AP POLYCET Syllabus 2027: SSC Class 10 Based, Subject Wise Topics and PDF Download

Euclid’s Division Lemma, Fundamental Theorem of Arithmetic, LCM and HCF, rational and irrational numbers, decimal expansions of rational numbers.

Set notation and representation, types of sets (finite, infinite, equal, null, singleton), union, intersection, complement, difference of sets, Venn diagrams, practical applications.

Degree and types of polynomials, zeroes of a polynomial, relationship between zeroes and coefficients, division algorithm, factorization.

Graphical representation, consistency of equations, algebraic methods: substitution, elimination, cross-multiplication, word problems.

Standard form, factorization method, completing the square, quadratic formula, nature of roots using discriminant (D = b² – 4ac), word problems.

Arithmetic Progression (AP): definition, general term aₙ = a + (n – 1)d, sum of first n terms Sₙ = n/2 [2a + (n – 1)d], word problems.

Distance formula, section formula (internal and external), midpoint formula, area of a triangle using coordinates, collinearity of points.

Similarity criteria (AA, SSS, SAS), Basic Proportionality Theorem and its converse, Pythagoras theorem and its converse, applications.

Tangent and secant definitions, tangents from an external point, tangent-radius perpendicularity, chord-angle relationships, area of sector and segment.

Surface area and volume of: cube, cuboid, cylinder, cone, sphere, hemisphere, frustum; problems on combination of solids; conversion of one solid to another.

Trigonometric ratios (sin, cos, tan, cot, sec, cosec), reciprocal identities, Pythagorean identities (sin²θ + cos²θ = 1 etc.), standard angle values (0°, 30°, 45°, 60°, 90°), trigonometric tables.

Angle of elevation, angle of depression, heights and distances word problems, problems with two right triangles in the same vertical plane.

Classical definition, sample space and events, sure and impossible events, complementary events, probability formula P(E) = favourable / total outcomes, problems on cards, dice, and coins.

Mean (direct method, assumed mean method, step deviation method), median and mode for grouped data, cumulative frequency distribution, ogive curves.

Temperature scales (Celsius and Kelvin), thermal expansion of solids, liquids, and gases, specific heat capacity, calorimetry, latent heat, methods of heat transfer: conduction, convection, and radiation with real-life examples.

Laws of reflection, types of mirrors (plane, concave, convex), key terms (pole, focus, centre of curvature, principal axis), mirror formula (1/v + 1/u = 1/f), magnification, sign convention, ray diagrams for image formation.

Laws of refraction (Snell’s law), refractive index, total internal reflection and critical angle, refraction through a glass slab (lateral displacement), dispersion of light through a prism.

Convex and concave lenses, key terms (optical centre, principal focus), lens formula (1/v – 1/u = 1/f), power of a lens P = 1/f, magnification, ray diagrams, lens combinations.

Structure and parts of the human eye, accommodation, defects of vision: myopia, hypermetropia, and presbyopia; correction using appropriate lenses, formation of a rainbow, atmospheric refraction.

Electric charge and current, potential difference, EMF, Ohm’s law (V = IR), factors affecting resistance, resistors in series and parallel with equivalent resistance formulae, Joule’s law of heating, electrical power P = VI = I²R = V²/R, domestic electrical energy.

Magnetic field due to a current-carrying conductor, right-hand thumb rule, Fleming’s left-hand rule, Faraday’s laws of electromagnetic induction, Fleming’s right-hand rule, working of DC motor and AC generator, AC vs DC.

Writing and balancing chemical equations, types of reactions: combination, decomposition, single displacement, double displacement, and oxidation-reduction (redox) reactions with examples.

Properties of acids and bases, acid-base indicators (litmus, phenolphthalein, methyl orange), pH scale, neutralization reactions, important salts: baking soda (NaHCO₃), washing soda (Na₂CO₃), plaster of Paris.

Physical and chemical properties of metals and non-metals, reactivity series, ionic bond formation, extraction of metals from ores, corrosion and its prevention by galvanization, painting, and alloying.

Covalent bonding, versatile nature of carbon (catenation and tetravalency), functional groups (alcohol, aldehyde, ketone, carboxylic acid, halide), homologous series, IUPAC nomenclature, properties of ethanol and ethanoic acid, soaps and detergents.

Döbereiner’s triads, Newlands’ law of octaves, Mendeleev’s periodic table and its limitations, Modern periodic law, Modern periodic table structure, periodic trends: atomic radius, ionization energy, electronegativity, and valency.

Ionic (electrovalent) bonds, covalent bonds, metallic bonds, Lewis dot structures, electrovalency and covalency, polar and non-polar covalent bonds, properties of ionic vs covalent compounds.

Physical and chemical properties of water, hard and soft water, temporary and permanent hardness, methods of removing hardness (boiling, addition of lime, Clark’s process, ion exchange resin), water purification.

Types of solutions, solute and solvent, solubility and factors affecting it, concentration expressions (mass percentage, molarity), true solutions vs colloidal solutions vs suspensions.