SUBODH PUBLIC SCHOOL,RAMBAGH CROSSING …...SUBODH PUBLIC SCHOOL, RAMBAGH CROSSING-JAIPUR MATHEMATICS ASSIGNMENT-2020-21 CLASS-SCHOLARS-1 (XI) Dear Students Warm Wishes To battle the

SUBODH PUBLIC SCHOOL,RAMBAGH CROSSING-JAIPUR

MATHEMATICS ASSIGNMENT-2020-21

CLASS-SCHOLARS-1 (XI) Dear Students

Warm Wishes

To battle the spread of Corona pandemic nationwide lockdown is ordered for the next 21 days by the

government of India . Our school too will remain closed till further notice. Towards best possible utilisation

of time during these hours and to curb down educational loss study material has been uploaded for you,

towards which following guidelines to be considered :

# Practice regular studies with proper timeline between 8 am to 1 pm.

# Before start studying meditate for a while.

# Take mini breaks in between to relax.

# Do not forget to nourish and hydrate yourself in between study hours.

# Go through each subject everyday as per the topics and content provided by the teacher. This can be

supplemented by ExtraMarks App. One can access it as given :

*Steps to download /access ExtraMarks app/website*

*Steps to download the app*:

Download The Learning App from play store >login>open the menu option >click on Redeem Voucher >

enter the code *GTS - RJ0093*-> click on apply

*Steps to access ExtraMarks Learning content on online portal* :

Open the link

www.extramarks.com > sign up, enter the required details and create your account > click on settings > click

on Redeem Voucher >enter the code *GTS - RJ0093*

# Follow one hour date wise schedule everyday per subject according to the working days mentioned in

calendar.

# Go through the contents of each subjects throughly and attempt the attached worksheets in either A4 size

sheets or left pages of previous year's register. Compile them in a file which will be assessed by the

respective subject teacher after regular school will resume.

# All revision work is to be carried out on mentioned holidays in calendar.

# One hour Testing ( PRACTICE TEST) of each subject for 25 marks for the provided content will be

conducted ( to be taken on separate sheets and compiled with file) as per mentioned schedule :

http://www.extramarks.com/

April 18 - English

April 20 - Physics / Accounts / Pol Sc

April 21 - Chemistry /Bst /Geography

April 22 - Math /German

April 23 - Biology /Economics

April 24 - IP /CS /Biotech/ PHE

Look forward for your diligent efforts and wish you all good health.

“Mathematics is the language with which God wrote the universe.

— Galileo”

Detailed learning and concept learning videos available on extramarks

(www.extramarks.com)Download app

HAPPY LEARNING


APRIL 03,2020

CHAPTER-4

PRINCIPLE OF MATHEMATICAL INDUCTION

NCERT e-BOOK( Chapter 4-Exercise 4.1)

Visit extramarks-Maths-Principle of Mathematical Induction-SLM(for videos and

slides)

LEARNING OUTCOMES

Student will understand how the Extended Principle of Mathematical Induction is closely related to the

original Principle., will understand the ideas of the basis step and the inductive step in a proof by

mathematical induction

Understand how to apply inductive arguments in a wide range of mathematical settings, including to

prove inequalities, formulas for derivatives,

Key Takeaways.

Mathematical induction is a method of mathematical proof typically used to establish that a given

statement is true for all natural numbers.

It is done by proving that the first statement in the infinite sequence of statements is true, and then

proving that if any one statement in the infinite sequence of statements is true, then so is the next one.

Inductive reasoning: The process of making inferences based upon observed patterns, or simple

repetition. Often used in reference to predictions about what will happen or does happen, based upon

what has happened.

Definition and steps of Mathematical Induction :

“Mathematical Induction is a method or technique of proving mathematical results or theorems”

The process of induction involves the following steps

Step 1 :

Represent every statement by P(n) for all ‘n’ belongs to natural number Verify that the statement is true for n = 1, that is, verify that P(1) is true. This is a kind to climbing the

first step of the staircase and is referred to as the initial step.

Step 2 : Assume that the statement is true for n = k this is referred to as a hypothetical step where k is a

positive integer.

Step 3 : Verify that the statement is true for n = k + 1 whenever it is true for n = k, where k is a positive

integer. This means that we need to prove that P(k + 1) is true whenever P(k) is true. This is referred

to as the inductive step.

If steps 1 and 2 have been established then the statement P(n) is true for all positive integers n.

Example 1 :

By the principle of mathematical induction,(PMI) prove that, for n ≥ 1

11 2 3 4 ..................

2

n nn

Solution :

Let 1

( ) :1 2 3 4 ..................2

n nP n n

Step 1 : put n = 1

1 1 1(1) :1 2 3 4 .................. 1

2P

1 1

Hence p(1) is true.

Step 2 : Let us assume that the statement is true for n = k (hypothetical statement)

1( ) :1 2 3 4 ..................

