AP POLYCET Syllabus 2027: Mathematics, Physics, Chemistry Topics, Weightage and PDF Download

Euclid’s Division Lemma and Algorithm, Fundamental Theorem of Arithmetic, Proof of irrationality of √2, √3, and √5, Decimal representation of rational numbers, Terminating and non-terminating decimals.

Types of sets (empty, finite, infinite, equal, equivalent), Operations on sets (union, intersection, difference, complement), Venn diagrams and their applications, Cardinality of sets, De Morgan’s laws.

Zeroes of a polynomial and their geometric meaning, Relationship between zeroes and coefficients for linear, quadratic, and cubic polynomials, Division algorithm for polynomials, Factorisation using zeroes.

Graphical representation of a pair of linear equations, Algebraic methods — substitution, elimination, cross-multiplication, Consistent and inconsistent systems, Conditions for unique/no/infinite solutions, Word problems.

Standard form ax² + bx + c = 0, Solutions by factorisation, completing the square, and quadratic formula, Discriminant (D = b² − 4ac) and nature of roots, Word problems based on quadratic equations.

Arithmetic Progression (AP): nth term formula aₙ = a + (n−1)d, Sum of n terms Sₙ = n/2[2a + (n−1)d], Geometric Progression (GP): nth term, sum of n terms, common ratio, Arithmetic and geometric means, Word problems.

Distance formula, Section formula (internal and external division), Midpoint formula, Area of a triangle using vertex coordinates, Slope and collinearity of three points, Applications in geometry.

Basic Proportionality Theorem (Thales’ Theorem) and its converse, Criteria for similarity of triangles (AA, SSS, SAS), Ratio of areas of similar triangles, Pythagoras Theorem and its converse, Applications in real-life problems.

Tangent to a circle — definition and properties, Number of tangents from an external point, Tangent-secant relationship, Length of tangent from an external point, Angle in alternate segment.

Surface area and volume of cube, cuboid, cylinder, cone, sphere, and hemisphere, Surface area and volume of combined solids, Conversion of one solid to another, Frustum of a cone — lateral surface area and volume.

Trigonometric ratios: sin, cos, tan, cosec, sec, cot, Values at standard angles (0°, 30°, 45°, 60°, 90°), Trigonometric identities (sin²θ + cos²θ = 1 and derived forms), Ratios of complementary angles.

Angle of elevation and angle of depression, Heights and distances — single-triangle and two-triangle problems, Real-life applications involving towers, buildings, and inclined planes.

Classical probability and empirical probability, Sample space, events, and outcomes, Mutually exclusive and complementary events, Addition rule of probability, Impossible and certain events.

Mean, median, and mode of grouped data, Cumulative frequency distribution (less than and more than), Ogive curves — drawing and interpretation, Relationship between mean, median, and mode.

Thermal expansion (linear, area, volumetric), Specific heat capacity and calorimetry, Latent heat of fusion and vaporisation, Modes of heat transfer — conduction, convection, radiation, Newton’s law of cooling.

Laws of reflection, Types of mirrors (plane, concave, convex), Image formation by spherical mirrors (ray diagrams), Mirror formula (1/v + 1/u = 1/f) and sign convention, Magnification and its formula.

Laws of refraction, Snell’s law (n₁ sin i = n₂ sin r), Absolute and relative refractive index, Total internal reflection (TIR) and critical angle, Applications of TIR — optical fibres, diamonds, prisms.

Types of lenses (convex/converging, concave/diverging), Image formation by lenses (ray diagrams), Lens formula (1/v − 1/u = 1/f) and sign convention, Magnification, Power of a lens (P = 1/f), Combination of lenses.

Structure of the human eye and accommodation, Defects of vision (myopia, hypermetropia, astigmatism, presbyopia) and corrections, Tyndall effect and Rayleigh scattering, Atmospheric refraction and its effects, Dispersion of white light and rainbow formation.

Electric charge, current, potential difference, and EMF, Ohm’s law and its limitations, Resistance and resistivity, Series and parallel combination of resistors, Heating effect of electric current (Joule’s law), Electric power (P = VI) and energy.

Magnetic field due to a straight current-carrying conductor and circular loop, Solenoid and its magnetic field, Right-hand thumb rule, Force on a current-carrying conductor in a magnetic field, Fleming’s left-hand rule, Working of an electric motor.

Faraday’s laws of electromagnetic induction, Lenz’s law, Fleming’s right-hand rule, AC generator and DC generator, Transformers (step-up and step-down), Advantages of AC over DC for power transmission.

Formation of coal and petroleum (fossil fuels), Types and grades of coal, Fractional distillation of petroleum and its products, Natural gas and its uses, Conservation of fossil fuels, Environmental impact.

Types of chemical reactions (combination, decomposition, displacement, double displacement, redox), Balancing chemical equations, Effects of heat, light, and electricity on reactions, Exothermic and endothermic reactions.

Properties and reactions of acids and bases, Neutralisation reaction, pH scale and its significance, Preparation and uses of important salts (NaCl, NaOH, Na₂CO₃, NaHCO₃, bleaching powder), Olfactory indicators.

Discovery of electrons, protons, and neutrons, Rutherford’s model and its limitations, Bohr’s model of the atom, Electronic configuration and shells (K, L, M, N), Atomic number and mass number, Isotopes and isobars.

Mendeleev’s periodic law and its limitations, Modern periodic law and the long-form periodic table, Groups and periods, Periodic trends — atomic radius, ionisation enthalpy, electronegativity, metallic and non-metallic character.

Ionic bond (electron transfer) and conditions for formation, Covalent bond (electron sharing), Lewis dot structures for molecules, Properties of ionic vs covalent compounds, Polar and non-polar covalent bonds.

Classical definitions and electron-transfer definitions of oxidation and reduction, Oxidising agents and reducing agents, Oxidation states and rules for assigning them, Balancing simple redox reactions, Applications (bleaching, corrosion, combustion).

Bonding in carbon — catenation and tetravalency, Allotropes of carbon (diamond, graphite, fullerene), Hydrocarbons (alkanes, alkenes, alkynes), Functional groups (-OH, -CHO, -COOH, -NH₂), IUPAC nomenclature, Chemical reactions (combustion, addition, substitution, oxidation), Soaps, detergents, and their cleaning action.

Minerals and ores — distinction, Concentration of ores (gravity separation, froth flotation), Extraction of iron, aluminium, copper, and zinc, Refining of metals, Reactivity series and its applications, Alloys and their uses, Corrosion and its prevention.

Physical and chemical properties of water, Hard water vs soft water — causes and effects, Methods of softening hard water (boiling, lime treatment, ion exchange), Water purification methods, Water pollution and conservation.

Types of solutions (solid-solid, liquid-liquid, gas-liquid), Solubility and factors affecting it (temperature, pressure), Concentration expressions — mass percent, molarity, Saturated, unsaturated, and supersaturated solutions, Henry’s law, Colligative properties (qualitative understanding).