Plus One

Kerala State Board New Syllabus Plus One Maths Notes Chapter 2 Relations and Functions.

Kerala Plus One Maths Notes Chapter 2 Relations and Functions

I. Cartesian Product or Cross Product:
The Cartesian product between two sets A and B is denoted by A × B is the set of all ordered pairs of elements from A and B.
ie; A × B = {(a, b): a ∈ A, b ∈ B}

Properties:

1. In general A × B ≠ B × A, but if A = B, A × B = B × A.
2. n(A × B) = n(A) × n(B)
3. n(A × B) = n(B × A)

II. Relations:
A relation R from a non-empty set A to a non-empty set B is a subset of the Cartesian product A × B.

Representation of a relation:

1. Roster form
2. Set builder form
3. Arrow diagram.

Universal relation from A to B is A × B.

Empty relation from A to B is empty set φ.

A relation in A is a subset of A × A.

The number of relation that can be written from A to B if n(A) = p, n(B) = q is 2pq.

Domain: It is the set of all first elements of the ordered pairs in a relation.

Range: It is the set of all second elements of the ordered pairs in a relation.
If R: A → B, then R(R) ⊆ B.

Co-domain: If R: A → B, then Co-domain of R = B.

III. Functions:
A relation f from A to B (f : A → B) is said to be a function if every element of set A has one and only one image in set B.

If f : A → B is a function defined by f(x) = y.

1. The image of x = y
2. The pre-image of y = x
3. Domain of f = {x ∈ A : f(x) ∈ B}
4. Range of f = {f(x) : x ∈ D(f)}
5. If f : A → B, then n(f) = n(B)n(A)

IV. Some Important Functions

Identity function: A function f : R → R defined by f(x) = x. Here D(f) = R, R(f) = R.
The graph of the above function is a straight line passing through the origin which makes 45 degrees with the positive direction of the x-axis.

Constant function: A function f : R → R defined by f(x) = c, where c is a constant.
Here D(f ) = R, R(f) = {c}.
The graph of the above function is a straight line parallel to the x-axis.

Polynomial function: A function f : R → R defined by
f(x) = a₀ + a₁x + ….. + a_nxⁿ, where n is a no-negative integer and a₀, a₁, …., a_n ∈ R.

Rational function: A function f: R → R defined by \(f(x)=\frac{p(x)}{q(x)}\), where p(x), q(x) are functions of x defined in a domain, where q(x) ≠ 0

Modulus function: A function f: R → R

Here D(f) = R, R(f) = [0, ∞).
The graph of the above function is ‘V’ shaped with a corner at the origin.

Signum function: A function f: R → R

Here D(f) = R, R(f) = {-1, 0, 1}.
The graph of the above function has a break at x = 0.

Greatest integer function f: R → R defined by

Here D(f) = R, R(f) = Z.
The graph of the above function has broken at all integral points.

V. Algebra of Functions

Let f : X → R and g : X → R be any two real functions, where X ⊂ R. Then, we define (f + g) : X → R by (f + g)(x) = f(x) + g(x) for all x ∈ X

Let f : X → R and g : X → R be any two real functions, where X ⊂ R. Then, we define (f – g) : X → R by (f – g)(x) = f(x) – g(x) for all x ∈ X

Let f : X → R be a real-valued function and k be a scalar. Then, the product kf : X → R by (kf)(x) = kf (x) for all x ∈ X

Let f : X → R and g : X → R be any two real functions, where X ⊂ R . Then, we define fg : X → R by fg(x) = f(x) × g(x) for all x ∈ X

Let f : X → R and g : X → R be any two real functions, where X ⊂ R. Then, we define \(\frac{f}{g}\) : X → R by
\(\left(\frac{f}{g}\right)(x)=\frac{f(x)}{g(x)}\) for all x ∈ X

Kerala State Board New Syllabus Plus One Maths Notes Chapter 1 Sets.

