Monday 24 September 2012


1
Summative Assessment - I
Sample Question Paper
Class X
ENGLISH-Language and Literature
MM-80 Time: - 3 Hours
Note; - The paper is divided into four sections.
Section A Reading comprehension 15 Marks
Section B Writing 15 Marks
Section C Grammar 15 Marks
Section D Text Books 35 Marks
General Instruction – All questions are compulsory.
Marks are indicated against each question.
Section -A
(Reading -15 Marks)
Q 1.
Read the following passage carefully and answer the questions by writing

the options that you consider the most appropriate in your answer sheet.
(5 Marks)

Fifty years ago people ate ice cream only in summer .Now it is eaten all the year
round. It originated in the Orient, centuries before English schoolboys first tasted it.
Marco Polo saw people eating ice cream there and brought back the idea to Italy.
From Italy the idea was carried to France, It became very popular in France with the
rich, and an effort was even made to keep the recipes a secret from the common
people. But, of course, they soon learned about this delicious new food and ice
cream became popular with everyone. Soon it spread all over the world. The first
factory to manufacture ice cream was started in Baltimore, Maryland, in 1851.
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However, the real development of ice cream and the ice cream business didn’t take
place until after 1900 with new developments in refrigeration.
The basis of all ice cream is cream, milk or milk solids, sugar, and sometimes
eggs. Vanilla, chocolate, berries, fruit ingredients, and nuts are added as flavors.
This is the usual proportion of ingredients in ice cream: about 80 to 85 percent
cream and milk products, 15 percent sugar, half to four and a half per cent
flavoring, and three-tenths of one per cent stabilizer.
A small amount of gelatin is used in order to retain the smoothness of the ice cream
by preventing the formation of ice crystals.
When you eat a third of a pint of vanilla ice cream, you are getting about as much
calcium, protein, and vitamin B as are in half a cup of whole milk, and as much
vitamin A and calories as are in one cup of milk.
A. The major change towards Ice cream is that
i.
it is eaten throughout the year
ii.
it is eaten as a desert
iii.
it is eaten in summer
iv.
it is eaten in winter
B. Ice cream became popular with everyone
i.
when the idea was carried from Italy to France
ii.
when English school boys tasted it
iii.
when the rich in France started eating it
iv.
when the common people learned about its recipe
C. The introduction of refrigeration led to the
i.
increased consumption of ice cream
ii.
development of the ice cream business
iii.
increase in the production of ice cream
iv.
improvement in the quality of ice cream
D. The smoothness of ice cream is retained by
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i. forming ice crystals
ii. using a small amount of gelatin
iii. using eggs
iv. using cream and milk
E. Find a word from the passage that means the same as “tasty”
i.
recipes
ii.
gelatin
iii.
delicious
iv.
flavouring
Q 2. Read the given poem carefully and answer the questions by writing options you
consider the most appropriate in your answer sheet against the correct question
number. (5 Marks)
PETE AT THE ZOO
I wonder if the elephant
Is lonely in his stall
When all the boys and girls are gone
And there is no shout at all,
And there is not one to stamp before,
No one to note his might.
Does he hunch up as I do,
Against the dark of night?
Gwendolyn Brooks
A. From these lines we understand that the speaker:
i. is fond of the dark
ii. is scared of being alone
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iii. enjoys being alone
iv. hates being left alone in the dark
B. The speaker wonders if the elephant is lonely because:
i. all the boys and girls have gone
ii. the boys and girls are no longer playing with the elephant
iii. the speaker has not visited the elephant
iv. the speaker herself is lonely
C. The elephant hunches up because
i. he is tired and lonely
ii. his back is aching
iii. he is frightened of the dark
iv. he is frightened of the other animals
D. With reference to the poem, what does
‘might’
mean?
i. Uncertainty
ii. Doubt
iii. Strength
iv. Ability
E. The last two lines suggest that the poet
i. enjoys being alone as she finds the children too noisy
ii. likes night because she is not very social
iii. does not like night because it makes her feel lonely
iv. does not like night because the elephant is not with her
Q3. Read the following passage carefully and answer the questions by writing the
option that you consider the most appropriate in your answer sheet.
(1X5 = 5 Marks)
Unconsciousness is a state where a person appears to be in deep sleep from where he/ she
cannot be awoken. The individual does not respond to any external stimuli, like sprinkling
clod water on the face, and for that matter even painful ones like piercing with a pin,
tingling a nerve etc. This insensible state is brought about by some interference in the
normal functioning of the brain and the nervous system.
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Unconsciousness when partial is called stupor and when complete is called coma. In cases
of stupor, the individual can be roused with difficulty but the eyelids cannot be opened due
to resistance by the individual. In a coma, however there is no response when an
individual is being called, the lid can be opened without any resistance.
The usual case of unconsciousness includes fainting, sunstroke, concussion (brain injury),
etc. Fainting is caused by the temporary reduction in the blood supply to the brain because
