Syllabus of XII Grade

Introduction:

The twelfth grade mathematics program is something that acquaints a person with the future scenario a student may face in future. The course structure of 12^th grade Mathematics program is precisely concentrated to give an overview of the broader mathematical fields that a student may get into in his or her higher studies. A student interested in pursuing mathematics in 12^th grade has wider prospects in higher studies and a much better career opportunity. A mathematics scholar of 12^th grade can opt from a wider choice of streams such as engineering, accountancy, graduation with mathematics which can further lead to career in research and development in premier organizations which deal with scientific operations.

The course structure of 12^th grade mathematics program is designed to meet the requirements to built a strong base for the future. There are eleven fields of mathematics that are dealt in basic in the 12^th grade math program. These eleven chapters are Algebra i, Algebra ii, Geometry and Measurement, Probability and Statistics, Ap Probability and Statistics, Trigonometry, Pre-calculus, Calculus, Linear Algebra, Mathematical Analysis and Mathematical Models with Applications.

1) Algebra: Let's first see what Algebra is all about. It's the branch of mathematics dealing with the study of the rules of operations and relations. It formats the constructions and concept that comes out, by the help of polynomials, equations and algebraic structures. Algebra is one of the most vital branch of mathematics.

Algebra has been divided into two distinct sub topics in 12^th grade mathematics:

Algebra (I)

Algebra (II)

Algebra (I) constitutes of sub-topics that show computational works on theoretical mathematical calculations and proofs. They are Linear equations/inequalities, Monomials and polynomials, Factoring second and third degree polynomials, Rational expressions/functions, Quadratic equations, Quadratic functions Exponents, factors, variation, exponential growth/decay, Hypothesis, counter examples, Correlation for data Patterns, relations, functions, Changing parameters of given functions, Graphs, matrices, sequences, series, recursive relations, Radical equations/inequalities and Limits and infinity.

Algebra (II) deals with the sub-topics that are related to higher engineering mathematics. These sub topics are Absolute value to solve equations/inequalities, Systems of linear equations/inequalities, Operations on polynomials, Factoring polynomials/trinomials, Operations on complex numbers, Operations on rational expressions, Graphing quadratic equations, Quadratic equations in complex number system, Quadratic functions, Laws and properties of logarithms, Fractional exponents, exponential functions, Conic sections, Ellipse, parabola, hyperbola, Binomial theorem, Types of series, Composition of functions, Continuous and discrete functions, Complex numbers for solutions of quadratic equations, Factoring, exponents, Systems of equations/inequalities, Estimation of solutions, Standard functions, Inverse of a function, Solutions of function equations and Slope, various forms of equation of line.

2) Geometry and Measurement: This topic deals with graphical and geometrical representations algebraic expressions and calculations of phenomena related to geometrical structures.
For this given task Geometry and Measurement has the given constituent subtopics that are, Logical reasoning, Geometric proofs, Euclidean/non-Euclidean geometries, Formal/informal proofs, Conditional statements, Pythagorean Theorem, Intersection of a plane with 3-d figures, Congruence, similarity, triangle inequality theorem, Properties of quadrilaterals, circles, parallel lines cut by a transversal, Angles of triangles and polygons, Basic constructions, Triangle congruence relationships, Similarity properties and transformations, trigonometric ratios, Pythagorean triples, Coordinate geometry, Special right triangles, Properties of inscribed/circumscribed polygons of circles, Rotations, translations, reflections, Planar cross-sections; perpendicular lines/planes, Effect of rigid motions on figures, isosceles triangle theorem; polyhedra, Parabolic functions (vertex, axis of symmetry) and Compound loci in the coordinate plane,

3) Probability and Statistics: Probability and Statistics is the branch of mathematics that measures the likeliness that a random event will occur or not.

