Mahesh

AP State Syllabus AP Board 7th Class English Textbook Solutions Chapter 6A A Hero Textbook Questions and Answers.

AP State Syllabus 7th Class English Solutions Chapter 6A A Hero

7th Class English Chapter 6A A Hero Textbook Questions and Answers

I. Read the following proverb and answer the questions that follow.

Question 1.
You may have heard of this proverb.before. Do you know what it means?
Answer:
This proverb says that timid or coward people cannot achieve anything. Only the brave or
the courageous can get on what they want. Here ‘Fortune’ means good result or benefit and this goes to the brave people.

Question 2.
Tell the class why the government rewards the brave and adventurous children.
Answer:
The government rewards the brave and adventurous children so as to inspire the younger ones to be brave like them and do adventurous things and to tell that the country needs the brave but not the timid.

Question 3.
Are you aware of any brave boy or girl who may have shown an act of bravery? Talk about his/her bravery to the class.
Answer:
Yes, my friend Chennakesava Sarma has shown an act of bravery. He saw a drowning child in the river Krishna through he was not a good swimmer, he at once jumped into the river and caught hold of the child by his hair. Later he shouted loudly. Some people nearby came and rescued both of them.

I. Answer the following questions.

Question 1.
According to the newspaper’s report, who fought with the tiger?
Answer:
According to the newspaper’s report, a village lad fought with the tiger.

Question 2.
Can you say why Swamis father read the hews to his son?
Answer:
His father read the news for Swami so that it would inspire his son and that his son would also do courageous things.

Question 3.
Did Swami believe the story? Give reasons for your answer.
Answer:
No, Swami did not believe the story. He told his father that the person fought with the tiger must be a grown-up person but not a boy. He felt that a boy could not fight with a tiger.

Question 4.
What did Swami’s father ask him to prove?
Answer:
Swami’s father asked him to prove his bravery by sleeping alone that night and thereafter too in his office room.

Question 5.
Why did Swami try to change the topic when his father asked him to sleep alone?
Answer:
Swami tried to change the topic because he was afraid to sleep alone as he had always slept beside his granny. So, he wanted to divert his father’s attention to cricket.

II. Read the following sentences and say whether they are true or false.

Write T for true and F for false statements in the brackets. Correct the false statements.
1. Swami said that he would sleep alone from the next week. ( )
2. Swami’s father looked like a ghost in darkness. ( )
3. When Swami was snoring, his grandmother pulled the blanket away. ( )
4. Swami was really afraid of darkness. ( )
5. Swami wished that the tiger had killed the boy. ( )
Answer:
1. F
2. T
3. F
4. T
5. T
Correction of false statements:
1. Swami said that he would sleep alone from the first of next month.
3. When Swami was snoring, his father pulled the blanket away.

III. Tick the correct option to make the sentence true.

1. Swami was almost faint with fear because
a) his father would beat him.
b) he was afraid of ghosts.
c) a ghost entered his room.
d) he had a terrible dream.

2. Swami clutched the leg of ………………………….
a) his father.
b) his grandmother.
c) a chair.
d) the thief.
Answer:
1. b (✓)
2. d (✓)

Vocabulary

I. Pick out the synonyms from the story for each of the following words.

1. clear
2. bravery
3. shameful
4. hide
5. upset
6. argued
7. swore
8. unpleasant
9. tapped
10. damage
Answer:
1) clear: detailed
2) bravery: courage
3) shameful: disgraceful
4) hide: cover
5) upset: pained
6) argued: mumbled/exclaimed/opined
7) swore: cursed
8) unpleasant: bitter
9) tapped: patted
10) damage: risk

II. Read the conversation given below and fill in the blanks with appropriate words from the box.

Ruchira: I don’t know why the teacher ……(1)…… to give his mobile number?
Suhas: He might be worried that you would ……(2)…… him with your phone calls.
Ruchira: I have great ……(3)..… for him. I will never behave in a ……(4)…… manner.
Suhas: I am ……(5)…… that our teacher will not give his number. Anyhow, I like your ……(6)…… We are all ……(7)…… him.
Ruchira: I don’t think our teacher is ……(8)…… but he says everything ……(9)…….
Once he gave me a wonderful gift so I am always ……(10)…… to him.
Answer:
1) hesitated
2) disturb
3) respect
4) disgraceful
5) certain
6) courage
7) afraid of
8) terrible
9) sternly
10) grateful

III. Read the following clues given below to complete the word ladder.

Clues

1. Sandhya said _____________ that she hated him.
2. Sridhar is a ____________ boy of 10 years old.
3. Jyothi used to sleep beside her _______________.
4. The garden is full of ________________ coloured flowers.
5. I met my friend Kumar on my _________________ home.
Answer:
1) crossly
2) young
3) granny
4) yellow
5) way

IV. Proverbs

A proverb is a short sentence, usually known to many people, stating something commonly experienced or giving advice. Here are some English proverbs:

• Tit for tat.
• Where there is a will there is a way.
• A bad workman always blames his tools.

Every language has proverbs. In Telugu we call them ‘saamethalu’. Here is one example from Telugu:
‘kukka kaatuki cheppu debba’. It is important to know the meaning of a proverb before you use it.

Match the parts under A and B to make some proverbs. You can use the clues given within the brackets.
A                                                                                                                     B
1. An apple a day(search for a profession)           [ ]                       a. is a friend indeed.
2. A friend in need (rhymes with friend)               [ ]                       b. saves nine.
3. Failure is (search for ‘achievement’)                  [ ]                       c. mightier than the sword.
4. A stitch in time (search for a number)               [ ]                      d. keeps the doctor away.
5. The pen is (search for a weapon)                       [ ]                      e. the stepping stone to success.
6. Empty vessels (search for noise)                        [ ]                       f. the mighty ocean.
7. Little drops of water make                                 [ ]                       g. seldom bite.
8. Honesty (ends with ‘cy’)                                     [ ]                       h. while the sun shines.
9. Make hay (search for planet)                              [ ]                       i. is the best policy.
10. Barking dogs (search for what dogs do)          [ ]                       j. make much noise
Answer:
l) d
2) a
3) e
4) b
5) c
6) j
7) f
8) i
9) h
10) g

Grammar

Simple Past Tense:

The second form of the verb (V₂ form) is used as simple past tense. It is used to express that some action was completed or not completed in the past.
In Affirmaive sentences, only the V₂ form, ‘did + V₁ form’ pattern is used for the simple past tense.
Example :
1. I went to Vikarabad yesterday.
2. He came to see me last night.
3. I did not go to school last Monday.
4. Sita did dance (Emphasizing the action) on this stage last month.

In interrogative sentences (Questions) and negative sentences, ‘did + V₁‘ pattern is used for the simple past tense.
Examples :
1. When did you see this film?
2. Did you give him the book yesterday?
3. I did not write the exam last Sunday.
4. Guruvardhan did not come here last Friday.