of fright, unexpected good or bad news etc. People held up in stuffy places like the
elevators often faint. A sudden fall in blood pressure can also cause fainting. The
individual appears pale, becomes weak and slow, breathing becomes shallow and skin
turns cold and clammy. Excessive summer heat can make the individual faint. Prolonged
exposure to sun may cause sunstroke, which starts with headache, vomiting, dizziness,
cramps or dryness of the throat.
Concussion commonly results in unconsciousness. Direct injury to the brain caused by
either a blow on the head or a fall from a height etc may result in concussion. The patient
may ‘black out’ for a short time. An individual could suddenly become unconscious due to
a heart attack. The initial signs are vomiting, profuse sweating and pain on the left side of
the chest.
A. Unconsciousness is caused
i.
by piercing with a pin
ii.
by tingling a nerve
iii.
by some interference in the normal functioning of the nervous system
iv.
by sprinkling cold water on the face
B. Stupor is
i. complete unconsciousness
ii.
partial unconsciousness
iii.
deep sleep
iv.
also known as coma
C. Temporary reduction in the blood supply to the brain usually results in
i. sleep
ii. coma
iii. fainting
iv. low blood pressure
D. The initial signs of heart attack are
i. vomiting, dizziness and cramps
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ii. low blood pressure and clod skin
iii. pale face and weakness
iv. vomiting, profuse sweating and pain on the left side of the chest
E. A word in the passage which means the same as ‘opposition’ is
i. interference
ii. resistance
iii. reduction
iv. concussion
Section-B
(Writing -15 Marks)
4. Write a letter to the editor of a newspaper expressing your views about “The Right
to Education” emphasising the importance of education in the life of people and the
measures that the government should take to make it a reality. You are Shashank,
a student of class X in Government Co-educational School, Kota.
(6 Marks)
OR
You are Shefali / Shashwat living in a hostel at Pune. Write a letter to your younger
brother Pranjal advising him to behave in a disciplined manner and to follow the
orders of his teachers during his trip to Jaipur with his class.
5. You are Mansi/ Manas, a student of Government Girls School, Dwarka. Your
mother is employed in a bank. You feel that working mothers lead a challenging
life and their children should play a supporting role. Prepare a speech in about 120
words to be delivered in the morning assembly of your school on the topic
‘Challenges of Working Mothers’ to make the students realize their role towards
working mothers
.
OR
Write an article to be published in your school magazine about the “Importance of
Games and Yoga”. You are Siddarth of Government Girls Senior Secondary School,
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Sector 2 Rohini.
(6 Marks)
.
6. Anuj decided to write a story to be published in a magazine for children but due to
high fever, he could not complete his story. Complete his story so that it could be
given for publishing.
Once upon a time there lived a king in a palace. He was very handsome and smart but
he was a great fool. One day he announced that --------------------- (80 words)
OR
Write a report about ‘A Book Fair” organised in your school by the National Book
Trust mentioning details like number of stalls, kinds of books, response of students,
discounts offered etc. You are Abhishek studying in classX of Government Model
School, Shalimar Bagh, Delhi.. (80 words)
(3 Marks)
SECTION-C
GRAMMAR-15 Marks
7. Choose the most appropriate options from the ones given below to complete the
following passage. Write the answers in your answer sheet against the correct
blank number. Do not copy the whole passage. (1/2x6=3 Marks)
Father wanted (a) _______ say something but the bus had started moving. I saw
(b)__________ father receding into the distance. I saw(c)_________________ the road we
had come by looked like a giant motionless rope. Father(d)_____________ use the same
road to go back home. Simultaneously our journey started(e)_____ two opposite directions,
with(f)_____________ seated in the luxurious seat of a bus and father walking back with
weary legs on the pebble stream road.
a. i) too ii)so iii)to iv)for
b. i) his ii) my iii) her iv) him
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c i) if ii) which iii) that iv)whether
d. i) could ii) would iii) should iv) will
e. i) at ii) in iii) of iv) for
f. i) him ii) us iii) he iv) me
Q 8 Rearrange the jumbled phrases to form meaningful sentences. The first one has
been done for you as an example. Write only the answers in your answer sheet.
(6 x ½= 3 Marks)
And a very / the king / named Acanthus / talented sculptor / Pygmalion was /of Cyprus
/of a village.
Pygmalion was the king of Cyprus and a very talented sculptor of a village named
Acanthus
a. had finished / he smiled / when he / the ivory statue / of a beautiful woman /one day.
b. smile /at having found /it was / the innocent /new and unique / of a child / something
c. by the beauty/ that /to worship it /he was / falling down / he felt like / so impressed/
on his knees / of the statue.
d. that he /a masterpiece / and called / he realized / this beauty, / had created / Galatea.
e. was a devoted / to the goddess / he prayed / to breathe life / into it / of Aphrodite,/
since he / follower.
f. to life and / married her / after the goddess/ his wish, / Pygmalion / Galatea came /
granted him.
9. Read the following dialogue and then complete the report by choosing the correct
options from the ones given below. Write your answers in your answer sheet with
the correct blank number.
(
1x3=3 Marks)
Do not copy the dialogue and the report:-

