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ACADEMIC ADVISORS KVS (HQ) NEW DELHI
ADVISORS KVS (RO) JAIPUR
CHIEF PATRON
SH. SANTOSH KUMAR MALL, IAS
COMMISSIONER
Sh. U. N. KHAWARE
ADDITIONAL COMMISSIONER (ACADEMICS)
Dr. (Sh.)SHACHI KANT JOINT COMMISSIONER
(TRAINING)
Dr. (Smt.) V.VIJAYLAKSHMI JOINT COMMISSIONER
(ACADEMICS)
Sh. NAGENDRA GOYAL DEPUTY COMMISSIONER
(ACADEMICS)
Sh. P.K. KAUL DEPUTY COMMISSIONER
(ACADEMICS)
Smt. SONA SETH ASSISTANT COMMISSIONER
(ACADEMICS)
Sh. Y. ARUN KUMAR ASSISTANT COMMISSIONER
(ACADEMICS)
Dr. (Smt.) V. GOWRI
OFFICIATING DEUPTY COMMISSIONER
JAIPUR REGION, JAIPUR
Sh. A. JYOTHY KUMAR
ASSISTANT COMMISSIONER
KVS (RO) JAIPUR
COURSE DIRECTOR
Sh. S.C.AGARWAL, PRINCIPAL
K.V.2 (ARMY), JODHPUR
ASSOCIATE COURSE DIRECTOR
Dr.(Sh.) M.M.A. USMANI
PRINCIPAL
K.V. (ARMY) BANAR, JODHPUR RESOURCE PERSONS
1. Sh. R.D. VAISHNAW, PGT MATHS K.V. NO. 2 (AFS) JODHPUR 2. Sh. JAIVINDRA YADAV, PGT MATHS K.V. NO. 1 (ARMY) JODHPUR 3. Sh. SUNIL GAUR, PGT MATHS K.V. BSF, JODHPUR
Venue: KV NO-2 Army Jodhpur
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CONTENTS
1. Preface
2. Schedule
3. List of participants
4. Group formation
5. Daily report
6. The Educational values of Mathematics
7. Gist of guest lectures
8. Group work
9. Quotations on Mathematics
10. Lists of important websites
11. List of reference book
From the desk of the course director…….…
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First of all I am thankful to the KVS authorities for providing an opportunity to me to
organize 12 days IN-SERVICE Course of TGT MATHS (Ist spell) in order to make them update in
the various spheres of teaching learning process.
A real teacher always remains keen to learn and who appreciate the thoughts of others.
Education is the systematic, purposeful process of reconstruction in experiences, which develop the
capacity of original thinking and raise our intellectual standards.
Modern education demands effective transaction of knowledge in the classroom viz.
activity based teaching, computer aided teaching and we the teachers of KENDRIYA
VIDYALAYA‟s better known as „Pace-Setters‟ can only accomplish this challenging task. There
is a very special quality in each one of us. If we think deeply and try to analyze, we will discover
the unique quality or characteristics in us that may be the secret of our success. This is what we
may call our unique success factor or USF.
In order to refresh the knowledge of a teacher, KVS has organizing In-Service Courses for
the teachers. In this connection this time my team consisting Sh. M.M.A. Usmani, Sh. R.D.
Vaishnaw, Sh. Jaivindra Yadav and Sh. Sunil Gaur has been given an opportunity to organize this
course. We have tried our level best to achieve the objectives of organizing this course. We have
worked on enrichment of content matter, Math‟s lab, latest trends in teaching methods, models of
teaching and skill development etc. Apart from the academics, the teacher were also apprised of the
life skill, Value Education, Communication skill, Guidance and counseling, Gender sensitization,
Work balance life, General awareness, constructivism, Yoga and Health , KVS Policies and
common Examination and evaluation and lots more which will further add up in proving their
excellence in noble profession.
All the official at KVS Headquarters, New Delhi as well as KVS regional office, Jaipur
really deserves a sense of real appreciation without that it was not possible for us to conduct this
course, effectively. On behalf of my team, I express my sincere gratitude for showing their faith in
me but also for providing proper guidance all the time and for encouraging me. I also extend my
sincere thanks to Chairman VMC K.V. No. 2 (Army) Jodhpur Brig. Shri B.S. Shekhawat, Sh.
M.M.A. Usmani as Associate Director, Principal K.V. Banar, Sh. R.D. Vaishnaw PGT Maths
K.V.AFS No. 2 Jodhpur, Sh Jaivindra Yadav K.V. No. 1 (Army) Jodhpur Sh Sunil Gaur K.V. BSF,
Jodhpur who are the pillars of the success. I am also thankful to my staff who has worked around
the clock for these 12 days.
S.C.Agarwal
Course Director and Principal
K.V. No.2 Army, Jodhpur
“A candle can‟t truly enlighten the world until it burns, a teacher can‟t truly teach until he learn”
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Participants List cum Contact Detail
SR. NO. NAME OF PARTICIPANT NAME OF KV
Mobile No. E-Mail
1 SH. NATENDRA SIGH KV NO. 1 (AFS) AGRA 9412331664 -
2 SH. MUKESH BHATIA NO.4 GWALIOR 9425307829 [email protected]
3 SH. KAUSHAL KUMAR NO2 JHANSI CANTT. JHANSI 9454866914 [email protected]
4 SH. RAM PRASHAD MRN, MATHURA 9412813284 [email protected]
5 SH. D. S. SHARMA MRN, MATHURA 9411065551 [email protected]
6 SH. SATISH RAWAT NO.2 (AFS) GWALIOR 9039676078 [email protected]
7 SH. KAMLESH KUMAR NO. 2 AGRA 9454378178 [email protected]
8 SMT.ARCHANA AWASTHI OEF, HAZRATPUR 9410877623 [email protected]
9 SH. B.M. TRIPATHI KV NO-3 BAAD, MATHURA 9411871789 [email protected]
10 SH.CHANDAN SINGH UPPER CAMP,D.DUN 9756820862 [email protected]
11 SH.N C PATHAK HALDWANI (IST SHIFT) 9411322619 [email protected]
12 SH.SANJAY KUMAR KASHIPUR 7417577515 [email protected]
13 SH.VINOD PUROHIT ONGC,D.DUN 7579080281 [email protected]
14 SH.LOKESH KUMAR ITBP,MERTHI 9899928129 [email protected]
15 SMT. ATIYA RIZVI MUZAFFARNAGAR 9410134373 [email protected]
16 SH.LAL SINGH RISHIKESH 9997701608 [email protected]
17 SH.R N YADAV CRPF,RAMPUR 9411291989 [email protected]
18 SH. S.K.NAYAK COD, JABALPUR 9425151322 [email protected]
19 SH. S.R.GAIKWAD AMBAJHARI 9822696741 [email protected]
20 SH. TARUN SHRIVASTAVA KATNI O.F. KATNI (M.P) 9424732440 [email protected]
21 SH.A.K.SINGH AJNI NAGPUR 7385378149 [email protected]
22 SH. BABU LAL SAINI KHETRI NAGAR 9636904481 [email protected]
23 SH. RAJ KUMAR KHANNA NO.5 (1ST SHIFT), JAIPUR 9928374441 [email protected]
24 SH. ANAND KUMAR KV KHAJUWLA 9414492245 [email protected]
25 SH.RAM NIWAS MEENA NO.1, ALWAR 8503993505 [email protected]
26 SMT. MUKESH GOTHWAL K.V.SIKAR 9461106325 [email protected]
27 SH. NARENDRA KUMAR SAINI K.V.SIKAR
9461413351 [email protected]
28 SH. KAUSHAL KISHORE VERMA KV.NO.6, JAIPUR
9461420808 [email protected]
29 SH. JAINENDRA CHOUHAN KV EME, BARODA 9033624791 [email protected]
30 SH. R.D.VAISHNAW KV 2 (AFS) JODHPUR 9462380565 [email protected]
31 SH. J.YADAV KV 1 (ARMY) JODHPUR 9414231884 [email protected]
32 SH. S. GAUR KV BSF, JODHPUR 9024256542 [email protected]
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Group formation
Ramanujan Group
1 Sh. Sanjay Kumar
2 Sh. Jinendra Chouhan
3 Sh. Satish Rawat
4 Sh. R N Yadav
5 Sh. Lokesh Kumar
6 Smt. Archana Awasthi
Brahmagupta Group
1 Sh. D S Sharma
2 Smt. Atiya Rizvi
3 Smt. Mukesh Gothwal
4 Sh. M C Pathak
5 Sh. Natendra Singh
6 MR. S.R.GAIKWAD
Arya Bhatt Group
1 Sh. Vinod Purohit
2 Sh. Chandan Singh
3 Sh. Lal Singh
4 Sh. Ramniwas Meena
5 Sh. Anand Kumar
6 Sh. Jainendra Chauhan
Bhaskaracharya Group
1 Sh. B N Tripathi
2 Sh. Babu Lal Saini
3 Sh. Narendra Kumar Saini
4 Sh. K K Verma
5 Sh. Rajkumar Khanna
6 Sh. Mukesh Bhatia
Varahmihir Group 1 Sh. S K Nayak
2 Sh. Kaushal Kumar
3 Sh. Ram Prasad
4 Sh. Kamlesh Tiwari
5 Sh. Tarun Shrivastava
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IN- SERVICE COURSE FOR TGT’s MATHS
3 June 2015 to 14 June 2015
Venue:- K.V. No. 2 (Army) Jodhpur
Date: - 03 June 2015
Report of I day of In-service course
All the participants were warmly welcomed by the Venue Director Mr. S.C. Agarwal & the
students of K.V. No. 2 Army Jodhpur at School premises. Then the ceremony began with the
lighting of lamp by the Chief Guest Mrs. Mamta Bhatia, Director of IGNOU Jodhpur Centre.
Associate Course Director Dr. M. M. Usmani, Principal K.V. Banar, Jodhpur addressed the
participants with an inspiring speech and expressed his views about the aims and objective of In
Service Course and its importance.
Then Chief Guest Mrs. Mamta Bhatia told about the importance of teaching learning process.
Then The Venue Director Shri S. C. Agarwal addressed the participants and assured them to
provide all the possible facilities for their comfortable stay at Jodhpur.