Kerala Plus One Maths Notes Chapter 1 Sets

I. Sets
Set is a well-defined collection of distinct objects.
Examples of sets.

• N: Set of Natural numbers.
• Z: Set of Integers.
• Q: Set of Rational numbers.
• R: Set of Real numbers.
• Z+: Set of Positive Integers numbers.
• Q+: Set of Positive Rational numbers.
• R+: Set of Positive Real numbers.

Representation of Sets:

1. Roster Form: All elements are listed, are separated by commas, and closed using brackets.
2. Set-builder Form: All elements of a set possess a single common property which is not possessed by any elements outside the set.
3. Venn Diagram: Here sets are represented by diagrams. These diagrams consist of rectangles and closed curves usually circles. The universal et is represented by a rectangle and its subsets by circles.

II. Types of Sets:

Empty set: Set contains no element, φ or {}.

Singleton set: Set containing one element.

Finite set: Set containing a definite number of elements.

Infinite set: Set containing an infinite number of elements..

Equivalent set: Sets containing an equal number of elements.

Equal set: Sets containing identical elements.

Subset: If every element of A is an element of B, denoted by A ⊂ B. For any set A, the set A and Empty set is a subset of A. If a set A has n elements, then it has 2n subsets.

Superset: B is a superset if A is a subset of B, denoted by B ⊃ A.

Proper Subset: If A ⊂ B and A ≠ B.

Power set: The set of all subsets of a set A, denoted by P(A). If n(A) = n, then n(P(A)) = 2n

Universal set: The superset of all subsets under discussion.

Intervals as subset of R:

1. [a, b] = {x : a ≤ x ≤ b}, closed interval.
2. (a, b] = {x : a < x ≤ b]
3. [a, b) = {x : a ≤ x < b}
4. (a, b) = {x : a < x < b}, open interval.

III. Operations on Sets

Union of Sets: The union of A and B is the set which consists of all elements of A and all elements of B except the common elements. In symbol we write as A ∪ B = {x : x ∈ A or x ∈ B}.
Venn diagram representation:

Properties:

1. A ∪ B = B ∪ A, Commutative.
2. (A ∪ B) ∪ C = A ∪ (B ∪ C), Associative
3. A ∪ φ = A, φ is the identity.
4. A ∪ A = A
5. U ∪ A = U

Intersection of Sets: The intersection of A and B is the set of common elements of both A and B.
In symbol, we write as A ∩ B = {x : x ∈ A and x ∈B}.
Venn diagram representation:

Properties:

1. A ∩ B = B ∩ A, Commutative.
2. (A ∩ B) ∩ C = A ∩ (B ∩ C), Associative
3. A ∩φ = φ
4. A ∩ A = A
5. U ∩ A = A
6. A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
7. n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
8. If A and B are disjoint, then n(A ∪ B) = n(A) + n(B)
9. n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(C ∩ A) + n(A ∩ B ∩ C)

Difference of Sets: The difference of the sets A and B in this order is the set of elements which belongs to A but not to B, denoted by A – B = {x : x ∈ A and x ∉ B}
Venn diagram representation:

Property: A – B ≠ B – A

Complement of a Set: The complement of a set A is the set of all elements of U which are not in A, denoted by
A’ = {x : x ∈ U and x ∉ A}
Venn diagram representation:

Properties:

1. A’ ∪ A = U, Commutative.
2. A’ ∩ A = φ, Associative
3. (A ∩ B)’ = A’ ∪ B’
4. (A ∪ B)’ = A’ ∩ B’
5. U’ = φ
6. φ’ = U
7. (A)’ = A
8. A – B = A ∩ B’
9. n(A – B) = n(A ∩ B’)
10. n(A) = n(A ∩ B’) + n(A ∩ B)
11. n(A ∪ B) = n(A ∩ B’) + n(A’ ∩ B) + n(A ∩ B)

Kerala State Board New Syllabus Plus One English Textbook Answers Unit 1 Glimpses of Greatness Text Book Questions and Answers, Summary, Notes.

