## Contents of NDA Math Book

Sets, Relations and Functions
Complex Numbers
Sequences and Series
Logarithms
Matrices
Determinant
Binomial Theorem
Permutations and Combinations
Probability
Binary Numbers
Trigonometric Ratios and Equations
Properties of Triangles
Height and Distance
Inverse Trigonometric Functions
Functions
Limits, Continuity and Differentiability
Differentiation
Application of Derivative
Indefinite Integration
Definite Integration
Area Bounded by Region
Differential Equations
Rectangular Cartesian System
The Straight Line
The Circle
Conic Sections
Vector Algebra
Three Dimensional Geometry
Statistics
Correlation and Regression

### Revised Syllabus Covered

Algebra

• Sets: Understanding the concept of sets, set operations, and Venn diagrams.
• De-Morgan Laws: Exploring De-Morgan’s laws in set theory.
• Cartesian Product: Introduction to the Cartesian product.
• Relations: Studying relations and equivalence relations.
• Real Numbers: Representation of real numbers on a number line.
• Complex Numbers: Basic properties, modulus, argument, and cube roots of unity.
• Binary System: Understanding the binary number system and conversion between binary and decimal.
• Progressions: Arithmetic, geometric, and harmonic progressions.
• Linear Inequalities: Solution of linear inequalities in two variables using graphical methods.
• Permutations and Combinations: Comprehending permutation and combination.
• Binomial Theorem: Applying the binomial theorem.
• Logarithms: Study of logarithms and their applications.

Matrices and Determinants

• Matrices: Types of matrices, matrix operations.
• Determinants: Understanding determinants, their basic properties.
• Adjoint and Inverse: Finding the adjoint and inverse of a square matrix.
• Applications: Solving systems of linear equations using Cramer’s rule and the matrix method.

Trigonometry

• Angles: Measurement of angles in degrees and radians.
• Trigonometric Ratios: Exploring trigonometric ratios.
• Identities: Trigonometric identities and sum and difference formulae.
• Multiple and Sub-Multiple Angles: Understanding multiple and sub-multiple angles.
• Inverse Trigonometric Functions: Introduction to inverse trigonometric functions.
• Applications: Applications of trigonometry in problems involving height, distance, and properties of triangles.

Analytical Geometry

• Coordinate System: Rectangular Cartesian Coordinate system.
• Equations of Lines: Equations of lines in various forms, angle between lines.
• Equations of Circles: Standard and general forms of the equation of a circle.
• Conic Sections: Standard forms of parabola, ellipse, and hyperbola, eccentricity, and axis.
• Three-Dimensional Space: Points in three-dimensional space, distance between two points.
• Direction Cosines and Ratios: Introduction to direction cosines and direction ratios.
• Equations of Planes: Equation of a plane and a line in various forms, angles between lines and planes.
• Equation of a Sphere: Introduction to the equation of a sphere.

Differential Calculus

• Real-Valued Functions: Concepts of real-valued functions, domains, ranges, and graphs.
• Limits: Notion of limit, standard limits, and continuity of functions.
• Derivatives: Derivatives of functions, interpretation, and applications.
• Rules of Differentiation: Derivatives of sums, products, quotients, and composite functions.
• Second Order Derivatives: Introduction to second-order derivatives.
• Maxima and Minima: Application of derivatives in maximum and minimum problems.

Integral Calculus and Differential Equations

• Integration: Integration as the inverse of differentiation, integration techniques.
• Definite Integrals: Evaluation of definite integrals and their applications.
• Differential Equations: Formation and solutions of differential equations of various types, applications in growth and decay problems.

Vector Algebra

• Vectors: Vectors in two and three dimensions, vector operations.
• Scalar and Vector Products: Scalar and vector products of vectors, applications.
• Work and Moment: Work done by a force and moment of a force, geometrical problems involving vectors.

Statistics and Probability

• Statistics: Classification of data, frequency distributions, and graphical representations.
• Measures of Central Tendency: Mean, median, mode, variance, and standard deviation.
• Correlation and Regression: Understanding correlation and regression.
• Probability: Probability theory, classical and statistical definitions, theorems, and random variables.
• Binomial Distribution: Examples of random experiments leading to binomial distribution.