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NEB Grade 11 & 12 New Syllabus: Mathematics
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NEB Grade 11 & 12 Mathematics Syllabus — Complete Overview

Mathematics is one of the core subjects available to students of the Science, Management, and Education streams under the National Examination Board (NEB), Nepal. It is also offered as a compulsory alternative to Social Studies for students who prefer a stronger quantitative foundation. The curriculum, developed by the Curriculum Development Centre (CDC), Sanothimi, Bhaktapur, under the Secondary Education Curriculum 2076 (revised 2078), organizes the subject into eight content areas — Algebra, Trigonometry, Analytic Geometry, Vectors, Statistics and Probability, Calculus, Computational Methods, and Mechanics — across both Grade 11 and Grade 12.

This page provides a complete, topic-accurate breakdown of the NEB Mathematics syllabus for both grades, including exam structure and preparation strategy.

Subject Information at a Glance

  • Subject Name: Mathematics (Compulsory alternative / Optional)
  • Subject Code: 401 (Grade 11, as per official NEB notices)
  • Streams: Science, Management, Education (compulsory alternative to Social Studies)
  • Developed by: Curriculum Development Centre (CDC), Government of Nepal
  • Curriculum: Secondary Education Curriculum 2078
  • Prescribed Textbook: Basic Mathematics Grade XI and Grade XII — Sukunda Pustak Bhawan (Authors: D.R. Bajracharya, R.M. Shrestha, M.B. Singh, Y.R. Sthapit, B.C. Bajracharya)
  • Teaching Hours: 160 working hours per grade
  • Total Full Marks: 75 (Theory) + 25 (Internal Evaluation) = 100, per grade
  • Exam Duration: 3 hours (students must bring their own graph paper, log table, and geometry instruments)

NEB Grade 11 Mathematics — Topic List by Content Area

Grade 11 Mathematics covers over 20 topics across eight content areas, totaling 160 working hours.

Content Area 1: Algebra (Largest Section)

  • 1.1 Logic and Set — statements, logical connectives, truth tables, set operation theorems
  • 1.2 Real Numbers — geometric representation, intervals, absolute value, field axioms, order axioms
  • 1.3 Function — domain and range, types of functions (injective, surjective, bijective), inverse and composite functions
  • 1.4 Curve Sketching — odd/even functions, periodicity, symmetry, monotonicity, graphs of quadratic, cubic, rational, trigonometric, exponential, and logarithmic functions
  • 1.5 Sequence and Series — arithmetic, geometric, harmonic progressions; AM, GM, HM and their relations; sum of infinite geometric series
  • 1.6 Matrices and Determinants — transpose, minors, cofactors, adjoint, inverse matrix, properties of determinants, solving linear equations
  • 1.7 Quadratic Equations — nature of roots (discriminant), root-coefficient relations, symmetric functions of roots, formation of equations
  • 1.8 Complex Numbers — algebra, Argand diagram, modulus, conjugate, square root, polar form

Content Area 2: Trigonometry

  • 2.1 Inverse Circular Functions — definition, principal values, domain and range of sin⁻¹x, cos⁻¹x, tan⁻¹x; relations between inverse functions
  • 2.2 Trigonometric Equations — general solutions of sinθ = sinα, cosθ = cosα, tanθ = tanα; solving using identities and factorization

Content Area 3: Analytic Geometry

  • 3.1 Straight Line — length of perpendicular from a point to a line, bisectors of angles between lines
  • 3.2 Pair of Straight Lines — general second-degree equation, condition for pair of lines, angle between lines, equation of bisectors
  • 3.3 Coordinates in Space — distance between two points in 3D, direction cosines and direction ratios

Content Area 4: Vectors

  • 4.1 Vectors — collinear and non-collinear vectors, coplanar and non-coplanar vectors, linearly dependent/independent vectors, linear combination of vectors

Content Area 5: Statistics and Probability

  • 5.1 Measures of Dispersion — standard deviation, variance, coefficient of variation, skewness (Karl Pearson and Bowley methods)
  • 5.2 Probability — sample space, events, two basic laws (addition and multiplication), independent events

Content Area 6: Calculus

  • 6.1 Limits and Continuity — limit theorems, standard limits (sin x/x, (eˣ−1)/x, ln(1+x)/x), indeterminate forms, continuity, types of discontinuity
  • 6.2 Derivatives — derivatives by first principle, basic rules (product, quotient, chain), parametric and implicit differentiation, higher order derivatives
  • 6.3 Applications of Derivatives — monotonicity, extreme values (maxima/minima), concavity, points of inflection, derivative as rate measure, tangents and normals
  • 6.4 Anti-derivatives — basic integrals, integration by substitution and by parts, definite integrals, area under a curve, area between two curves