Utkarsh: I have lost my wallet
Inspector: How did you lose it?
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Utkarsh: My pocket was picked
Inspector: Where did it happen?
Utkarsh: In the local market, sir.
Utkarsh reported to the inspector (A)_______lost his wallet. The inspector asked
him (B)___________Utkarsh replied(C)________.The inspector further asked him
where it had happened. Utkarsh replied that it had happened in the local market.
a. i) that I had ii) that he had
iii) that he has iv) that I have
b. i) how he has lost it ii) how he had lost it.
iii) how had he lost it. iv) how he had lost that
c. i) my pocket has been picked ii) if his pocket had been picked
iii) that his pocket had been picked iv) whether his pocket has been picked
10. Complete the following passage by choosing the correct passive forms of the verbs
given in brackets from the alternatives given below the passage. Write only your
answers in the answer sheet against the blank number.
(1x3=3 Marks)
An exhibition (A)________ (hold) in Andhra Pradesh. A young girl (B)________ (ask)
not to allow anyone to enter without a ticket. When Nehruji tried to enter without a ticket,
she stopped him saying that no one (C)__________(allow) to enter without a ticket.
a. i) held ii) was held iii) is held iv) will be held
b. i) asked ii) was asked iii) is asked iv) has asked
c. i) allowed ii) was allow iii) was allowed iv) is allowed
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11. Complete the dialogue by choosing the correct alternative from those given below.
Write your answers in the answer sheet against the correct number.
(1x3=3 Marks)
Swati: Your sister is very beautiful. Please tell me(A)_____________.
Mohit: I want to tell you (B)________.
Swati: Then please tell me (C)_________________.
Mohit: She is in fact my niece who has come to spend her holidays with us.
a. i) what she was doing ii) what was she doing?
iii) what she is doing iv) what is she doing?
b .i) if she was not his sister ii) whether is she not my sister
iii) that she is not my sister iv) that she was not my sister
c. i) who she is ii) whose she is.
iii) who is she iv) whom she is
SECTION-D
(Text Books-35 Marks)
12. (a) Read the following passage carefully and answer the questions by writing the
option that you consider the most appropriate in your answer sheet.
(4Marks)
The class roared. I had to laugh too though I’d nearly exhausted my ingenuity on the topic
of chatterboxes. It was time to come up with something else, something original. My
friend, Sanne who is good at poetry, offered to help me write the essay from beginning to
end in verse and I jumped for joy. Mr. Keesing was trying to play a joke on me with this
ridiculous subject, but I’d make sure the joke was on him.
A. The class laughed heavily because_____
a. the teacher had cracked a joke
b. a student had fallen down
c. the teacher had made fun of a student
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d. the teacher had given a funny homework to Anne.
B. This time Anne decided to counter the insult
a. by insulting the teacher
b. by insulting the students who laughed at her
c. by writing the easy in verse as a joke on the teacher.
d. by writing a short story about the teacher
C. This incident reveals that Anne was
a. revengeful and nasty
b. creative and mischievous.
c. selfish and unsocial.
d. imaginative and insulting.
D. Find out a word from the passage which means the same as ‘tired’.
a. ridiculous
b. exhausted
c. ingenuity
d. chatterbox
12 (b) Read the following passage carefully and answer the question by
writing the option that you consider the most appropriate in your
answer sheet.(4 Marks)
With a satisfied expression, he regarded the field of ripe corn with its flowers,
draped in a curtain of rain. But suddenly a strong wind began to blow and along
with the rain very large hailstones began to fall. These truly did resemble new
silver coins .The boys, exposing themselves to the rain ,ran out to collect the
frozen pearls.
It’s really getting bad now,” exclaimed the man.” I hope it passes quickly.” It
did not pass quickly .For an hour the hail rained on the house, the gardens, hill
side, the cornfield, on the whole valley. The field was white, as if covered with
salt.
A. Lencho looked satisfied because---------
a. the fields were green.
b. the corn was ready for harvesting.
c. it had started raining.
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d. the harvest was quite good.
B. “the frozen pearls” refers to-----
a. white pearls kept in the fridge.
b. pearls frozen to look beautiful.
c. hail stones.
d. big rain drops.
C. The field was white because-----
a. white plants were growing there.
b. it was covered with salt.
c. it was covered with hail stones.
d. it was painted white.
D. Find a word in the passage which means the same as ‘to look like’’
a. expression
b. hailstones
c. resemble
d. draped
13. Read the following extracts carefully and answer the questions by writing the
options that you consider the most appropriate in your answer sheet.
[Attempt any two] (2x3=6 Marks)
a. But if it had to perish twice,
I think I know enough of hate
To say that for destruction ice
Is also great
And would suffice.
A. “It” here refers to -----
a. hate
b. love
c. world
d. life
B. The poet compares hate to ice because
a . both represent lack of warmth and love.
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b. both are destructive.
c. both are found in life.
d. both are opposed to fire and desire.
C. The rhyming scheme of the poem is
a. a b a b a
b. a a a b b
c. a a b b a
d. a b b a b
b. Money is external
He is learning, well behind his desperate eyes,
The epistemology of loss, how tp stand up
Knowing what every man must one day know
And most know many days, how to stand up.
A. The ‘He’ in the above lines is
a. a child
b. an infant
c. a young man
d. an old man
B. He is learning
a. to be like a grown up
b. to be happy
c. to deal with loss
d. not to lose things
C. The big truth of life that he learns is
a. not to lose things
b. to value things
c. to lose and forget
d. the need to understand the nature of loss
c
. I think I could turn and live with animals, they are
so placid and self-contain’d,
I stand and look at them long and long.
A. The poet wishes