Kerala Plus One English Textbook Glimpses of Greatness Questions and Answers Unit 1

Let’s begin

Question 1.
“Some are born great; some achieve greatness; some have greatness thrust upon them. ”-William Shakespeare (Twelfth Night).
Is greatness an innate trait? Is it acquired by the successful or thrust upon them? Discuss.
Answer:
I don’t think greatness is an innate trait. It is acquired by successful people. Look at the examples of Abraham Lincoln, Mahatma Gandhi, Nelson Mandela, Mother Theresa and Dr. APJ Abdul Kalam. They all acquired their success by hard work, perseverance, courage and determination. Success is not thrust upon them. They worked for it and they got it.

Question 2.
What qualities make people great? Discuss with your friends and write them in the boxes below:

Question 3.
We strive to reach heights, achieve greatness and be successful ¡n life. But at times, it seems difficult. Now, look at the picture below:

What thoughts and feelings does it evoke in you?
Answer:
The boy has stage-fright and he is not confident to perform before the judges and the audience. He is trying to get away but he is being forced by his teacher to say something or sing.

Question 4.
Give a suitable caption to the picture.
Answer:
“The Reluctant Performer”.

Question 5.
Have you had any similar experience? If so, share it with your friends.
Answer:
Yes, J had. I was in the 10th Standard and I was asked to make a Welcome Speech on the School Day. I was not keen on doing it. But my Principal insisted that I should do it. I prepared a speech and studied it by heart. When I got on the stage on the School Day, I started shivering and shaking and my mind went blank. I could not say a word. The Principal had to prompt me to speak some words. I somehow stammered something and fled from the stage. It was the worst day of my life as my classmates teased me about my ‘Speech’.

Think And Respond

Question 1.
What made little Abe stand on the dry goods box and deliver the speech?
Answer:
Little Abe stood on the dry goods box and delivered the speech because he was replying to a stump speaker, who made the speech standing on the stump of a tree.

Question 2.
Do you think good dress, appearance, position in society, etc., are needed to present yourself before the public for a speech?
Answer:
I think in normal circumstances good dress, appearance, position in society, etc., are needed to present ourselves before the public for a speech. But in the case of some famous people like Abraham Lincoln and Mahatma Gandhi, good dress, appearance, etc., did not seem to matter. But these are exceptions and not the rule.

Question 3.
What is the role of Dennis in bringing out the best in young Abe?
Answer:
Dennis was like a catalyst in bringing out the best in young Abe. Dennis recognised the capabilities of Abe and encouraged him to show them to the public. Dennis was a good friend of Abe and he wanted Abe to shine.

Question 4.
Do you think that everybody has some potential in them? Some people take the initiative, while others do not dare to showcase their talents. What do you think are the reasons for this? Write down your views.
Answer:
I think that everybody has some potential in them. Some people do not dare to showcase their talents because of many reasons:

• Lack of opportunity
• Lack of confidence
• Lack of encouragement
• Fear of failure

I. Read and Reflect

Question 1.
We are going to read the story of a young seagull. He was afraid to make his first flight. His parents helped him into action and thus made him ready to face the challenges of life.

Glimpses Of Greatness About This Unit

“Success is not final, failure is not fatal: it is the courage to continue that counts.” Sir Winston Churchill.

Success is surely the fruit of perseverance. The great achievement of others can inspire us. Similarly, we can be an inspiration to many others. This Unit highlights the personality traits of some great people. It emphasises the qualities that are to be developed to become successful in life.

This Unit has the following:
a) An anecdote from the life of Abraham Lincoln – ‘Abe’s First Speech’.
b) A Story by Liam O’Flaherty – ‘His First Flight’.
c) A Speech by Dr. APJ Abdul Kalam – 7 will Fly’.
d) A Short Biographical Sketch of Stephen Hawking – ‘Quest for a Theory of Everything’.
e) A Poem by Rudyard Kipling – ‘If’.