Past Continuous Tense:

Structure of this tense is as follows, was/were + Verb with ‘ing’ form.
Ex: was going, were doing, was singing, were writing, was teaching etc.
Use: We use the past continuous tense to express that certain action was going on at a certain time in the past.
Examples: Affirmative sentences
1. At 11 a.m. yesterday, I was writing the exam.
2. My mother was cooking when the postman came.
3. We were chatting when our English teacher entered the classroom.

Negative sentences
1. They were not studying at this time last night.
2. We were not playing when he arrived here.

Questions (Interrogative sentences)
1. What were you doing then?
2. Were they playing at this time yesterday?
3. Was he sleeping in your period this morning?

Look at the following sentences from the text.
1. Father was sitting under the lamp and reading the newspaper.
2. He looked over the newspaper.
Sentence 1 is in the past continuous form. It coveys that the action was in progress at a particular point of time in the past.
In sentence 2, the verb ‘looked’ is in the simple past tense. It shows that the action was completed in the past.

I. Pick out 5 sentences from the story that use the Simple Past Tense and 5 sentences that use the Past Continuous Tense. Write them down in your notebook.

5 sentences that use the Simple Past Tense:
1) The newspaper gave a detailed account of the boy’s fight with the tiger.
2) At last, some people came that way and killed the tiger.
3) Swami rose quietly from his place.
4) He cursed the newspaper that had printed the tiger’s story.
5) Swami hurriedly got up and spread his bed under the bench and crouched there.

5 sentences that use the Past Continuous Tense:
1) Father was standing over him.
2) Father was only joking.
3) A tiger was chasing him.
4) Something was moving in the darkness.
5) Swami was following the whole conversation from under the blanket.

II. Read the following paragraph and fill in the blanks with the simple past or the past continuous forms.

While Swami’s father ………………… (read) the newspaper, Swami …………………(listen) to it. His father ………………… (ask) him to sleep alone. But he ………………… (be) afraid of ghosts. He ………………… (want) to sleep in his grandmother’s room. While he ………………… (sleep), he …………………(have) a terrible dream. A tiger ………………… (chase) him and he …………………(try) to escape.
Answer:
1) was reading
2) was listening
3) asked
4) was
5) wanted
6) was sleeping
7) had
8) was chasing
9) was trying

Writing

I. Summarize the story using the following hints.

Swami ___ the news report ___ about a boy’s fight ___ father’s advice ___ sleeps in his grandmother’s room ___ father insists on sleeping alone ___ a terrible dream ___ catches a thief ___ becomes a hero.
Answer:
One day Swami’s father read out some news in some newspaper for his son, Swami. The news was about the bravery of a village lad who was returning home by the jungle path. The newspaper gave a detailed account of the boy’s fight with the tiger.

After listening to the news, Swami said that a boy could not be brave enough to fight with a tiger. Then Swami’s father asked him to prove his courage. For that, his father advised him . to sleep for some nights alone in his office room. He wanted his son to do it that night itself. But Swami went into the porch and slept beside his granny. Swami never slept alone. He always slept beside his granny.

Then his father came to Swami and woke him up. He insisted Swami on his sleeping alone in the office room that night. Swami tried to escape but in vain. So he had to sleep alone in darkness in his.father’s room that night. Then Swami had a terrible dream. He could not sleep. Suddenly he heard that someone was coming towards him. He thought he was a ghost. So, at once, to protect himself, Swami bit into the knee of a thief. The thief cried out. Father and a servant came and caught the thief. Swami became a hero.

II. Write about an act of bravery that you or your family member or any one of your friends may have shown at some stage in your life.

An act of my bravery

My father runs a jewellery shop. The shop is open on all days. But it is closed on Sundays.

One Sunday evening, I was returning home. after playing cricket with my friends. I was coming on my bicycle. On my way home, when I came to my father’s shop, I found my father’s shop was kept open. I was surprised to see it open as it was a Sunday. I got down my bicycle and put it behind a tree and stood there silently to see what was going to happen. A few minutes later, I saw two thieves coming from the shop with a bag of jewellery and keeping it in their car, kept outside the shop. They later, went again into the shop to bring some more.

At once, without any hesitation, I ran towards the car and took out the air from all the tyres. Then I rode on my bicycle to the nearby police station and informed the police about the theft.

The police took me in their jeep and came to the spot. Seeing the police, the thieves began to run. But the police chased them and caught hold of them. All our jewellery was kept back in the shop and then it was locked.
The police congratulated me on my act of bravery. All my friends and neighbours praised me for my bravery. I felt happy as I had saved our property.

III. Change the story of ‘A Hero’ into a drama and enact it.

• Read Swami’s story once again.
• Identify the characters.
• Pick out the dialogues of the characters.
• Identify the locations of the events.
• Decide scenes and setting accordingly.
• Assign roles to the members of the groups.
• Enact the drama before the whole class.

Answer:
Scene – I
Swami’s house with father sitting in a chair and reading a newspaper and his son Swami standing behind him.
Characters: Swami, his father and his granny.
Father: listen, Swami! I’ll read out an interesting news for you.
Swami: What’s it, Dad?
Father: it’s about the bravery of a village lad who was returning home by the jungle path.
Swami: What’s there in it about his bravery?
Father: He came face to face with a tiger and fought with it. Later he climbed on tâ thetop branch of a tree and stayed there for half-a-day. Later some village people came that way and killed the tiger.
Swami: That couldn’t be. I think he must be a grown-up person.
Father: Don’t think so. Age and strength don’t matter with regard to courage/bravery.
Swami: Suppose I am very brave. Can I fight with a tiger?
Father: O.K. I will test your courage. Tonight, sleep alone in the dark in my office room and prove your bravery.
Swami: I will do it next month. Please put it off.
Father: No, come on with me.
(Father puts Swami alone in his office room. He leaves him in the dark but keeps the doors open)

Scene – II
Place: Father’s office room. Swami is sleeping under a bench.
Characters: Swami, a burglar, Father.
Swami to himself: I don’t know why father is cruel to me in this manner. I wish the tiger had not spared the village lad.
A burglar to himself: The door is open. I will enter the room and steal the valuable things. (The burglar walks ¡n and steals something. He comes near the boy.
(Swami hears the sound of his walkin close to him.)
Swami to himself: What is this sound? I think a devil is coming to kill me. I must do something now. I will dig my teeth into its leg.
(When the burglar comes nearer, Swami digs his teeth into the knee of the burglar.)
The burglar: Oh! I was bitten.
(Hearing the sound, Father and a servant come into the room and catch the thief.)

Scene – III
Place: School
Characters: Swami, his friends, a teacher and the Headmaster.
Teacher: Oh! You have acted bravely. I appreciate you.
Swami: Thank you, teacher.
Friends: Swami, you have done a marvellous thing. Congrats.
Swami: It’s O.K.
H.M.: Swami, you are a true scout. You have proved y.our bravery. We are proud of you.
Swami: Thank you, Sir.
(But the next day on wards, Swami sleeps in his usual place.)