Content Area 7: Computational Methods

  • 7.1 Numerical Computation — finding roots of equations using bisection method and Newton-Raphson method
  • 7.2 Numerical Integration — trapezoidal rule, Simpson’s one-third rule

Content Area 8: Mechanics

  • 8.1 Statics — parallelogram law of forces, composition and resolution of forces, resultant of coplanar forces, triangle law, Lami’s theorem
  • 8.2 Dynamics — uniform acceleration equations (v = u + at, s = ut + ½at², v² = u² + 2as), motion under gravity, motion on smooth inclined planes

NEB Grade 12 Mathematics — Topic List by Content Area

Grade 12 Mathematics covers 19 topics across the same eight content areas. The subject is officially titled Compulsory Mathematics (Basic Mathematics Grade XII) and is prescribed for Science, Management, and Education stream students.

Content Area 1: Algebra (7 topics)

  • Chapter 1: Permutation and Combination — basic counting principle, permutations of distinct and non-distinct objects, combinations, applications
  • Chapter 2: Binomial Theorem — binomial theorem for positive integral index, general term, binomial coefficients, applications
  • Chapter 3: Elementary Group Theory — binary operations, definition of a group, properties of groups, examples
  • Chapter 4: Complex Numbers — De Moivre’s theorem, applications in finding roots of complex numbers, properties
  • Chapter 5: Quadratic Equations — nature and roots, relation between roots and coefficients, formation of quadratic equations with given roots
  • Chapter 6: Sequence and Series — Mathematical Induction; sum of finite natural numbers, squares, and cubes of first n natural numbers
  • Chapter 7: Matrix-Based System of Linear Equations — consistency of systems, solving using Cramer’s rule and matrix inversion method

Content Area 2: Trigonometry (2 topics)

  • Chapter 8: Inverse Circular Functions — advanced treatment, properties, simplification of inverse trigonometric expressions
  • Chapter 9: Trigonometric Equations and General Values — general solutions, solving equations with multiple conditions

Content Area 3: Analytic Geometry (2 topics)

  • Chapter 10: Conic Section — standard equations and properties of parabola, ellipse, and hyperbola; focus, directrix, eccentricity
  • Chapter 11: Coordinates in Space — advanced 3D geometry, equations of lines and planes, distance in three dimensions

Content Area 4: Vectors (1 topic)

  • Chapter 12: Product of Vectors — scalar (dot) product, vector (cross) product, scalar triple product, geometrical applications

Content Area 5: Statistics and Probability (2 topics)

  • Chapter 13: Correlation and Regression — Karl Pearson’s correlation coefficient, rank correlation (Spearman’s), regression lines, regression equations
  • Chapter 14: Probability — dependent cases, conditional probability, Bayes’ theorem, binomial distribution

Content Area 6: Calculus (3 topics)

  • Chapter 15: Derivatives — L’Hôpital’s rule, Rolle’s theorem, Mean Value theorem, tangents and normals (advanced), applications of derivatives
  • Chapter 16: Anti-derivatives — integration techniques, definite integrals, application to areas and volumes
  • Chapter 17: Differential Equations — formation of differential equations, order and degree, solving variable-separable and homogeneous types

Content Area 7: Computational Methods (2 topics)

  • Chapter 18: Linear Programming Problems — graphical method, feasible region, optimization of objective functions
  • Chapter 19: System of Linear Equations (Numerical Methods) — Gaussian elimination, iterative methods

Content Area 8: Mechanics (2 topics) + Applied Mathematics

  • Chapter 20: Parallel Forces and Moments — moments, couples, conditions of equilibrium
  • Chapter 21: Dynamics — projectile motion, motion in a straight line under variable force
  • Chapter 22: Mathematics for Economics and Finance (additional topic for Management stream students)

NEB Mathematics Exam Structure

  • Theory Examination: 75 marks (3-hour written exam conducted by NEB)
  • Internal Evaluation: 25 marks (project work and continuous assessment conducted by the school)
  • Students must bring their own graph paper, log table, and geometry instruments; electronic devices are strictly prohibited
  • NEB does not publish official chapter-wise marks distribution for either grade; the CDC teaching-hour grid is explicitly for time distribution only

The theory paper typically includes short answer questions testing specific concepts, long answer/derivation questions, and numerical problem-solving questions across different content areas. Calculus and Algebra together consistently account for the highest combined marks across recent board papers, reflecting their larger teaching-hour allocation.

