## Karnataka Class 12 Commerce Maths Best Books For 2017 Exams

Karnataka Class 12 Commerce Maths Best Books : Here we provides complete details about Karnataka Class 12 Commerce Maths Best Books and other Karnataka Class 12 Commerce Maths Best Study materials in pdf format. Here we provide direct links to buy Karnataka Class 12 Commerce Maths Best Books . Buy these Karnataka Class 12 Commerce Maths Best Books, Download here Karnataka Class 12 Commerce Maths study materials , question paper and read well.

### Karnataka Class 12 Commerce Maths Best Books For 2017 Exams

Karnataka Class 12 Commerce Maths Best Books : ** **Commerce is a useful stream as this discipline has great demand in different job oriented fields. Subjects like Economics, Accountancy, Business studies and others are included in this stream. After completion of their 10 standard, students can opt for this stream in class 11 and 12 and they can also take this stream in graduation level. The CBSE board is known for its well-evaluated syllabus and suitable question papers. To maintain its praiseworthy recognition, the board has prepared a comprehensive syllabus for class 11 commerce. All essential subjects and their relevant topics are incorporated in this syllabus by maintaining a proper order. Hence, students get thorough knowledge from this syllabus.

**Karnataka class 12 commerce maths study material:**

Key Features:

- Calculate the total time for studies
- Weigh your subjects
- Division of days for studding each subject
- Division of subject areas as per the allotment of days
- Weekly plan of study

**Karnataka class 12 commerce maths study material:**

- Time management is more important.
- Firstly do not ignore your health.
- Get proper sleep and eat a balanced nutritious diet.
- A good relaxed mind and healthy food is important for you to retain what you study.
- Besides know your strengths and weaknesses. Give more time to your weaker subjects but also take care that you do not ignore any subject altogether because a piled up syllabus in even one subject might bring down your percentage.
- Do not try to spend hours in front of books if you are not retaining what you study.Plan to study such that you do not study for long stretches and get enough break every hour or two.
- Also be positive and optimistic about scoring well. A happier you will be a more successful you.

#### Mathematics Paper Analysis.

Part A – This part comprised one mark questions, mostly formulae and simple calculations. There were totally ten questions.

Part B – This is a little tedious section comprising 14 two marks questions with a choice to answer any ten. Each question carried two marks.

Part C – Part C is the toughest in the paper. Ten to attend of any three marks questions in this section.

Part D – Students has the option to write any six out of the ten given questions. This is the section that is a breather for students after the tricky part c.

Part E – This is the last part that carried ten marks. Only two questions were given with a choice to answer any one.

### Karnataka Class 12 Commerce Maths Best Books For 2017 Exams

The CBSE board is known for its well-evaluated syllabus and suitable question papers. To maintain its praiseworthy recognition, the board has prepared a comprehensive syllabus for class 11 commerce. All essential subjects and their relevant topics are incorporated in this syllabus by maintaining a proper order. Hence, students get thorough knowledge from this syllabus.

**Class 11th Calculus Integration – VIEW****class 11th Derivatives Calculus – VIEW****Matrices and Determinants – VIEW****11th Maths Full Course – VIEW****Probability – VIEW****11th Accounts Full Course Cum CPT by Mansi Jain and M K jain – VIEW****Rectification of Error, Bills of Exchange & Bank Reconciliation Statement – VIEW**

### Karnataka class 12 commerce maths best faculty:

**Class 11th Partnership – VIEW****Class 11 – Demand and Supply By M K Jain – VIEW****Basics of Accounting upto PL and BS – VIEW****Class 11 – Theory of Cost and Laws of Production By M K Jain – VIEW**

### Karnataka Class 12 Commerce Maths Best Books For 2017 Exams

Karnataka Class 12 Commerce Maths Best Books : The basic concepts of sets and functions are topics covered in high school math courses and are thus familiar to most university students. We take the intuitive point of view that sets are underscored collections of objects. We first recall some standard terminology and notation associated with sets. When we speak about sets, we usually have a “universal set” U in mind, to which the various sets of our discourse belong.

1. Sets

Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of a 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. Practical Problems based on sets.

2. Relations & Functions

Ordered pairs, Cartesian product of sets. Number of elements in the cartesian product of two finite sets. Cartesian product of the sets of real (upto R x 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 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 quotients of functions.

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

A set is an underscored collection of distinct objects. We use the notation x ∈ S to mean “x is an element of S” and x /∈ S to mean “x is not an element of S.” Given two subsets (sub collections) of U, X and Y , we say “X is a subset of Y ,” written X ⊆ Y , if x ∈ X implies that x ∈ Y . Alternatively, we may say that “Y is a super set of X.” X ⊆ Y and Y ⊇ X mean the same thing. We say that two subsets X and Y of U are equal if X ⊆ Y and Y ⊆ X. We use braces to designate sets when we wish to specify or describe them in terms of their elements: A = {a, b, c}, B = {2, 4, 6, . . .}. A set with k elements is called a k-set or set with carnality k. The cardinality of a set A is denoted by |A|.

Since a set is an unordered collection of distinct objects, the following all describe the same 3-element set

{a, b, c} = {b, a, c} = {c, b, a} = {a, b, b, c, b}.

Class 11 Commerce Maths Sets And Functions : The first three are simply listing the elements in a different order. The last happens to mention some elements more than once. But, since a set consists of distinct objects, the elements of the set are still just a, b, c. Another way to think of this is:

Two sets A and B are equal if and only if every element of A is an element of B and every element of B is an element of A.

### Karnataka Class 12 Commerce Maths Best Books For 2017 Exams

Karnataka Class 12 Commerce Maths Best Books : This topic “Relations and Functions” is a foundation or fundamental of algebra in mathematics. Relations and functions are two different words having different meaning mathematically. Many us you might be confused in their difference. We shall study both these concepts in detail here.

Same as the relations which we have in our daily life, a kind of relations also exists in algebra. In daily life, relations are like brother and sister, friends, student and teacher and many more. In mathematics also we see some relations like a line is parallel or perpendicular to another, any one variable is greater or less than the another variable. Any Set A is subset of B, all these are examples of relations.

One thing which we see in common while studying relations, that it required two different objects to link two different objects via relations.

**What is the meaning of Relation in math?**

Understanding Relations requires basic knowledge of sets. A Set is a collection of well defined objects of particular kind. For Example a set of outcomes of dice, a set of English alphabet.

Relation is always studied between two sets. If we have two non void (or null/empty) sets A and B then the relation R from set A to set B is represented by aRb, where a is the set of elements belonging to set A while b belongs to set B.

Relation from a set A to a set B is the subset of the Cartesian product of A and B i.e. subset of A x B. Relation in other way can also be defined as an collection of ordered pairs (a, b) where a belongs to the elements from set A and b from set B and the relation is from A to B but not vice versa.

### Recommended read : KARNATAKA class 11 commerce Maths fast track revision notes

### Karnataka Class 12 Commerce Maths Best Books For 2017 Exams

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