Mathematics Curriculum for Quiz – Level 4
1. Sets, Relations, and Functions
- Sets: Representations, Types (Empty, Finite, Infinite), Subsets, Operations (Union, Intersection, Difference, Complement).
- Relations & Functions: Cartesian Product, Domain, Codomain, Range.
2. Trigonometric Functions
- Angles: Degree and Radian Measure.
- Functions: Identities, Signs in Quadrants, Equations, Graphs.
3. Algebra
- Complex Numbers & Quadratics: Modulus, Conjugate, Solutions of Quadratics with Complex Roots.
- Permutations & Combinations: Factorial, Fundamental Counting Principle, Arrangements vs. Selections.
- Binomial Theorem: Expansion for Positive Integral Indices, General and Middle Terms.
- Sequence & Series: Arithmetic (AP) and Geometric (GP) Progressions, Sum to (n) Terms.
4. Coordinate Geometry
- Straight Lines: Slope, Intercepts, Various Forms of Equations, Distance Formulas.
- Conic Sections: Circle, Parabola, Ellipse, Hyperbola (Standard Equations and Parameters).
- 3D Geometry: Coordinate Axes/Planes in 3D, Distance Formula, Section Formula.
5. Calculus
- Limits: Limits of Polynomials and Trigonometric Functions.
- Derivatives: Definition, Derivatives of Standard Functions, Product/Quotient Rules.
6. Statistics and Probability
- Statistics: Mean, Median, Mode, Dispersion (Range, Mean Deviation, Variance, Standard Deviation).
- Probability: Sample Space, Events (Mutually Exclusive, Exhaustive), Axiomatic Approach.