The Unit aims at equipping the students to face the challenges of life with courage, confidence and perseverance and to become unique in their own ways, upholding the values of life. The Unit also aims at building confidence in the students to use English effectively in different situations of their lives.

Glimpses Of Greatness About This Author

Abraham Lincoln (Abe) is one of the greatest American statesmen. He is known for his famous speeches. Here is the story of his first speech as a small boy.

Abe’S First Speech

Abe made his first speech when he was a boy. He was without shoes. One suspender held up his trousers. He wore a cheap straw hat. Through a hole in it, some of his hair stuck out.

Abe attended a political meeting with his friend Dennis Hanks. Dennis was Abe’s companion in splitting logs to make rail fences. The meeting was addressed by one stump speaker. Stump speakers were those trained political speakers who addressed the audience standing upon tree stumps. The speaker was shouting at the top of his voice and he was making wild signs with his hands.

At the end of the speech, Abe and Dennis did not agree with the views of the speaker. Dennis thought Abe could make a better speech than what the speaker had made. He got a dry goods box and asked Abe to reply to the earlier speaker.

Abe threw his straw hat to the ground. He got on to the dry goods box and delivered a speech. The crowd listened to the speech attentively and applauded him. Even the first speaker admitted that Abe’s was a fine speech and it answered every point in the speech made by him.

Dennis Hanks was very happy. He thought that Abe was the greatest man that ever lived. He went on saying how Abe was a better speaker than the trained campaign speaker.

(From ‘Abe Lincoln’s Anecdotes and Stories’ by R.D. Wordsworth)

Glimpses Of Greatness Glossary

Kerala State Board New Syllabus Plus One English Textbook Answers Unit 6 Leaps and Bounds Text Book Questions and Answers, Summary, Notes.

Kerala Plus One English Textbook Leaps and Bounds Questions and Answers Unit 6

“That’s one small step for a man one giant leap for mankind.”

– Neil Armstrong

Let’s begin

Look at the pictures on page 163 carefully:

Question 1.
Can you identify the actor in these visuals?
Answer:
It is Charlie Chaplain.

Question 2.
What do these pictures communicate to you?
Answer:
They communicate to me the wonder-world of technology and machines.

Question 3.
Do you think that technology and its various aspects must be studied in detail to get a serious understanding of society?
Answer:
No, I don’t think so. Technology is just one aspect of the society and not everybody understands it.

Question 4.
Write a short paragraph on the role of technology in modern society and share the ideas with your friend.
Answer:
In modern society, technology is an inevitable part of our everyday life. It has a role in everything we do even though we sometimes do not realize it. Thanks to development in technology there have been many breakthroughs in different fields such as communication, transportation, education, medicine, entertainment and agriculture. Our life has become simpler and more enjoyable than before. We have mobile phones and so we can talk with anybody, anytime, anywhere in the world. The planes, trains, buses and trucks transport people and goods fast from one place to another.

In medicine, X-ray, Scanning etc. help doctors to diagnose the disease. Laser treatment and surgery is common. We have video, audio and TV to keep us entertained all the time. Even in religion, technology is playing a role. Using powerful sound system, cassettes and CDs, religious leaders propagate their beliefs. Agriculture is revolutionized by the use of technology.

About the Unit

Science and technology have brought about big changes in every walk of life. Technology has transformed every corner of the world. It caters to the demands of everyone including the differently abled. This progress is, however, not without some hazards.

This Unit starts with an article ‘The Cyber Space’ by Esther Dyson on the use and abuse of cyberspace. ‘Is Society Dead?’ by Andrew Sullivan is a humorous but strong write-up on the i-Pod generation which is in a way disconnected from societal interactions. The short story titled ‘Conceptual Fruit’ by Thaisa Fank, presents the efforts of a loving father to enable his differently abled daughter to make sense of the world around her, with the help of technology.

