ECAT (Engineering) 10-Day Plan

Natural numbers, integers, rational, irrational, real numbers, surds, and operations on different number sets.

Algebraic expressions, polynomials, factorization, simultaneous equations, and algebraic identities.

Solution of quadratic equations by factorization, completing square, and quadratic formula.

Trigonometric ratios, identities, solving triangles, heights and distances, and applications.

Cartesian system, distance formula, section formula, equation of lines, slope, and conic sections.

Lines, angles, triangles, quadrilaterals, circles, polygons, congruence, similarity, and theorems.

Area and perimeter of 2D shapes, surface area and volume of 3D solids.

Set theory, Venn diagrams, operations on sets, types of functions, domain, range, and inverse functions.

SI units, dimensional analysis, measurement techniques, and precision in physical quantities.

Motion in one and two dimensions, displacement, velocity, acceleration, and equations of motion.

Newtons three laws of motion, friction, momentum, impulse, and their applications.

Work done by forces, kinetic and potential energy, conservation of energy, and power.

Centripetal force, orbital motion, gravitational field, and Keplers laws.

Fluid statics, Pascals law, Archimedes principle, Bernoullis equation, and fluid dynamics.

Simple harmonic motion, wave properties, sound waves, and wave equation analysis.

Heat transfer, specific heat, thermodynamics laws, entropy, and heat engine efficiency.

Electron configuration, atomic orbitals, quantum numbers, and periodic properties of elements.

Ionic, covalent, metallic bonds, VSEPR theory, hybridization, and molecular geometry.

Gaseous state (gas laws), liquid state, solid state (crystal structures), and phase transitions.

Internal energy, enthalpy, Hess law, entropy, Gibbs free energy, and spontaneity.

Reversible reactions, equilibrium constant, Le Chateliers principle, and equilibrium factors.

pH scale, buffer solutions, indicators, neutralization, hydrolysis, and titrations.

Redox reactions, electrochemical cells, Nernst equation, electrolysis, and corrosion.

Reaction rates, rate laws, order of reactions, activation energy, and collision theory.