Two topics in 12^th grade mathematics deals with the course of probability and statistics :

Probability and Statistics

Ap Probability and Statistics

Probability and Statistics: Probability and Statistics is an introduction to the field of the probability with mathematical concept and has the sub topics such as Types of events, Measures of central tendency/dispersion, quartiles, interquartiles, Permutations and combinations, Methods of data representation, Statistical experiments (more than one variable) and Correlation and causation.

Ap Probability and Statistics: Ap Probability and Statistics is the higher and more complex version of probability. It teaches to apply the mathematical approach to the probability problems. The sub topics under this heading are Probability problems with finite sample spaces, conditional probability worksheet, Discrete/continuous random variables, Mean, variance of discrete random variable , Standard distributions, Mean, standard deviation of normally distributed random variable, Central limit theorem, Line of best fit - least squares regression, Correlation coefficient, Statistics of a distribution, Mean, standard deviation of sampling distribution, Mean, standard deviation of population distribution, Confidence intervals, P-value for a statistics and Chi-square distribution/test.

Trigonometry: In trigonometry, students will study triangles and the relations between their sides and the acquired angles. Trigonometry is all about trigonometric functions showing relations and its applications to cyclical phenomena for example waves. For this topic, several subtopics that a person may deal with are Graphing functions, Trigonometric functions, Formulas for sines and cosiness, Polar/rectangular coordinates, Complex numbers in polar form, DeMoivre's theorem, Inverse, trigonometric functions and Area of triangle (one angle and 2 adjacent sides).

Pre-calculus and Calculus: In these two topics, a 12^th grade student will firstly go through Pre-calculus, get acquainted with several terms and fundamentals that are used in Calculus. And, then he or she shall get into an interesting journey of Calculus that brings differentiations and integrations of expressions.
Pre-calculus has sub topics like Limits of sequences, series, Continuity, end behavior, asymptotes, limits, Regression, Law of Sines/Cosines, area formulas, Parametric/rectangular forms of functions

Vectors, Even/odd functions, significant values, Functions and operations, Conic sections- applications and Sequences and series.

Calculus, after going through pre-calculus, may get easier for a being and he or she shall easily understand calculus topics like Limits- operations on functions, Continuity of a function, Intermediate value, extreme value theorem, Derivatives, differentiability, Derivatives of functions

Chain rule, Rolle's theorem, mean value theorem, and L'Hopital's rule, Maxima, minima, inflection points, intervals, Newton's method (approximating the zeros of a function), Differentiation to solve problems, Definite/indefinite integrals, Riemann sums, Fundamental theorem of calculus, Definite integrals problems, Techniques of integration, Inverse trigonometric functions, Integrals of functions, Simpson's rule, Newton's method, Improper integrals (limits of definite integrals), Tests for convergence/divergence of sequences/series, Power series, Taylor series/polynomials and Elementary differential equations.

Linear Algebra: Linear algebra deals with vector spaces, also called linear spaces, along with linear functions that input one vector and output another. So, this topic deals with Types of linear systems, Gauss-Jordan elimination, Gauss-Jordan method, Vectors and vector addition, Geometrical solution sets of systems of equations, Rectangular matrices to row echelon form, Matrix multiplication, Inverse to a square matrix, Determinants of 2 by 2 and 3 by 3 matrices, Row reduction methods, Cramer's rule and Scalar (dot) product.

Mathematical Analysis: Mathematical Analysis is a branch of mathematics that consist s of the theories of differentiation, integration and measure, limits, infinite series and analytic functions. Various forms of complex numbers, Mathematical induction, Roots and poles of rational functions

Graphing rational functions – asymptotes and Limits of sequence/function are the sub topics that are studied under this topic.

Mathematical Models with Applications: The mathematical model is a study of a system using mathematical concepts and language. This section covers Theoretical/empirical probability , Probability models, Studying patterns and analyzing data, Rates, linear functions, direct/inverse variation, Problems related to personal income, credit, financial planning, Transformations and symmetry.

Best of luck for your foundational step into the world of mathematics towards the brightest future ever!

In upcoming posts we will discuss about Polynomials in XII Grade and interquartiles. Visit our website for information on Tamilnadu education board