IV. Have a discussion in the whole class on how the performance could be improved in terms of delivery of dialogues, costumes, action, settings, etc.
A Skit on ‘A Hero’.
The performance could be improved and made humorous if it was as follows.
When father exits the office room –

Swami: I am afraid I can’t be alone. What should I do? idea! I shall go unnoticed to himself into my father’s bed room, pick up his cell-phone and call my close friend, Guruvardhan.
(The boy tiptoes into his father’s bed room, picks up his mobile, comes out and makes phone call to his friend, Guruvardhan.)
Swami: HelIo Guru! I’m Swami.
Guruvardhan: Hello Swami ! What’s the matter? Why are you calling me at this time? Any problem?
Swami: Yes, Guru. Can you come to my house now and spare an hour with me?
Guruvardhan: Why?
Swami: I’ll tell you here. Please do come soon.
(Swami deletes the number of his friend from his father’s mobile from dialed numbers, keeps it there and comes back into his father’s office room. Half an hour later, his friend enters the room)

Swami : Hai! Come in. I feel bored being alone.
Guruvardhan: Why alone here?
Swami: My father does this as a test for my bravery. Give me some idea.
(Guruvardhan think over it for a while)
Guruvardhan: I’ll take some valuable things from this office room and throw them scattered at the gate of your house and go back home. Half an hour later, you cry out Thief, thief, I can’t chase him. Please help” and walk hurriedly to the gate. Your father comes. Tell him you are trying to catch the thief who entered and stole the things. Also tell him he has left them there and escaped. Your father then appreciates your bravery. How is it?
Swami: It’s a good idea. Let’s do it at once.
(They implement their plan. His friend has gone home, leaving the things at the gate)
Swami: Thief, thief! catch him. (Shouts loudly)
(His father and a servant come there with a torchlight in hands.)
Father: Where is the thief? What has happened?
Swami: Dad! A thief has entered the office room and stole some valuable things.
I heard the sound and cried. He began to run. I tried to catch him. But he escaped, leaving these things here.
Father: (looking at them) Oh! these are very valuable. Had I lost them, I would have been in great trouble. Really you have done a very good job. I appreciate your bravery.
(All the members of his family praise him.)

Can you solve these letter riddles?
1. What letter of the alphabet is an insect?
2. What letter is a part of the head?
3. What letter is a drink?
4. What letter is a body of water?
5. What letter is a pronoun like “you”?
6. What letter is an exclamation?
7. What letter is looking for causes?
8. Why is the letter “T” like an island?
Answer:
1. the letter is’B’.
2. the letter is ‘I’.
3. the letter is ‘T’.
4. the letter is ‘C’.
5. the letter is ‘U’
6. the letter is’O’
7. the letter is ‘Y’
8. ‘T’ is like an island because it is in the middle of water.

Study Skills

Change the words given in the box into different parts of speech. Some words may not have all the forms given in the table. You may use a dictionary if you like.

Try these tongue twisters

Three grey geese in a green field grazing.
Double bubble gum bubbles double.
Selfish Sal sells shell-fish.
How much wood would a woodchuck chuck if a woodchuck could chuck wood?

Listening and Speaking

I. Your teacher will read the story ‘Carried away by an Eagle’. Listen carefully and answer the questions that follow.

We often speak in fun about a bird carrying away a child. A mother might say to her little one, “Don’t be naughty, or a crow will carry you away.” But do such things really happen?

The following story however, is from real life. The place was a farmhouse near Trondheim in Norway. It was June 1932. A four-year-old child, Svenhild Hansen, was playing in the yard in front of the farmhouse. Suddenly a large eagle came down. It caught hold of the child in its claws and flew up. Luckily, only the child’s dress was held in his claws, so the child was not hurt.

The big bird carried the child for more than a kilometre. It was flying towards its nest. Eagles build their nests on high rocks. This one’s nest was on the side of a mountain.Growing tired, the bird put the child down on a flat rock. This rock was eight hundred feet high on the side of the mountain. The bird’s nest was just fifty feet away.

But by this time, the child’s mother and father, and a large party of men had set out to look for the child. They noticed the eagle flying round and round over a rock in the mountain. They thought that the child might be there, and climbed quickly to the place. But they did not have much hope that they would find her alive.

When they finally reached there, the little Svenhild was fast asleep. She was not even hurt except for a few scratches.

People say that usually, an eagle kills the animal it catches, before taking it to its nest. Why didn’t the eagle kill the child? We do not know. We can only say that the child was very, very lucky.
Svenhild is now a grown-up woman. She is married. But she still keeps the tom dress she wore during this amazing adventure.

1. How old was the child when she was picked up by the eagle?
Answer:
She was four years old.

2. In which country did the child live when she was picked up by the eagle?
Answer:
Norway.

3. Why did the eagle leave the child on a rock?
Answer:
Because the eagle grew very tired then.

4. Why did the eagle fly round and round over the rock?
Answer:
Because the girl was put down on that rock.

5. Why do you think that the girl was lucky?
Answer:
Because she was neither killed nor hurt.

6. Why do you think Svenhild still keeps the tom dress?
Answer:
To remember that amazing adventure.

II. Work in groups and retell the story ‘Carried away by an Eagle’ in your own words.

A four-year old girl named Svenhild Hansen, was in the yard in front of the farm house near Trondheium in Norway, in June 1932. Suddenly, she was picked up by the a large eagle in its claws. The bird was carrying the child away towards its nest on the side of a mountain. The girl’s dress was held in the claws of the eagle and so she was not hurt.

Being tired, the eagle put the girl on a flat rock on the side of a mountain. The bird’s nest was just 50 feet away.

Then the child’s parents came there with a large party of men who had noticed the eagle flying round and round over a rock in the mountain. They thought that the eagle might have killed the girl there. They climbed quickly to the place.

To their surprise and happiness, they found the girl fast asleep. She was not hurt except for a few scratches. Really she was lucky. The girl grew up and got married. But she kept the tom dress with her to recollect that amazing adventure.

A Hero Summary in English

One day Swami’s father was sitting under the hall lamp and reading the newspaper. When Swami came to him, he read out the news of the bravery of a village lad who was returning home by the jungle path. The lad, then, came face to face with a tiger. But he was not frightened. Instead, he flew up to a tree and stayed on it for half a day. At last some people came that way and killed the tiger. Then Swami told his father that a boy could not fight a tiger. His father said that courage is everything; strength and age don’t matter much. Swami’s father told Swami to prove his courage by sleeping alone in his office room that ^r night. Swami could not sleep alone. He always slept beside his granny in the porch. He would be trembling and awake all night if he did not sleep beside his granny. So he requested his father to let him do it from the first of next month. But his father did not agree. When Swami was sleeping by his granny as usual, his father came and woke him up. He then took him into his office room and order him to sleep on one of the benches in the room, alone. He put out the lights, but left the door open and went out. Swami was alone. He was afraid.

Swami spread his bed under the bench and crouched there. Soon he fell asleep. He had a dream that a tiger was chasing him. Swami tried to open his eyes but failed. So he groaned in despair.

Suddenly Swami heard a little rustling noise in the darkness. Swami was afraid that a devil was coming. But it was nothing but a thief that entered the office room as the door was kept open. The thief came very close to him. At once Swami clutched his leg and dug his teeth in.        .