After that the resource persons introduced themselves then vote of thanks was given by Mr. R.D.
Vaishnav PGT (Maths) K.V. No. 2 AFS which ended with a melodious Bhajan. After that an Ice
breaking session was conducted for the introduction of participants. After that all the 29
participants of four regions were divided into 05 groups namely Arya Bhatt Group,
Bhaskaracharya Group, Ramanujan Group, Varahmihir Group, and Brahmagupta Group and then
work was assigned for each group.
Consisting of one SA-I paper for each group.
Question Bank
05 questions from each topic for slow learners
Project/ Activity
Mathematical Facts
Quiz
Puzzles
P. S.A.
Then after lunch break. A pre-test was conducted to test the basic knowledge of the participants
with this the program ended for the first day.
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Date:- 04 June 2015
Report of II day of In-service course
Morning session started with morning assembly followed by previous day report.
Lecture was delivered by Course Director Mr. S. C. Agarwal (Principal) on trigonometry by
innovative method to simplify the complication in trigonometry especially in trigonometric
identities, height and distance problems.
Lecture by Guest faculty Dr. Rashmi Mathur Asst. Professor in NLU Jodhpur on Communication
skill. She explains different types of skills verbal and non-verbal in a very simple and effective
manner and co-related it to various fields of our daily life.
Resource person Mr. R. D. Vaishnav delivered lecture on number system. He explains different
types of numbers using question answer method.
Col. Veer Singh (Nominee Chairman) addressed the participants and gave many motivational
thought related to life.
Demo lesson was given by S.K. Nayak National Awarded teacher. He shared his experience how to
get national award.
Demo lesson was delivered by D. S. Sharma on construction of triangles with PPTs.
Demo Lesson was delivered by Natendra Singh on lines and angles by PPTs.
Date:- 05 June 2015
Report of III day of In-service course
Third day of the course was started by group II Bhaskaracharya Group. It began with morning
assembly including prayer, pledge thought of the day, news and special item.
Dr. M. M. Usmani in the first session explained on New Approach of Teaching and Learning
Mathematics. He described about Aims and Objectives of Teaching and Learning Mathematics
and challenges faced by a teacher in the classroom situation. He also described about the various
ways to make the teaching and learning Mathematics joyful.
Lecture was delivered by Dr. Prasant Mehta Professor in Law University Jodhpur on life skills. He
focused on to be flexible in life to cop up the challenges in the changing world.
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Resource person Mr. Sunil Gour delivered lecture on Vedic Mathematics. He explained about the
origin, how it can be used in Algebra, Trigonometry and in our daily life. He explained Sutra’s of
Vedic Mathematics and its uses to make our calculations easy.
Demo lesson given by Mukesh Bhatia K.V 4 Gwalior on the topic pair of linear equations in two
variables.
Demo lesson was delivered by Kaushal Kumar K.V 2 Jhansi on Polynomials
Demo Lesson was delivered by Ram Prasad K.V. Refinery Nagar Mathura on Statistics.
A lecture on RTE 2009 was conducted by Mr. J. Yadav (Resource Person). He explained about RTE
2009.
The day ended with group activities by different groups.
Date:- 06 June 2015
Report of IV day of In-service course
Fourth day of the course was started by group 2 Bhaskaracharya Group. It started with morning
assembly including prayer, pledge, thought of the day, news and special item.
In the Ist session, Mr. S.C. Agarwal Hon. Principal K.V. 2 army Jodhpur and course Director of In
service course TGT (Maths) explained the proof of Pythagoras Theorem and derived general
formula to find out area of regular polygon. He gave some easier methods for students.
Mr. A.S. Bhati, Hon. Principal K.V. 2AFS Jodhpur delivered a lecture on constructivism in detail. He
also described about 5 E’s.
Resources person Mr. Sunil Gaur delivered a lecture on Vedic mathematics to describe
multiplication and cube root.
After lunch break Demo lesson was delivered by Satish Rawat K.V. No. 2 Gwaliour, Kamlesh
Tiwari, K.V. No.2 Agra gave a demonstration lesson on Area & Perimeter.
A lecture on RTE-2009 was delivered by Mr. J. Yadav (Resource Person)
The day ended with group activities by different groups.
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Date:- 07 June 2015
Report of V day of In-service course
Fifth day of the course was started by group 3 (Ramanujan Group). It started with morning
assembly including prayer, pledge, Thought of the day, and news.
In the I session Dr. M. M. Usmani, Principal K.V. Banar & Associate Director of the In-service
course For TGT Maths delivered a lecture on integral approach of maths in which he explains how
to connect Arithmetic to Geometry, To relate Mensuration with Geometry.
Mr. T.C. Meena, PGT Comp.Sc. explained about E- CTLT.
After tea break Mr. R. D. Vaishnav (resource person) resumed his lecture on number system.
Mr. J. Yadav (resource person) discussed questions of higher difficulty Level in which the course
Director Mr. S. C. Agarwal Hon. Principal K.V. 2 army Jodhpur and course Director of In service
course TGT (Maths) also gave some important tips and shortcut methods for solving various
questions.
After Lunch break Mr. Chandan Singh TGT (Maths) Upper camp Dehradun, Mr N C Pathak , TGT
K.V. Haldwani Ist shift and Mr. B.M. Tripathi TGT (Maths) K.V. No. 3 Baad Mathura gave
demonstration lessons.
After tea break, group activity was carried out by all the 5 groups
Date:- 08 June 2015
Report of VI day of In-service course
6th day of the 1st spell of the in-service course for T G T (Maths ) began with the morning
assembly in the presence of the course director and venue Principal, Mr. S.C. Agrawal; associate
course director, Mr. Usmani Sir Principal K V Barnard and three resource persons Mr. R D
Vaishnav , Mr. J Yadav & Mr. Sunil Gaur. The assembly was organized by the Ramanujan Group
group in a very effective manner. Report of 5th day was presented by covering all the activities of
the entire day. Under the special item a devotional song was presented by Mr. D S Sharma, the
song endorsed our feelings and annexed our trust in almighty which gave forth positive energy for
the whole day.
Thereafter, one of the resource person, Mr. R D Vaihnav started to give lecture on the topic “C S
Number”, before his lecture he brought out the instinct of a mathematics teacher. He quoted-“If
you are a good mathematics teacher, students remember you, If not, they will never forget you.”
Which motivated participants to be justified towards their profession? Mr.Vaishnav elaborated
the topic and brought out the knowledgeable and noteworthy concepts of “C S Number” In
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addition to it he made aware the participants to understand the techniques of solving problems
related to reasoning. It was interactive and fruitful lecture.
This was followed by a guest lecture from eminent personality of Jodhpur Law University Madam
Manisha Mirdha on Counseling & Guidance. She imparted valuable knowledge about counseling
and guidance. She also clarified the difference between them. She enlighted everyone with the
thought that there should be job satisfaction and teacher should be more and more interactive
with the students.
After tea break, one and half hour Mid -Test carrying 50 marks, it was conducted in the
observation and control of course director, Assistant Course Director and Resources persons. All
the participants appeared in the test and tried their level best to be a high scorer.
Post- lunch session began at 2:00 pm with demo lessons by the participants. Three participants
from different KV’s gave demo lessons, on Real numbers & Measurement of central tendency.
Demo lessons were very effective. Participants also interacted and put up their queries and gave
valuable suggestion for betterment. After tea break all the participants went to computer lab for
the assigned group work under the valuable guidance of our resource persons. At 5:00 pm the
course director, Mr. S C Agrawal, informed about the pre decided spot of educational tour and
asked opinion to make the trip informative and joyful.
The whole day passed in a fruitful manner.
Date:- 09 June 2015
Report of VII day of In-service course
On 7th day i.e. on 09/06/2015 after having tea all participants visited to Osian a famous tourist
place and saw the world famous temple Devi Sachchiyan and other spots. At Osian every one
enjoyed the desert and saw the famous dame. Around 2: 00 pm trip came back the Geeta Dham
and took the delicious lunch and moved to visit the Mehrangarh fort. It was educational &
enjoyable tour for all participants.
Date:- 10 June 2015
Report of VIII day of In-service course
The 10th day of the In-service course Ist spell began with a very pleasant morning. A cool breeze
was blowing, After having a delicious and healthy breakfast, all the participants gathered in the
conference hall. The morning assembly was started at sharp 8:30 am in the esteemed presence of
our course director Mr. S. C. Agrawal, principal KV2 (Army) Jodhpur, Associate course director,
Mr. M. M. Usmani Sir Principal K V Banar and the team of our worthy resource persons. Morning
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assembly was conducted by Varahmihir Group Group followed by a moral talk in good manners
by Kamlesh Kumar. He said that good habit play an important role in behavior. Generally people
pretends to behave in a well behaved manners but it is actually not so.
First session started with interesting and interactive presentation on Relation & Function by our
learned resource person Mr. Sunil Gaur. He mainly focused on relation of two sets. Later on he
discussed many different ways of finding function.
The day was very special for us because we got an opportunity to have a guest lecture on
“Gender sensitization” by the Assistant Professor Dr. Kranti Kapoor from Law University Jodhpur.
She explained a very complicated topic of “Gender sensitization” in a very easy and interesting
way which enriched our social skills. Mr. Rawat proposed vote of thanks.
After tea break interactive session was started by an eminent personality Dr. Neeti
Mathur from Law University Jodhpur. She summarized the key points by emphasizing on
importance of positive attitude & Quality of workplace. She said we should always be positive and
the world will be positive to us.
After having nutritious, high calorie and delicious lunch we all again assembled in the hall for the
post lunch session. Post lunch session was started by many flash presentation presented by our
three participants as demo lessons namely Mr. R. L. Yadav on “pair of linear equation”, Madam
Atiya Rizvi on “Circles” and Mr. Lal Singh on “Square of numbers”. Then we assembled for group
photograph.
After tea break participants moved to computer lab to complete the group work assigned i.e. to
prepare PSA question paper and MLL material for all classes.
The day ended with lot of enthusiasm as the participants were eagerly looking forward to learn
more interesting topics in the forthcoming day.
