HPRCA Mathematics Teacher Syllabus 2026

HPRCA Mathematics Teacher Syllabus 2026: Complete Exam Syllabus

The Himachal Pradesh Rajya Chayan Ayog (HPRCA) has released the official syllabus for the Mathematics Teacher recruitment exam. The syllabus is divided into three main sections: Mathematics (Post Graduation Level), B.Ed subjects, and General Awareness. Below is the detailed topic-wise breakdown HPRCA Mathematics Teacher Syllabus 2026.

1. Mathematics (Post Graduation Level)

This section covers advanced mathematical concepts ranging from Algebra to Calculus and Numerical Methods.

a) Algebra and Number Theory

• Number Systems: Rational/Irrational numbers, Fundamental Theorem of Arithmetic.
• Polynomials & Equations: Quadratic, Cubic, and Biquadratic equations, Relationship between roots and coefficients.
• Matrices & Determinants: Types of matrices, Inverse, System of linear equations, and Eigenvalues.
• Modern Algebra: Groups (Abelian/Non-abelian), Cyclic groups, Subgroups, Lagrange’s theorem, and Normal subgroups.
• Complex Numbers: Polar representation, Fundamental Theorem of Algebra, and Square-root of Complex numbers.

b) Calculus and Analysis

• Real Analysis: Limits, Continuity, Differentiability, Cauchy convergence criterion, and Series tests (Root, Ratio, Leibnitz).
• Derivatives: Chain rule, Mean Value Theorems (Rolle’s, Lagrange’s, Cauchy’s), Maxima & Minima, and Curvature.
• Integrals: Definite and Indefinite integrals, Area under curves, and Length of curves.
• Differential Equations: Linear equations, Homogeneous equations, Exact differential equations, and PDEs (Classification into elliptic, parabolic, hyperbolic).

c) Geometry and Vectors

• Two-Dimensional Geometry: Conic sections (Circle, Parabola, Ellipse, Hyperbola) and General equation of a line.
• Three-Dimensional Geometry: Direction cosines, Planes, Lines, Coplanar/Skew lines, and Angle between planes.
• Vectors: Dot and Cross products, Gradient, Divergence, Curl, and Laplacian operator.

d) Statistics, Probability, and Discrete Math

• Statistics: Mean, Median, Mode, Variance, and Standard Deviation.
• Probability: Conditional probability, Bayes’ theorem, Binomial distribution, and Random variables.
• Permutations & Combinations: Fundamental principle of counting and Binomial Theorem.
• Sequence & Series: AP, GP, HP, and Special series.

e) Other Important Topics

• Trigonometry: Identities, Inverse Trigonometric Functions, and Height & Distance.
• Sets, Relations & Functions: Types of functions (Domain/Range), Venn diagrams, and Equivalence relations.
• Numerical Methods: Newton’s method, Trapezoidal rule, Simpson’s rule, and Euler’s method.

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2. Subjects of B.Ed (Teaching Methodology)

This section tests the pedagogical skills of the candidate:

• Learning and Teaching.
• Assessment for Learning.
• Teaching of Mathematics.
• Lesson Planning, Assessment, and Evaluation.
• ICT in Teaching-Learning Process.
• Guidance and Counseling.

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3. General Awareness

Common for all streams, this section includes:

• General Knowledge: HP GK and Current Affairs.
• Everyday Science and Logical Reasoning.
• Social Science (10th Standard level).
• General English & General Hindi (10th Standard level).

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