The thief, then,, cried out that something had bitten his leg. Everyone in the house was awakened by the loud noise. Father and a servant came running with a light. Both of them caught hold of the thief. The thief was later taken a way by the police.

The next day, Swami’s classmates praised him. His teacher patted him for his courage and bravery. The headmaster said that Swami had bitten into the knee of a notorious house ­breaker and the police were grateful to him. ,

When father returned home that night, Swami, instead of sleeping alone in the office room, was seen sleeping beside his granny. His mother stopped his father from wakening him up.

A Hero Glossary

crossly (adv): a little angrily

scowl (n): an angry look or expression.

porch (n): a covered entrance to a building; a verandah.

sternly (adv): seriously and strictly.

disgraceful (adj): very bad; shameful.

tiptoed (v): walked quietly on the tips of his toes

curled (v): drew up his legs close to the body and curved his back

snoring (v): breathing roughly and noisily while sleeping

stirred (v): moved slightly

groaned (v): made a deep sad sound.

pleaded (v): requested

scorpions (n): small creatures with a poisonous sting in the long tail

laughing-stock: someone or something which seems stupid

tumbling (v): falling helplessly

scout (n): one who is trained in doing acts of public service

notorious (adj): well-known for some bad quality or act

faint (v): likely to lose consciousness

crouched (v): bent the knees close to the body in fear

encased (v): covered himself completely

crawled (v): moved slowly, keeping the body close to the ground

bravery (n): courage

lad (n): boy

path (n): way

jungle (n): forest

account (n): a written or spoken description of something that has happened,

coward (n): timid

beside (prep): by the side of

tremble (v): shake in a way that you cannot control

humbly (adv): politely

quietly (adv): silently (without making a noise)

whispered (v): spoke in a very low voice so that others could not hear it well

commanded (v): strongly ordered

AP State Syllabus AP Board 6th Class Maths Solutions Chapter 9 2D-3D Shapes Unit Exercise Textbook Questions and Answers.

AP State Syllabus 6th Class Maths Solutions 9th Lesson 2D-3D Shapes Unit Exercise

Question 1.
Give examples for each shape in the table.

Sphere	Cylinder	Cube	Cone
1.
2.
3.	.

Solution:

Sphere	Cylinder	Cube	Cone
1. Marbles	Chalk piece	Dice	Heap of rice
2. Laddu	Road roller	Ice cube	Tent
3. Tennis ball	Pillar of building	Rubic cube	Joker cap

Question 2.
Look at the adjacent figure and answer the following questions,
(i) What is the name of the triangle?
(ii) Write all sides, angles and vertices of the triangle.
Solution:
i) Name of the given triangle is ΔPQR.
ii) The sides of ΔPQR are \(\overline{\mathrm{PQ}}, \overline{\mathrm{QR}}\) and \(\overline{\mathrm{PR}}\) .
The angles of ΔPQR are ∠P, ∠Q and ∠R.
The vertices of ΔPQR are P, Q and R.

Question 3.
Look at the adjacent figure and answer the following questions.
(i) Write the name of this polygon.
(ii) Write the pairs of adjacent sides and adjacent angles.
(iii) Write all vertices, pairs of opposite sides and pairs of opposite angles.
Solution:
i) Name of the given polygon is quadrilateral EFGH.
ii) EH and FG are pair of adjacent sides of EF.
EF’ and GH are pair of adjacent sides of FG.
FG and EH are pair of adjacent sides of GH.
EF and HG are pair of adjacent sides of EH.
Adjacent angles of E are ∠H and ∠F.
Adjacent angles of F are ∠E and ∠G.
Adjacent angles of G are ∠F and ∠H.
Adjacent angles of H are ∠G and ∠E

iii)Vertices of the quadrilateral EFGH are E, F, G and H.
Opposite side of EF is GH.
Opposite side of FG is EH.
Pairs of opposite angles are ∠E, ∠G and ∠F, ∠H.

Question 4.
Say true or false.
(i) We can locate only one centre in a circle. [ ]
(ii) All chords are called diameters. [ ]
(iii) A square pyramid has squares as its faces. [ ]
Solution:
i) True
ii) False
iii) False

AP State Syllabus AP Board 6th Class Maths Solutions Chapter 9 2D-3D Shapes Ex 9.4 Textbook Questions and Answers.

AP State Syllabus 6th Class Maths Solutions 9th Lesson 2D-3D Shapes Ex 9.4

Question 1.
Write the shapes of the following.
(i) A brick (ii) A road roller (iii) Foot ball (iv) Joker cap
Solution:
i) Shape of a brick is cuboid.
ii) Shape of a road roller is cylinder.
iii) Shape of a foot ball is shpere.
iv) Shape of a joker cap is cone.

Question 2.
Fill in the blanks.
(i) The shape of heap of grain
(ii) The shape of a dice
(iii) The shape of a bubble
(iv) The shape of a candle
Solution:
i) Cone ii) Cube iii) Sphere

Question 3.
Match the following.

Solution:

Question 4.
Fill in the table.

Shape	No.of faces	No. of vertices	No. of edges
Cube
Triangular prism
Square pyramid
Cuboid

Verify Euler’s Formula for the data in the table.

We know that, the F + V = E + 2is Euler’s formula.
In the above table given shapes satisfy the Euler’s formula.

AP State Syllabus AP Board 6th Class Maths Solutions Chapter 9 2D-3D Shapes Ex 9.3 Textbook Questions and Answers.

AP State Syllabus 6th Class Maths Solutions 9th Lesson 2D-3D Shapes Ex 9.3

Question 1.
Look at the given quadrilateral and answer the following questions.
i) What are the sides of the given quadrilateral?
ii) What is the opposite side of \(\overline{\mathrm{AB}}\) ?
iii) What is the opposite vertex of B?
iv) What is the opposite angle of ∠C ?
v) How many pairs of adjacent angles are there? What are they?
vi) How many pairs of opposite angles are there? What are they?

Solution:
In the given quadrilateral ABCD,
i) It has four sides. They are \(\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{CD}} \text { and } \overline{\mathrm{AD}}\)
ii) Opposite side of \(\overline{\mathrm{AB}}\) is \(\overline{\mathrm{DC}}\)
iii) Opposite vertex to B is D.
iv) Opposite angle of ∠C is ∠BAD (or) ∠A.
v) It has four pair of adjacent angles are there. They are :
Adjacent angles of ∠A are ∠B and ∠D.
Adjacent angles of ∠B are ∠A and ∠C.
Adjacent angles of ∠C are ∠B and ∠D.
Adjacent angles of ∠D are ∠A and ∠C.
vi) It has two pairs of opposite angles are there. They are ∠A and ∠C; ∠B and ∠D.

Question 2.
Find the number of lines of symmetry in the following.

Solution:
i) Given adjacent figure is a square.
Number of lines of symmetry to a square are 4

ii) Given adjacent figure is a circle.
Number of lines of symmetry to a circle are infinite (many).

iii) Given adjacent figure is a triangle.
Number of lines of symmetry to the triangle are three.
(If it is an equilateral triangle).