Date:- 11 June 2015
Report of IX day of In-service course
The ninth day of the in service course began with morning assembly conducted by VARAHMIHIR
GROUP group. After this the course director Mr. S.C. Agarwal explained some useful and
innovative methods for finding squares of numbers, tables and divisibility tests for 7,11,13,17,19
and many more numbers. After that the learned resource person Mr. R.D. Vaishnaw explained
the terms related to probability and cleared doubts related to the concepts. After tea break all
the participants were benefitted by watching an inspiring video named “Life changing experience
by Sandeep Maheshwari”. After this all are gathered to have lunch. In the post lunch session
demo lessons were presented by Mrs. Archana Awasthi on coordinate geometry, Mr.A.K.Singh on
Surface area of cylinder ,Mr. S.R.Gaikwad on Central Tendencies and Mr. Tarun Srivastava on
Similar Triangles. After tea break all the participants gathered for group activities. As such the
day was proved to be very fruitful.
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Date:- 12 June 2015
Report of X day of In-service course
The tenth day of the in service course started with morning assembly conducted by Brahamgupta
group. After morning assembly the course director Mr. S.C.Agarwal explained very useful and
essential topics related to calculation of income tax, interest on GPF, gratuity, encashment of EL
and HPL, calculation of pension with or without commutation. He cleared all the doubts and
answered the quarries of the participants. After the tea break associate course director Mr.M.M.
Usmani delivered a lecture on learning with generous joy and explained the topic derivative. After
this the resource person Mr. J.Yadav has given a lecture on proofs in mathematics and took the
topic deductive and inductive reasoning. In the post lunch session demo lessons were presented
by Mr. Babu Lal on Pythagoras theorem, Mr.Rajkumar Khanna on Introduction to Trigonometry
and Mr. Ramniwas Meena on Surface Area and Volumes .After tea break all the participants were
assembled for group work. In this way the tenth day of in service course ended successfully.
Date:- 13 June 2015
Report of XI day of In-service course
The 11th day of the first spell of in service course started with the shiny morning. After having
breakfast participants assembled in conference hall. The morning assembly was conducted by
Brahmagupta group in the presence of course Director Mr.S. C. Agrawal, the Associate Course
Director Mr.M. M. A. Usmani , Resource Person Mr.R. D. Vaishnav , Mr.J Yadav , Mr. Sunil Gaur .The
programe of assembly were presented with new ideas and it was appreciated. Devotional bhajan was
presented by our Resource Person Mr.R. D. Vaishnav and Mr. D S Sharma.
The first interesting session was taken up by resource person Shri J Yadav on “Proof in Mathematics”
& “Euclid Geometry”. He explained about Axioms and postulates, ”The importance of Mathematics”.
He made us aware about the “Proof in Mathematics” and how can we develop the perception of
“Proof in Mathematics” among children.
After that a guest lecture was delivered Dr. R.N. Agrawal. Dr. Agrawal threw light on a very significant
topic that is General Awareness in Mathematics. He openly discussed and interacted with the
participants about them how they can make aware their students effectively in the classroom.
The day was very special for us because we got an opportunity to have a guest lecture on
“Stress Management” by Mr. A. S. Bhati Principal K V NO2 AFS Jodhpur.
The post test was conducted from 11:30 am to 12:30 pm under the keen observation of all the
resource persons.
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Post lunch session was started by many flash presentation presented by our four participants
as demo lessons namely Madam Mukesh Gothwal on “ reasoning”, Mr. N. K. Saini on “ Lines and
angles , Mr. K. K. Verma on “ fractions” and Mr. Jitendra Chouhan on ,” polyhedron”.
After tea break participants moved to computer lab to complete the group work and presented their
own exhibits.
The day ended with lot of enthusiasm as the participants were eagerly looking forward to learn
more interesting topics in the forthcoming day.
Date:- 14 June 2015
Report of XII day of In-service course
The 12th day of the first spell of in service course started with the shiny morning.
After having breakfast participants gathered in conference hall. The morning assembly was conducted
by Brahmagupta group in the presence of course Director Mr.S. C. Agrawal, the Assocoiate Course
Director Mr.M. M. Usmani , Resource Person Mr.R. D. Vaishnav , Mr.J Yadav , Mr. Sunil Gaur .The
program of assembly were presented with new ideas and was appreciated.
After that Mr.T. C. Meena PGT(Comp.Sci.) threw light on a very significant topic that is ICT. He
openly discussed and interacted with the participants about them how they can use the ICT to make
their lesson. Next session started with interesting and interactive presentation on “Vedic
Mathematics” by our learned resource person Mr. Sunil Gaur. He mainly focused on sixteen sutra and
thirteen sub sutra from “Arthaveda”. Later on he discussed many different ways of calculation
through “Vedic Mathematics”.
After tea break interactive session was started by an eminent personality our Associate
Course Director Mr. M. M. A. Usmani, Principal K.V. Banar, Jodhpur. He summarized the key points
by emphasizing on importance of construction.
Thereafter, one of the resource person, Mr. R D Vaishnav delivered a lecture on the topic
“Factorization”. Mr.Vaishnav elaborated the topic and brought out the knowledgeable and
noteworthy concepts of “Factorization”. It was interactive and fruitful lecture.
After lunch, all the participants assembled for valedictory function. Mr. A. S. Bhati, Principal
K.V .NO. 2 AFS Jodhpur graced the occasion as chief guest.
Various participants expressed their views and thanked the course director to make course a
tool to sharper their weapons by which they can make their teaching effective.
16
The Educational values of Mathematics
“Mathematics is a great motivator for all humans, because its begins with zero and it never
ends (infinity)”
Mathematics has a powerful language and with the advent of computer its importance has
increase manifold. Mathematics promotes innovation and creativity but it should not be
imprisoned in the four walls of class or a school should be an ideal place where new
mathematical ideas and innovations can be promoted.
Every teacher of mathematics need to be informed and convinced about the educational value
of Mathematics as a subject. There are a number of question which need to be answered at this
stage.
There are a number of questions which need to be answered at this stage. Why should
everybody learn mathematics? Why should this subject be taught to everybody? What is the
place of mathematics in any scheme of education? What is the importance of this subject in life
and in a school curriculum? What shall be the advantage of devoting so much of efforts, time
and money to the teaching of mathematics? What are the purpose and aims of teaching
mathematics? How does it make any contribution in the development of individual? It will be
seen that these question pertain to the same aspect viz., the educational value of mathematics.
The knowledge of its value and aim will stimulate and guide the teacher to adopt effective
methods devices and illustrative materials knowledge of educational values helps the teacher
to avoid aimlessness in teaching. Values are the springboard of aim and versa. There is nothing
controversial about two. One aims at the thing because one values it: or by aiming at a thing,
on shall taste its value. “we aim at teaching mathematics because we know its values or when
we teach mathematics in the light of its aim, we shall realize its values.” Aimless teaching will
realize no values.
There are some definite motives for which the students are sent to schools. Schooling should be
purposeful affair. Everything done in the school should be the outcome of the aims and purpose
of schooling.
Broadly speaking there are three main considerations for which a child sent to school.
Education must contribute toward the acquirement of these values:
1) Knowledge and skill
2) Intellectual habits and powers
3) Desirable attitude and ideas
These three values can be called utilitarian, disciplinary and cultural values of education
respectively.
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Practical Value or Utilitarian value
One cannot do without the use of fundamental process of this subject in daily life. A common
man can get on sometime every well without learning how to read and write, but he can never
pull on without learning how to count and calculate. Any person ignorant of maths will ne at
the mercy of other and will be easily cheated. The knowledge of its fundamental process and
the skill to use them are the preliminary requirement of a human being these days.
Counting, notation, addition, subtraction, multiplication division, weighting selling, buying and
any more are simple and fundamental process of mathematics which has immense practical
values in life. The knowledge and skill in these processes can be provided in an effective and
systematic manner only by teaching mathematics in schools.
Disciplinary value
“Mathematics is away to settle in the mind a habit of reasoning” it trains or disciplines the
mind. Due to its very nature, it possesses a real disciplinary value. It is exact, true and to the
point knowledge, and therefore creates a discipline in the mind. Its truths are definite and
exact.
It develops reasoning and thinking powers more and demands less from memory.
1) Characteristics of simplicity: there is a vast scope for simple reasoning in this subject. It
teaches that definite facts are always expressed in a simple language and definite facts
are always easily understandable.
2) Characteristics of accuracy: without accuracy there is no chance of progress and credit in
mathematics. Accurate reasoning, thinking and judgment are essential for its study. It is
in the nature of this subject that it cannot be learnt through vagueness of thought and
argument.
3) Characteristics of certainty of result: there is no place for subjectivity and personal
equation in mathematics. The answer is either right or wrong.
4) Characteristics of original: most work in mathematics demands original thinking.
Reproduction and cramming of ideas of others is not very much appreciated.
5) Characteristics of similarity to the reasoning of life: clear and exact thinking is as
important in daily life as in mathematical study.
6) Characteristics of verification of results: results can be easily verified. This verification of
result is also likely to include the habit of self- criticism and self-evaluation.
7) Application of knowledge: secondly, knowledge itself becomes real and useful only
when the mind is able to apply it to now situations. In mathematics, there is again a vast
scope for application; ability to apply knowledge to new situations is inculcated in
student.
18
Cultural Value
“Mathematics is the mirror of civilization” mathematics has got its cultural value, and this value
is steadily increasing day by day. It helped man to overcome difficulty in the way of his
progress. It has laid a major role in bringing into such advance stage of development.
The prosperity of man and his cultural advancement have depended considerably upon the
advancement of mathematics.
Modern civilization owes its advancement to the progress of various occupations such as
agriculture, engineering, surveying, medicine, industry, navigation, rail board, building etc.
These occupations build up culture and they are its backbone.
Disciplinary Value
“Mathematics is a way to settled in a mind a habit of reasoning”. Said locke.
It trains or disciplines the mind. Due to its very nature, it possesses a real disciplinary value. It is
exact, true and to the point, and creates a discipline in the mind. Its truths are definite and
extract. It develops reasoning and thinking power more and demand less from memory.
Social Value
“Mathematics plays an important role in the organization and maintenance of our social
structure. It enable us to understand the inter- relations of individual and possibilities of
various group.
Society is a phenomena of balancing and counter- balancing of various social forces.