Read And Reflect

The advent of the www (world wide web) has brought a revolutionary change in the spread of information. A cultural transformation from the printed space to the cyber space took place. It redefined the spatial dimensions of our universe.

Kerala State Board New Syllabus Plus One English Textbook Answers Unit 5 Harmony of Life Text Book Questions and Answers, Summary, Notes.

Kerala Plus One English Textbook Harmony of Life Questions and Answers Unit 5

Good health is a state of complete physical, social and mental well-being, and not merely the absence of disease or infirmity Health is a resource for everyday life, not the object of living, and is a positive concept emphasizing social and personal resources as well as physical capabilities.

– WHO

Look at the Logo give below.

Question 1.
Can you identify the words that appear with the entry ‘wellness’ in the logo?
Answer:
The words are Health, exercise, flexibility, movement, balance, energy.

Question 2.
What is your idea of wellness?
Answer:
My idea of wellness is a state of complete physical, social, financial and mental well-being. In other words I should be physically healthy, free from diseases. Socially I must be accepted by others and they should like me. Financially I should be free so that I can have all the material that I think I need for my comfort and happiness. Mental well-being is a state which always keeps me happy, optimistic and contented, free from tensions, worries and anxieties.

Question 3.
Does it pertain to the physical realm alone?
Answer:
No. It also pertains to the social, mental and financial realms.

Question 4.
What are the activities conducted by your School Health Club for promoting wellness?
Answer:
Our School Health Club conducts many activities for promoting wellness. There is a trainer who gives the members yoga classes. Every day a few minutes are spent on physical exercises. Twice a week we have compulsory outdoor games at least for an hour. Once a month we go out trekking. We also have made it a regular practice to plant trees around the compound, or take care of the existing ones. As part of our program the members are asked not to overeat and oversleep. Whenever possible they are encouraged to swim. We also tell the members to come to the school on foot, and not in vehicles, if the distance is not much.

Question 5.
Prepare a logo, (This should be done by each student, ensuring that the logo reflects some of the aims (goals) of the Club.)
Answer:

Harmony of Life About the Unit

The holistic concept of wellness is the basic premise of this unit. It has a short story, a poem and an essay. The short story ‘Gooseberries’ by Anton Chekhov reflects on the belief in following one’s dream and doing whatever it takes to achieve that. The poem To Sleep’ by William Wordsworth stresses the importance of good sleep. The essay ‘Going out for a walk’ by Max Beerbohm challenges the notion that walking is a productive mental exercise – especially if one is with a talkative companion.

I. Read And Reflect

Chekhov’s ‘Gooseberries’ is a story of two brothers who pursue happiness in their own ways. The story gives plenty of opportunities to critically examine the ways they have chosen. The extent to which they succeed is a/so worth our consideration.

Kerala State Board New Syllabus Plus One English Textbook Answers Unit 2 Words and Deeds Text Book Questions and Answers, Summary, Notes.

Kerala Plus One English Textbook Words and Deeds Questions and Answers Unit 2

Let’s Begin

Question 1.
“Deeds must be an execution of words. Mahatma Gandhi was true to his words in his deeds. His life was a message.” This is what Albert Einstein wrote about Gandhi on his 70th birthday, in 1939:
Answer:
Mahatma Gandhi: He was a leader of his people, unsupported by any outward authority. He was a politician whose success did not rest upon craft or the mastery of technical devices but simply on the convincing power of his personality. He was a victorious fighter who always refused to use force. He was a man of wisdom and humility. He was armed with resolve and inflexible consistency. He devoted all his strength to the uplifting of his people and the betterment of their condition. He faced the brutality of Europe with the dignity of a simple human being.

Generations to come, it may be, will scarce believe that such a one as this, ever in flesh and blood, walked upon this earth.