AP State Syllabus AP Board 6th Class Maths Solutions Chapter 9 2D-3D Shapes InText Questions and Answers.

AP State Syllabus 6th Class Maths Solutions 9th Lesson 2D-3D Shapes InText Questions

(Page No. 125)

Question 1.
Draw six different types of rough sketches of polygons in your notebook. In which case, it is not possible to form a polygon ?
Hence, what is the least number of sides needed to form a polygon ? Obviously three.
Solution:

From the above figure we conclude that with one side and two sides cannot form a polygon. So, atleast three sides needed to form a polygon.

Check Your Progress (Page No. 127)

Look at the adjacent figure.

Question 1.
Which points are marked in the interior of A GHI ?
Solution:
The points marked in the interior of AGHI are A, B and 0.

Question 2.
Which points sure marked on the triangle?
Solution:
The points marked on the triangle are G, P, H, I and Y.

Question 3.
Which points are’marked in the exterior of A GHI ?
Solution:
The points marked in the exterior of AGHI are M, R, S, X and Z.

(Page No. 130)

Question 1.
Take a rectangular sheet (like a post-card). Fold it along its length so that one half fits exactly over the other half. Is this fold a line of symmetry ? Why ?
Solution:
Yes. Because the two parts of the rectangular sheet (post-card) coincide exactly with each other.
So, the folded line is the line of symmetry.

Question 2.
Open it up now and again fold along its width in the same way. Is this second fold also a line of symmetry ? Why ?
Solution:
Yes. Because the two parts of the rectangular sheet (post-card) coincide exactly with each other.
So, the second folded line also a line of symmetry.

Question 3.
Do you find that these two lines are the lines of symmetry ?
Solution:
Yes. These two lines are the lines of symmetry. One is line of symmetry along length and the other is line of symmetry along width.

Project (Page No. 130)

Question 1.
Collect symmetrical figures from your surroundings and prepare a scrap book.
Solution:

AP State Syllabus AP Board 6th Class Maths Solutions Chapter 9 2D-3D Shapes Ex 9.2 Textbook Questions and Answers.

AP State Syllabus 6th Class Maths Solutions 9th Lesson 2D-3D Shapes Ex 9.2

Question 1.
Look at the given triangle and answer the following questions.
i) Which points are marked in the exterior of the triangle?
ii) Which points are marked on the triangle?
iii) Which points are marked in the interior of the triangle?

Solution:
i) The points marked in the exterior of the triangle are X, Y and Z.
ii) The points marked on the triangle are A, I, B, J and C.
iii) The points marked in the interior of the triangle are K, L and O.

Question 2.
Look at the adjacent figure. Answer the following questions.
i) How many sides are there in the triangle? What are they?
ii) How many vertices lie there on the triangle? What are they?
iii) What is the side opposite to the vertex P?
iv) What is the vertex opposite to \(\overline{\mathrm{PR}}\) ?

Solution:
In the given ∆PQR,
i) It has three sides. They are \(\overline{\mathrm{PQ}}, \overline{\mathrm{QR}}\) and \(\overline{\mathrm{PR}}\)
ii) It has three vertices. They are P, Q and R.
iii) The side opposite to the vertex P is \(\overline{\mathrm{QR}}
iv) The vertex opposite to the side [latex]\overline{\mathrm{PR}}\) is Q.

Question 3.
Look at the given triangle and answer the following questions.
i) How many angles are there in the triangle? What are they?
ii) What is the angle opposite to \(\overline{\mathrm{MN}}\) ?
iii) Where is the right angle in the given triangle ?

Solution:
In the given ∆MON,
i) It has three angles, they are ∠MNO, ∠NOM and ∠OMN.
ii) Angle opposite to the side \(\overline{\mathrm{MN}}\) is ∠MON or ∠O.
iii) In the triangle ∠MON is the right angle.

AP State Syllabus AP Board 6th Class Maths Solutions Chapter 9 2D-3D Shapes Ex 9.1 Textbook Questions and Answers.

AP State Syllabus 6th Class Maths Solutions 9th Lesson 2D-3D Shapes Ex 9.1

Question 1.
What is the name of four sided polygon? Draw the rough sketch.
Solution:
A four sided polygon is called a quadrilateral.

ABCD is a quadrilateral.

Question 2.
Draw a rough sketch of pentagon.
Solution:
A five sided polygon is called a pentagon.
So, pentagon has five sided figure.

ABCDE is a pentagon.

Question 3.
Write all the sides of the given polygon ABCDEF.
Solution:
Given polygon ABCDEF is a Hexagon.
Its six sides are \(\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{CD}}, \overline{\mathrm{DE}}, \overline{\mathrm{EF}} \text { and } \overline{\mathrm{FA}}\)
So, it is called a Hexagon.

Question 4.
Write the interior angles of the polygon PQRST.
Solution:
Given the polygon PQRST has five sides.
So, it is called a Pentagon.
It has five interior angles.
They are ∠TPQ, ∠PQR, ∠QRS, ∠RST and ∠STP.
They can also be written as ∠P, ∠Q, ∠R, ∠S, ∠T.

Question 5.
Measure the length of the sides of the polygon PQRST.
Solution:
The given polygon has five sides.
They are \(\overline{\mathrm{PQ}}\) = 2cm; \(\overline{\mathrm{QR}}\) = 2.5 cm;
\(\overline{\mathrm{RS}}\) .= 2.4 cm; \(\overline{\mathrm{ST}}\) = 2.2 cm, \(\overline{\mathrm{PT}}\) = 2.5 cm
It’s a pentagon.

SCERT AP 7th Class Maths Solutions Pdf Chapter 7 Ratio and Proportion Ex 7.1 Textbook Exercise Questions and Answers.

AP State Syllabus 7th Class Maths Solutions 7th Lesson Ratio and Proportion Ex 7.1

Question 1.
Pavan and Roshan started a business with ₹ 1,50,000 and ₹ 2,00,000 respectively. After nine months Roshan left the business. At the end of the year, they got a profit of ₹ 45,000. Then find the profits shared by Pavan and Roshafi.
Answer:
Given Pavan’s investment =₹ 150000
Pavan’s period in business = 1 year = 12 months
Roshan’s investment = ₹ 200000
Rohan’s period in business = 9 months

The ratio of investments of Pavan to Roshan = 150000 : 200000 = 3 : 4
The ratio of periods of business of Pavan to Roshan = 12 : 9 = 4 : 3
The profit should be distributed on the basis of the compound ratio of investments and period = 3 : 4 and 4 : 3 is
3 × 4 : 4 × 3 = 12 : 12

Therefore, compound Ratio =1:1 (i.e.,) they should share profit equally. Profit = ₹ 45,000
Total parts = 1 + 1 = 2
Pavan’s profit = 45000 × \(\frac{1}{2}\) = ₹ 22500
Roshan’s profit = 45000 – 22500 = ₹ 22,500