Mathematics helps in creating a social order in this phenomenon. Its regulates the functioning
of society in many ways.
Moral Value
The study of mathematics helps in moral development and character formation. It helps in
developing proper moral attitude as there is no place for prejudiced feeling, biased outlook,
doubts and half-truths, discrimination misdistribution of resources, unreasonableness and
irrationally in the learning of this subject. It is the only subject which helps in objective analysis,
correct reasoning, valid conclusion and impartial judgment. The Greek philosopher Dutton has
rightly remarked that….” Gossip, flattery, slander, deceit – all speak for slovenly mind that has
not been trained by mathematics.
Aesthetic Value
People wrongly consider mathematics as something mundane but for a true student of
mathematics, the subject is all beauty, symmetry, balanced, harmony, fineness, art and music.
19
There is a great pleasure in successfully solving a mathematical problem. It was the reason why
Pythagoras sacrificed one hundred oxen to the goddess for celebrating the discovery of the
theorem that goes by his name. in the same way Archimedes forgot his nakedness while
announcing to the discovery of his principle.
Leibnitz has rightly said – “Music is a hidden exercise in arithmetic unconscious of dealing with
numbers”.
Vocational Value
The study of mathematics prepares us for various occupations like engineering, accountancy,
auditing, taxation, banking, surveying, trade, designing, teaching, agriculture, planning
financing, weights and measure inspection, quality control, budgeting, construction, computer
application etc.
These occupations have immensely benefitted from mathematics in achieving vocational
efficiency in many spheres. Almost every location involves investment, loans, interest, profit,
loss, percentage etc. Which can be better managed with the help of mathematical knowledge
and understanding.
A sound vocational life demands a sound mathematical background.
Almost every vocation involves mathematics.
Intellectual Value
The study of mathematics helps us in development of many intellectual tricks like power of
thinking and reasoning, induction, analysis, originality, generalization, discovery etc. Every
mathematical problem possesses an intellectual challenge and a unique mental exercise.
The subject is taught for the development of power rather then knowledge. Its problem solving
is helpful in the development of one’s mental faculties. It develops our powers of acquiring
knowledge, thinking reasoning, judgment and generalization.
International Value
Mathematics is a universal subject and it helps in creating international understanding. Its
history presents a very good picture of the overall development of our civilization. What we
possess in the form of mathematical knowledge today is the fruit of the combined efforts of all
human beings, the inhabitants of all the corner of the world, the scholars of all ages, the
followers of all religion and member of all the races. Mathematics is a common heritage of
mankind and it is not an exclusive property of any particular nation, race or country. All
mathematicians irrespective of their caste, color or creed worked devotedly towards a common
cause.
Mathematics is a symbol of agreement all over the world, it is the same everywhere.
20
The man – made barriers of boundary cannot restrict or check the free flow of mathematics
doesn’t take much time to become an international asset. The diverse country have at least
some common platform in the sphere of scientific and mathematical knowledge. We may differ
from one another in many ways but in the field of mathematics we find our difference
removed.
S.C.Agarwal
Principal
K.V.No.2 Army, Jodhpur
Guest lecture
LIFE SKILLS
(BY Mr.PRASHANT MEHTA, FACULTY,NLU,JODHPUR)
21
Living in a global society, where every day we interact with individuals different
than ourselves, it has become necessary for everyone to understand how to
effectively carry out personal and professional interactions. The lack of knowledge,
skills, and practices surrounding diversity can result in the loss of friends, diminished
profits/market shares, poor customer service, employee turnover, low job
satisfaction, and unnecessary legal battles. Recent demographic trends indicate the
demand for well informed and trained employees. This workshop provides a
framework of how diversity interfaces with all aspects of our lives including the roles
of language, culture, social psychology, and personality to determine how these work
together to create the magnification and maintenance of stereotypical differences
between and among groups. The main goal of the workshop is to enable the
participants to understand how to effectively and efficiently manage themselves and
their role in a diverse environment to establish a positive climate for all
stakeholders. Come learn how you can be a P.O.P. (Proponent of People) and live
more meaningfully in a diverse world.
GENDER SENSITIZATION
(BY Ms.KANTI KAPOOR, FACULTY,NLU,JODHPUR)
Gender sensitization refers to theories which claim that modification of the
behavior of teachers and parents (etc.) towards children can have a causal effect on
gender equality.
Gender sensitizing "is about changing behavior and instilling empathy into the views
that we hold about our own and the other sex." It helps people in "examining their
personal attitudes and beliefs and questioning the 'realities' they thought they know.
CONSTRUCTIVISM & CONTINOUS AND COMPRHENSIVE EVALUATION
(BY Mr A.S.Bhati,Principal , KV-2 AFS,JODHPUR)
Constructivism is basically a theory, based on observation and scientific study
about how people learn. It says that people construct their own understanding
and knowledge of the world, through experiencing things and reflecting on those
experiences
• BENEFITS OF CONSTRUCTIVISM:
• Children enjoy and learn more when they are actively involved rather than
passively listening.
• Education works best when it concentrates on thinking and understanding
rather than on rote memorization
• Constructivist learning is transferable. Students create organizing principles
that they can take to other learning settings
• Constructivism gives students ownership of what they learn and often the
students have a hand in designing the assessment as well
QUALITY OF WORK LIFE BY NEETI MATHUR
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Love and work are said to be the cornerstones of being human and both are very
important for happiness. Yet juggling the demands of each can be difficult. By
thinking differently, we can perhaps find ways to have a better balance between work
and home.
Being more mindful of the different potential sources of conflict between work and
family life, including time, demands, strain and behaviour , can help us to start to be
more conscious of the patterns we tend to fall into and so help us to think of effective
strategies to guard against these way in which we think about the demands upon us
makes a huge difference to how we feel and how effective we are at responding.
Think of the ways in which your family life and the skills you use at home can make
you more effective at work and how your work and the skills you use there can be
effectively used at home. Also, why not try out some of Action for Happiness's
resilient thinking tactics.
ARYABHATT GROUP
MINIMUM LEVEL LEARNING (CLASS - VI)
23
CHAPTER – 1.KNOWING OUR NUMBERS.
Q1.One Km is how many centimeters ?
(i) 100000 (ii) 10000 (iii) 1000 (iv) 100
Q2.Population of a town in the year 2000 was 200000 .In the year 2005 ,it was found to be
increased by 10359 . What was the population of the town in 2005.
(i) 220359 (ii) 210000 (iii) 210359 (iv) 20359
Q3.A machine , on an average , manufactures 2825 screws a day. How many screws did it
manufacture in the month of January ?
(i) 84750 (ii) 87575 (iii) 81925 (iv) 79100
Q4.A vessel has 4 litres& 500 ml of milk. In how many glasses , each of 25 ml capacity, can it be
filled?
(i) 150 (ii) 160 (iii) 170 (iv) 180
Q5.Which of the following is the Roman Numeral for 69
(i) LXXI (ii) LXIX (iii) CXIX (iv) CXXI
CHAPTER – 2.WHOLE NUMBERS.
Q1.Which is the successor of 1099999 ?
(i) 1100001 (ii) 1100000 (iii) 1099998 (iv) 9999999
Q2.Which is the predecessor of 208090 ?
(i) 208089 (ii) 208091 (iii) 218090 (iv) 198090
Q3.What is the value of 8x1769x125
(i) 1769000 (ii) 1768000 (iii) 1768010 (iv) 1769010
Q4.What is the value of 81265x169 – 81265x 69
(i) 81265000 (ii) zero (iii) 8126500 (iv) 8026500
Q5.Which of the following is the additive identity in the set of Whole numbers ?
(i) 1 (ii) zero (iii) -- 1 (iv) any number
CHAPTER – 3.PLAYING WITH NUMBERS.
Q1. Which of the following is the factor of every number ?
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(i)-- 1 (ii) zero (iii) 1 (iv) any number
Q2.How many factors does 36 have ?
(i) 5 (ii) 6 (iii) 7 (iv) 9
Q3. Which of the following is the smallest prime number?
(i) 1 (ii) 2 (iii) 3 (iv) 5
Q4.How many prime numbers are there between 1 &20 ?
(i) 7 (ii) 8 (iii) 9 (iv) 10
Q5. Which of the following is the smallest composite number?
(i)2 (ii) 3 (iii) 4 (iv) 5
Q5. Which of the following is the HCF of the numbers 20,28 &36 ?
(i)20 (ii) 36 (iii) 4 (iv) 5
CHAPTER – 4.BASIC GEOMETRICAL IDEAS.
Q1.How many lines can pass through two given points?
(i)1 (ii) 2(iii) 3 (iv) Infinite
Q2.How many vertices are there in a hexagon?
(i)5 (ii) 6(iii) 7 (iv) 8
Q3.How many diagonals are there in a pentagon?
(i)2 (ii) 3(iii) 4 (iv) 5
Q4.What is the length of the diameter of a circle of radius 8 cm ?
(i)4cm (ii) 8cm(iii) 16cm (iv)2cm
Q5.An angle divides the plane in to how many regions ?
(i)2 (ii) 3(iii) 4 (iv) 5
CHAPTER –5.UNDERSTANDING ELEMENTARY SHAPES.
Q1.What is the angle measure for half a revolution?
(i)600 (ii) 900(iii) 1800 (iv) 2700
25
Q2.What fraction of a clockwise revolution does the hour hand of a clock turn through, when it
goes from 3 to 9?
(i)1/2 (ii)1/3(iii) 1/ 4 (iv)1/5
Q3.Where will the hand of a clock stop if it starts at 5 & makes 1/4 of a revolution, clockwise?
(i)7 (ii) 8(iii) 9 (iv) 10
Q4.Which direction will you face if you start facing south & make one full revolution?
(i)East (ii) West (iii) North (iv) South
Q5.Where will the hour hand of a clock stop if it starts from 6 & turns through one right angle?
(i)7 (ii) 9(iii) 8 (iv) 10
CHAPTER –6.INTEGERS.
Q1.Which of the following is the simplest form of (--8) +(--7) -- (--2)
(i)-- 17 (ii) 13(iii) -- 13 (iv) 17
Q2.What is the value of 50 – (--40) – (--2)
(i)-- 12 (ii) 8(iii) 92 (iv) 88
Q3.Which of the following lies to the left of –24 ?
