NEB Mathematics Science grade 11 and 12 Syllabus based on New Curriculum

Q: What are the 8 content areas in NEB Mathematics?

Both NEB Class 11 and Class 12 Mathematics cover 8 content areas: Algebra, Trigonometry, Analytic Geometry, Vectors, Statistics and Probability, Calculus, Computational Methods, and Mechanics (or Mathematics for Economics and Finance). Each content area builds progressively from Class 11 foundations to Class 12 advanced topics.

Q: How many teaching hours are in NEB Class 11 Mathematics?

NEB Class 11 Mathematics has 120 theory teaching hours plus 40 additional hours for practical and project activities, totalling 160 working hours. Theory hours are distributed as: Algebra 31 hrs, Trigonometry 8 hrs, Analytic Geometry 13 hrs, Vectors 7 hrs, Statistics & Probability 9 hrs, Calculus 31 hrs, Computational Methods 10 hrs, and Mechanics/Mathematics for Economics 11 hrs.

Q: How many teaching hours are in NEB Class 12 Mathematics?

NEB Class 12 Mathematics also has 120 theory teaching hours plus 40 hours for practical and project activities. The hour distribution per content area is identical to Class 11, but topics are more advanced — for example, Calculus in Class 12 covers differential equations and L'Hôpital's rule, while Algebra covers Group Theory, De Moivre's theorem and matrix-based systems.

Q: What new topics are introduced in NEB Class 12 Mathematics Algebra?

NEB Class 12 Algebra (31 hrs) introduces: Permutation and Combination, Binomial Theorem (positive integral and any index), Elementary Group Theory (binary operations, abelian groups), De Moivre's theorem and complex roots, Quadratic Equations (nature of roots, symmetric roots), Sums of natural number series by mathematical induction, and solving systems of linear equations by Cramer's rule and matrix methods.

Q: What does NEB Class 12 Calculus cover?

NEB Class 12 Calculus (31 hrs) covers: derivatives of inverse trigonometric, exponential, logarithmic and hyperbolic functions by definition; L'Hôpital's rule (0/0 and ∞/∞ forms); Rolle's theorem and Mean Value theorem; anti-derivatives of standard integrals and rational functions using partial fractions; and first-order differential equations (separable, homogenous, linear and exact types).

Q: Is Mechanics compulsory in NEB Mathematics Class 11 and 12?

No. NEB Mathematics offers a choice in the 8th content area (11 hrs per grade): students can study either Mechanics (Statics and Dynamics) or Mathematics for Economics and Finance. Class 11 Mechanics covers parallelogram of forces, composition and resolution of forces, and motion under gravity. The Economics option covers demand-supply functions, elasticity, cost-revenue-profit functions and equilibrium/break-even conditions.

Curriculum at a Glance

8Content Areas per Grade

120Theory Hours per Grade

40Practical Hours per Grade

NCFNational Curriculum Framework 2076

+2Grade 11–12 (Secondary Level)

About this curriculum: The NEB Mathematics syllabus for 2081 BS (2024–25) follows Nepal’s National Curriculum Framework (NCF 2076). Designed for Grade 11 and 12 students, it covers 8 content areas — Algebra, Trigonometry, Analytic Geometry, Vectors, Statistics & Probability, Calculus, Computational Methods, and Mechanics or Mathematics for Economics & Finance. Students have 160 working hours per grade (120 theory + 40 practical/project activities).