Question 2.
Salman started a hotel with an amount of ₹ 75,000. After 5 months Deepak joined with an amount of ₹ 80,000. At the end of the year they earned a profit of ₹ 73,000. How will they share their profit?
Answer:
Given Salman’s investment = ₹ 75000
Salman’s period in business = 1 year = 12 months
Deepak’s investment = ₹ 80000 Deepak’s period in business = 7 months
The ratio of investments of Salman to Deepak = 75000 : 80000 = 15 : 16
The ratio of periods of business of Salman to Deepak = 12 : 7

The profit should be distributed on the basis of compound ratio of 15 : 16 and 12 : 7 is
15 × 12 : 16 × 7 = 180 : 112
= 45 : 28
Therefore, compound ratio = 45 : 28
Profit = ₹ 73,000
Total parts = 45 + 28 = 73

∴ Salman’s profit = 73000 × \(\frac{45}{73}\)
= ₹ 45000

Deepak’s profit = 73000 × \(\frac{28}{73}\)
= ₹ 28,000

Question 3.
Ramayya took a grass field for rent for grazing his 24 cows. After 5 months, Somayya also joined with him for his 40 cows. At the end year they paid a rent of ₹ 35,500. What would be the rent paid by each of them?

Answer:
Given number of cows grazed by Ramayya = 24
Grazed months 1 year =12 months.
Number of cows grazed by Somayya = 40
Grazed months = 7 months.

The ratio number of grazed cows
= 24 : 40 = 3 : 5

The ratio of months grazed = 12 : 7
The rent should be distributed on the basis of compound ratio of 3 : 5 and 12 : 7 is
3 × 12 : 5 × 7 = 36 : 35

Therefore, compound ratio = 36 : 35
Annual Rent = ₹ 35,500
Total parts = 36 + 35 = 71

Rent paid by Rarnavya = 35,500 × \(\frac{36}{71}\)
= ₹ 18,000
Rent paid by Somaa = 35,500 × \(\frac{35}{71}\)
= ₹ 17,500

Question 4.
Ravi started a business with ₹ 2,10,000. After a few months, Prakash joined the business with an amount of ₹ 3,60,000. At the end of the year if they got a profit of ₹ 1,20,000 each, then find after how many months did Prakash join in the business?
Answer:
Given Ravi’s investment = ₹ 2,10,000
Ravi’s period in business = 1 year = 12 months
Prakash’s investment = ₹ 3,60,000

Let, Prakash’s period in business = x months
The Ratio of investments of Ravi and Prakash = 210000 : 360000 = 7 : 12
The ratio of periods of business of Ravi to Prakash = 12 : x

The profit should distributed on the basis of compound ratio of 7 : 12 and 12 : x is
7 × 12 : 12 × x = 84 : 12x
= 7 : x
Therefore, compound ratio = 7 : x
They got equal profits.

So, Total profit = 120000 + 120000 = ₹ 2,40,000
Total parts = 7 + x
So, x = 7
So Prakash joined after (12 – 7) = 5 months
Prakash’s period in business = x
= 7 months
So, Prakash joined in business after (12 – 7) = 5 months.

AP State Syllabus AP Board 7th Class English Textbook Solutions Chapter 3C The Magic of Silk Textbook Questions and Answers.

AP State Syllabus 7th Class English Solutions Chapter 3C The Magic of Silk

7th Class English Chapter 3C The Magic of Silk Textbook Questions and Answers

I. Answer the following questions.

Question 1.
Who do you think the old man is? Justify your reasons.
Answer:
The old man, I think, is God or a messenger from God because a man could not do such miracle.

Question 2.
Do you believe in miracles?
Do you think that magic and miracles are the same? If not, give your reasons.
Answer:
Yes, I believe in miracles as I believe in the Almighty.
Magic and Miracles are not the same.
A Miracle is an act or event that does not follow the laws of nature and is believed to be caused by God. But ’magic’ is the secret power of appearing to make impossible things happen by saying special words or doing special things. A man can do magic but not miracles. So, they are not the same.

Question 3.
If you were Siew Mei, how would you feel?
Answer:
If I were Siew Mei, I would highly get astonished to see the change of long white beard into the finest silk thread. I would feel it a miracle and get immense happiness and the feeling that luck favoured me.

What is an anagram?
An anagram is the rearrangement of the letters of a word, name, phrase, sentence, title, or the like into another word or phrase. But ALL the letters of the name or phrase must be used ONCE and only ONCE. This is the basic rule of anagramming. The best anagrams are meaningful and relate in some way to the original subject. Example: if we take the word ‘the classroom’ and rearrange the letters in it, we get ‘school master’. So, ‘school master’ is an anagram of‘the classroom’ and vice versa. Here are some other anagrams: mother-in-law _ woman Hitler; debit card _ bad credit; dormitory _ dirty room; eleven plus two _ twelve plus one.
Write some anagrams and display them on the wall magazine.
Answer:

Original expression	Changed expression
the classroom	school master
mother-in-law	woman Hitler
debit card	bad debit
dormitory	dirty room

The Magic of Silk Summary in English

Long ago, there lived an old woman with her daughter, Siew Mei in a hut in the forest. Her husband had been killed by a tiger, some years ago.

Siew Mei helped her mother. She did cooking and cleaning herself. They had a garden in front of their hut. Siew Mei looked after the silkworms, growing in the garden. Siew Mei made beautiful silk from the fine silk thread given by the silkworms. She sold the silk to the travellers in the village market and got money. With that money, she bought items of food and other things.

One day as Siew Mei was returning home, it started to rain heavily and it wats getting dark. So, Siew Mei ran into the first hut she saw. She found nobody in the hut. Then Siew Mei swept the dirty floor and washed the unwashed bowls and pots. She kept the hut clean and tidy. When the rain stopped, Siew Mei came out of the hut. There she saw a long-bearded old man, aged about a hundred years. The man saw the girl and looked at the clean and tidy hut. He understood what the girl had done. He was so pleased that he cut off a little of his white beard and put it in a piece of cloth. He tied it up and gave her the bundle.

The old man told Siew Mei not to give the bundle to anyone. He also told her to open the bundle at her home.

Siew Mei reached her hut with the bundle. She told her mother what had happened. Then she opened the bundle to show the old man’s beard. When the handle was opened, they were surprised to see the finest silk thread in the whole of China, in that bundle. With that finest silk thread, they made the finest silk that they had ever seen. They also noticed that the bundle of silk thread still remained exactly the same size as before.

With the luck they got, the old woman and her daughter, Siew Mei became famous and lived happily together.

By this jesson, one should know that unselfish service fetches a person fame as well as happiness. One can understand by reading this story, how the miracle happened and who the person who did the miracle might be.

The Magic of Silk Glossary

enough (adj): sufficient

had better (aux.v.): should

strange (adj): unknown

a present (n): a gift

beard (n): hair on the cheeks, on and under the chin.

glad (adj): happy

surprise (n): wonder (or) astonishment

noticed (v): observed

far (adv): distant

AP State Syllabus AP Board 6th Class Maths Solutions Chapter 8 Basic Geometric Concepts InText Questions and Answers.

