Showing posts with label class11-maths. Show all posts
Showing posts with label class11-maths. Show all posts

Thursday 22 December 2022

National Mathematics Day #eduvictors

National Mathematics Day

National Mathematics Day #eduvictors


National Mathematics Day is observed annually on December 22nd to mark the anniversary of the eminent mathematician Srinivasa Ramanujan's birth.


Thursday 28 July 2022

Class 11 - Maths - Trigonometric Functions Notes, Solved Problems and NCERT Exercise 3.2 Solutions #eduvictors #class11Maths #Trigonometry

Class 11 - Maths - Trigonometric Functions Notes, Solved Problems and NCERT Exercise 3.2 Solutions

Class 11 - Maths - Trigonometric Functions Notes, Solved Problems and NCERT Exercise 3.2 Solutions #eduvictors #class11Maths #Trigonometry



Q1. What are quadrantal angles?

Answer: All angles which are integral multiples of π/2 are called quadrantal angles.

Therefore, for quadrantal angles, we have

Monday 27 June 2022

Class 11 - Maths - Trigonometric Functions - Angle on Circular System + NCERT 3.1 Answers. (Part-1) #class11Maths #eduvictors #trigonometry

Class 11 - Maths - Trigonometric Functions - Angle on Circular System + NCERT 3.1 Answers. (Part-1)

Class 11 - Maths - Trigonometric Functions - Angle on Circular System + NCERT 3.1 Answers. (Part-1)

The phrase "measuring the sides of a triangle" is how the word "trigonometry" is obtained from the Greek words "trigon" and "metron." The field was initially created to address triangle-related geometric issues. The surveyors who mapped out the new territories, the engineers, and other people studied it for navigation. Currently, numerous fields, including the science of seismology, the design of electrical circuits, the description of the condition of an atom, forecasting ocean tide heights, analysing musical tones, and many other things.

You should remember 

1. In the sexagesimal system, we measure angles in degrees, minutes and seconds.

1 right angle = 90° 

1° = 60′  (minute) and 

1′ = 60′′ (second)


2. In the circular measure, we measure angles in radians.

Thus,

πc = 180° 

Friday 25 March 2022

Methods of Differentiation - CBSE Class 11 - Mathematics - Limits and Derivatives Part-11 #class11Maths #limits #calculus #differentiation #eduvictors

Methods of Differentiation 

CBSE Class 11 - Mathematics - Limits and Derivatives Part-11 

Methods of Differentiation - CBSE Class 11 - Mathematics - Limits and Derivatives Part-11 #class11Maths #limits #calculus #differentiation #eduvictors


#class11Maths  #calculus 

Working rule for finding the derivative of implicit functions

First method:

Differentiate every term of f (x, y) = 0 with respect to x.

Tuesday 15 February 2022

DIFFERENTIATION OF STANDARD FUNCTIONS- CBSE Class 11 - Mathematics - Limits and Derivatives Part-10 #class11Maths #limits #calculus #differentiation #eduvictors

 

DIFFERENTIATION OF STANDARD FUNCTIONS

CBSE Class 11 - Mathematics - Limits and Derivatives Part-10

DIFFERENTIATION OF STANDARD FUNCTIONS- CBSE Class 11 - Mathematics - Limits and Derivatives Part-10 #class11Maths #limits #calculus #differentiation #eduvictors


 #class11Maths #Limits

You have learnt theorems of differentiation part-9. Let us proceed further. Here is a list of differentiation of some standard functions: 

Sunday 6 February 2022

THEOREMS ON DIFFERENTIATION - CBSE Class 11 - Mathematics - Limits and Derivatives Part-9 #class11Maths #limits #calculus #differentiation #eduvictors

THEOREMS ON DIFFERENTIATION 

CBSE Class 11 - Mathematics - Limits and Derivatives Part-9

THEOREMS ON DIFFERENTIATION - CBSE Class 11 - Mathematics - Limits and Derivatives Part-9  #class11Maths #limits #calculus #differentiation #eduvictors


 #class11Maths #Limits

You have learnt about finding derivatives using the first principle in part-7 and part-8. Let us proceed further. Here is a summary of theorems on differentiation.

Sunday 30 January 2022

CBSE Class 11 - Mathematics - Limits and Derivatives Part-8 Differential CoEfficient and Derivatives Using First Principle #class11Maths #limits #calculus #differentiation #eduvictors

CBSE Class 11 - Mathematics - Limits and Derivatives Part-8

CBSE Class 11 - Mathematics - Limits and Derivatives Part-8 Differential CoEfficient and Derivatives Using First Principle #class11Maths #limits #calculus #differentiation #eduvictors
Differentiation


In the previous post[Part-7], we learned about some important derivatives using the First Principle.