Chapter-wise Syllabus

∑ Algebra

#	Topic / Sub-unit	Key Concepts
1.1	Logic and Set⏱ Part of 31 hrs	Introduction to Logic, statements and logical connectives Truth tables and basic laws of logic Theorems based on set operations; proof of set identities Field axioms and order axioms of real numbers Interval, absolute value and geometric representation of real numbers
1.2	Functions⏱ Part of 31 hrs	Review of functions; domain and range Inverse function and composite function Functions of special types: algebraic (linear, quadratic, cubic), trigonometric, exponential, logarithmic Odd and even functions; periodicity, symmetry and monotonicity Curve sketching of polynomials, rational functions, trigonometric, exponential and logarithmic functions
1.3	Sequence and Series⏱ Part of 31 hrs	Arithmetic, geometric and harmonic sequences and series Properties and relations among A.M, G.M and H.M Sum of infinite geometric series
1.4	Matrices and Determinants⏱ Part of 31 hrs	Transpose of a matrix and its properties Minors, cofactors, adjoint, inverse matrix Determinant and properties of determinants (without proof) Solving problems using determinant properties
1.5	Complex Numbers⏱ Part of 31 hrs	Definition of complex number and imaginary unit Algebra of complex numbers; geometric representation Conjugate, modulus and their properties; square root of a complex number Polar form of complex numbers

Total working hours for Algebra: 31 hrs

△ Trigonometry

#	Topic / Sub-unit	Working Hours	Key Concepts
2.1	Properties of a Triangle⏱ Part of 8 hrs		Sine law, cosine law, tangent law Projection laws and half angle laws Solution of triangles (simple cases)

Total working hours for Trigonometry: 8 hrs

◯ Analytic Geometry

#	Topic / Sub-unit	Key Concepts
3.1	Straight Lines⏱ Part of 13 hrs	Length of perpendicular from a given point to a given line Bisectors of the angles between two straight lines General equation of second degree in x and y — condition for pair of lines Homogeneous second-degree equation: angle between pair of lines, angle bisectors
3.2	Circle⏱ Part of 13 hrs	Condition of tangency of a line at a point to a circle Equations of tangent and normal to a circle at a given point
3.3	Parabola⏱ Part of 13 hrs	Standard equation of a parabola Equations of tangent and normal to a parabola at a given point

Total working hours for Analytic Geometry: 13 hrs

→ Vectors

#	Topic / Sub-unit	Working Hours	Key Concepts
4.1	Vectors and Scalar Product⏱ 7 hrs		Collinear and non-collinear vectors; coplanar and non-coplanar vectors Linear combination of vectors Scalar (dot) product of two vectors; angle between two vectors Geometric interpretation of scalar product; properties Condition of perpendicularity; applications in trigonometry and geometry

Total working hours for Vectors: 7 hrs

📊 Statistics & Probability

#	Topic / Sub-unit	Working Hours	Key Concepts
5.1	Measures of Dispersion⏱ Part of 9 hrs		Standard deviation and variance Coefficient of variation Skewness (Karl Pearson’s and Bowley’s methods)
5.2	Probability⏱ Part of 9 hrs		Random experiment, sample space, events; equally likely, mutually exclusive, exhaustive and independent events Mathematical and empirical definition of probability Two basic laws of probability (without proof)

Total working hours for Statistics & Probability: 9 hrs

∫ Calculus

#	Topic / Sub-unit	Key Concepts
6.1	Limits and Continuity⏱ Part of 31 hrs	Limits of a function; indeterminate forms Algebraic properties of limits (without proof) Theorems on limits of algebraic, trigonometric, exponential and logarithmic functions Continuity of a function; types of discontinuity; graphs of discontinuous functions
6.2	Derivatives⏱ Part of 31 hrs	Derivative by first principle (algebraic, trigonometric, exponential, logarithmic) Rules of differentiation: sum, difference, product, quotient, chain rule, power rule Derivatives of parametric and implicit functions; higher order derivatives Geometric interpretation of derivative; monotonicity; extreme values; concavity; points of inflection Derivative as rate of measure
6.3	Anti-derivatives (Integration)⏱ Part of 31 hrs	Integration as reverse of differentiation; basic integrals Integration by substitution and integration by parts Definite integral; definite integral as area under the curve Area between two curves

