UP Board Syllabus 2027: Subject-Wise Topics, Weightage and PDF Download

Real Numbers; Euclid’s Division Lemma; Fundamental Theorem of Arithmetic; decimal expansions of rational numbers (terminating and non-terminating recurring); proof of irrationality of √2, √3, √5

Polynomials: Zeros of a polynomial; relationship between zeros and coefficients of quadratic polynomials; division algorithm for polynomials.

Pair of Linear Equations in Two Variables: Graphical method; algebraic methods — substitution, elimination, cross-multiplication; equations reducible to linear form.

Quadratic Equations: Standard form ax² + bx + c = 0; solutions by factorisation, completing the square, and quadratic formula; discriminant and nature of roots.

Arithmetic Progressions: nth term; sum of first n terms; application problems.

Distance formula; Section formula (internal and external division); Area of a triangle using coordinates; Collinearity of three points

Triangles: Similarity criteria (AA, SSS, SAS); Basic Proportionality Theorem and its converse; Pythagoras Theorem and its converse; areas of similar triangles.

Circles: Tangent to a circle; number of tangents from an external point; equal tangents; tangent-radius perpendicularity.

Constructions: Division of a line segment in a given ratio; tangents to a circle from an external point.

Trigonometric Ratios: sin, cos, tan, cosec, sec, cot; standard angle values (0°, 30°, 45°, 60°, 90°); relationships between ratios.

Trigonometric Identities: sin²A + cos²A = 1; 1 + tan²A = sec²A; 1 + cot²A = cosec²A; applications in simplification and proof.

Heights and Distances: Angle of elevation; angle of depression; word problems on a single plane.

Areas Related to Circles: Area of sector and segment; areas of combinations of plane figures.

Surface Areas and Volumes: Combinations of any two solids (cuboid, cone, cylinder, sphere, hemisphere); conversion of solid from one shape to another; frustum of a cone.

Statistics: Mean, median, mode of grouped data; cumulative frequency distribution; ogive curves; comparison of two distributions.

Probability: Classical definition; simple problems on single events (not using set notation).

Relations and Functions: Types of relations — reflexive, symmetric, transitive, equivalence; types of functions — one-one, onto, bijective; composition; inverse of a function.

Inverse Trigonometric Functions: Definition, domain, range, principal value branches; graphs; elementary properties; problems on sin⁻¹, cos⁻¹, tan⁻¹ and their combinations.

Matrices: Types (zero, identity, diagonal, symmetric, skew-symmetric, triangular); operations (addition, scalar multiplication, matrix multiplication); non-commutativity; invertible matrix; uniqueness of inverse.

Determinants: Determinant of square matrices up to 3×3; properties; minors and cofactors; adjoint; inverse of a non-singular matrix; solution of system of linear equations by matrix method.

Continuity and Differentiability: Continuity; differentiability; chain rule; implicit differentiation; exponential and logarithmic functions; logarithmic differentiation; parametric differentiation; second-order derivatives; Rolle’s Theorem; Lagrange’s Mean Value Theorem.

Applications of Derivatives: Rate of change; increasing and decreasing functions; tangents and normals; approximations; maxima and minima — first and second derivative tests.

Integrals: Integration as inverse of differentiation; integration by substitution, by parts, by partial fractions; Bernoulli’s rule; definite integrals; properties of definite integrals; Fundamental Theorem of Calculus.

Applications of Integrals: Area under simple curves (line, circle, parabola, ellipse); area between two curves.

Differential Equations: Order and degree; general and particular solutions; formation; variable separable method; homogeneous differential equations; linear differential equations of first order.

Vectors: Vectors and scalars; magnitude and direction; direction cosines and direction ratios; types of vectors; position vector; addition; scalar multiplication; dot product; cross product; scalar triple product; geometrical applications.

Three-Dimensional Geometry: Direction cosines and direction ratios of a line; equation of a line in Cartesian and vector form; angle between two lines; skew lines; shortest distance between two skew lines; equations of a plane; angle between two planes; distance of a point from a plane; coplanarity of two lines.

