**Linear inequalities class 11 Commerce ncert solutions**

**linear inequalities class 11 Commerce ncert solutions: **The CBSE board has etched an indelible position owing to its well-revised educational programs. It aims to give valuable learning to students so that they can attain zenith of success in their academic career.

After class 10 exams, students get options to select an ideal stream out of three different streams including science, arts, and commerce. Apart from science and arts stream, many students opt for commerce as a suitable career option.

Commerce is a popular subject among students especially for those, who want to pursue a career in banking, trade and business domains.

The CBSE commerce subjects class 11 are English, Maths, Business Studies, Accounts, Economics, Multimedia, Psychology, Painting, Physical Education, etc.

Students can easily collect well-evaluated syllabus and sample papers of the CBSE subjects for Class 11 commerce online.

Mathematics is an old, broad, and deep discipline (field of study). People working to improve math education need to understand.

Mathematics as a formal area of teaching and learning was developed about 5,000 years ago by the Sumerians.

They did this at the same time as they developed reading and writing. However, the roots of mathematics go back much more than 5,000 years. Throughout their history, humans have faced the need to measure and communicate about time, quantity, and distance.

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**Linear inequalities class 11 Commerce ncert solutions Mathematics as a Discipline**

**linear inequalities class 11 Commerce ncert solutions: **A discipline (an organized, formal field of study) such as mathematics tends to be defined by the types of problems it addresses, the methods it uses to address these problems, and the results it has achieved. One way to organize this set of information is to divide it into the following three categories (of course, they overlap each other):

**Mathematics as a human endeavor.**For example, consider the math of measurement of time such as years, seasons, months, weeks, days, and so on. Or, consider the measurement of distance, and the different systems of distance measurement that developed throughout the world. Or, think about math in art, dance, and music. There is a rich history of the human development of mathematics and mathematical uses in our modern society.**Mathematics as a discipline.**You are familiar with lots of academic disciplines such as archaeology, biology, chemistry, economics, history, psychology, sociology, and so on. Mathematics is a broad and deep discipline that is continuing to grow in breadth and depth. Nowadays, a Ph.D. research dissertation in mathematics is typically narrowly focused on definitions, theorems, and proofs related to a single problem in a narrow subfield in mathematics.**Mathematics as an interdisciplinary language and tool.**Like reading and writing, math is an important component of learning and “doing” (using one’s knowledge) in each academic discipline. Mathematics is such a useful language and tool that it is considered one of the “basics” in our formal educational system.

**linear inequalities class 11 Commerce ncert solutions**

**linear inequalities class 11 Commerce ncert solutions: **To a large extent, students and many of their teachers tend to define mathematics in terms of what they learn in math courses, and these courses tend to focus on #3.

The instructional and assessment focus tends to be on basic skills and on solving relatively simple problems using these basic skills. As the three-component discussion given above indicates, this is only part of mathematics.

Even within the third component, it is not clear what should be emphasized in curriculum, instruction, and assessment. The issue of basic skills versus higher-order skills is particularly important in math education.

How much of the math education time should be spent in helping students gain a high level of accuracy and automatically in basic computational and procedural skills?

How much time should be spent on higher-order skills such as problem posing, problem representation, solving complex problems, and transferring math knowledge and skills to problems in non-math disciplines?

**Download Class 11 commerce ncert solution of linear inequalities in PDF Format.**

**class 11 Commerce Maths ncert Syllabus **

**Unit-I: Sets and Functions**

**Sets****(20 Periods):-**Sets and their representations.Empty set.Finite and Infinite sets.Equal sets.Subsets.Subsets of a set of real numbers especially intervals (with notations). Powerset. Universal set. Venn diagrams. Union and Intersection of sets.The difference of sets. The complement of a set. Properties of Complement Sets.**Relations & Functions:****(20 Periods):-**Ordered pairs, the Cartesian product of sets.The number of elements in the cartesian product of two finite sets. Cartesian product of the set of reals with itself (up to R x R x R). Definition of relation, pictorial diagrams, domain, co-domain, and range of a relation. Function as a special type of relation. Pictorial representation of a function, domain, co-domain, and range of a function. Real-valued functions, domain, and range of these functions, constant, identity, polynomial, rational, modulus, Signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product, and quotient of functions.**Trigonometric Functions:****(20 Periods):-**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. Signs of trigonometric functions. Domain and range of trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple applications.

**Unit-II: Algebra**

**The principle of Mathematical Induction:****(10 Periods):-**Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications.**Complex Numbers and Quadratic Equations****(15 Periods):-**Need for complex numbers, especially {tex}\surd -1{/tex}, to be motivated by an inability to solve some of the quadratic equations. Algebraic properties of complex numbers.Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, a solution of quadratic equations (with real coefficients) in the complex number system. The square root of a complex number.**Linear Inequalities****(15 Periods):-**Linear Inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line.Graphical representation of linear inequalities in two variables.Graphical method of finding a solution of the system of linear inequalities in two variables.**Permutations and Combinations****(10 Periods):-**Fundamental principle of counting. Factorial*n.*(n!) Permutations and combinations, derivation of formulae for {tex}{{n}_{{{p}_{r}}}}{/tex} and {tex}{{n}_{{{c}_{r}}}}{/tex} and their connections, simple applications.**Binomial Theorem****(10 Periods):-**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****(10 Periods):-**Sequence and Series. Arithmetic Progression (A. P.). Arithmetic Mean (A.M.) Geometric Progression (G.P.), general term of a G.P., sum of first*n*terms of a G.P., infinite G.P., and its sum, geometric mean (G.M.), relation between A.M. and G.M. Formulae for the following special sums

**Unit-III: Coordinate Geometry**

**Straight Lines****(10 Periods):-**Brief recall of two-dimensional geometry from earlier classes. Shifting of origin. The slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, point-slope form, slope intercept form, two-point form, intercept form and normal form. The general equation of a line.The equation of the family of lines passing through the point of intersection of two lines.The distance of a point from a line.**Conic Sections****(20 Periods):-**Sections of a cone: circle, ellipse, parabola, hyperbola, a point, a straight line and a 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****(10 Periods):-**Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. The distance between two points and section formula.

**Unit-IV: Calculus**

**Limits and Derivatives****(30 Periods):-**Derivative introduced as the rate of change both as that of distance function and geometrically.The intuitive idea of the limit.Limits of polynomials and rational functions trigonometric, exponential and logarithmic functions. Definition of derivative relates it to the scope of the tangent of the curve, Derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

**Unit-V: Mathematical Reasoning**

**Mathematical Reasoning****(10 Periods):-**Mathematically acceptable statements. Connecting words/ phrases – consolidating the understanding of “if and only if (necessary and sufficient) condition”, “implies”, “and/or”, “implied by”, “and”, “or”, “there exists” and their use through variety of examples related to real life and Mathematics. Validating the statements involving the connecting words, Difference between contradiction, converse, and contrapositive.

**Unit-VI: Statistics and Probability**

**Statistics****(15 Periods):-**Measures of dispersion: Range, mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances.**Probability****(15 Periods):-**Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set-theoretic) probability, connections with other theories studied in earlier classes. The probability of an event, the probability of ‘not’, ‘and’ and ‘or’ events.

**Conclusion linear inequalities class 11 Commerce ncert solutions**

**linear inequalities class 11 Commerce ncert solutions: **In this article, we discussed all information about linear **inequalities class 11 Commerce ncert solutions**, the points are –

**About linear inequalities class 11 Commerce ncert solutions****Syllabus of class xi math.****Class 11 commerce ncert solution of linear inequalities in PDF Format.**

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