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Academic Syllabus Insights
High-precision topic mapping for competitive exams. Click subjects to expand details.
Mathematics Syllabus
Weightage IncludedSets, Relations & Functions
Key Sub-topics
- Sets and their representation
- Union, intersection and complement of sets
- Algebraic properties of sets
- Relation, Types of relations
- Functions; Types of functions
- Composition of functions and invertible functions
Complex Numbers & Quadratic Equations
Key Sub-topics
- Complex numbers as ordered pairs of reals
- Argand diagram
- algebra of complex numbers
- modulus and argument
- Quadratic equations in real and complex number system
- Relations between roots and co-efficients
Matrices & Determinants
Key Sub-topics
- Matrices, algebra of matrices
- Types of matrices
- Determinants and matrices of order two and three
- Properties of determinants
- Adjoint and evaluation of inverse of a square matrix
- Solution of simultaneous linear equations
Permutations & Combinations
Key Sub-topics
- Fundamental principle of counting
- Permutation as an arrangement
- Combination as selection
- Meaning of P (n,r) and C (n,r)
- Simple applications
Binomial Theorem & its Applications
Key Sub-topics
- Binomial theorem for a positive integral index
- General term and middle term
- Properties of Binomial coefficients
- Simple applications
Sequences & Series
Key Sub-topics
- Arithmetic and Geometric progressions
- Insertion of arithmetic and geometric means
- Relation between A.M. and G.M.
- Sum up to n terms of special series
- Arithmetico-Geometric progression
Limit, Continuity & Differentiability
Key Sub-topics
- Real-valued functions
- Algebra of functions
- Limits, continuity and differentiability
- Differentiation of the sum, difference, product and quotient of two functions
- Differentiation of exponential and logarithmic functions
- Applications of derivatives
Integral Calculus
Key Sub-topics
- Integral as an anti-derivative
- Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions
- Integration by substitution, by parts and by partial fractions
- Evaluation of definite integrals
- Area under simple curves
Differential Equations
Key Sub-topics
- Ordinary differential equations, their order and degree
- Formation of differential equations
- Solution of differential equations by the method of separation of variables
- Solution of homogeneous and linear differential equations
Coordinate Geometry
Key Sub-topics
- Cartesian system of rectangular coordinates
- Straight lines
- Circles
- Conic sections (Parabola, Ellipse, Hyperbola)
- Standard forms
Three Dimensional Geometry
Key Sub-topics
- Coordinates of a point in space
- Distance between two points
- Section formula
- Direction cosines and direction ratios
- Equation of a line and a plane
Vector Algebra
Key Sub-topics
- Vectors and scalars
- Addition of vectors
- Components of a vector in two and three dimensional space
- Scalar and vector products
- Scalar and vector triple product
Statistics & Probability
Key Sub-topics
- Measures of Dispersion
- Calculation of mean, median, mode
- Probability of an event
- Addition and multiplication theorems of probability
- Bayes' theorem
- Bernoulli trials and Binomial distribution
Trigonometry
Key Sub-topics
- Trigonometrical identities and equations
- Trigonometrical functions
- Inverse trigonometrical functions and their properties
- Heights and Distances
Strategy Insight
High: Calculus (35%), Algebra (30%), Coordinate Geometry (20%)
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