2

k kP k k

……………………….(1)

Now We need to show that P(k + 1) is true. Considering P(k) is true,

Step 3 : Observe that the terms in the sequence in L.H.S. is increasing by 1,therefore adding k + 1 both sides

in equation (1) we have

1

1 2 3 4 .................. 1 12

k kk k k

1 2 3 4 .................. 1 1 12

21 2 3 4 .................. 1 1

2

1 21 2 3 4 .................. 1

2

1 1 11 2 3 4 .................. 1

2

kk k k

kk k k

k kk k

k kk k

Thus it is valid for n = k + 1 also

Hence, by the principle of mathematical induction, for n≥1

1( ) :1 2 3 4 ..................

2

n nP n n

Example 2:

WORKSHEET -01

OBJECTIVE TYPE QUESTIONS

Choose the correct answer out of the given four options in each of the Exercises

1. If 10n + 3.4n+2+ k is divisible by 9 for all n ∈∈N, then the least positive integral value of k is

(a) 5 (b) 3 (c) 7 (d) 1

2. For all n ∈N, 3.52n+1 + 23n+1 Is divisible by

(a) 19 (b) 17 (c) 23 (d) 25

3. If xn – 1 is divisible by x – k, then the least positive integral value of k is

(a) 1 (b) 2 (c) 3 (d) 4

4 Let ( ) : "2 1"nP n is Prime then,

(a) P(1) is not true (b) P(2) is not true

(c) P(3) is not true (d) P(5) is not true

5 2( ) : " 41"P n n n is Prime then

(a) P(1) is not true (b) P(2) is not true

(c) P(41) is not true (d) None of these

Fill in the Blanks :

6. If P(n) : 2n < n, n ∈∈ N, then P(n) is true for n ≥ …………

7 If 23 1n is divisible by for all n N .then is equal to………….

8 The statement 2( ) : " "P n n n is an even integer is true for ………….

9 If 2( ) :1 3 5 .................. 2 1 nP m m m then ( 1)P m is……………….

10If 3( ) : " 4"P n n n then find P(1), P(2), P(3), P(5).

APRIL 04,2020

CHAPTER-4

PRINCIPLE OF MATHEMATICAL INDUCTION

WORKSHEET -02

(1) By the principle of mathematical induction, prove that, for n ≥ 1

2

3 3 3 3 3 11 2 3 4 ..................

2

n nn


22 2 2 2 1 2 1

( ) :1 3 5 .................. 2 13

m m mP m m

(3) Prove that the sum of the first n non-zero even numbers is n2 + n.


1 2

( ) :1.2 2.3 3.4 4.5 .................. 13

n n nP n n n

(5) Using the Mathematical induction, show that for any natural number n ≥ 2,

2 2 2 2

11 1 1 1( ) : 1 1 1 .................. 1

2 3 4 2

nP n

n n

(6) Using the Mathematical induction, show that for any natural number n ≥ 2,

2 2 2 2 2 1 2 1( ) :1 2 3 4 ..................

6

n n nP n n

APRIL 05,2020-

SUNDAY-Revision through extramarks

content-MCQ

APRIL 06,2020

Holiday (Mahaveer Jayanti)

Revision of the previous content and

solving examples of NCERT chapter 4

APRIL 07 & 08, 2020

WORKSHEET -03[HOTS]

(1) Using the Mathematical induction, show that for any natural number n,

2( ) : 2 4 6 .................. 2P n n n n


3 1

( ) :1 4 7 .................. 3 22

n nP n n

(3) Prove by Mathematical Induction that

( ) :1 5 9 .................. 4 3 2 1P n n n n


x2n − y2n is divisible by x + y.

(5) Use induction to prove that n3 − 7n + 3, is divisible by 3, for all natural numbers n.

(6) Use induction to prove that 10n + 3 × 4n+2 + 5, is divisible by 9, for all natural numbers n.

APRIL 10,2020

Good Friday(holiday)

Revision through extramarks-Practice

test

APRIL 09 & 11 2020

CHAPTER-6

Linear Inequalities

LEARNING OUTCOMES-

# Solving algebraic inequalities in one variable using a combination of the properties of inequality.

# Represent inequalities on a number line

Key Takeaways.

NCERT e-BOOK( Chapter 6-Exercise 6.1)

Detailed learning video available on extramarks to understand the concept and method

to solve linear inequalities (1-21 slides)

(www.extramarks.com)Download app

Definition: A statement of any one of the following types

(1) 0ax b (2) ax b (3) ax b (4) ax b is called as Linear inequations (or inequality) in one variable.

To solve a linear inequation in one variable,take all terms containing the

variable on L.H.S. and all terms not containing the variable on R.H.S.