Let’s discuss :

Question 2.
What impression of Gandhiji do you get from the brief description given above? Discuss.
Answer:
The impression I get is that Gandhiji was one of the greatest men the world has ever seen. He did not have any political authority but he was a true leader of the people. He was not a shrewd politician who was a master of all latest technologies, but he impressed people with his powerful personality. He always advocated non-violence. Even the might of England could not defeat this ‘Naked Fakirfrom India’ as Winston Churchill once called him. He was a man of wisdom and humility.

He would never run away from any risk and he was determined to succeed. His ambition in life was giving the people of his country freedom and good life which they could enjoy in peace and brotherhood. He advocated tolerance and he believed that God is one known by different names – Ishwar, Allah, God. All human beings are the sons and daughters of the same Father. Gandhi was not only a nationalist but a great internationalist who believed in the fraternity of the humankind all over the world. Gandhiji is the greatest son of India.

Question 3.
What kind of a ‘fighter’ is Gandhi?
Answer:
Gandhi is a fighter who believed in non-violence. He would never give up, fearing defeat. He was even willing to sacrifice his life to attain his goals which he believed to be just and right.

Question 4.
‘One must practise what one preaches.’ How far is the statement true of Mahatma Gandhi?
Answer:
Mahatma Gandhi always practised what he preached. He strongly believed that “Deeds must be an execution of words.” Empty words never came out of his mouth. If he said something people could be sure that he would do it. He even gave up his life to practise what he preached.

Read and Reflect

Question 1.
Jawaharlal Nehru writes about the timely arrival of Gandhiji to Indian politics. India was in great need of such a leader. Gandhiji was like a beam of light that removed the darkness. Nehru makes a right assessment of Gandhiji in his book ‘Discovery of India’. Here is an excerpt.

“Keep your thoughts positive
because your thoughts become your words
Keep your words positive
because your words become your behaviour.”

Words and Deeds About this Unit:

– Mahatma Gandhi

The theme of this unit is the need for the symbiotic relationship between words and deeds. The unit aims at inculcating the right values through a few examples. It has an essay by Nehru titled “And Then Gandhi Came”, a story written by Prabhat Kumar Mukhopadhyay with the title The Price of Flowers’, translated by Lila Ray, and a poem ‘Death the Leveller’ by James Shirley.

The texts and the activities are designed to help the students to imbibe the values of good citizenship. They also enable them to acquire a strong linguistic foundation.

Kerala State Board New Syllabus Plus One English Textbook Answers Unit 4 Braving The Hazards Text Book Questions and Answers, Summary, Notes.

Kerala Plus One English Textbook Braving The Hazards Questions and Answers Unit 4

Let’S Begin

1. Examine the picture given below:

Let’s Discuss

Question 1.
What do these pictures tell us about?
Answer:
They tell us about disasters.

Question 2.
Note down all the ideas that come to your mind about them.
Answer:
Upper Row:
Picture 1 : aWhirlwindorablastofanuclearbomb.
Picture 2 : a Tsunami
Picture 3 : High tide or Storm in the sea

The row beneath :
Picture 1 : An earthquake
Picture 2 : A forest fire

Read and Reflect

Question 1.
Share your thoughts with your friends. Collect ideas from them, and enrich your understanding of the subject.

Question 2.
Disasters – both natural and man-made cause widespread damage and destruction. It is high time that we became aware of and equipped ourselves to face impending disasters. Here is an essay about disasters and their management in the Indian context.

Braving The Hazards About the Unit:

Disasters, both natural and man¬made, have become very common today. Thousands die each year in disasters. They also cause a lot of destruction and damage. It is necessary to be informed and equipped to face impending disasters. The idea of disaster management is taken up seriously throughout the world.

This unit has 3 texts. One is an essay by Anjana Majumdar about disaster management in India. The 2nd is a short story by A.J. Cronin. The 3rd is a poem by Benjamin Peck Keith about the wreck of the Titanic. In addition, there is a newspaper report and an excerpt from the essay ‘On Courage’ by A.G. Gardiner. The texts and activities aim to make the learners aware of different disasters and to equip them to act promptly in moments of crisis.