a. to live in a jungle
b. to be like animals
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c. to live with animals
d. celebrate with animals
B. The poet likes animals because
a. they are strong and swift
b. they are beautiful and elegant
c. they are wise and intelligent
d. they are calm and self-reliant
C. Thinking about animals, the poet feels
a. jealous
b. happy
c. melancholic
d. thoughtful
14. Answer any three of the following questions in 40-50 words each (2x3= 6 Marks)
1. Nelson Mendela speaks of twin obligations. What are they?
2. What did the hungry seagull find on the ledge? How did he feel?
3. Where did Wanda Petronski usually sit? Why?
4. What were Anne’s views about writing a diary? Why did she write it?
15. Answer the following question in about 80 words. (5 Marks)
The systems of government in Mandela’s country in the first decade, and in the final
decade of the twentieth century were a total contrast. What were the differences?
OR
The pilot in the Black Aeroplane had a supernatural experience. What was it?
16. Answer the following question in about 80 words. (4 Marks)
Mrs. Pumphery was responsible for Tricki’s illness. Justify.
OR
Appearances can be very misleading. How did Fowler discover this truth?
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17. Answer any two of the following questions in 40-50 words each (2x3 = 6 Marks)
a) Why did Hari think it would be easy to deceive Anil?
b) How did the lady in red convince Horace to open the lock?
c) What important documents did Ausable have in his possession?
EXAMINATION SPECIFICATIONS
English Language and Literature
Code No. 184
CLASS – X
Division of Syllabus for Term I (April-September) Total Weightage Assigned
Summative Assessment I
Section Marks
20%
Reading 15
Writing 15
Grammar 15
Literature 35
Formative Assessment
20%
TOTAL 40%
Division of Syllabus for Term II (October-March) Total Weightage Assigned
Summative Assessment II
Section Marks
Reading 15
40%
Writing 15
Grammar 15
Literature 35
Formative Assessment
20%
TOTAL
60%

Note
:
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1. The total weightage assigned to Summative Assessment (SA I&II) IS 60%. The total weightagwe
assigned to Formative Assessment (FA1, 2, 3, &4) is 40%. Out of the 40% assigned to Formative
Assessment, 10% weightage is assigned to conversation skills (5% each in Term I&II) and 10%
weightage to the Reading Project (at least 1 Book is to be read in each term and the Project will carry a
weightage of 5% in each term)
2.
The Summative Assessment I and Summative Assessment II is for eighty marks. The weighatge
assigned to Summative Assessment I is 20% and the weightage assigned to Summative Assessment II is
40%.

SECTION A: READING
15 Marks
30 periods
Qs 1-3 Three unseen passages
of total 500 words followed by 15 marks Multiple Choice
Questions of 1 mark each. Out of the 15 marks,
3 marks will be for vocabulary. The
questions will test inference, evaluation and analysis. The passages may be extracts from
poetry/ factual/ literary/ discursive texts.

Section B: WRITING 15 Marks
40 periods
Q 4 Letter Writing: One out of two letters (formal/informal/email)
in not more than 100 words
based on verbal stimulus and context provided.
Types of letter: Informal – personal, such as to family and friends.
Formal – letters to the Editor.
Email – formal letters to prince[pal of the school or to the editor of a Newspaper or a Magazine.
6 Marks
Q 5 Writing
an article, speech or debate based in visual or verbal stimulus in not more than 120 words (One out
of two).
6 Marks
Q 6
Writing a short composition in the form of dialogue writing/story or report of minimum 80 words (One
out of two). 3 Marks
Section C: GRAMMAR 15 Marks
45 periods
This section will assess Grammar items in context for 5 marks. It will carry 5 questions of 3 marks each.
Qs 7-11
. A variety of short questions involving the use of particular structures within a context. Text types
used will include gap – filling, sentence-completion, sentence-reordering, dialogue-completion and sentence
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transformation (including combining sentences). The Grammar syllabus will include the following areas in
class IX:
1. Tenses
2. Modals (have to/had to, must, should, need, ought to and their negative forms)
3. Use of passive voice
4. Subject – verb concord
5. Reporting
(i). Commands and requests
(ii). Statements
(iii). Questions
6. Clauses:
(i) Noun clauses
(ii) Adverb clauses of condition and time
(iii)Relative clauses
7. Determiners, and
8. Prepositions
Note: No separate marks are allotted for any of the grammatical items listed above.
All questions will be
multiple choice questions. The questions will be based on a sample of grammar items
taught in class IX.