Divide by the coefficient of the variable preserving the inequality signif the coefficient is [ositive and changing the inequality sign if the coefficient is negtive

Example1- Solve for x: -(x-3)+4 < -2x+5

Solution: -(x-3)+4 < -2x+5

Add -4 on both sides

-(x-3)+4-4 < -2x+5-4

-(x-3)<-2x+1

-x+3< -2x+1

Add -3 on both sides


-x+3-3< -2x+1-3

-x< -2x-2

-x+2x<-2

x<-2

Therefore solution is (-∞, −2)

WORKSHEET -01

Solve for x:

1. 7x + 3 < 5x + 9.

2. 𝑥

3 >

𝑥

2 + 1

3. 1

2(

3𝑥

5+ 4) ≥

1

3(𝑥 − 6)

4. 2

𝑥−3< 0

5.𝑥−5

𝑥−2< 0

APRIL12,2020

Sunday- Visit Extramarks-Maths-

LinearInequalities-SLM(for videos and

slides)

APRIL 13 &15,2020

To understand the concept of number line kindly watch detailed learning video (slides 22-32)

on extra marks

Example: Solve the linear inequality 3x+17<2(1-x) and represent the solution on number line

Solution: 3x+17>2(1-x)

3x+17 >2-2x

5x> -15

x> -3

The graph for x > -3

WORKSHEET -02 Solve the linear inequalities and represent the solution on number line 1. 3(x-2) ≤ 5x+8

2. 3(𝑥−2)

5 ≥

5(2−𝑥)

3.

3. −2 −𝑥

4≤

1+𝑥

3

4. I3-2xI< 7

5. 𝑥−3

𝑥+5> 0

APRIL 14,2020-

Ambedkar Jayanti –Holiday-Revision

through extramarks content-MCQ’s

APRIL 16 & 17,2020

To understand the concept of graphical solution of linear inequations in two variables kindly

watch detailed learning video (slides 33-45) on extra marks

Example: Solve the inequality graphically

y≥-x+1

Solution:

WORKSHEET -03

Solve the following linear inequations graphically:

1. x+2y > 2

2. 3x+2y≤12

3. x-y<0

4.-5x+4y≥ 0

APRIL 19,2020-

SUNDAY-Revision through extramarks

content-Practice test-HOTS

APRIL 18,20 &21,2020

To understand the concept of graphical solution of system of linear inequations in two

variables kindly watch detailed learning video (slides 46-56) on extra marks and practice

worksheet 4

WORKSHEET -04

Solve the following system of linear inequations graphically

1.2x+3y≥ 3, -5x+4y≤0, 3x+4y≤18, x,y≥0

2. x+y≤ 5, x≥ 2, y≥1

3. 2x+y≥2, y-x≥-1,x+2y≤ 8,x,y≥0

4 The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is160 cm, then find its breadth. 5 In drilling a hole in the earth, it is observed that the temperature T in degree Celsius, x km

Below the surface of earth, was given by : T = 25(x -3) + 30, 3 < x <15 .

APRIL 22,2020

TEST-DAY

APRIL 23 &24,2020

Simple Trigonometric identities

1 sin sin cos cos sinA B A B A B

2 cos cos cos sin sinA B A B A B

3 tan tan

tan A±B =1 tan tan

A B

A B

4 sin sin 2sin cosA B A B A B

5 sin sin 2cos sinA B A B A B

6 cos cos 2cos cosA B A B A B

7 cos cos 2sin sinA B A B A B

8 sin2 2sin cosA A A

9 2

2 tansin 2

1 tan

AA

A

10 2 2cos2 cos sinA A A

11 2cos2 2cos 1A A

12 2cos2 1 2sinA A

13 2

2

1 tancos2

1 tan

AA

A

_

14 3sin 3 3sin 4sinA A A

15 3cos3 4cos 3cosA A A

WORKSHEET – 01

USING TRIGONOMETRIC IDENTITIES PROVE THAT:

1 0 0 2cos2 1tan 60 tan 60 =

2cos2 1

AA A

A

2 0 0 1sin 45 sin 45 = cos2

2A A A

3 0 0tan 45 +tan 45 =2sec2

4 0 0tan 45 -tan 45 =2tan2

5 Find sin2 if sin cos 1

6 cos 2 cot2 cotec A A A

7 sin 2

cot1 cos2

AA

A

Refer NCERT chapter-4 & 6(solved examples and exercises)

FACULTY : Scholars - Mathematics

1 Dr.Y. K. Sharma

2 Mr.B.K. Sharma

3 Ms.Simarpreet kaur

4 Ms.Shivani Kotwal

Documents

SUBODH PUBLIC SCHOOL,RAMBAGH CROSSING …...SUBODH PUBLIC SCHOOL, RAMBAGH CROSSING-JAIPUR MATHEMATICS ASSIGNMENT-2020-21 CLASS-SCHOLARS-1 (XI) Dear Students Warm Wishes To battle the