AP State Syllabus 6th Class Maths Solutions 8th Lesson Basic Geometric Concepts InText Questions

(Page No. 111)

i) How many rays are there ?
Solution:
Four

ii) How many coins are close to player Q ?
Solution:
B, C and D coins are close to player Q.

iii) While striking with striker there is a possibility of a coin touches with any other. Draw all such possibilities in the given picture by means of the line segments.
Solution:
\(\overline{\mathrm{CB}}\) and \(\overline{\mathrm{DE}}\) .

iv) How many such line segments can be drawn in the picture ?
Solution:
\(\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{ED}}, \overline{\mathrm{AC}}, \overline{\mathrm{AE}}, \overline{\mathrm{CD}}, \overline{\mathrm{CE}}, \overline{\mathrm{AD}}, \overline{\mathrm{BD}} \text { and } \overline{\mathrm{BE}}\)

Let’s Do (Page No. 112)

Question 1.
Observe the table and their notations and fill the gaps.

Solution:

Lets Explore (Page No. 114)

Question 1.
Measure the lengths of all line segments in the given figures by using divider and scale. Then compare the sides of the given figures.

Solution:
i) In ΔABC; \(\overline{\mathrm{AB}}\) = 2.2 cm; \(\overline{\mathrm{BC}}\) = 2 cm and \(\overline{\mathrm{AC}}\) = 2.2 cm ‘
2.2 cm = 2.2 cm > 2 cm i.e., \(\overline{\mathrm{AB}}=\overline{\mathrm{AC}}>\overline{\mathrm{BC}}\)
Two sides are equal and one side is different in length.

ii) In PQRS rectangle \(\overline{\mathrm{PS}}=\overline{\mathrm{QR}}\) = 2.7 cm; \(\overline{\mathrm{P Q}}=\overline{\mathrm{RS}}\) = 1.8 cm and \(\overline{\mathrm{PR}}=\overline{\mathrm{QS}}\) = 3.2 cm.
Opposite sides are equal and diagonals are equal in length,

iii) In KLMN square \(\overline{\mathrm{KL}}=\overline{\mathrm{LM}}=\overline{\mathrm{MN}}=\overline{\mathrm{KN}}\) = 1.8 cm
All sides are equal in length.

Let’s Do (Page No. 115)

Question 1.
(i) Find the parallel lines in the below figure. Name, write and read them.

Solution:
a) l, m are parallel lines.
We denote this by writing l || m and can be read as l is parallel to m.
b) n, o are parallel lines.
We denote this by writing n||o and can be read as n is parallel to o.
c) p, q are parallel lines.
We denote this by writing p||q and can be read as p is parallel to q.

ii) Find the intersecting lines in the above figure. Name, write and read them.
Solution:
Intersecting lines are (l, q); (m,q); (m, r); (n,q); (p, r); (o, r); (o, q); (q, r);

iii) Find the concurrent lines in the above figure. Name, write and read them.
Solution:
Three or more lines passing through the same point are called concurrent lines. Concurrent lines are (l, o, p) & (m, n, p).

iv) Find the perpendicular lines in the above figure. Name, write and read them.
Solution:
a) p, o are perpendicular lines.
We denote this by writing p ⊥ o and can be read as p is perpendicular to o.
b) p, n are perpendicular lines.
We denote this by writing p ⊥ n and can be read as p is perpendicular to n.
c) n, q are perpendicular lines.
We denote this by writing n ⊥ q and can be read as n is perpendicular to q.
d) q, o are perpendicular lines.
We denote this by writing q⊥ o and can be read as q is perpendicular to o.

(Page No. 119)

Question 1.
Measure the angles at the vertices.

Solution:

In triangle ABC,
m∠BAC = 60°
m∠ABC = 60°
m∠ACB = 60°

In triangle XYZ,
m∠YXZ = 40°
m∠XYZ = 70°
m∠XZY = 70°

In triangle PQR,
m∠QPR = 35°
m∠PQR = 38°
m∠PRQ = 107°

AP State Syllabus AP Board 7th Class English Textbook Solutions Chapter 3B Home They Brought Her Warrior Dead Textbook Questions and Answers.

AP State Syllabus 7th Class English Solutions Chapter 3B Home They Brought Her Warrior Dead

7th Class English Chapter 3B Home They Brought Her Warrior Dead Textbook Questions and Answers

I. Answer the following questions.

Question 1.
How do you think the warrior lost his life?
Answer:
The warrior must have fought bravely in the battle field. He must have been killed by an enemy soldier.

Question 2.
What was unnatural with the warrior’s wife?
Answer:
Even though the dead body of her husband was placed before her, she neither swooned nor uttered a cry. Her maidens did their best to make her cry but they all failed. It was unusual.

Question 3.
What did the maidens do to make her cry?
Answer:
They praised the warrior as worthy to be loved, and the truest friend and the noblest foe. A maiden took the face-cloth from the face of the dead warrior.

Question 4.
Why did they want her to cry?
Answer:
They wanted her to cry because they thought that she would die if she did not cry.

Question 5.
Who succeeded in making the woman cry?
Answer:
A nurse of ninety-years succeeded in making the woman cry.

Question 6.
Look at the word order in the title. Normally we say “They brought her dead warrior home.”
Why do you think the poet changed the word order? Is it beautiful? Discuss. Find other lines with a similar order in the poem.
Answer:
The poet changed the word order so as to make the title attract the reader’s attention.

Project

I. Here is a list of India’s neighbouring countries. Collect the information mentioned below in the table. After collecting this information display it in “Our Reading Corner” (ORC).

Answer:

Home They Brought Her Warrior Dead Summary in English

A warrior died in a war. His dead body was brought home by some of his friends, the other soldiers. His wife was too sensitive. When she heard the news of her husband, she was greatly shocked. In her shock, she almost went into a typical semi-unconscious state. She neither fainted nor cried. The maidens, who were watching her, said that she would die, if she did not cry. They made all possible attempts to bring her to normal state.

They praised the warrior as worthy to be loved. Some praised him as the truest friend and the noblest foe. All their admiration and praising words of the soldier failed to bring her to her normal state. She did not speak a single word. She was totally unmoved.

A maiden made another attempt. She slowly went to the dead body and removed the face-cloth from his face. Her trial also failed. The state of the dead warrior’s wife remained the same. She did not move. She did not cry.

A nurse of ninety-years attempted. She put the child of the dead warrior in the lap of the woman. The touch of her child had a magical charm. The woman shed tears. She cried out that she would live for the sake of the child. She regained her full consciousness. She realised that she had to live to look after her child.

Home They Brought Her Warrior Dead Glossary

wanlor(n): soldier good at fighting

swooned(v): became unconscious

stole(v): moved silently

foe(n): enemy

tempest(n): storm in the ocean

they (here): the other soldiers

uttered (v): spoke

maidens (n): noble ladies

praised (v): admired

soft and low (adv): slowly and gently

worthy (adj): rightly fit or suitable

for thee (prn): for your sake

AP State Syllabus AP Board 6th Class Maths Solutions Chapter 7 Introduction to Algebra InText Questions and Answers.