(i)--23 (ii) 25(iii) -- 25 (iv) 23
Q4.Which of the following numbers do you get if you subtract --40 from --50
(i)10 (ii)-- 10(iii) -- 90 (iv) 90
Q5.Which of the following numbers is ‘2’ less then four times of ‘5’ ?
(i)18 (ii)-- 18(iii) 3 (iv) 13
CHAPTER - ALGEBRA .
Q1.If Sarita’s present age is ‘x’ years, what will be her age 5 years from now?
(i)(x—5)yrs. (ii) (x +5)yrs(iii) 5x yrs (iv) 5/x yrs
Q2 .Ram’s bank balance is Rs.500 more then 3 times his friend’s bank balance. If his friend’s bank
balance is ‘ y ‘, what is Ram’s bank balance.
(i)y+500 (ii) 3y + 500(iii) 3y (iv) 3y – 500
Q3.The length of a rectangular hall is 4 metres less then 3 times the breadth of the hall. What is
the length , if the breadth is ‘b’ meters ?
26
(i)b + 4 (ii) b -- 4(iii) 3b -- 4 (iv) 3b + 4
Q4.If 2x + 3 = 5 , which of the following is the value of ‘x’ ?
(i)1 (ii) -- 4(iii) 4 (iv)– 1
Q5.Find which of the following is the solution of the equation 3y – 5 = 7 ?
(i)1 (ii) -- 4(iii) 4 (iv) – 1
CHAPTER – RATIO &PROPORTION .
Q1.Which of the following is the ratio of one rupee to 50 paisa ?
(i)1:1 (ii) 2:1(iii) 1: 2 (iv) 1:50
Q2.Which of the following is the equivalent ratio of 6:4?
(i)3:2 (ii) 6:8(iii) 12:4 (iv) 1:1
Q3.IfRs.60 is divided between X&Y in the ratio of1:2,which of the following is the share of X?
(i)50 (ii) 20(iii) 40 (iv) 180
Q4.There are 100 teachers in a school for 3000 students. Which of the following is the teacher
student ratio?
(i)3:100 (ii) 1:1(iii) 30:1 (iv) 1:30
Q5.If the cost of six pens is Rs.60 , which of the following is the cost of 10 such pens?
(i)10 (ii) 100(iii) 600 (iv) 6
HIGHER ORDER THINKING SKILLS (CLASS - VI)
Chapter - Area and Perimeter 1. Find perimeter of rectangle whose length =6m8dm and breadth =4n6dm
2. Find the cost of fencing a rectangular field 24m long and 18m wide at Rs. 6.25 per meter.
3. The length and breadth of rectangular field are in ratio 5:3. If its perimeter is 64m. Find the dimensions.
4. The cost of fencing a rectangular field at Rs. 14.60 per m is 1606. If the width of the field is 23m find its length.
5. The length and breadth of rectangular field are in ratio 3:2. The cost of fencing the field at Rs. 6.50 per m is Rs. 520. Find the dimensions of the field.
Chapter.CIRCLE 1. Find the circumference of circle if r=14cm
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2. Find the diameter of circle if circumference is 66cm
3. Find the diameter of circle if circumference is 75 cm
4. The diameter of wheel of a car is 70cm. Find the distance traveled by wheel of car in 1000 revolutions.
5. Find the circumference of circle if diameter of circle is 10m.
Chapter.AREA OF RECTANGLE
1. Find the area of a rectangle whose length and breadth 45cm and 16cm respectively. Also find perimeter of rectangle
2. A room is 5m 40cm long and 3m 75cm wide. Find the area of the carpet needed to cover the floor.
3. Find the cost of cultivating a rectangular field 34m long and 18m wide at Rs. 4.50 per sqmetre. Also find the cost of fencing the field at Rs. 2.25 per meter.
4. A room is 9.68m long and 6.3m wide. Its floor is to be covered with rectangular tiles of size 22cm by 10cm. Find the total cost of the tiles at Rs. 5 per tiles.
5. The area of rectangle is 650 sq cm and one of its side is 13cm. Find the perimeter of rectangle.
Chapter.RATIO AND PROPORTIONAL 1. Find the ratio of (i)40 paisa to Rs 4 (II) 24 min. to an hr (III) 125 ml to 2 litres (IV) 4m to 36 cm (V) Dozen to Score 2. Find the ratio the price of coffee to that of tea, when coffee cost rupees 24 per100 gm and tea Rs 80 per kg? 3. Two numbers are in ratio 2:7. If the sum of the numbers are 81. Find the numbers? 4. Divide the number 642 in ratio 1: 2: 3 among A, B, C 5. The ratio of Length and breadth of rectangle is 5:3. Find lts dimension if perimeter is 256?
Chapter.UNITARY METHOD 1. A truck runs 495 km on 36 liter petrol. How many km can it run on 35 liter petrol? 2. 12 men can reap a field in 25 days. in how many days can 20 man reap field ? 3. In a camp, there were provisions for 425 men for 30 days. However, 375 men attend the camp. How many provision last? 4. If 48 boxes are needed for 6000 pens. How many boxes will be needed for 1875 pens? 5. A bus travel 36 km in hr. If it maintains a uniform speed, how long will it takes to cover162 km? How for does it travel in 8 hrs. ?
Chapter.Ratio and Proportional 1. First, second, fourth term of a proportional are 45, 25, 35, Find third term.
2. If 36 , x , x , 16 are in proportional Find value of x
3. Find value of x if 25,35, x are in proportional
4. An electrical pole cast shadow length 20 m at a time when a tree of 6 cm cast shadow of 8 m. Find the height of pole.
5. The length of the side of a triangle are in ratio 1: 3 : 5 .If perimeter of triangle is 90 cm find its largest side .
Algebraic expression
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1. Numerical coefficient of 8x3yz2is ________
2. Find value: (a) 8 - x + y if x = 7 and y = 9 (b) 6x - y +30 if x = 2 and y = 6
3. Write like terms from 2x2, 2x, 2x3, - 5x, 11x4
4. Write numerical coefficient of . 3x3yza2
5. Find area of rectangle with sides 3x and 5y
Chapter. Geometry
1. Draw a circle of radius 5 cm. Draw and measure the largest chord.
2. Using ruler and compass construct angle : 1350, 22.50, 450, 900, 112.50
3. Draw an angle of 900 and using protector to construct an angle of 600by dividing it .
4. Use protector to draw 600, By dividing into 4 part and draw an angle of 150
5. What is a triangle? Define all its 6 types.
ACTIVITY (CLASS - VI)
Commutative, Associative and Distributive
Learn the difference between Commutative, Associative and Distributive Laws by
creating:
Comic Book Super Heroes
You will need:
Coloring pencils
Paper
29
Imagination!
Activity 1
Step 1: The "Commutative Laws" say you can swap numbers over and still get
the same answer ...
... when you add:
a + b = b + a
Example:
... or when you multiply:
a × b = b × a
Example:
Step 2: Does order of numbers matter when multiplying or adding?
Step 3: Using this information, try to draw a super hero whose super powers
incorporates the fact that order doesn't matter.
Your super hero could be a man, a woman, a dog, a robot, anything!
Step 4: Label your super hero Commutative (Man/Woman/Dog/Whatever)
30
Activity 2:
Step 1: The "Associative Laws" say that it doesn't matter how you group the
numbers (i.e. which you calculate first) ...
... when you add:
(a + b) + c = a + (b + c)
... or when you multiply:
(a × b) × c = a × (b × c)
Step 2: Do the way we group numbers matter when multiplying or adding?
Step 3: Using this information, try to draw a super hero whose super powers
incorporates the fact that the way we group numbers doesn't matter
Step 4: Label your super hero Associative (Girl/Boy/Dog/Whatever)
Activity 3
Step 1: The "Distributive Law" says:
a × (b + c) = a × b + a × c
This is what it lets you do:
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3 lots of (2+4) is the same as 3 lots of 2 plus 3 lots of 4
Step 2: Though they kind of look the same, what's different between Associative
and Distributive. Notice that one uses multiplication and addition, but the other
uses either multiplication or addition. What else can you notice
Step 3: Using this information, try to draw a super hero whose super powers are
distributive
Step 4: Label your super hero Distributive
(Woman/Man/Hamster/Whatever)
PROBLEM SOLVING ASSESSMENT (CLASS - VI)
1. What should come in the place of question mark in the following series? a. 3, 8, 6, 10, 9,?
32
a) 11 b)12 c)10 d)14
2. Which of the following number is divisible by 9?
a) 823519 b)270351 c)602591 d)748802
3. Rohan is 18th
from either end of a row of boys. How many boys are there in
that row?
a) 26 b) 36 c) 37 d) 35
4. Which of the following statement is true?
a) (-7)+(-3) = -4 b) (-4)+(0)=0
c) (-2) +(1)= -1 d) (8)+(9)= -17
5. What is the decimal form of ½+1/4+1/8 ?
a) 0.750 b) 0.875 c) 0.825 d) 0.625
6. Loveleen went 12 km north from his house. Then he turned west and covered
8 km. Then he turned south and covered 5 km. Finally he covered 8 km
turning to his east .In which direction is he from his house now?
a) south b) west c) north d) east
7. Find odd one out in the series 1, 5,7 ,17,23,29
a ) 5 b ) 7 c) 23 d) 1
8. The area of a square plot of side 8 m is
a) 16 sqm b) 32 sqm c) 64 sqmd) 8 sqm
9. The correct sum of 0.009+5.4+28.03 is
a) 33.439 b) 32.439 c) 33.934 d) 33.349
10. The number of vertices in a cube is
a) 12 b) 6 c) 4 d) 8
QUIZ (CLASS - VI)
1. 158=___ + 106.What number will come in the blank to make the number sentence true?
A. 52
B. 152
C. 158
D. 264
2. Shown below is a part of a triangle with one of its angles missing. The measure of the missing
angle is
A. 90
B. Less then 90
C. More then 90
D. (we cannot say any of the above definitely.)
33
3. Faizal has 918 marbles. he wants to make packets of marbles, with 9 marbles in each packet.
how many packets will he be able to make?