Kerala State Board New Syllabus Plus One English Textbook Answers Unit 3 Beyond The Horizon Text Book Questions and Answers, Summary, Notes.

Kerala Plus One English Textbook Beyond The Horizon Questions and Answers Unit 3

Let’s Begin

Question 1.
Look at the illustration given below.

Give a suitable caption to it.
Answer:
Travel

Question 2.
What more would you like to include in this illustration?
Answer:
An aeroplane, a train, a mountain, a beach, a big hotel, a city, skiing, dancing

Question 3.
Travel is an integral part of modern life. It opens up new horizons and experience. Imagine that you are planning a tour to a place of importance.
What are your criteria for selecting your tourist destination?
Answer:
a) Scenic beauty
b) Good accommodation and good food
c) Entertainment
d) Travel facilities and Safety

Read and discuss :

The lush beauty of a place is a real feast for the eyes. It never fails to attract us. Here is an account of the magical beauty of nature-the panoramic view from the top of Thamarasseri Ghats orThamarasseri Churam (a hilly highway with 9 hairpin curves from Adivaram to Lakkidi, in Wayanad) towards the Arabian Sea.

Read the material given below.
‘High mountains rise to the left with water glistening on bare black rocks like tears of gladness in the eyes of sorrow; forests stretch away here with gentle slope and easy undulation; far below lie swamps choked with thorny thickets and rank coarse grasses in whose bosoms are stored the streams which water those large stretches of rice fields, here sere and yellow after the sickle of the reaper, there whitening unto harvest or again a vivid green where the second crop matures.

Hills everywhere, some arid, red and unfruitful, more covered in the feathery foliage of the Eastern orchards… As the distance grows farther, hill and field all merge into one green plain, and beyond gleams the sea, hard to be discerned from heaven that bends down and meets it. The thought rises from the heart that in such fair and well-ordered beauty, the affairs of this world may perchance appear… so strange, so little comprehendible by us, the dwellers, amid its hills and valleys.

– (Wayanad: It’s Peoples and Traditions by C. Gopalan Nair, 1911)

Question 4.
Discuss the colours mentioned in the passage.
Answer:
Black rocks, yellow rice fields, whitening into harvest, green crops, red hills, green plain.

Question 5.
What gives Thamarasseri its well-ordered beauty?
Answer:
The high mountains with water glistening on bare black rocks, the forests that stretch with gentle slope and easy undulation, the swamps choked with thorny thickets, the harvested rice fields, the vivid green second crops, the hills, the green plain, and he gleaming sea and the sky that bends down to meet the sea gives Thamarasseri its well-ordered beauty.

Question 6.
Pick out the word pictures found in the passage.
Answer:
Thorny thickets coarse grasses sere and yellow

Question 7.
Think of a place in your locality which is noted
for its scenic beauty. Is it attractive and beautiful as the place described in the above passage? Discuss with your friends. (3 Mark)

Read and Enjoy

Question 1.
Travel is an eye-opener. It opens up new, refreshing snapshots before us and often helps us to change our philosophy of life.

… all experience is an arch wherethrough’
Gleams that untravelled world whose margin fades Forever and forever when I move.

Beyond The Horizon About the Author:

– Alfred Lord Tennyson

Ulysses is the speaker of Tennyson’s poem. For him travel is the means to satisfy his unquenchable thirst for knowledge. With his strong determination, ‘to strive, to seek, to find, and not to yield’, he plans to go beyond horizons of knowledge and experience. Nowadays the amenities of travel have improved. The opportunities of travel have also increased.

This Unit focuses on travel and the different experience it gives. It takes the students through different areas of travel – adoration of natural beauty, a desire for adventure and an exploration of new cultures, customs and traditions.

It has three lessons:
a) Sunrise on the Hills (a poem)
b) The Trip of Le Horla (a short story)
c) The Sacred Turtles of Kadavu (a Fijian Legend)

Kerala State Board New Syllabus Plus One Maths Notes Chapter 16 Probability.