Total working hours for Calculus: 31 hrs

💻 Computational Methods

#	Topic / Sub-unit	Working Hours	Key Concepts
7.1	Numerical Computation⏱ Part of 10 hrs		Characteristics of numerical computing: accuracy, rate of convergence, numerical stability and efficiency Roots of algebraic and transcendental equations by bisection method Newton-Raphson method; approximate error estimation
7.2	Numerical Integration⏱ Part of 10 hrs		Trapezoidal rule Simpson’s ⅓ rule

Total working hours for Computational Methods: 10 hrs

⚖️ Mechanics or Math for Economics

#	Topic / Sub-unit	Key Concepts
8.1	Statics (Mechanics option)⏱ Part of 11 hrs	Forces and resultant forces; parallelogram law of forces Composition and resolution of forces Resultant of coplanar forces acting on a point Triangle law of forces and Lami’s theorem
8.2	Dynamics (Mechanics option)⏱ Part of 11 hrs	Motion of particle in a straight line Motion with uniform acceleration; motion under gravity Motion down a smooth inclined plane
8.3	Mathematics for Economics and Finance (alternative option)⏱ 11 hrs	Mathematical models and functions; demand and supply functions Cost, revenue and profit functions Elasticity of demand, supply and income Budget and cost constraints Equilibrium and break-even conditions

Total working hours for Mechanics / Math for Economics: 11 hrs

∑ Algebra

#	Topic / Sub-unit	Key Concepts
1.1	Permutation and Combination⏱ Part of 31 hrs	Basic principle of counting Permutation: all different, not all different, circular, with repetition Combination of things all different; properties of combination
1.2	Binomial Theorem⏱ Part of 31 hrs	Binomial theorem for positive integral index; general term; binomial coefficients Binomial theorem for any index (without proof); application to approximation Euler’s number; expansion of eˣ, aˣ and log(1+x) (without proof)
1.3	Elementary Group Theory⏱ Part of 31 hrs	Binary operations on sets of integers and their properties Definition of a group; finite and infinite groups Uniqueness of identity, uniqueness of inverse, cancellation law Abelian group
1.4	Complex Numbers (Advanced)⏱ Part of 31 hrs	De Moivre’s theorem and its proof Finding roots of a complex number using De Moivre’s theorem Properties of cube roots of unity Euler’s formula
1.5	Quadratic Equations⏱ Part of 31 hrs	Nature of roots of a quadratic equation Relation between roots and coefficients Formation of a quadratic equation; symmetric roots; one or both roots common
1.6	Series and Mathematical Induction⏱ Part of 31 hrs	Sum of first n natural numbers; sum of squares and cubes of first n natural numbers Principle of mathematical induction
1.7	Matrix-based System of Linear Equations⏱ Part of 31 hrs	Solution of system of linear equations by Cramer’s rule (up to 3 variables) Matrix method: row-equivalent and inverse matrix methods (up to 3 variables)

Total working hours for Algebra: 31 hrs

△ Trigonometry

#	Topic / Sub-unit	Working Hours	Key Concepts
2.1	Inverse Circular Functions⏱ Part of 8 hrs		Definition of inverse circular (trigonometric) functions Establishing and using relations on inverse circular functions
2.2	Trigonometric Equations⏱ Part of 8 hrs		General solution of trigonometric equations General values of sin, cos, tan, and their inverses

Total working hours for Trigonometry: 8 hrs

◯ Analytic Geometry

#	Topic / Sub-unit	Working Hours	Key Concepts
3.1	Conic Sections (Ellipse & Hyperbola)⏱ Part of 13 hrs		Standard equation of an ellipse Standard equation of a hyperbola
3.2	Coordinates in Space (3D Geometry)⏱ Part of 13 hrs		Direction cosines and direction ratios of a line General equation of a plane; intercept and normal form Plane through 3 given points; plane through intersection of two planes Parallel and perpendicular planes; angle between two planes Distance of a point from a plane