A. 12
B. 102
C. 120
D. 1062
4. Which of these lies between 6.3 and 6.6?
A. 6.2
B. 6.9
C. 6.05
D. 6.41
5. A teacher brought some toffees to her class. after giving 3 toffees each to 15 students who had
completed their assignments, she has 60 toffees left with her. how many toffees did she bring to
the class?
A. 15
B. 45
C. 78
D. 105
6. Which of these numbers has only two factors, 1 and the number itself?
A. 37+1
B. 37+37
C. 37X1
D. 37X37
7. Meena divides a number by 2. she then divides the answer by 2. this is the same as dividing the
orginal number by
A. 1
B. 2
C. 4
D. Cannot be said as the original number is not known
8. John has stamps of different countries. 1/3rd of them are India stamps. if he has 36 Indian
stamps, how many stamps does he have in total?
A. 12
B. 36
C. 48
D. 108
9. 1024+1025+___=1025+1025+1025.what number will come in the blank to make the number
sentence true?
A. 1024
B. 1025
C. 1026
D. 5124
10. Minu has bought 6 pens. the cost of each pen was between Rs.25 and Rs. 30. which of these
could be the total cost of the pens?
A. Rs.55
B. Rs.126
C. Rs.173
D. Rs.330
34
PUZZLE
ADDITION EQUATIONS
Summative Assessment-1
Time : 2 ½ Hrs. Class-VI –Maths [ M.M. : 60] ------------------------------------------------------------------------------------------------
General Instructions – All questions are compulsory.
(Section-A) 1 8=8
1. How many centimeters make a meter- (a) 100 cm (b) 10 cm (c) 1000 cm (d) 10000 cm
2. Which is the smallest whole number- (a) 0 (b) 1 (c) -1 (d) 2
3. The matchsticks pattern of letter T: (a) 2n (b) 4n (c) 3n (d) 6n
4. Lines that do not meet are said to be- (a) Intersecting lines (b) Parallel lines
(c) Perpendicular lines (d) None of these
5. A four sided polygon is called a- (a) Triangle(b) Quadrilateral
(c) Pentagon (d) Hexagon
6. A triangle with all three sides are of equal lengths, called : (a) Equilateral (b) Isosceles (c) Scalene(d) none of above
7. Which is greatest negative integer- (a) -2 (b) -1 (c) -3 (d) -4
8. What is the sum of (-2) + 6 –
Across 1. x + 8 = 24 2. x + 2 = 17 3. x + 3 = 17 5. x + 12 = 25 6. x + 21 = 40 7. x + 3 = 19 8. x + 6 = 24 9. x + 10 = 30 11. x + 20 = 30 12. x + 7 = 21
Down
1. x + 6 = 19 2. x + 10 = 24 3. x + 5 = 18 4. x + 3 = 22 5. x + 12 = 28 6. x + 18 = 36 7. x + 3 = 15 8. x + 10 = 20 9. x + 30 = 50 10. x + 12 = 26
35
(a) -4 (b) 8 (c) 4 (d) -8
(Section-B) 2 6=12
9. Give prime factorization of 56. 10. using the number line write the integer which is- (a) 3less then -2 (b) (-5) + 10
11. Draw a rough sketch of a quadrilateral KLMN. State-
(a) Two pair of opposite sides (b) Two pair of opposite angles
12. Find the common factor of- 5,15 and 25
13. Find usingdistributive method- 5437 x 1001
14. Find the value of the following- 54279 x 92 + 8 x 54279
(Section-C) 3 8=24
15. Find the difference between the greatest and the least number that
can be written using the digits 6,2,7,4,3 each only once.
16. Give an estimate-
(a) 439 + 334 + 4317 (rounding off to nearest hundred)
(b) 8325 – 491 (nearest tens rounding off)
17. Find the HCF of-
(a) 30, 40 (b) 24 and 36
18. What shape is:
(a) Your instrument box (b) A brick (c) A sweet laddu . 19. Write the following numbers with appropriate signs-
(a) 100 m below sea level (b) C above C temperature
(c) C below C temperature
20. Write in Roman numerals-
(a) 73 (b) 92 (c) 33
21.Give expressions in the following cases-
(a) 5 times y to which 3 is added
(b) y is multiplied by 5 and the result is subtracted from 16.
22. Draw rough diagrams to illustrate the following-
(a) Open curve (b) Closed curve
(Section-D) 4 4=16
23. From the figure identify-
E
D
A B
C
O
.P
P
36
(a) The center of circle (b) Three radii
(c) A diameter (d) A chord
(e) A sector (f) A segment
24.Say True or False:
(a) The measure of an acute angle<90 degree.
(b)The measure of an obtuse angle<90 degree.
(c) The measure of an reflex angle>180 degree.
(d) The measure of one complete revolution=360 degree.
25. Complete the following table and by inspection of the table find the
solution to the equation m+10=16.
m 1 2 3 4 5 6 7 8 9 10
m+10
26. Find the least number which when divided by 12, 16, 24 and 36
Leaves a remainder 7 in each case.
OR
Determine the largest 3-digit number exactly divisible by 8, 10 and 12.
BHASKARYACHARYA GROUP
MINIMUM LEVEL LEARNING (CLASS - VII)
37
Integers Q.1: Listthreeintegersbetween–2and8.
Q.2: Write additive identity and multiplicative identity.
Q.3 Find the product (-1) × 225
Q.4 Evaluate (-36) / (-9)
Lines and Angles
Q.5 Write complementary angle of 600
Q.6 Can two angles be supplementary if both of them are obtuse?
Q.7 Find the value of x, y and z
Q.8 Define vertically opposite angle.
Rational Numbers
Q.9 Writethefollowingrationalnumbersinascendingorder:
( )
( )
( )
Q.10: Find the sum: (i)
(ii)
(iii)
Q-11: Find the sum of:
Q.12 Findtheproduct:
(i)
(
) (ii)
X (-9) (iii)
X
Q.13: Findthevalueof: (i)
(ii)
(iii)
The Triangle and its Properties Q.14 Is there a triangle whose sides have lengths 10.2 cm, 5.8 cm and 4.5 cm?
x y
z
50
38
Q.15 ABC is a triangle, right-angled at C. If AB = 25 cm and AC = 7 cm, find BC. Q.16 A tree is broken at a height of 5m from the ground and its top touches the ground at a distance of 12m from the base of the tree. Find the original height of the tree. Q.17 Write angle sum property. Simple Equations Q.18 Solve the equation. 5p + 2 = 17 Q.19 Set up equations. a. Add 4 to eight times a number; you get 60 b. When I subtracted 11 from twice a number, the result was 15.
Q.20 Write in statement form
P + 4 = 15
Q.21 Write algebraic equation and solve One fifth of a number minus 4
gives 3.
Practical Geometry Q.22 Draw an angle of measure 600.
Q.23 Construct ΔXYZ in which XY = 4.5 cm, YZ = 5 cm and ZX = 6 cm.
Q.24 Construct Δ DEF such that DE = 5 cm, EF = 3 cm, angle D = 900
Exponents and Powers Q.25 Find the value of 5
4.
Q.26 Simplify 2 × 103.
Q.27 Simplify using law of exponents,
38 × 3
-2 × 3
4
Q.28 Express as a product of prime factors.
729 × 64
Data Handling Q.29 Find the mean of the first 5 whole numbers. Q.30 Find the mode and median of the data 13, 16, 12, 14, 19, 12, 14, 13, 14
HIGHER ORDER THINKING SKILLS (CLASS - VII)
39
Q.1 The next Number in the pattern. -62, -37, -12________is
a) 25 b) 13 c) 0 d) -13
Q.2 On the number line the value of -3 X 3 lies on right hand side of
a) -10 b) -4 c) 0 d) -11
Q.3 Evaluate the following using distributive “ 68 X (-17) +-68 X 3
Q.4 Check whether -5 and +5 are additive inverse?
Q.5 Taking today as 0 on the number line, if the day before yesterday is 17
January.What is the date three days after tomorrow.
Q. 6 2/5 X 1/5 =
a) -1 b) 1 c) 0 d) 2/25
Q.7 Value of 25.4 X 100=
a) 254 b) 2.54 c) 2540 d) 0
Q.8 Divide 3/10 by ( 1/3 of 3/5 )
Q.9 The range of data : 3,4,5,6,7,2,3 ?
Q.10 The median of the data : 2,3,6,8,4, 11?
Q.11 Calculate the Mean, Median and Mode of the following data : 70, 62, 54, 57,
54, 62, 62, 75 ?
Are the all three same?
Q.12 Observe the given data and draw the bar graph.
Days Monday Tuesday Wednesday Thursday Friday Saturday
No. of Mobiles sold
50 45 30 55 27 60
Q.13 If x + 7 = 16 then find value of x?
Q.14 x exceeds three by 7, the equation is
a) 2x +15=1 b) x-3 =7 c) x-7 =3 d) none
Q.15 Check whether 5 is solution of the equation 3 x + 2 = 17
40
Q.16 Make the equations:
A) 13 subtracted from twice of a number gives 3.
b) One fifth of a number is five less then that number.
Q.17 Radha got Rs. 17480 as her monthly salary and overtime. Her salary exceeds
the over time by rs. 10000. What is her monthly salary?
Q.18 Find the complementary angle of 79 degree.
Q.19 For a rectangle length is 60 c.m. and a diagonal is 61 c.m. then find breadth.
Q.20 0.07 is equal to
a) 70% b) 7 % c) 0.7% d) 0.07%
PROBLEM SOLVING ASSESSMENT(CLASS - VII)
1. Which observation in the following has maximum frequency?
1, 1, 2, 4, 3, 2, 1, 2, 2, 4
a) 4 b) 3 c) 2 d) 1
2. Which fraction does the one part of the given figure represent?
a)1/5 b) 5/1 c) 5/5 d)0 /5
3If P=0.7,Q=0.27, R=0.327 then P+Q+R is equal to
41
a) 2.327 b) 2.214 c) 1.297 d) 12.97
4 If 7*1=16, 3*9=24, then 6*5=
a) 22 b) 30c) 11 d) 1
5. Equivalent ratio of 6:4 is
a)12:8 b) 1:2 c) 4:6 d) 2:3
6. What time should last watch show?
7. Find the number which will replace x
5 12 x
6 8 18
7 9 20
a) 21 b) 10 c) 13 d) 15
8. The HCF of two consecutive odd numbers is
a) 0 b)2 c) 1 d) none of these
9. 13 is to 17 as x as to 12 where “as to” stands for addition
a) 221 b) 18 c) 31 d) 112
10. Which number should come in place of x?
10. 1/7+2/7+x/7=10/7
a) 1 b) 2 c)3 d) 7
QUIZ (CLASS - VII)
1- Find the number of triangles in the figure given below.
