**CBSE class 11 commerce Maths fast track revision notes**

**CBSE class 11 commerce Maths fast track revision notes**:- we will provide complete details of CBSE class 11 commerce Maths fast track revision notes in this article.

**CBSE class 11 commerce Maths fast track revision notes**

CBSE Class 11 Commerce Maths Mathematical Reasoning : CBSE conducts the final examinations for Class 10 and Class 12 every year in the month of March. The results are announced by the end of May. The board earlier conducted the AIEEE Examination for admission to undergraduate courses in engineering and architecture in colleges across India. However the AIEEE exam was merged with the IIT-Joint Entrance Exam (JEE) in 2013. The common examination is now called JEE (Main).

CBSE also conducts AIPMT (All India Pre Medical Test) for admission to major medical colleges in India. In 2014, the conduct of the National Eligibility Test for grant of junior research fellowship and eligibility for assistant professor in institutions of higher learning was outsourced to CBSE. Apart from these tests, CBSE also conducts the central teachers eligibility test and the Class X optional proficiency test. With the addition of NET in 2014, the CBSE has become the largest exam conducting body in the world

**CBSE class 11 commerce Maths fast track revision notes**

CBSE Class 11 Commerce Maths Mathematical Reasoning : Mathematics can, broadly speaking, be subdivided into the study of quantity, structure, space, and change (i.e. arithmetic, algebra, geometry, and analysis). In addition to these main concerns, there are also subdivisions dedicated to exploring links from the heart of mathematics to other fields: to logic, to set theory (foundations), to the empirical mathematics of the various sciences (applied mathematics), and more recently to the rigorous study of uncertainty. While some areas might seem unrelated, the Langlands program has found connections between areas previously thought unconnected, such as Galois groups, Riemann surfaces and number theory

**Complete Details Of CBSE Class 11 Commerce Maths Mathematical Reasoning**

CBSE Class 11 Commerce Maths Mathematical Reasoning : We provides here CBSE Class 11 Commerce Maths Calculus Important topics and Free download notes for CBSE Class 11 Commerce Maths Calculus in Pdf Format. Download these files and read well.

**Unit-V: Mathematical Reasoning**

**1. Mathematical Reasoning**

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 contraceptive.

Download here pdf format CBSE Class 11 Commerce Maths Mathematical Reasoning

**CBSE class 11 commerce Maths fast track revision notes**

CBSE Class 11 Commerce Maths Mathematical Reasoning : Every lesson is followed with a variety of fun, colorful activities to ensure concept mastery. The lessons and activities spiral slowly, allowing students to become comfortable with concepts, but also challenging them to continue building their problem-solving skills. These books teach more than mathematical concepts; they teach mathematical reasoning, so students learn to devise different strategies to solve a wide variety of math problems. All books are written to the standards of the National Council of Teachers of Mathematics.

**Logic**

Logic is the subject that deals with the method of reasoning. It provides us rules for determining the validity of a given argument in proving theorem.

**Statement (Proposition)**

A statement is an assertive sentence which is either true or false but not both a true statement is called valid statement. Otherwise it is called invalid statement. Statements are denoted by the small letters i.e., p, q, r … etc.

**Open and Compound Statement**

A sentence which contains one or more variable such that when certain values are given to the variable it becomes a statement, is called an open statement. If two or more simple statements are combined by the use of words such as ‘and’, ‘or’, ‘not’, ‘if’, ‘then’, ‘if and only if ‘, then the resulting statement is called a compound statement.

**Truth Value and Truth Table**

A statement can be either ‘true’ or ‘false’ which are called truth values of a .statement and it is represented by the symbols T and F, respectively. A. truth table is a summary of truth values of the resulting statements for all possible assignment of values to the variables appearing in a compound statement. Number of rows depends on their number of statements.

**Truth Table for Two Statements (p, q)**

Number of rows = 22 = 4 p q T T T F F T F F Elementary Operation of Logic

p q

T T

T F

F T

F F

**Elementary Operation of Logic**

(i) Conjunction A compound sentence formed by two simple sentences p and q using connective ‘and’ is called the conjunction of p and q and it is represented by p ∧ q.

(ii) Disjunction A compound sentence formed by two simple sentences p and q using connectives ‘or’ is called the disjunction of p and q and it is represented by p ∨ q.

(iii) Negation A statement which is formed by changing the truth value of a given statement by using the word like ‘no’, ‘not’ is called negation of given statement. If p is a statement, then negation of p is denoted by ~ p.

(iv) Conditional Sentence (Implication) Two simple sentences p and q connected by the phase, if and then, is called conditional sentence of p and q arid it is denoted by p => q.