Introduction; terminology (objective function, constraints, feasible region, corner points); graphical method of solution for problems in two variables; feasible and infeasible regions; bounded and unbounded regions; optimal feasible solution; types of LP problems (manufacturing, diet, transportation) with up to three non-trivial constraints.

Conditional probability; multiplication theorem; independent events; total probability; Bayes’ theorem; random variable and its probability distribution; mean and variance of a random variable; Bernoulli trials; Binomial distribution — mean, variance, and problems.

Chemical reactions and equations; types of chemical reactions; Acids, bases and salts; Metals and non-metals; Carbon and its compounds — functional groups, homologous series; Periodic classification of elements

Life processes — nutrition, respiration, transportation, excretion; Control and coordination — nervous system, hormones; Reproduction — asexual and sexual reproduction in plants and humans; Heredity and evolution — Mendel’s laws, sex determination, Darwin’s theory

Reflection of light; spherical mirrors — mirror formula; Refraction of light — glass slab and prism; Lenses — lens formula, power; Human eye — structure, defects and correction; Scattering of light — Tyndall effect, colour of sky

Ohm’s Law; resistance; series and parallel combination; electric power; heating effect; Magnetic effects of electric current — Oersted’s experiment, electric motor; Faraday’s law of electromagnetic induction; domestic electric circuits

Sources of energy — conventional and non-conventional; Our environment — food chain, trophic levels, ozone depletion; Management of natural resources — forests, water, coal and petroleum

Sandhi (joining of words); Samas (compound words); Alankar (figures of speech); Ras (emotional essence in poetry); Chhand (metre); Paryayvachi Shabd (synonyms); Vilom Shabd (antonyms); Muhavare and Lokoktiyan (idioms and proverbs); Vakya Shuddhi (sentence correction); one-word substitutions

Tenses (all forms); Active and Passive Voice; Direct and Indirect Speech; Modals; Prepositions; Determiners; Subject-Verb Agreement; transformation of sentences; error identification and correction; fill-in-the-blanks

The Rise of Nationalism in Europe; Nationalism in India (Non-Cooperation, Civil Disobedience movements); The Making of a Global World; The Age of Industrialisation; Print Culture and the Modern World

Resources and Development; Forest and Wildlife Resources; Water Resources; Agriculture; Minerals and Energy Resources; Manufacturing Industries; Lifelines of National Economy (transport, communication, trade)

Power Sharing; Federalism; Democracy and Diversity; Gender, Religion and Caste; Popular Struggles and Movements; Political Parties; Outcomes of Democracy; Challenges to Democracy

Development; Sectors of the Indian Economy; Money and Credit; Globalisation and the Indian Economy; Consumer Rights

Reproduction in organisms (asexual, sexual); Sexual reproduction in flowering plants (pollination, fertilisation, seed and fruit development); Human reproduction (male and female systems, gametogenesis, fertilisation, embryo development); Reproductive health (contraception, STDs, ART)

Heredity and variation (Mendel’s laws, chromosomal theory, linkage and crossing over, sex determination, mutations); Molecular basis of inheritance (DNA structure, replication, transcription, translation, gene regulation — lac operon); Evolution (origin of life, Darwinism, Hardy-Weinberg principle, adaptive radiation, human evolution)

Human health and disease (common diseases, immunity, vaccines, cancer, AIDS, drugs and alcohol); Strategies for food production (animal husbandry, plant breeding, single cell protein, tissue culture); Microbes in human welfare (biogas production, sewage treatment, industrial products, biocontrol agents)

Principles and processes of biotechnology (recombinant DNA technology, PCR, gel electrophoresis, cloning vectors, competent host); Applications (GMOs in agriculture, transgenic animals, bioremediation, gene therapy, ELISA, Bt cotton, Golden Rice)

Organisms and populations (niches, population interactions); Ecosystem (structure, productivity, energy flow, nutrient cycling — carbon and phosphorus cycles); Biodiversity and conservation (hotspots, endangered species, IUCN categories, in-situ and ex-situ conservation); Environmental issues (pollution, global warming, ozone depletion, biomagnification)