Section D: TEXT BOOKS 35 Marks
95 periods
First Flight-NCERT Text Book for Class IX 25 Marks
Q 12 Two
reference to context Multiple Choice Questions from Prose or Play.
Up to one mark in each extract will be for vocabulary, at least one question will be used for testing local and
global comprehension and one question will be in interpretation.

(20-30 words) 4x2= 8 Marks
Q 13 Two out of three
reference to context stanza from a poem followed by 3 Multiple Choice Questions to
test local and global comprehension of the set text.)
(20-30 words)
3x2=6 Marks
Q 14 Three out of four Short Answer questions
based on Prose or Play to test local and global
comprehension of theme and ideas.
(40-50 words) 2x3=6 Marks
Q 15 One out of two Long Answer questions
extrapolative in nature based on prose or Play.
(Upto 80 words) 5 Marks
Footprints without Feet: NCERT Supplementary Reader for Class IX
10 Marks
Q 16 One out of Two Long Answer Questions
from Supplementary Reader to interpret, evaluate and analyse
character, plot or situations occurring in the lessons to be answered in about
80 words.
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4 Marks
Q 17 Two out of three Short Answer Type Questions
based on factual aspects, interpretation or evaluation of
a lesson.
(40-50 words) 3x2=6 Marks
Syllabus for SA I
Literature Reader (First Flight)
PROSE
1. A Letter to God
2. Nelson Mandela: Long Walk to Freedom
3. His First Flight (Lesson)
4. Black Aero Plane
5. From the Diary of Anne Frank
6. Hundred Dresses – I
7. Hundred Dresses – II
POETRY
1. Dust of Snow: Fire and Ice
2. A Tiger in the zoo
3. How to tell Wild Animals
4. The Ball Poem
Supplementary Reader (Footprints without Feet)
1. A Triumph of Surgery
2. The Thief’s Story
3.The Midnight Visitor
4. A Question of Trust

Monday 17 September 2012

maths sample paper solved

Paper:
Class-X-Math: Summative Assessment I:5
Total marks of the paper:
90
Total time of the paper:
3.5 hrs
General Instructions:

1. All questions are compulsory.

2. The question paper consists of 34 questions divided into four sections A, B, C, and D. Section – A comprises of 8 questions of 1 mark each, Section – B comprises of 6 questions of 2 marks each, Section – C comprises of 10 questions of 3 marks each and Section – D comprises of 10 questions of 4 marks each.

3. Question numbers 1 to 8 in Section – A are multiple choice questions where you are to select one correct option out of the given four.

4. There is no overall choice. However, internal choice has been provided in 1 question of two marks, 3 questions of three marks each and 2 questions of four marks each. You have to attempt only one of the alternatives in all such questions.

5. Use of calculator is not permitted.

6. An additional 15 minutes has been allotted to read this question paper only.


Questions:


1]
The mean of a dataset with 12 observations is calculated as 19.25.
If one more value is included in the data, then for the new data with
13 observations mean becomes 20. Value of this 13th observation is:
[Marks:1]
A.
31
B.
30
C.
28
D.
29
2]
If A and B are the angles of a right angled triangle ABC, right angled
at C then 1+cot2A =          
[Marks:1]
A.
cot2B
B.
tan2B
C.
cos2B
D.
sec2B
3]
Which of the following numbers is irrational?
[Marks:1]
A.
0.23232323   
B.
0.11111….
C.
2.454545…
D.
0.101100101010…….
4]
If a and β are the zeroes of the quadratic polynomial f (x) =x2 +2x+1, then is
[Marks:1]
A.
2
B.
0
C.
-1
D.
-2
5]
The pair of equations y = 0 and y = -7 has :
[Marks:1]
A.
infinitely many solutions
B.
two solutions
C.
one solution
D.
no solution
6]
How many prime factors are there in prime factorization of 5005?
[Marks:1]
A.
7
B.
6
C.
2
D.
4
7]
Which of the following is defined?
[Marks:1]
A.
sec 90°
B.
cot 0° 
C.
tan 90°
D.
cosec 90°     
8]
If sin (A - B) = and cos (A + B) = , then the value of B is :
[Marks:1]
A.
B.
60°    
C.
45°
D.
15°
9]
Use Euclid's division lemma to show that square of any positive integer is either of form 3m or 3m + 1 for some integer m.
[Marks:2]
10]
What must be added to polynomial f(x) = x4 + 2x3 - 2x2 + x - 1 so that the resulting polynomial is exactly divisible by x2 + 2x - 3?
[Marks:2]
11]
Determine a and b for which the following system of linear equations has infinite number of solutions 2x - (a -4)y = 2b + 1; 4x - (a -1) y = 5b - 1.
[Marks:2]
12]
In figure ÐBAC = 90°, AD BC. Prove that: AB2 + CD2 = BD2 + AC2.
[Marks:2]
13]
If tan q = 3 sin q, then prove that sin2 q - cos2 q = .
OR
If 7 sin2 q + 3 cos2 q = 4, then prove that sec q + cosec q = 2 + .
[Marks:2]
14]
Construct a more than cumulative frequency distribution table for
the given data :
Class Interval
50 - 60
60 - 70
70 - 80
80 - 90
90 - 100
100 - 110
Frequency
12
15
17
21
23
19
        