Difference Between Grade 11 and Grade 12 Mathematics

Grade 11 Mathematics builds the conceptual and computational groundwork: logic and sets, functions and curve sketching, sequences and series, matrices and determinants, basic complex numbers, inverse circular functions and trigonometric equations, coordinate geometry including pair of lines and 3D coordinates, vectors, measures of dispersion, basic probability, limits and calculus through integration, numerical methods, and introductory mechanics. Grade 12 Mathematics assumes all of this and extends significantly: Algebra adds permutations, combinations, binomial theorem, group theory, and De Moivre’s theorem; Analytic Geometry expands to conic sections; Vectors adds scalar and vector products with applications; Statistics adds correlation, regression, and binomial probability; Calculus adds L’Hôpital’s rule, Mean Value theorem, differential equations, and applied integration; Computational Methods adds linear programming; and Mechanics extends to moments and projectile motion.

Tips to Score High in NEB Mathematics Examination

  • Master Algebra first: Algebra is the largest content area and underpins almost every other topic. Be completely comfortable with functions, complex numbers, and matrices before advancing to calculus or analytic geometry.
  • Understand derivations rather than memorizing formulas: Many board questions directly ask for derivations — the quadratic formula, general solutions of trigonometric equations, Newton-Raphson iteration, trapezoidal and Simpson’s rules, integration by parts, and mechanics results. Writing them from first principles is both faster and more reliable than rote recall.
  • Practice calculus problems daily: Calculus topics (limits, derivatives, integration, and in Grade 12, differential equations) carry significant combined weight and reward the habit of daily structured practice — at least 3–5 problems per session.
  • Build a personal formula sheet chapter by chapter: Record every formula, key theorem, standard limit result, and integration formula in one organized notebook as you complete each topic. This becomes your most valuable revision tool before the exam.
  • Practice conic sections thoroughly (Grade 12): Conic sections (parabola, ellipse, hyperbola) is a major Grade 12 Analytic Geometry topic that introduces entirely new forms of problems. Work through all standard types of questions — finding focus, directrix, eccentricity, and tangent/normal equations.
  • Prioritize correlation and regression (Grade 12): These chapters involve both conceptual understanding and calculations (Karl Pearson’s coefficient, Spearman’s rank correlation, regression equations). They are consistently tested and relatively straightforward to score well in with systematic practice.
  • For linear programming (Grade 12), sketch accurately: Linear programming questions require constructing feasible regions graphically. Accurate, clearly labeled graphs are essential for full marks.
  • Bring the right instruments to the exam hall: The NEB Mathematics exam requires you to bring your own graph paper, log table, and geometry instruments (compass, protractor, ruler). Forgetting any of these puts specific question types at risk.

Frequently Asked Questions (FAQs)

How many topics are there in NEB Mathematics for Grade 11 and Grade 12?

Grade 11 Mathematics covers over 20 topics across eight content areas: Algebra (8 topics), Trigonometry (2), Analytic Geometry (3), Vectors (1), Statistics and Probability (2), Calculus (4), Computational Methods (2), and Mechanics (2). Grade 12 Mathematics covers 19 main topics (chapters) across the same eight content areas, plus Mathematics for Economics and Finance for Management stream students.

What is the prescribed textbook for NEB Mathematics?

The standard prescribed textbook is Basic Mathematics Grade XI (for Grade 11) and Basic Mathematics Grade XII (for Grade 12), both published by Sukunda Pustak Bhawan and authored by D.R. Bajracharya, R.M. Shrestha, M.B. Singh, Y.R. Sthapit, and B.C. Bajracharya. This is the primary study resource for both grades.

Is Mathematics compulsory or optional in NEB Grade 11 and 12?

Mathematics is offered as a compulsory alternative to Social Studies (Sol.005/Sol.006) for Science, Management, and Education stream students. Students who choose Mathematics instead of Social Studies take it as a required subject. It is also available as an additional optional subject for some streams.

How many teaching hours are allocated for NEB Mathematics?

Both Grade 11 and Grade 12 Mathematics are allocated 160 working hours each — more than Physics or Chemistry (128 hours each), reflecting the subject’s broad content coverage across eight areas.

Does NEB publish official chapter-wise marks distribution for Mathematics?

No. As with all NEB subjects, the official CDC syllabus document states that the teaching-hour grid is for time distribution purposes only, not marks allocation. Students should prepare across all content areas rather than selectively targeting specific chapters based on unofficial predictions.

Which Mathematics topics are most important for the board exam?

Based on teaching-hour allocation and consistent board paper patterns, Calculus (limits, derivatives, integration, and in Grade 12, differential equations) and Algebra (particularly complex numbers, quadratic equations, and in Grade 12, permutations/combinations and binomial theorem) consistently carry the highest combined marks. Conic Sections, Correlation and Regression, and Product of Vectors are also high-priority Grade 12 topics.

Where can I find Mathematics notes and important questions for Grade 11 and 12?

You can find Mathematics study resources on nneducation.com. Browse our courses from the Courses section. The official syllabus PDF is also embedded at the top of this page for your reference.

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