📘 Class 12 Basic Mathematics Solutions & Syllabus

Ch 1 Permutation & Combination 📑 Open Notes

Fundamental principle of counting, factorial notation, permutations (linear & circular), combinations, applications in real-life problems, and derivation of formulae. Includes NEB past questions.

Ch 2 Binomial Theorem 📑 Open Notes

Binomial expansion for positive integer index, general term, middle term, binomial coefficients, properties of binomial coefficients, and simple applications using Pascal’s triangle.

Ch 3 Complex Number 📑 Open Notes

Definition, algebra of complex numbers, conjugate, modulus, argument, polar form, De Moivre’s theorem, roots of complex numbers, and geometrical representation.

Ch 4 Sequence & Series 📑 Open Notes

Arithmetic progression (AP), geometric progression (GP), harmonic progression (HP), sum of n terms, arithmetic mean, geometric mean, infinite GP and applications.

Ch 5 Matrix Based System of Linear Equation 📑 Open Notes

Matrix notation, types of matrices, determinant, inverse, solving system of linear equations using matrix inversion and Cramer’s rule, row reduction method.

Ch 6 Properties of Triangle 📑 Open Notes

Sine rule, cosine rule, projection formula, tangent rule, half-angle formulae, circumcircle, incircle, exradii, and relation between sides and angles.

Ch 7 Solution of Triangle 📑 Open Notes

Solving triangles when three sides, two sides and included angle, two angles and side are given. Application of trigonometric identities in solving triangles (height & distance problems).

Ch 8 Conic Section 📑 Open Notes

General equation of conics: Circle, parabola, ellipse, hyperbola. Standard forms, eccentricity, focus, directrix, latus rectum, tangents, normals, and equations in shifted axes.

Ch 9 Product of Vectors 📑 Open Notes

Scalar (dot) product, vector (cross) product, scalar triple product, vector triple product, geometric interpretations, work done, area of parallelogram, volume of parallelepiped.

Ch 10 Correlation & Regression 📑 Open Notes

Bivariate data, scatter diagram, Karl Pearson’s correlation coefficient, Spearman’s rank correlation, regression lines, coefficient of determination, interpretation.

Ch 11 Probability 📑 Open Notes

Basic probability, laws of probability, conditional probability, independent events, Bayes’ theorem, random variables, expectation, and simple problems.

Ch 12 Derivatives 📑 Open Notes

Definition of derivative, rules of differentiation (product, quotient, chain rule), derivatives of algebraic, trigonometric, exponential, logarithmic functions, higher order derivatives.

Ch 13 Applications of Derivatives 📑 Open Notes

Geometrical meaning of derivative, tangent & normal, rate of change, maxima and minima, increasing/decreasing functions, concavity and optimization problems in real-life.

Ch 14 Antiderivatives 📑 Open Notes

Integration as inverse of differentiation, standard integrals, integration by substitution, integration by parts, definite integrals, properties of definite integrals.

Ch 15 Differential Equations 📑 Open Notes

Order and degree of differential equations, formation, solution of first order first degree DE: variable separable, homogeneous, linear differential equations (integrating factor).

Ch 16 System of Linear Equation 📑 Open Notes

Numerical methods to solve linear systems: Gaussian elimination, Gauss-Jordan method, iterative methods (Jacobi, Gauss-Seidel). Consistency of system.

Ch 17 Linear Programming 📑 Open Notes

Linear inequalities, graphical solution of linear programming problems (LPP), feasible region, corner point method, maximization and minimization problems, applications in business.

Ch 18 Statics 📑 Open Notes

Forces, equilibrium of coplanar forces, parallel forces, moments, couples, center of gravity, friction on horizontal and inclined planes, ladders, wedges.

Ch 19 Dynamics: Newton’s Law of Motion 📑 Open Notes

Newton’s laws of motion, impulse, conservation of momentum, motion under constant force, projectile motion, connected bodies, motion on smooth/inclined planes, pulley problems.