Total working hours for Analytic Geometry: 13 hrs

→ Vectors

#	Topic / Sub-unit	Working Hours	Key Concepts
4.1	Vector Product⏱ 7 hrs		Vector (cross) product of two vectors Geometric interpretation of vector product Properties of vector product Application of vector product in geometry and trigonometry

Total working hours for Vectors: 7 hrs

📊 Statistics & Probability

#	Topic / Sub-unit	Working Hours	Key Concepts
5.1	Correlation and Regression⏱ Part of 9 hrs		Correlation and nature of correlation Correlation coefficient by Karl Pearson’s method; interpretation and properties (without proof) Rank correlation by Spearman’s method Regression equation; regression line of y on x and x on y
5.2	Probability (Advanced)⏱ Part of 9 hrs		Dependent events and conditional probability (without proof) Solving probability problems using combinations Binomial distribution; mean and standard deviation of binomial distribution (without proof)

Total working hours for Statistics & Probability: 9 hrs

∫ Calculus

#	Topic / Sub-unit	Key Concepts
6.1	Advanced Derivatives⏱ Part of 31 hrs	Derivatives of inverse trigonometric, exponential and logarithmic functions by definition Relationship between continuity and differentiability Hyperbolic functions and inverse hyperbolic functions; differentiation rules L’Hôpital’s rule for 0/0 and ∞/∞ forms Differentials; tangent and normal using derivatives Rolle’s theorem and Mean Value theorem: geometrical interpretation and verification
6.2	Anti-derivatives (Advanced Integration)⏱ Part of 31 hrs	Anti-derivatives of standard integrals Integrals reducible to standard forms Integrals of rational functions (using partial fractions)
6.3	Differential Equations⏱ Part of 31 hrs	Differential equation: order and degree First order, first degree differential equations Separable variable method Homogeneous differential equations Linear and exact differential equations

Total working hours for Calculus: 31 hrs

💻 Computational Methods

#	Topic / Sub-unit	Working Hours	Key Concepts
7.1	Linear Programming Problems (LPP)⏱ Part of 10 hrs		Linear programming problem formulation Simplex method (maximization problems only)
7.2	System of Linear Equations — Gauss Elimination⏱ Part of 10 hrs		Gauss Elimination method for solving system of linear equations (up to 3 variables)

Total working hours for Computational Methods: 10 hrs

⚖️ Mechanics or Math for Economics

#	Topic / Sub-unit	Key Concepts
8.1	Statics — Parallel Forces (Mechanics option)⏱ Part of 11 hrs	Resultant of like and unlike parallel forces
8.2	Dynamics — Newton’s Laws & Projectile (Mechanics option)⏱ Part of 11 hrs	Newton’s laws of motion Projectile motion
8.3	Mathematics for Economics and Finance (alternative option)⏱ 11 hrs	Consumer and producer surplus Quadratic functions in economics; input-output analysis Dynamics of market price Difference equations; Cobweb model Lagged Keynesian macroeconomic model

Total working hours for Mechanics / Math for Economics: 11 hrs

Practical & Project Activity Hours (per Grade)

Students are required to complete 40 practical and project activity hours in each of Grade 11 and Grade 12 (in addition to 120 theory hours). These are distributed across all 8 content areas as shown below.