(a) 8 (b) 12 (c) 10 (d) 14
1:2
0
1:1
2
1:0
4
42
2- If 23 +13 = 3x , then x is
(a) 1 (b) 2 (c) 3 (d) 6
3- The sides of two squares in the ratio 2:3 , then the ratios of
their areas will be
(a) 2:3 (b) 3:2 (c) 9:4 (d) 4:9
4- If a , b , c are the sides of right angle triangle, which one is possible
(a) a2˃ b2+c2
(b) a2=b2+c2
(c ) a2< b2+c2
(d) none of the these
5- The product of 43.07 x 1000 is (a)4.307 (b) 4307 (c) 430.7 (d) 43070 6-What is the digit in the thousandths place in the product of 4.15x0.021 ? • 5 (b) 0 (c) 7 (d) 8 7- Find the number that should replace the blank 12:21 :: 8:_____
• 14 (b) 16 (c) 18 (d) 24 8- Which number should come in place of □
(a) 1 (b) 2 (c) 3 (d) 7 9-How many prime factors 1000 have? • 2 (b) 4 (c) 25 (d) 100 10-Find x
5 12 X
6 8
18
43
7 9 20
(a) 10 (b) 21 (c) 13 (d) 15
PUZZLE (CLASS - VI)
ACROSS
1. Three or more lines passing through the same point.
5. Abbreviated form to prove two triangles congruent when
exactly one angle is equal.
8. A number which neither prime nor composite.
9. Chord passing through the centre
11. Number which are integers or fractions.
1 2 3
4 5
6
7
8
9 10
11
44
DOWN
1. Abbreviated form to prove two right triangles congruent.
2.Point of intersection of medians.
3. A quadrilateral having one pair of sides of parallel.
4. A solid figure whose length, breath and height are equal.
6. Numbers of the type 1, 2 , 3 , . . . . . .
7.The observation occurring maximum number of times.
10. L .C .M. OF 2 and 5.
SUMMATIVE ASSESSMENT – 1
Time : 2 ½ Hrs. Class-VI –Maths [ M.M. : 60]
Section- A( 1 mark of each question)
Q.1. The perpendicular line – segment drawn from a vertex of a triangle to the opposite side is
called its
(a) Altitude (b) median (c) angle bisector (d ) none of these
Q.2. Theline – segment joining a vertex of a triangle to the midpoint of opposite side is called
its (a) Altitude (b) median (c) angle bisector (d ) none of
these
45
Q.3. The compliment of 15° is
(a) 65° (b) 165° (c) 75° (d) 245°
Q.4. The solution of equation 3x = 12 is
(a) 6 (b) 9 (c) 7 (d) 4
Q.5. The difference between the highest and the lowest observation is called
(a) range (b) median (c) mode (d ) mean
Q.6. The additive inverse of –6 is
(a) 6 (b) 0 (c) –5 (d) –7
Q.7. If a number is greater then1 , then its reciprocal is ……………………..
(a) equal to 1 (b) greater then 1 (c) less then 1 (d ) none of these
Q.8. 35 mm is equal to
a) 0.35 km b) 3.5 cm c) 0.035 cm d) 350 cm
Section- B( 2 marks of each question)
Q.9. Find (i)
of
(ii)
of 27
Q.10. Find (i) 0.05 x 7 (ii) 211.02 x 4
Q.11. Solve the equation : 3x - 2 = 46
Q.12. Find the supplement angle of each of the following angles (i) 105 ° (ii) 87 °
Q.13. Find the value of x in the following figure. X
50 °60 °
Q.14. Fill in the blanks.
(i) For a triangle ABC ,A + B + C = ……………
(ii) In a right triangle , the side opposite to 90° is called ………………..
Section- C(3 marks of each question)
Q.15. Find the perimeter of triangle ABC.( in the figure.)
A
cm
cm
B C
cm
Q.16. Evaluate each of the following
(i) ( 31 ) [( 30 ) + ( 1 ) ] (ii) [( 6 ) + ] [( 2 ) + 1 ]
Q.17. Find (i) 0.04 2 (ii) 2.48 4 (iii) 14.49 7
Q.18. Solve the equation : 5 (x - 2) = 4
Q.19. Set up an equation and solve to find the solution of the following case
46
“Add 4 to eight times a number, you get 60.”
Q.20. Find the values of unknown ‘ x ‘ and ‘ y ‘ in the following diagram:
Q.21. Construct a triangle XYZ in which XY = 4.5cm, YZ = 5 cm and ZX = 6 cm.
Q.22. Find (i)
1
(ii)
Section- D( 4 marks of each question)
Q.23. The mean mark (out of 100) of a group of student is 60. If their marks are 85, 62, 36, 48,
72, x, 75 and 39, then find the value of x.
Q.24. Find the following
(i) (-2) x (-5 ) (ii) 12 + (-4) (iii) o ÷ 5 (iv) 0 x14
Q.25. ABC is a triangle, right angled at C. If AB = 25 cm and AC = 7 cm , find BC.
Q.26. Construct a triangle ABC in which mA = 60° , mB = 30° and AB = 5.8 c
RAMANUJAN GROUP
MINIMUM LEVEL LEARNING (CLASS - VIII)
CHAPTER –1.RATIONAL NUMBERS.
Put a tick mark(√) on the correct answer :
Q1.Which of the following numbers is the additive inverse of 7/29
(i) 29/7 (ii)—29/7 (iii)–7/29 (iv) 7/29
Q2.Which of the following numbers is the multiplicative inverse of 15/31
(i) 31/15 (ii)—31/15 (iii)–15/31 (iv) 15/31
47
Q3.Which of the following numbers has no multiplicative inverse
(i) zero (ii) 1 (iii)– 1 (iv) none of these
Q4.Which of the following numbers is the product of 6/13 & -- 26/3
(i) 1(ii)—4 (iii)–266/133 (iv) 266/133
Q5.Which of the following numbers is its own reciprocal
(i) 10 (ii) zero (iii)1/5(iv) 1
Q6.Which of the following numbers is the decimal form of 1/4
(i)-- 0.25 (ii) 2.5(iii)0.25 (iv) – 2.5
CHAPTER –2. LINEAR EQUATIONS IN ONE VARIABLE
Put a tick mark(√) on the correct answer :
Q1. If (x/3) + 1 = ( 7/15) then the value of ‘x’ is
(i) 22/5 (ii)—8/5 (iii) 7/5 (iv) 3
Q2.What is the degree of the equation x2 + 2x – 3 = x2 + 7x -- 23
(i) zero (ii) one (iii) two (iv) three
Q3.What is the length of the rectangle whose breadth is 10 cm & perimeter 60 cm.
(i) 15cm (ii) 16cm (iii) 20cm (iv) 25cm
Q4.What should be added to –3/5 to get – 7/5
(i) 4/5(ii) 1 (iii) –4/5(iv) 2
Q5.If x % of 50 is 10 , then the value of ‘x’ is
(i) 30(ii) 15 (iii) 10(iv) 20
CHAPTER –3.UNDERSTANDING QUADRILATERALS.
Put a tick mark(√) on the correct answer :
Q1.How many diagonals does a convex quadrilateral has ?
(i)one (ii)two (iii)three (iv)four
Q2.What is the sum of all interior angles of a pentagon ?
(i) 1800 (ii)3600 (iii)5400 (iv)7200
Q3. How many sides a regular polygon has whose each exterior angle is 450?
48
(i)eight (ii)seven (iii)six (iv)five
Q4.What is the minimum interior angle possible for a regular polygon?
(i) 600 (ii)800 (iii) 1200 (iv)1600
Q5.What is the maximum exterior angle possible for a regular polygon?
(i) 600 (ii) 800 (iii) 1200 (iv)1600
CHAPTER –4 & 10. PRACTICAL GEOMETRY & VISUALISING SOLID SHAPES
Put a tick mark(√) on the correct answer :
Q1.What the point of intersection of the medians of a triangle called ?
(i) circumcentre (ii) In centre (iii) centroid (iv) orthocentre
Q2.What the point of intersection of the altitudes of a triangle called ?
(i) circumcentre (ii) In centre (iii) centroid (iv) orthocentre
Q3.What the point of intersection of the side bisectors of a triangle called ?
(i) circumcentre (ii) In centre (iii) centroid (iv) orthocentre
Q4.What the point of intersection of the angle bisectors of a triangle called ?
(i) circumcentre (ii) In centre (iii) centroid (iv) orthocentre
Q5.Which of the following is a three dimensional figure ?
(i) Square (ii) Trapezium (iii) Cube (iv) Parallelogram
CHAPTER –5.DATA HANDLING.
Q.1 Adjoining pie chart gives the expenditure (In percentage) on various items & savings of a
family during a month. Answer the following questions on the basis of the information given in
the pie chart.
(a)On which item, the expenditure is maximum?
(i) House rent (ii) Food (iii) Others (iv) Education
(b)Expenditure on which item is equal to the total savings of the family?
House rent, 10% Transport, 5%
Education, 15%
Food, 25%
Clothes, 10%
Savings, 15%
Others, 20% House rent
Transport
Education
Food
Clothes
49
(i) House rent (ii) Food (iii) Clothes (iv) Education
(c)If the monthly savings of the family is Rs.3000 , what is the monthly expenditure on clothes ?
(i)Rs. 2000 (ii)Rs. 3000 (iii) Rs.1000 (iv) Rs.4000
Q2.What are the possible number of outcomes if a coin is tossed twice ?
(i)one (ii)two (iii)three (iv)four
Q3.What are the possible number of outcomes if a die is tossed once ?
(i) six (ii)five (iii)three (iv)four
Q4.What are the possible number of outcomes if a card is drawn from a pack of 52 cards?
