Class 12 Math Syllabus

1. Algebra

1.1 Permutation and Combination

• Basic principle of counting
• Permutations
• Combinations

1.2 Binomial Theorem

• Theorem for a positive integer
• General term and binomial coefficient
• Theorem for any index
• Applications to approximation
• Euler’s number
• Expansion of e^x, a^x and log(1 + x)

1.3 Complex Numbers

• Polar form
• De Moivre’s theorem & applications
• Properties of cube roots of unity
• Euler’s formula

1.4 Sequence and Series

• Sum of natural numbers
• Sum of squares
• Sum of cubes
• Principle of mathematical induction

1.5 Matrix-based System of Linear Equations

• Cramer’s rule
• Matrix method (row equivalent & inverse)
• Up to three variables

2. Trigonometry

2.1 Properties of a Triangle

• Sine law
• Cosine law
• Tangent law
• Projection laws
• Half-angle laws

2.2 Solution of Triangle

• Simple cases

3. Analytic Geometry

3.1 Conic Section

• Condition of tangency to a circle
• Tangent & normal to a circle
• Standard equation of parabola
• Equations of tangent & normal to a parabola
• Standard equations of ellipse & hyperbola

4. Vectors

4.1 Product of Vectors

• Scalar product
• Vector product
• Geometric interpretations
• Properties & applications

5. Statistics and Probability

5.1 Correlation and Regression

• Karl Pearson’s correlation coefficient
• Rank correlation
• Regression equations

5.2 Probability

• Dependent cases
• Conditional probability

6. Calculus

6.1 Derivatives

• Derivatives of hyperbolic & inverse hyperbolic functions
• L'Hospital’s rule (0/0, ∞/∞)
• Differentiate & differentials
• Tangent & normal
• Derivative as rate of measure

6.2 Anti-derivatives

• Standard integrals
• Integrals reducible to standard forms
• Integrals of rational functions

6.3 Differential Equations

• Order & degree
• First order & first degree equations
• Separable, homogeneous, linear & exact equations

7. Computational Methods or Mechanics

Computational Methods

• Gauss Elimination method
• Gauss-Seidel method
• Linear programming: Simplex method

Mechanics

• Resultant forces: parallelogram law, triangle law, Lami’s theorem
• Newton’s laws of motion and projectile
• Resultant of coplanar forces
• Motion of a particle in a straight line