(v) Bi-conditional Sentence (Bi-implication) The two simple sentences connected by the phrase, ‘if and only if this is called biconditional sentences. It is denoted by the symbol ‘<=>’.

**Table for Basic Logical Connections Tautology and Contradiction**

The compound statement which are true for every value of their components are called tautology. The compound statements which are false for every value of their components are called contradiction (fallacy).

**Quantifiers and Quantified Statements**

In this statements, there are two important symbols are used.

(i) The symbol ‘∀’ stands for ‘all values of ‘. This is known as universal quantifier.

(ii) The symbol ‘∃’ stands for ‘there exists’. The symbol ∃ is known as existential quantifier.

**CBSE class 11 commerce Maths fast track revision notes**

CBSE Class 11 Commerce Maths Mathematical Reasoning : Forget boring math lessons and dreaded drill sheets. These fun, colorful books use engaging lessons with easy-to-follow explanations, examples, and charts to make mathematical concepts easy to understand. They can be used as textbooks or comprehensive workbooks with your textbooks to teach the math skills and concepts that students are expected to know in each grade—and several concepts normally taught in the next grade.

Beginning 1, Beginning 2, and Level A Contents

• Counting

• Identifying

• Matching

• Ordering

• Position

• Comparing and Estimating

• Addition

• Subtraction • Locating

• Writing

• Grouping

• Patterns

• Geometric Shapes

• Measurement

• Data/Probability

• Fractions

Level B, Level C, Level D, Level E, Level F, and Level G Contents

**CBSE class 11 commerce Maths fast track revision notes**

CBSE Class 11 Commerce Maths Mathematical Reasoning : This is a one-year Algebra I course for Grades 7-9. Students who have a solid algebra background will have no trouble with the algebra problems from SAT and even the GRE. This 384-page book highlights vocabulary and notation, and has examples from the history of math.

What makes this book unique and different from other algebra textbooks is that it is built from the experiences of an award-winning algebra teacher with more than 30 years of teaching experience. Many textbooks are written by a committee of authors, and many of those authors have little experience teaching beginning algebra students in middle school or high school.

**CBSE class 11 commerce Maths fast track revision notes**

Understanding Algebra I presents the most essential concepts and skills needed to fully understand and gain confidence in algebra in a step-by-step fashion, teaching students that algebra is generalized arithmetic. It helps students see the connection between mathematics that they already know and algebra, so that learning algebra becomes easier and less abstract. This book provides students with real strategies to succeed in solving word problems by using charts and translating strategies that guarantee success.

**Understanding Algebra I Contents**

• Set and Set Notation

• Number Lines

• Graphing

• Rationals

• Operations

• Expressions

• Equations

• Inequalities

• Word Problem

• Percent Problems

• Ratio Problems

• Motion Problems • Work Problems

• Absolute Value

• Polynomials

• Factoring

• Radicals

• Linear Functions

• Slope

• Elimination

• Graphing

• Substitution

• Absolut Value

• Algebraic Fractions

**CBSE class 11 commerce Maths fast track revision notes**

**CBSE class 11 commerce Maths fast track revision notes** : The successful completion of this colorful 272-page book will virtually guarantee a student’s success in high school geometry. Although the geometric concepts of perimeter, area, and volume are taught piecemeal from elementary school through middle school, too many students enter high school without the skills and knowledge to succeed in high school geometry. Unfortunately, middle school students receive very little education on the properties of parallelograms and the tools needed to succeed at doing geometric proofs. The result is a high number of students who struggle with high school geometry and standardized testing. Geometry is a fundamental subject in high school standardized testing.

This book teaches students an understanding of the reasoning behind the properties taught in geometry–instead of merely asking them to memorize them. Students are also taught the basics of geometric proofs and coordinate geometry in a way middle school students can understand. A glossary of terms that every student must master is included. This book can be used as a classroom textbook in Grades 7, 8, or 9 (usually over a two-year period). In many high schools this book can also be used as a one-year high school geometry course. This book follows the National Math Standards in mathematics but it goes further.

**Understanding Geometry Contents**

• Geometry Notation

• Lines

• Planes

• Angles—Types and Properties

• Pythagorean Theorem

• Polygons

• Quadrilateral Properties

• Parallelogram Properties

• Perimeter

• Circumference • Pi

• Trapezoids

• Geometric Constructions

• 3D Shapes—Prism, Cylinders, Pyramids, and Cones

• Symmetry

• Transformations—Reflection, Translations, Rotations, and Dilations

• Tessellations

• Proofs

• Congruency

• Slopes

**CBSE class 11 commerce Maths fast track revision notes**

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**CBSE class 11 commerce Maths fast track revision notes**

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