[Marks:2]
15]
Prove that 3 - is an irrational number.
OR
Prove that is an irrational number.
[Marks:3]
16]
Solve for x and y:
= 2; ax - by = a2 - b2
[Marks:3]
17]
Find the missing frequency for the given data if mean of distribution is 52.
          Wages (In Rs.)
10 - 20
20 - 30
30 - 40
40 - 50
50 - 60
60 - 70
70 - 80
No. of workers
5
3
4
f
2
6
13
OR
Find the mean of following distribution by step deviation method.         
Daily Expenditure :
100 - 150
150 - 200
200- 250
250 - 300
300- 350
No. of householders :
4
5
12
2
2
[Marks:3]
18]
Prema invests a certain sum at the rate of 10% per annum of interest and another sum at the rate of 8% per annum get an yield of Rs 1640 in one year's time. Next year she interchanges the rates and gets a yield of Rs 40 less than the previous year. How much did she invest in each type in the first year?
OR
Six years hence a man's age will be three times his son's age and three years ago, he was nine times as old as his son. Find their present ages.
[Marks:3]
19]
If one solution of the equation 3x2 = 8x + 2k + 1 is seven times the other. Find the solutions and the value of k.
[Marks:3]
20]
If and f are the acute angles of a right triangle, and
[Marks:3]
21]
In figure ABCD is rectangle in which segments AP and AQ are drawn. Find the length (AP + AQ).
[Marks:3]
22]
In figure sides XY and YZ and median XA of a triangle XYZ are
respectively proportional to sides DE, EF and median DB of DDEF.
Show that DXYZ ~ DDEF.
[Marks:3]
23]
In the figure below triangle AED and trapezium EBCD are such that the area of the trapezium is three times the area of the triangle. Find the ratio .
         
[Marks:3]
24]
Find the median for the following frequency distribution:
        
Class Interval
10 - 19
20 - 29
30 - 39
40 - 49
50 - 59
60 - 69
70 - 79
Frequency
2
4
8
9
4
2
1
[Marks:3]
25]
Find all zeroes of polynomial.
4x4 - 20x3 + 23x2 + 5x - 6 if two of its zeroes are 2 and 3.
[Marks:4]
26]
Prove the following :
If a line is drawn parallel to one side of a triangle to intersect the
other two sides in distinct points, the other two sides are divided in
the same ratio.
OR
Prove that in a right triangle, the square of the hypotenuse is equal
To the sum of the squares of the other two sides.
[Marks:4]
27]
OR
= cosec q + cot q.
[Marks:4]
28]
Find the value of
[Marks:4]
29]
Form the pair of linear equations in the following problems, and find
the solution graphically.
"10 students of Class X took part in a Mathematics quiz. If the
number of girls is 4 more than the number of boys, find the number
of boys and girls who took part in the quiz."
[Marks:4]
30]
The following table gives production yield per hectare of wheat of
100 farms of a village.
Production yield (in kg/ha)
50 - 55
55 - 60
60 - 65
65 - 70
70 - 75
75 - 80
Number of farms
2
8
12
24
38
16
Change the distribution to a more than type distribution and draw ogive.
[Marks:4]
31]
Prove that ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides.
[Marks:4]
32]
Prove that:
[Marks:4]
33]
Show that the square of any positive integer cannot be of the form 5q + 2 or 5q + 3 for any integer q.
[Marks:4]
34]
Calculate the mode of the following frequency distribution table.
Marks
No. of Students
above 25
above 35
above 45
above 55
above 65
above 75
above 85
52
47
37
17
8
2
0



Paper:
Class-X-Math:Summative Assessment I:5
Total marks of the paper:
90
Total time of the paper:
3.5 hrs
General Instructions:

1. All questions are compulsory.

2. The question paper consists of 34 questions divided into four sections A, B, C, and D. Section – A comprises of 8 questions of 1 mark each, Section – B comprises of 6 questions of 2 marks each, Section – C comprises of 10 questions of 3 marks each and Section – D comprises of 10 questions of 4 marks each.

3. Question numbers 1 to 8 in Section – A are multiple choice questions where you are to select one correct option out of the given four.

4. There is no overall choice. However, internal choice has been provided in 1 question of two marks, 3 questions of three marks each and 2 questions of four marks each. You have to attempt only one of the alternatives in all such questions.