Let us talk about what differential co-efficient is?

Differential coefficient: Let y = f (x) be a continuous function of a variable quantity x, where x is independent and y. is a dependent variable quantity.

Wednesday 12 January 2022

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-7) Derivatives Using First Principle #class11Maths #limits #calculus #differentiation #eduvictors

CBSE Class 11 - Mathematics - Limits and Derivatives Part-7

Derivatives Using First Principle

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-7)  Derivatives Using First Principle #class11Maths #limits #calculus #differentiation #eduvictors



In the previous post[Part-6], we learned about the Derivative of a function at a point. Let us focus on some important derivatives using the First Principle.


Theorem 1: From the first principle, we have 

Friday 31 December 2021

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-6) - Derivative of a Function At a Point #limits #class11Maths #calculus #eduvictors

Class 11 - Mathematics - Limits and Derivatives (Part-6) - Derivative of a Function At a Point 

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-6) - Derivative of a Function At a Point #limits #class11Maths #calculus #eduvictors



In the previous blog post Limits and derivatives Part-5, we learned about the limits. Let us understand the derivative of a function at a point.

Q1: What is the derivative of a function at a point?

Answer: Let y = f(x) is a continuous function. It means the value of y changes as the value of x changes.

At x = a, is a point in its domain of definittion. The derivative of f at a is defines as: 

Saturday 25 December 2021

Class 11 and 12 Maths - Probability - Part 1 (Solved Questions) #probability #class11Maths #class12Maths #cbse202122 #eduvictors

Class 11 & 12 Maths - Probability - Part 1 (Solved Questions)

Class 11 and 12 Maths - Probability - Part 1 (Solved Questions) #probability #class11Maths #class12Maths #cbse202122 #eduvictors


Let us revisit the basic terminology used in probability.

Q1: Define probability. What can the probability never predict?

Answer: Probability gives us a measure of the likelihood that something will happen. However, probability can never predict the number of times that an occurrence actually happens.


Q2: Define experiment.

Answer: An action or operation resulting in two or more well-defined outcomes. 

e.g. tossing a coin, throwing a die, drawing a card from a pack of well-shuffled playing cards etc.

Wednesday 22 December 2021

National Mathematics Day #mathematics #eduvictors

National Mathematics Day 

National Mathematics Day #mathematics #eduvictors

India celebrates National Mathematics Day on December 22 every year. The day marks the birth anniversary of famous mathematician Srinivasa Ramanujan.

*Typo in the graphic new = knew


Sunday 19 December 2021

CBSE Class 11 - Mathematics - Limits and Derivatives Part-5 #class11Maths #eduvictors #limits #calculus

CBSE Class 11 - Mathematics - Limits and Derivatives Part-5

CBSE Class 11 - Mathematics - Limits and Derivatives Part-5 #class11Maths #eduvictors #limits #calculus


In the previous blog post Limits and derivatives Part-4, we learned about the  trigonometric limits. Let us solve other problems related to Limits

Wednesday 1 December 2021

CBSE Class 11 - Mathematics - Limits and Derivatives Part-4- Limits of Trigonometric Functions #class11Maths #eduvictors #limits

CBSE Class 11 - Mathematics - Limits and Derivatives Part-4- Limits of Trigonometric Functions

CBSE Class 11 - Mathematics - Limits and Derivatives Part-4- Limits of Trigonometric Functions #class11Maths #eduvictors #limits



In the previous blog post Limits and derivatives Part-3, we learn about the algebra of limits. Now, let us study few theorems before we discuss about trignometric limits.


Theorem 1: Let f(x) and g(x) be two real valued functions with same domain such that f(x) ≤ g(x) for all x.
For some a, if $\lim_{x\rightarrow a} f(x)$ and $\lim_{x\rightarrow a} g(x)$ exist then $\lim_{x\rightarrow a} f(x) \leq  \lim_{x\rightarrow a} g(x)$

Theorem 2: Sandwich Theorem or Squeeze Theorem
Let f(x) and g(x) be two real valued functions with same domain such that f(x) ≤ g(x) ≤ h(x) for all x in common domain.
For some a, if $\lim_{x\rightarrow a} f(x) = l = \lim_{x\rightarrow a} h(x)$, then $\lim_{x\rightarrow a} g(x) = l$

Sunday 14 November 2021

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-3) Questions and Answers #class11Maths #Limits #eduvictors

CBSE Class 11 - Mathematics - Limits and Derivatives 

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-3) Questions and Answers #class11Maths #Limits #eduvictors

Part-3  Algebra of Limits  

#class11Maths #Limits 

In the previous post Limits and derivatives Part-2, we get basic ideas of the algebra of limits and also learned about rules and properties of limits.