∑ Algebra11 hrs

△ Trigonometry2 hrs

◯ Analytic Geometry5 hrs

→ Vectors3 hrs

📊 Statistics & Probability3 hrs

∫ Calculus11 hrs

💻 Computational Methods2 hrs

⚖️ Mechanics / Math for Econ.3 hrs

Quick Comparison – Class 11 vs 12

Area	📐 Class 11 Focus	∫ Class 12 Focus
Algebra	Logic, Sets, Functions, Sequences, Matrices, Complex Numbers	Permutation & Combination, Binomial Theorem, Group Theory, De Moivre’s, Quadratic Equations, Cramer’s Rule
Trigonometry	Properties of Triangles, Solution of Triangles	Inverse Circular Functions, Trigonometric Equations (General Solution)
Analytic Geometry	Straight Lines, Pair of Lines, Circle, Parabola	Ellipse, Hyperbola, 3D Coordinates, Equations of Planes
Vectors	Scalar (Dot) Product, Properties, Applications	Vector (Cross) Product, Properties, Applications
Statistics & Probability	Measures of Dispersion, Basic Probability Laws	Correlation & Regression, Conditional Probability, Binomial Distribution
Calculus	Limits, Continuity, Differentiation, Basic Integration, Definite Integrals	Advanced Derivatives, L’Hôpital’s Rule, Mean Value Theorem, Partial Fractions, Differential Equations
Computational Methods	Bisection Method, Newton-Raphson, Trapezoidal & Simpson’s Rule	Simplex Method (LPP), Gauss Elimination Method
Mechanics / Econ.	Parallelogram of Forces, Lami’s Theorem, Uniform Motion / Demand-Supply, Elasticity	Parallel Forces, Projectile & Newton’s Laws / Consumer Surplus, Cobweb Model, Difference Equations

Frequently Asked Questions

What are the 8 content areas in NEB Mathematics?

Both NEB Class 11 and Class 12 Mathematics cover 8 content areas: Algebra, Trigonometry, Analytic Geometry, Vectors, Statistics and Probability, Calculus, Computational Methods, and Mechanics (or Mathematics for Economics and Finance). Each area builds progressively from Class 11 foundations to advanced Class 12 topics.

How many teaching hours are in NEB Class 11 Mathematics?

NEB Class 11 Mathematics has 120 theory teaching hours plus 40 practical and project activity hours, totalling 160 working hours. Theory hours: Algebra 31, Trigonometry 8, Analytic Geometry 13, Vectors 7, Statistics & Probability 9, Calculus 31, Computational Methods 10, Mechanics/Math for Economics 11.

How many teaching hours are in NEB Class 12 Mathematics?

NEB Class 12 Mathematics also has 120 theory hours + 40 practical hours = 160 total working hours. The hour distribution per content area is identical to Class 11, but the topics are more advanced — Class 12 Calculus covers differential equations, while Class 12 Algebra covers Group Theory, De Moivre’s theorem and matrix-based systems of equations.

What new Algebra topics are introduced in NEB Class 12?

Class 12 Algebra (31 hrs) introduces entirely new topics: Permutation and Combination, Binomial Theorem (including any-index form and Euler’s number), Elementary Group Theory (binary operations, abelian groups), De Moivre’s theorem and complex roots, Quadratic Equations (nature of roots, symmetric roots), sums of series by Mathematical Induction, and solving linear systems by Cramer’s rule and matrix methods up to 3 variables.

What does NEB Class 12 Calculus cover that Class 11 does not?

Class 12 Calculus (31 hrs) extends beyond Class 11 with: L’Hôpital’s rule (0/0 and ∞/∞), derivatives of inverse trigonometric and hyperbolic functions, Rolle’s theorem and Mean Value theorem, integration of rational functions using partial fractions, and first-order differential equations (separable variables, homogeneous, linear and exact types). These are absent from the Class 11 syllabus.

Is Mechanics compulsory in NEB Mathematics Class 11 and 12?

No, it is not compulsory. The 8th content area (11 hrs per grade) offers a choice between Mechanics (Statics and Dynamics) and Mathematics for Economics and Finance. Class 11 Mechanics covers parallelogram of forces, Lami’s theorem and motion under gravity. The Economics option covers demand-supply, elasticity, cost-revenue-profit and equilibrium/break-even analysis. Students and schools select one option.

What is the NEB Mathematics curriculum framework for 2081 BS?

The NEB Mathematics syllabus for 2081 BS (2024–25) follows Nepal’s National Curriculum Framework (NCF 2076). It is designed for Grade 11 and 12 students and focuses on developing logical reasoning, problem-solving skills, and computational competence aligned with secondary-level education goals. The curriculum prepares students for higher education in science, technology, economics and related fields.