5. Use of calculator is not permitted.

6. An additional 15 minutes has been allotted to read this question paper only.


Solutions:


1]
Let x1,x2,x3……..,x12 be the 12 values of the given data. Let the 13th observation be x13.
                x1+x2+x3……..+x12 = 12x19.25 = 231       
                x1+x2+x3……..,x12+x13= 13x20=260
                (x1+x2+x3……..+x12)+x13= 260
                x13=260-231 = 29
2]
Given, triangle ABC is right angled at C. Therefore,
A+B=90o or A=90o-B
1+cot2A = 1 + cot2(90o-B) = 1+tan2B = sec2B
3]
A real number is an irrational number when it has a non terminating non repeating decimal representation.
4]
x2 +2x+1= (x+1)2
Þ x = -1
? = ?= -1
1/ ? and 1/? are also -1. 1/ ? + 1/? = -2
5]
Since the x-axis y=0 does not intersect y=-7 at any point.
6]
Since .
7]
Because cosec 90°=1, others are not defined.
8]
9]
If a and b are one two positive integers. Then a = bq + r, 0 r b Let b = 3 Therefore, r = 0, 1, 2 Therefore, a = 3q or a = 3q + 1 or a = 3q + 2                                       If a = 3q a2 = 9q2 = 3(3q2) = 3m or where m = 3q2 a = 3q + 1 a2 = 9q2 + 6q + 1 = 3(3q2 + 2q) + 1 = 3m + 1 where m = 3q2 + 2q or a = 3q + 2 a2 = 9q2 + 12q + 4 = 3(3q2 + 4q + 1) + 1                                                = 3m + 1 where m 3q2 + 4q + 1                                                   Therefore, the squares of any positive integer is either of the form 3m or 3m + 1.
10]
Given polynomial P(x) = x4 + 2x3 - 2x2 + x -1
Let g(x) must be added to it.
                                                       
So, number to be added=-(-x+ 2) = x - 2               
11]
For infinite number of solution,
Consider
Again,
12]
                                                                                                  
AC2 = AD2 + CD2 … (2)
[By Pythagoras theorem]                                            
(1) - (2) gives,
Hence proved.
13]
                                                                                                              
OR
Consider,
7 sin2 q + 3 cos2 q = 4
7Sin2 + 3 (1 - sin2 ) = 4                                                                     
7Sin2 + 3 - 3sin2 = 4
4Sin2 = 1
Sin =                                                             
Thus,     Sec 30o + Cosec30o =
14]
Class Interval
Cumulative Frequency
More then 50
More then 60
More then 70
More then 80
More then 90
More then 102
108
95
80
63
42
19
15]
Let 3 - be a rational number.                                                                                                                              
3 - = [ p,q are integers, 2 0]                                 
Here,                    
LHS = Rational No.
RHS = irrational No.        
But, Irrational no Rational no
our assumption is wrong is an irrational.
OR
Let us assume to the contrary, that is a rational number.
is rational.
(n-1)+(n+1)-2 is rational
2n+2 is rational
But we know that is an irrational number
So 2n+2 is also an irrational number
So our basic assumption that the given number is rational is wrong.
Hence, is an irrational number.
16]
                            … (1)                                                                     
                   … (2)
Multiplying (1) with a and (2) with b, we get                                                                                       
               
From (1), bx + ab = 2ab
bx = ab
x = a
Hence, x = a and y = b.
17]
C.I
Fi
Xi
Fi. .Xi
10 - 20
5
15
75
20 - 30
3
25
75
30 - 40
4
35
140
40 - 50
F
45
45f
50 - 60
2
55
110
60 - 70
6
65
390
70 - 80
13
75
975
33+f
1765+45f
Mean =                                                                                                                                              
OR
C.I
fi
xi
di
fidi
100 - 150
4
125
-2
-8
150 - 200
5
175
-1
-5
200 - 250
12
225
0
0
250 - 300
2
275
1
2
300 - 350
2
325
2
4
-7
Where:                 
18]
Let us assume that Prema invests Rs x @10% and Rs y @8% in the first year.
We know that
Interest =                
ATQ,
+ =1640
Þ 10x + 8y = 164000 …(i)
After interchanging,
+ =1600       
we get 10y+8x=160000
8x+10y=160000 ...(ii)
Adding (i) and (ii)
18x+18y=324000
Þ x + y = 18000 ... (iii)
Subtracting (ii) from (i),
2x-2y=4000
Þ x - y = 2000 ...(iv)
Adding (iii) and (iv)
2x=20000
Þ x = 10000.
Substituting this value of x in (iii)
y=8000
So the sums invested in the first year at the rate 10% and 8% are Rs 10000 and Rs 8000 respectively.
                                                                                               
OR
                                                                                                               
                                                                                          
Solving (1) and (2), we get
x = 30 y = 6.        
19]
Let is one zero. = 7 is another zero then                                   
+ 7 =
8 =            = and =                                                      
Now,
20]
The two angles and f being the acute angles of a right triangle, must be complementary angles.
So,                                                                         
Substituting, in above equation
                                                        