Kerala Plus One Maths Notes Chapter 16 Probability

I. Random Experiments
An experiment is called a random experiment if it satisfies the following two conditions:

• It has more than one outcome.
• It is not possible to predict the outcome in advance.

Sample space: The set of all possible outcomes of a random experiment is called sample space. Generally denoted by S.

Event: Any subset E of a sample space S is called an event.

Types of Events:
1. Impossible event and sure event: The empty set φ and the sample space S describe the impossible event and sure event respectively.

2. Simple event: An event E having only one sample point of a sample space.

3. Compound event: An event having more than one sample point of a sample space.

Algebra of events:

1. Event ‘not A’ = A’
2. Event ‘A or B’ = A ∪ B
3. Event ‘A and B’ = A ∩ B
4. Event ‘A but not B’ = A ∩ \(\bar{B}\) = A – B

If A ∩ B = φ, then A and B are mutually exclusive events or disjoint events.

If E₁ ∪ E₂ ∪ E₃ ∪ …… ∪ E_n = S, then we say that E₁, E₂, E₃, …….., E_n are exhaustive events.

If E₁ ∪ E₂ ∪ E₃ ∪ …… ∪ E_n = S, and E_i ∩ E_j = φ, i ≠ j then we say that E₁, E₂, E₃,…….., E_n are mutually exclusive events and exhaustive events.

II. Probability of an Event
Let S is a sample space and E be an event, such that n(S) = n and n(E) = m. If each outcome is equally likely, then it follows that P(E) = \(\frac{m}{n}\).

P(Impossible event) = 0 and P(Sure event) = 1, hence 0 ≤ P(E) ≤ 1.

If A and B are any two events, then P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

If A and B are mutually exclusive events, then P(A ∪ B) = P(A) + P(B)

If A is any events, then P(A’) = 1 – P(A)

P(A ∩ \(\bar{B}\)) = P(A) – P(A ∩ B)

Kerala State Board New Syllabus Plus One Maths Notes Chapter 15 Statistics.

Kerala Plus One Maths Notes Chapter 15 Statistics

Statistics deals with data collected for specific purposes and making decisions about the data by analyzing and interpreting it.

I. Measure of Dispersion
This gives a measure of the dispersion of the observation around the measure of central tendency of the data collected.

1. Range = Maximum value – Minimum value.
2. Mean Deviation.

Where,
x_i – observations
a – Any measure of central tendency.

Grouped data:
i. Discrete frequency distribution.
ii. Continuous frequency distribution.

Where,
x_i – Observations/midpoints of class intervals
a – Any measure of central tendency.

Median class is the class in which the \(\left(\frac{N}{2}\right)^{t h}\) observation lies.

l – The lower limit of the median class.
f₀ – Cumulative frequency of the class preceding the median class.
f₁ – Frequency of the median class.
C – Width of the class interval.

3. Variance and Standard Deviations.
Standard Deviation (σ) = √Variance
Ungrouped data:

Where, x_i – observations
\(\bar{x}\) – Mean
n – number of observations

Grouped data:
i) Discrete frequency distribution.
ii) Continuous frequency distribution.

Where,
x_i – Observations/mid points of class intervals.
\(\bar{x}\) – Mean
f_i – Frequency.

Short cut method of finding variance and standard deviation:
Let A be the assumed mean and the scale be reduced to \(\frac{1}{h}\) times (h being the width of class intervals). Let the new value be y_i and prepare the required tables using y_i. i.e; y_i = \(\frac{x_{i}-A}{h}\)
Find the variance and standard deviation of y_i using the above-mentioned method, let it

II. Coefficient of Variation

The distribution having greater CV has more variability around the central value than the distribution having a smaller value of the CV.

Less the CV more consistent is the data.

For distributions with equal means, the distribution with lesser standard deviation is more consistent or less scattered.