This section contains the following topics:

• Set theory, set operations, and Venn diagrams.
• De Morgan laws, relation, and the Cartesian product of equivalence.
• Real numbers are represented on a line.
• Conversion of a number between the binary and decimal systems.
• Basic characteristics, modulus, argument, and cube roots of unity of complex numbers.
• Binary number system.
• Graph-based solutions to two-variable linear equations.
• Progressions in geometry, harmony, and arithmetic.
• Real-coefficient quadratic equations
• Combination and Permutation.
• The binomial theorem and its uses.
• Applications for logarithms.

2) Matrices and Determinants:

This section contains the following topics:

• Matrix types and Matrix operations
• Basic characteristics of determinants, a matrix’s determinant.
• Inverse and adjacent to a square matrix.
• Applications include the use of Cramer’s rule and the Matrix method to solve a system of linear equations with two or three unknowns.

3) Trigonometry:

The NDA exam syllabus 2023 for this section is as follows:

• Angles and their degrees and radians measurements.
• Ratios of trigonometry.
• Formulas for the sum and difference of trigonometric identities.
• Sub-multiple and Multiple angles.
• Trigonometric operations in inverse.
• Applications include height and distance as well as triangular properties.

4) Analytical Geometry of two and three Dimensions:

This section contains the following topics:

• Cartesian coordinates with a rectangular shape.
• Distance calculation.
• Many variations of a line’s equation and angles between two lines.
• A Point’s separation from a line.
• Circle equation in standard and general form.
• Parabola, ellipse, and hyperbola are in their standard forms.
• A conic’s eccentricity and axis.
• Distance between two points at a point in three dimensions.
• Cosines and ratios of directions.
• The equation for two points
• Different equations involve a plane and a line.
• Angles between two planes and two lines.
• The equation for a sphere.

5) Differential Calculus

This section contains the following topics:

• Real-valued function concept, including domain, range, and function graph.
• Functions that are composite, one-to-one, onto, and inverse.
• Examples of a limit concept and standard limits.
• Examples and algebraic operations on continuous functions for the concept of function continuity.
• Application of derivatives to maxima and minima problems.
• Applications for the geometrical and physical interpretations of a derivative of a function at a point.
• Derivatives of a function for another function, derivatives of the sum, product, and quotient of functions, and derivatives of composite functions.
• Derivatives of the second order.
• Functions for increasing and decreasing.

6) Integral Calculus and Differential Equations

This section contains the following topics:

• Standard integrals using algebraic expressions, and trigonometric, exponential, and hyperbolic functions include integration as the inverse of differentiation, integration by substitution, and integration by parts.
• Applications for evaluating definite integrals include calculating the areas of flat regions bordered by curves.
• Definition of a differential equation’s order and degree, as well as examples of how to construct one.
• Examples include the general and specific solutions to differential equations, as well as the solutions to first-order and first-degree differential equations of various forms.
• application in growth and decay problems.

7) Vector Algebra

This section contains the following topics:

• Vectors in two and three dimensions, including a vector’s magnitude and direction.
• Unit and null vectors, vector addition, vector scalar multiplication, scalar product, or dot product of two vectors are all examples of vectors. Cross product of two vectors, or vector product.
• Applications include the work carried out by a force and its moment, as well as geometrical problems.

8) Statistics & Probability

Statistics-

This section contains the following topics:

• Data classification, frequency distribution, and cumulative frequency distribution and their examples.
• Mean, median, and mode constitute central tendency measures.
• The graphical representation includes frequency polygons, histograms, and pie charts and their examples.
• Comparison and determination of variance and standard deviation.
• Correlation and regression.

Probability-

This section contains the following topics:

• Random experiment, events, mutually exclusive and exhaustive events, outcomes and associated sample space, impossible and certain events.
• Intersection and Union of events.
• Simple problems with basic probability theorems.
• Elementary, Complementary and composite events.
• Examples and a definition of probability, both classical and statistical.
• Simple problems include conditional probability and Bayes’ theorem.
• Using a random variable as a sample space function.
• Examples of random experiments that gave rise to the binomial distribution.