21]
                                                                    
                                        
Now, AP + AQ = 120 + 60 = 180 cm
22]
23]
Let the area of triangle =x sq units
Area of trapezium = 3x sq units
Area triangle ABC = x + 3x = 4x sq units                 
Now,
Consider triangles AED and ABC,
ED ll BC...given
ÐAED = ÐABC Corresponding angles
ÐA = ÐA Common
?AED ~ ?ABC                               [By AA rule]                                                       
= (since Ratio of areas of two similar triangles is equal to ratio of square of corresponding sides)
So                                                                                                                                                       
24]
C.I
F
Cf
9.5 - 19.5
2
2
19.5 - 29.5
4
6
29.5 - 39.5
8
14
32.5 - 49.5
9
23
49.5 - 59.5
4
27
59.5 - 69.5
2
29
69.5 - 79.5
1
30
Here,     l = 39.5 c.f = 14 f = 9 h = 10                           
M = 39.5 +                                                                
25]
Given 2 and 3 are the zeroes of the polynomial.
Thus(x - 2) (x - 3) are factors of this polynomial.                                                                                
                                             
4x4 - 20x3 + 23x2 =5x - 6 = (x2 - 5x + 6) (4x2 - 1)
Thus, 4x4 - 20x3 + 23x2 +5x-6=(x - 2) (x - 3) (2x - 1) (2x + 1)
Therefore, 2,3,
26]
Given: A triangle ABC in which a line parallel to side BC intersects other two sides AB and AC at D and E respectively
                To prove that
                Construction: Let us join BE and CD and then draw DM AC and EN AB.
                Proof: Now, area of
Note that BDE and DEC are on the same base DE and between the same parallels BC and DE.
So, ar(BDE) = ar(DEG)
Therefore, from (1), (2) and (3), we have :
                        
OR
Given: A right triangle ABC right angled at B.
To prove: that AC2 = AB2 + BC2
Construction: Let us draw BD AC (See fig.)
Proof:
Now, ADB ABC (Using Theorem: If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse ,then triangles on both sides of the perpendicular are similar to the whole triangle and to each other)
                So,                                  (Sides are proportional)
                Or, AD.AC = AB2                               … (1)
                Also, BDC ABC                    (By Theorem)
                So,
                Or, CD. AC = BC2               … (2)
                Adding (1) and (2),
                AD. AC + CD. AC = AB2 + BC2
                OR,         AC (AD + CD) = AB2 + BC2
                OR,         AC.AC = AB2 + BC2
                OR          AC2 = AB2 + BC2
Hence proved.
27]
OR
Dividing numerator and denominator of LHS by sin , we get
    
28]
29]
Let the number of girls and boys in the class be x and y respectively.
According to the given conditions, we have:
x + y = 10
x - y = 4
x + y = 10 Þ x = 10 - y
Three solutions of this equation can be written in a table as follows:
x
5
4
6
y
5
6
4
x - y = 4 Þ x = 4 + y
Three solutions of this equation can be written in a table as follows:
x
5
4
3
y
1
0
-1
The graphical representation is as follows:
From the graph, it can be observed that the two lines intersect each other at the point (7, 3).
So, x = 7 and y = 3.
30]
We can obtain cumulative frequency distribution of more than type as following:
Production yield
(lower class limits)
Cumulative frequency
more than or equal to 50
100
more than or equal to 55
100 - 2 = 98
more than or equal to 60
98 - 8 = 90
more than or equal to 65
90 - 12 = 78
more than or equal to 70
78 - 24 = 54
more than or equal to 75
54 - 38 = 16
Now taking lower class limits on x-axis and their respective cumulative frequencies on y-axis we can obtain its ogive as following.
31]
Statement: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Given: DABC ~ DPQR To Prove: Construction: Draw AD^BC and PS^QR                                                          Proof:                                                                         DADB ~ DPSQ (AA)                 Therefore,                     … (iii)                                                                     But DABC ~ DPQR            Therefore,                               … (iv)                                                     Therefore,     Therefore,                                                      From (iii)                             
32]
                                                                                       
                                                                                                   
                                                                                  
               
                                                                                                                                                                                                                                                                                                                                       
                Hence, L.H.S = R.H.S
33]
Let 5q + 2, 5q + 3 be any positive integers
(5q + 2)2 = 25q2 + 20q + 4
                = 5q (5q + 4) + 4 is not of the form 5q + 2                                              
Similarly for 2nd
(5q + 3)2 = 25q2 + 30q + 9
=5q(5q+6)+ 9 is not of the form 5q+3
So, the square of any positive integer cannot be of the form5q+2 or 5q+3
For any integer q
34]
Marks
Frequency
25 - 35
5
35 - 45
10
45 - 55
20
55 - 65
9
65 - 75
6
75 - 85
2
Total
52
                                                                                                               
Here the maximum frequency is 20 and the corresponding class is 45-55.So,45-55 is the modal class.
We have,l=45,h=10,f=20,
Mode = +          
Mode=49.7