NDA Syllabus 2025 - Paper 1 (Mathematics)
The comprehensive UPSC NDA syllabus 2025 for mathematics paper is given in this article:
Unit 1: Trigonometry {Approx. Number of Questions: 25- 30}
- Arcs and angles
- Trigonometric Ratios
- Trigonometric Identities
- Heights and Distances
- Inverse Trigonometry
- Properties of a Triangle
Unit 2: Algebra {Approx. Number of Questions: 25- 30}
- Sets and Venn diagrams
- Quadratic Equations
- Sequence and Series
- Permutation and Combinations
- Logarithm
- Bionomial Theorem
Unit 3:Matrices and Determinants {Approx. Number of Questions: 5- 10}
- Matrices: Types; Operation on Matrices; Adjoint of a matrix; Inverse of a matrix; order of a matrix; Non zero triangular matrix
- Determinants: Rules governing determinants; Value of determinant; Minor and Cofactors; Creamers law
Unit 4: Geometry- 2 D {Approx. Number of Questions: 10- 15}
- Cartesian System: Distance formula; Section Formula;
- Line: Equation of a line; Slope of a line; Intersection of lines; Parallel and perpendicular lines; System of lines
- Triangles: Types of triangles; Properties; Points related to a triangle; Similarity of triangles
- Circle: Equation; Properties; Concentic circles; Tangents; Chords
- Parabola
- Ellipse
- Hyperbola
Unit 5: Geometry- 3 D {Approx. Number of Questions: 5- 10}
- Points in three dimensional space: 3-D Distance formula; Section Formula
- Direction Ratios
- Direction Cosines
- Plane: Equation; Parallel and perpendicular planes
- Sphere: Equation; Points in a sphere; radius of a sphere
Unit 6: Calculus {Approx. Number of Questions: 25- 30}
- Relations and functions
- Limits
- Differentiation
- Integration
- Differential equations
- Application of derivatives
- Definite Integrals
- Maxima and Minima
Unit 7: Statistics and Probability {Approx. Number of Questions: 15- 20}
- Central Tendency: Mean; Median; Mode
- Mean: Types of Mean; Combined mean
- Median: Using Formula
- Mode: Using Formula
- Variance
- Mean Deviation; Standard Deviation
- Graphs: Bar Graph; Pie Chart; Histogram; Frequency Polygon; Ogive
- Correlation and Regression
- Probaility: Definition; General Formula; Mutually exhaustive and inclusive events; Complementary Probability
- Bayes Theorem
- Probability Distribution
Unit 8: Vector Algebra {Approx. Number of Questions: 5- 10}
- Vectors: Definition; Two and Three Dimensional Vectors; Unit Vector; Position vector
- Operations on a vector
- Scalar Multiplication; Vector Multiplication
- Vector Product: Dot Product; Cross Product
- Applications: Force; Work Done; Moment of Force