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Mathfirst principles.

11TH • RIGOROUS CURRICULUM.

Chapter-by-chapter theory notes, step-by-step textbook exercises, video lectures, and SLO-aligned board examination prep for Mathematics (11th).

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Syllabus

Curriculum Syllabus

Course chapter sequence roadmap and learning outcomes.

Mathematics (11th)

1. Complex Numbers

1.1 Complex Numbers
1.2 Equality and Square Roots
1.3 Complex Polynomials
1.4 Roots of Unity
1.5 Polar Form and Applications

2. Functions and Graphs

2.1 Concept of Function
2.2 Intersecting Points
2.3 Square Root Graphs
2.4 Cube Root Graphs
2.5 Real Life Applications

3. Theory of Quadratic Functions

3.1 Quadratic Function
3.2 Inverse of Quadratic Function
3.3 Absolute Value Quadratic
3.4 Equations Reducible to Quadratic
3.5 Real World Quadratic

4. Matrices and Determinants

4.1 Introduction to Matrices
4.2 Matrix Operations
4.3 Matrix Properties
4.4 Determinants
4.5 Adjoint and Inverse
4.6 Row Operations and Echelon Form
4.8 Non-Homogeneous Systems
4.9 Homogeneous Systems
4.10 Applications of Matrices

5. Partial Fractions

5.1 Partial Fractions Intro
5.2 Repeated Linear Factors
5.3 Irreducible Quadratic Factors
5.4 Repeated Quadratic Factors

6. Sequences and Series

6.1 Sequences
6.2 Arithmetic Progression
6.3 Arithmetic Mean
6.4 Arithmetic Series
6.5 Geometric Progression
6.6 Geometric Mean
6.7 Geometric Series
6.8 Arithmetico-Geometric Progression
6.9 Harmonic Progression
6.10 Miscellaneous Series
6.11 Real Life Applications

7. Permutations and Combinations

7.1 Fundamental Counting
7.2 Permutations
7.3 Objects Not All Different
7.4 Combinations

8. Mathematical Inductions and Binomial Theorem

8.1 Mathematical Induction
8.2 Binomial Theorem
8.3 Binomial Series
8.4 Pascal's Triangle
8.5 Applications of Binomial Theorem

9. Division of Polynomials

9.1 Polynomials and Division
9.2 Applications of Remainder and Factor Theorems

10. Trigonometric Identities

10.1 Fundamental Law of Trigonometry
10.2 Allied Angles
10.3 Further Applications of Basic Identities
10.4 Double, Half and Triple Angles
10.7 Product–Sum Formulas

11. Trigonometric Functions and Their Graphs

11.1 Domains and Ranges
11.2 Even, Odd and Periodicity
11.4 Graphs of Trigonometric Functions
11.5 Maximum, Minimum and Applications

12. Limit and Continuity

12.1 Limit of a Function
12.2 Limits of Important Functions
12.3 Continuity and Discontinuity
12.4 Applications of Limits

13. Differentiation

13.1 Tangent and the Derivative
13.2 Differentiation from First Principles
13.3 Differentiation Theorems
13.4 Applications of Differentiation

14. Vectors in Space

14.1 Vectors in Space
14.2 Dot Product
14.3 Cross Product
14.4 Scalar Triple Product
INTERACTIVE LAB • CALCULUS & VECTORS

Explore Dynamic Tangent Secants & Riemann Sums

Visualize derivatives as tangent limits, integrate Riemann area under curves, and inspect vector geometry in 2D & 3D space.

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