# Class 12 Maths

Class 12 maths is highly crucial for students to perform well in various competitive exams like IIT, JEE and others. In class 12 maths students continue to consolidate their understanding of secondary level math skills. Thus, learning class 12 maths requires students to have a deep conceptual knowledge of important skills acquired in previous grades.

## Class 12 Maths Syllabus

Students often find class 12 maths ambiguous due to the improper understanding of concepts and topics. To understand the various concepts and topics it is necessary to have a clear understanding of the complete syllabus covered under class 12 maths.

### SETS AND FUNCTIONS

**Sets**

Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of the set of real numbers, especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and intersection of sets. Difference of sets. Complement of a set, Properties of Complement sets.

**Relations and Functions**

Ordered pairs, Cartesian product of sets. Number of elements in the Cartesian product of two finite sets. Cartesian product of the reals with itself (upto R × R × R). Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation of a function, domain, co-domain and range of a function. Real valued function of the real variable, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum and greatest integer functions with their graphs. Sum, difference, product and quotients of functions.

**Trigonometric Functions**

Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin2x + cos2x = 1, for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin (x+ y) and cos (x + y) in terms of sin x, sin y, cos x and cos y. Deducing the identities.

### ALGEBRA

**Principle of Mathematical Induction (Periods 06)**

Process of the proof by induction, motivating the application of the method by looking at naturalnumbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications.

**Complex Numbers and Quadratic Equations**

Need for complex numbers, especially −1, to be motivated by inability to solve every quadratic equation. Brief description of algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system, Square-root of a Complex number.

**Linear Inequalities**

Linear inequalities, Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Solution of system of linear inequalities in two variables - graphically.

**Permutations and Combinations**

Fundamental principle of counting. Factorial n. Permutations and combinations derivation of formulae and their connections, simple applications.

**Binomial Theorem**

History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, general and middle term in binomial expansion, simple applications.

**Sequence and Series (Periods 10)**

Sequence and Series. Arithmetic Progression (A.P.), Arithmetic Mean (A.M.), Geometric Progression (G.P.), general term of a G.P., sum of n terms of a G.P. Arithmetic and geometric series, infinite G.P. and its sum, geometric mean (G.M.). Relation between A.M. and G.M. Sum to n terms of the special series.

### COORDINATE GEOMETRY

**Straight Lines (Periods 09)**

Brief recall of 2-D from earlier classes, shifting of origin. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axes, point-slope form, slope-intercept form, two-point form, intercepts form and normal form. General equation of a line. Equation of family of lines passing through the point of intersection of two lines. Distance of a point from a line.

**Conic Sections (Periods 12)**

Sections of a cone: Circles, ellipse, parabola, hyperbola, a point, a straight line and pair of

intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.

**Introduction to Three-dimensional Geometry (Periods 08)**

Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.

CALCULUS

Limits and Derivatives (Periods 18)

Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit.

## Develop class 12 Maths Skills

Class 12 maths is outlined to impart the knowledge of analytical and practical skills in students. It develops a basic understanding of applying maths, for instance, using trigonometric functions to calculate the height or applying algebraic formulas to solve real-life problems. Students can acquire an understanding of these class 12 maths concepts through various interactive activities and visualization. Here are some key class 12 maths skills that students need to develop.

**Trigonometric Functions**

Trigonometry functions and their applications are important topics covered under class 12 maths that students should understand and apply in solving various problems.

**Algebra**

Algebra is an important part of class 12 maths that enables students to write, read and apply expressions, rational numbers and polynomials. It also helps students to utilize these skills and knowledge to solve practical problems.

**Geometry**

It is important for students to understand the geometric transformation covered in class 12 maths that involves angles, circles, perpendicular lines, parallel lines, and line segments.

## Class 12 Maths Tips and Tricks

Practice Daily

Class 12 maths is crucial for developing higher-level maths skills thus students must practice daily and track their progress sincerely to improvise their skills.

**Practice Past Years Question Papers**

Practicing question papers from past years will help students to get an idea of the complexity level of the exam. It will also benefit students in enhancing their speed and accuracy

**Cover Full Syllabus**

Covering full syllabus of class 12 maths is a must for students to clarify all their doubts before exams.

**Refer Reliable Study material**

Refer reliable study material like NCERT Solutions and NCERT textbooks for the preparation of class 12 maths. These are the best preparation resources as the class 12 maths exam is set according to them.

visual curriculum