AP State Syllabus 6th Class Maths Solutions 7th Lesson Introduction to Algebra InText Questions

Let’s Explore (Page No. 102)

Question 1.
Arrange 2 matchsticks to form the shape Continue the same shape for 2 times, 3 times and 4 times. Frame the rule for repeating the pattern.
Solution:
To make the given shape 2 matchsticks are needed.
To make the given 2 shapes 4 matchsticks are needed.
To make the given 3 shapes 6 matchsticks are needed.
To make the given 4 shapes 8 matchsticks are needed.
Continue and arrange the information in the following table.

Number of matchsticks required = 2 × Number of shapes to be formed
= 2 × x = 2x

Question 2.
Rita took matchsticks to form the shape
She repeated the pattern and gave a rule.
Number of matchsticks needed = 6.y, where y is the number of shapes to be formed. Is it correct ? Explain.
What is the number of sticks needed to form 5 such shapes ?
Solution:

To make the given shape 6 matchsticks are needed.
To make the given 2 shapes 12 matchsticks are needed.
To make the given 3 shapes 18 matchsticks are needed.
Continue and arrange the information in the following table.

Yes, it is correct.
Number of matchsticks required = 2 × Number of shapes to be formed
= 2 × y = 2y
Number of matchsticks needed to form 5 such shapes = 6 × 5 = 30

Let’s Explore (Page No. 103)

Question 1.
A line of shapes is constructed using matchsticks.

Shape-1 Shape-2 Shape-3 Shape-4
i) Find the rule that shows how many sticks are needed to make a line of such shapes ?
ii) How many matchsticks are needed to form shape -12 ?
Solution:

Number of matchsticks 3 5 7 9
i) Let us know the pattern
S₁ = 3 = 2 + 1 = (1 × 2) + 1
S₂ = 5 = 4 + 1 = (2 × 2) + 1
S₃ = 7 = 6 + 1 = (3 × 2) + 1
S₄ – 9 = 8 + 1 = (4 × 2) + 1
Now the rule for this pattern is number of matchsticks.

ii) Used to make ‘n’ number of shapes is Sn = (n × 2) + 1 = 2n + 1
Number of matchsticks needed to form shape – 12 is
S₁₂ = 2(12) + 1 = 24 + 1 = 25 sticks.

Check Your Progress (Page No. 105)

Question 1.
Fill the following table as instructed. One is shown for you.

S.No.	Expression	Verbal Form
1.	y + 3	Three more than y
2.	2x – 1
3.	5z
4.	\(<table border=”2″>\)

Solution:

S.No.	Expression	Verbal Form
1.	y + 3	Three more than y
2.	2x – 1	One less than the double of x
3.	5z	5 times of z
4.	\(<table border=”2″>\)	Half of the m

Let’s Explore ? (Page No. 106)

Question 1.
Find the general rule for the perimeter of a rectangle. Use variables T and ‘b’ for length and breadth of the rectangle respectively.
Solution:
Given length of rectangle = l
breadth of rectangle = b
We know that the perimeter of rectangle is twice the sum of its length and breadth.
Sum of length and breadth = l + b
Twice the sum of length and breadth = 2 × (l + b)
Rule for the perimeter of a rectangle = 2(l + b)

Question 2.
Find the general rule for the area of a square by using the variable ‘s’ for the side of a square.
Answer:
Given side of a square = s
We know that the area of a square is the product of side and side.
Area of a square = side × side
Rule for the area of a square = s.s

Side	Area
1	1 × 1
2	2 × 2
3	3 × 3
4	4 × 4
………..	…………
s	S × s

(Page No. 107)

Question 1.
Find the nth term in the following sequences.
0 3, 6, 9, 12, ii) 2, 5, 8, 11, iii) 1, 4, 9, 16,
Solution:
i) Given number pattern is 3, 6, 9, 12,……………..
To find the nth term in the given pattern, we put the sequence in a table.

First number = 3 × 1
Second number = 3 × 2
nth number = 3 × n = 3n
So, the nth term of the pattern 3, 6, 9, 12, is 3n.

ii) Given number pattern is 2, 5, 8, 11,
To find the nth term in the given pattern, we put the sequence in a table.

First number = 2 = 3 × 1 – 1
Second number = 5 = 3 × 2 – 1
Third number = 8 = 3 × 3 – 1
nth number = 3 × n – 1 = 3n – 1
So, the nth term of the pattern 2, 5, 8, 11 is 3n – 1.

iii) Given number pattern is 1, 4, 9, 16,
To find the nth term in the given pattern, we put the sequence in a table.

First number =1 = 1 × 1
Second number = 4 = 2 × 2
Third number =9 = 3 × 3
nth number = n × n = n²
So, the nth term of the pattern 1, 4, 9, 16 is n².

Check Your Progress (Page No. 108)

Question 1.
Complete the table and find the value of ‘p’ for the equation \(\frac{\mathbf{p}}{\mathbf{3}}\) = 4

p	\(\frac{\mathbf{p}}{3}\) = 4	Condition satisfied ? Yes/ No
3
6
9
12

Solution:

p	\(\frac{\mathbf{p}}{3}\) = 4	Condition satisfied ? Yes/ No
3	\(\frac{3}{3}\) ≠1 ≠ 4	No
6	\(\frac{6}{3}\) ≠2 ≠ 4	No
9	\(\frac{9}{3}\) ≠ 3 ≠ 4	No
12	\(\frac{12}{3}\) ≠ 4 ≠ 4	Yes

Question 2.
Write LHS and RHS of following simple equations.
i) 2x + 1 = 10
ii) 9 = y – 2
iii) 3p + 5 = 2p + 10
Solution;
i) 2x+ 1 = 10
Given equation is 2x + 1 = 10
L.H.S = 2x + 1
R.H.S = 10

ii) 9 = y – 2
Given equation is 9 = y – 2
LHS = 9
RHS = y – 2

iii) 3p + 5 = 2p + 10
Given equation is 3p + 5 = 2p + 10
LHS = 3p + 5
RHS = 2p + 10

Question 3.
Write any two simple equations and write their LHS and RHS.
Solution:
i) Consider 8x + 3 = 4 is a simple equation.
L.H.S = 8x + 3
RHS = 4

ii) Consider 5a + 6 = 8a – 3 is a simple equation.
LHS = 5a + 6
RHS = 8a – 3

Let’s Explore (Page No. 109)

Observe for what value of m, the equation 3m = 15 has both LHS and RHS become equal.
Solution:
Given equation is 3m = 15
If m = 1, then the value of 3m = 3(1) = 3≠15 ∴ LHS ≠RHS
If m = 2, then the value of 3m = 3(2) = 6 ≠ 15 ∴ LHS ≠ RHS
If m = 3, then the value of 3m = 3(3) = 9≠15 ∴ LHS ≠ RHS
If m = 4, then the value of 3m = 3(4) = 12 ≠ 15 ∴ LHS ≠ RHS
If m = 5, then the value of 3m = 3(5) = 15 = 15 ∴ LHS = RHS
From the above when m = 5 the both LHS and RHS are equal