent & Normal, Maxima & Minima, Rate of Change
Integration & Definite Integrals
Standard Integrals, Rules, Definite Integrals, Area Under a Curve, Area Between Two Curves
Differential Equations
Order & Degree, Variable Separable, Homogeneous, Linear & Exact Differential Equations, Integrating Factor
Unit 6 — Vectors & Their Products
Vectors in Plane & Space
Algebra of Vectors, Linear Combination, Linearly Dependent and Independent Set of Vectors
Products of Vectors
Scalar (Dot) Product, Vector (Cross) Product, Scalar Triple Product, Geometric Applications
Unit 7 — Statistics & Probability
Measures of Location & Dispersion
Mean, Median, Mode, Range, Variance, Standard Deviation, Coefficient of Variation
Correlation & Regression
Pearson's Correlation Coefficient, Regression Lines, Scatter Diagrams, Line of Best Fit
Probability & Distributions
Conditional & Compound Probability, Additive & Multiplicative Rules, Bayes' Theorem, Binomial Distribution
Chapter Quiz
Answer all questions below