Let us try to solve few problems:


Q1: Evaluate the given limit $\lim_{r\rightarrow 1} \pi r^2$

Answer: $\lim_{r\rightarrow 1} \pi r^2 = \pi(1)^2 = \pi$


Wednesday 10 November 2021

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-2) Questions and Answers #class11Maths #Limits #eduvictors

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-2) 

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-2) Questions and Answers #class11Maths #Limits #eduvictors


Questions and Answers                                                                     #class11Maths #Limits 


In the previous blog post Limits and derivatives Part-1 , we learn


$\lim_{x\rightarrow a} f(x) = l$ and it is called limit of the function f(x)


The two ways x could approach a number an either from left or from right, i.e., all the values of x near a could be less than a or could be greater than a.


In this case the right and left hand limits are different, and hence we say that the limit of f(x) as x tends to zero does not exist (even though the function is defined at 0).

Saturday 6 November 2021

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-1) Questions and Answers #class11Maths #Limits #eduvictors

CBSE Class 11 - Mathematics - Limits and Derivatives

Part-1 - Questions and Answers

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-1) Questions and Answers #class11Maths #Limits #eduvictors

Q1: Define Calculus.

Answer: Calculus is that branch of mathematics that mainly deals with the study of change in the value of a function as the points in the domain change. 


👉Note: The chapter "Limits and Derivatives" is an introduction to Calculus.

👉Calculus is a Latin word meaning ‘pebble’. Ancient Romans used stones for counting.


Q2: Who are called pioneers of Calculus (who invented Calculus)?

Answer: Issac Newton (1642 - 1727) and G. W. Leibnitz(1646 - 1717).

Both of them were invented independently around the 17th century.



Q3: What is the meaning of 'x tends to a' or x → a?

Answer: When x tends to a (x  → a), x is nearly close to a but never equals to a.

e.g. x → 3 means the value of x maybe 2.99 or 2.999 or 2.999...9 is very close to 3 but not exactly equal to 3. Similarly, x may be 3.01, 3.001, 3.0001... from the right side and gets closer to 3.

Friday 8 October 2021

CBSE Class 11 Maths Term 1 MCQs For Practice (#class11Maths)(#cbse2021)(#term1mcqs)(#eduvictors)

CBSE Class 11 Maths Term 1 MCQs For Practice 

CBSE Class 11 Maths Term 1 MCQs For Practice  (#class11Maths)(#cbse2021)(#term1mcqs)(#eduvictors)


No. of Questions: 15 

Time: 30 minutes

Chapters: Sets, Relations and Functions, Complex Numbers, Sequence and Series, Straight Lines, Limits and Statistics



Q1: The set {1, 2, 3, ...} is _______ set. Fill in the blank.

(a) null

(b) finite

(c) infinite

(d) singleton

Sunday 15 August 2021

Class 11 - Maths - Complex Numbers - Solved Problems - Part 1 (#class11Maths)(#eduvictors)(#cbsenotes)

Class 11 - Maths - Complex Numbers - Solved Problems - Part 1

Class 11 - Maths - Complex Numbers - Solved Problems - Part 1 (#class11Maths)(#eduvictors)(#cbsenotes)


Q1: What are imaginary numbers?


Answer: If the square of a given number is negative then such a number is called an imaginary number.


Q2: Name the mathematician who was the first to introduce the symbol i (iota) for square root of -1.


Answer: Euler.


Q3: Evaluate i⁹ + i¹⁹

Tuesday 6 July 2021

CBSE Class 11 Maths - Relations - Domain, Range and Co-Domain (#class11Maths)(#eduvictors)(#cbse2021)

CBSE Class 11 Maths - Relations - Domain, Range and Co-Domain

CBSE Class 11 Maths - Relations - Domain, Range and Co-Domain (#class11Maths)(#eduvictors)(#cbse2021)


RELATION 

Let A and B be two nonempty sets. Then, a relation R from A to B is a subset of (A × B).

Thus, R is a relation from A to B ⇔ R ⊆ (A × B).


If (a, b) ∈ R then we say that ‘a is related to b‘ and we write, a R b. 


If (a, b) ∉ R then ‘a is not related to b‘ and we write, $a \not \mathrel{R} b$.



Q1: Let A = {-1, 2, 4} and B = {1, 3}. Show A × B as arrow diagram.