(i) 20 (ii)30 (iii)42 (iv)52
Q5.What is the probability of getting a king if a card is drawn from a pack of 52 cards?
(i) 1/52 (ii)2/52 (iii)3/52 (iv)4/52
CHAPTER –6.SQUARES & SQUARE ROOTS.
Put a tick mark(√) on the correct answer :
Q1. If a number has ‘1’ or ‘9’ in the unit’s place, then its square roor ends in which of the
following numbers.
(i) 1 (ii) 4 (iii) 5 (iv) 6
Q2. There are how many non-perfect squares between 100 &121 ?
(i) 10 (ii) 15 (iii) 20 (iv) 25
Q3.What will be the unit’s digit of 526982
(i) zero (ii) 4 (iii) 5 (iv) 6
Q4.The sum of first ‘n’ odd natural numbers is given by
(i) 2n (ii) n2 (iii) (n + 1) (iv) n2 + 1
Q5.Which of the following numbers is not a perfect square ?
(i) 62500 (ii) 57600 (iii) 90000 (iv) 63147
CHAPTER –7. CUBES&CUBE ROOTS.
Put a tick mark(√) on the correct answer :
Q1.Which of the following numbers must be subtracted from 345 to get a perfect cube ?
(i) 121 (ii) 131 (iii) 2 (iv) 24
50
Q2.Which of the following numbers is a perfect cube ?
(i) 343 (ii) 443 (iii) 543 (iv) 643
Q3.Which of the following numbers must be multiplied to 392 to get a perfect cube ?
(i) 2 (ii) 3 (iii4 (iv) 7
Q4. By which of the following numbers 10648 must be divided to get a perfect cube ?
(i) 2 (ii) 4 (iii) 5 (iv) 7
Q5.What is the volume of a cube whose each side is 4cm ?
(i) 24cm3 (ii) 48cm3 (iii) 64 cm3 (iv) 125cm3
CHAPTER –8.COMPARING QUANTITIES.
Put a tick mark(√) on the correct answer :
Q1.Find which of the following represents 3 : 4 ?
(i) 25% (ii) 40% (iii) 50% (iv) 75%
Q2.If 60% of x is 1200 , then the value of ‘x’ is
(i) 1000 (ii) 2000 (iii) 3000 (iv) 4000
Q3.The list price of an article is Rs.220. If it is sold at a discount of 20% , what is its selling price
(i) 100 (ii) 44 (iii) 176 (iv) 200
Q4. A table marked at Rs.15000 is available for Rs.14400 .Find the discount percent?
(i) 2% (ii) 4% (iii) 5% (iv) 7%
Q5.The cost price of an article is Rs 500. If it is sold at a profit of 20% , what is its selling price
(i) Rs. 600 (ii) Rs. 700 (iii) Rs. 400 (iv) Rs. 520
CHAPTER –9.ALGEBRAIC EXPRESSIONS AND IDENTITIES.
Put a tick mark(√) on the correct answer :
Q1.What is the sum of 7xy + 5yz – 3xz & 2xy + 4yz + 2xz ?
(i) 8xy + yz -- xz (ii) 9xy + 9yz -- xz (iii) 9xy + 9yz + xz (iv) 9xy + 9yz + 5xz
Q2. What should be subtracted from 2x2 – 5y2 + 7z2 to get x2 – y2 + z2
(i) x2 –4 y2 +6 z2 (ii) x2 –3 y2 +6 z2 (iii)3 x2 – 2y2 +2 z2 (iv) x2 – y2 + z2
51
Q3.What is the product of 3xy, 4xy &2xz ?
(i) 24xyz (ii) 24x2yz (iii) 24 x3y2z (iv) 24 x3y2z2
Q4.What is the area of the rectangle of length 4xy & breadth 2xy ?
(i) 8xy2 (ii) 8x2y (iii) 4 x3y2z (iv) 8 x2y2
Q5.What is the volume of the cuboid of length 8xy , breadth 3xy & height xy ?
(i) 24xy2 (ii) 24x2y (iii)2 4 x3y2 (iv) 24 x3y3
CHAPTER – 11. MENSURATION
Q1.What is the area of a rhombus whose diagonals are of lengths 10cm & 8.2 cm?
(i) 24cm2 (ii) 41cm2 (iii) 42 cm2 (iv) 25cm2
Q2.What is the area of a trapeziumwhose two parallel sides are 10 cm & 12cm & height 4cm?
(i) 42cm2 (ii) 44cm2 (iii) 46 cm2 (iv) 48cm2
Q3.The area of a rhombus is 240 cm2.If one of its diagonals is 16 cm ,what the length of its other
diagonal is?
(i) 32cm (ii) 30cm (iii) 45 cm (iv) 48cm
Q4.If each side of an equilateral triangle is doubled, then its area becomes how many times?
(i) 2 (ii) 3 (iii) 4 (iv) 8
Q5.What is the total surface area of a cuboid of dimensions 4cm, 5cm &6cm ?
(i) 142cm2 (ii) 144cm2 (iii) 146 cm2 (iv) 148cm2
CHAPTER – 12.EXPONENTS & POWERS.
Q1. Which of the following is the multiplicative inverse of (3 x 4)--2
(i) 12 (ii)1/ 144 (iii) 144 (iv) 1 / 12
Q2.What is the value of ‘ m ‘ if (-- 2)2 x (-- 5)3 = 50 m ?
(i) 10 (ii) -- 10 (iii) 100 (iv) -- 100
Q3.What is the scientific notation of 0.0023 ?
(i) 2.3 X 10--3 (ii) 23 X 10--3 (iii) 2.3 X 103 (iv) 23 X 103
Q4.What is the usual form of 7.54 x 10--3 ?
(i) 0.0754 (ii) 0.00754 (iii)0.000754 (iv) 0.0000754
Q5.What is the value of ( 30+ 40+ 50) ?
52
(i) 7 (ii) -- 7 (iii) 3 (iv) -- 3
CHAPTER – 13.DIRECT & INVERSE PROPORTIONS.
Q1.An electric pole, 14metres high, casts a shadow of 10metres. What will be the height of a tree
that casts a shadow of 15 metres under similar conditions?
(i) 14 m (ii) 20 m (iii) 21 m (iv) 24 m
Q2.A train is running at a speed of 75 km/hr. What distance will it cover in 20 minutes ?
(i) 15km (ii) 20km (iii) 23 km (iv) 25 km
Q3.A machine manufactures 840 bottles in six hours. Find the number of bottles it can
manufacture in five hours ?
(i) 600 (ii) 650 (iii) 700 (iv) 750
Q4.The scale of a map is given as 1:30000000 . If two cities are 4 cm apart on the map , what is
the actual distance between them ?
(i) 600 km (ii) 1400 km (iii) 1300 km (iv) 1200 km
Q5.If 15 workers can build a wall in 48 hours, how many workers will be required to do the same
work in 30 hours ?
(i) 15 (ii) 14 (iii) 24 (iv) 30
CHAPTER – 14.FACTORISATION.
Q1.What is the HCF of 2x2y &3xy2 ?
(i) 6xy (ii) 6x2y2 (iii) xy (iv) x2y2
Q2. Which of the following is a factor of 6xy – 4y + 6 – 9x ?
(i) 2x + y (ii) x -- y (iii) 2x -- 3 (iv) 3x -- 2
Q3. Which of the following is a factor of y2 – 7y + 12 ?
(i) 2y + 3 (ii) y + 3 (iii) y -- 3 (iv) 2y – 2
Q 4.Which of the following is a factor of m4 – 256 ?
(i) m + 4 (ii) m2 + 4 (iii) m2 -- 4 (iv) m + 16
Q 4.Which of the following is a factor of z2 – 4z -- 12 ?
(i) z + 6 (ii) z -- 6 (iii) z2 -- 12 (iv) z + 2
Q5.What is the value of 2x – 3y + 4z at x=2, y = 0 & z =1
(i) 4 (ii) 6 (iii) 8 (iv) 10
53
CHAPTER – 14 & 15.INTRODUCTION TO GRAPHS & PLAYING WITH NUMBERS.
The following graph shows the temperature forecast & the actual temperature for each day of a
week. On the basis of the graph , answer the following questions .
Q1.On which days was the forecast temperature the same as the actual temperature ?
(i)Mon day, Tuesday (ii)Tuesday, Friday ,Sunday
(i)Mon day, Tuesday, Wed.day (ii)Tuesday, Saturday ,Sunday
Q2.What was the maximum forecast temperature during the week ?
(i) 350C (i) 450C (i) 300C (i) 150C
Q3.What was the minimum forecast temperature during the week ?
(i) 350C (i) 250C (i) 300C (i) 150C
Q4.On which days did the actual temperature differ the most from the forecast temperature ?
(i)Mon day (ii)Tuesday (iii) Wed.day (iv) Thursday
CHAPTER – 15.PLAYING WITH NUMBERS.
Q1.Find the value of ‘A’ & ‘B’ from the following ?
3 A
+ 2 5
B 2
(i) 2 & 3 (ii) 7& 6 (iii) 8 & 6 (iv) 1 & 7
0
10
20
30
40
Monday Tuesday wed.day Thursday Friday Saturday Sunday
Forest
Actual
Column1
54
Q2.Find the value of ‘A’ & ‘B’ from the following ?
A B
X 6
B BB
(i) 7 & 4 (ii) 7& 2 (iii) 2 & 6 (iv) 4 & 7
Q2.Find the value of ‘A’ & ‘B’ from the following ?
1 2 A
+ 6 A B
A 0 9
(i) 3 & 4 (ii) 5& 2 (iii) 8 & 1 (iv) 4 & 8
Q3. If the three digit number 24x is divisible by ‘9’ , what is the value of ‘x’
(i) 3 (ii) 5 (iii) 8 (iv) 4
Q4. If 21z5 is a multiple of ‘9’ , where ‘z’ is a digit , find the value of ‘z’ ?
(i) 2 (ii) 3 (iii) 8 (iv) 1
HIGHER ORDER THINKING SKILLS (CLASS - VIII)
1. The product of two rational numbers is -
. If one of the numbers is
, find
the other.
2. Divide the sum of
and
by their difference.
3. Represent -
on the number line.
4. Solve using appropriate property:
x
-
-
x
5. The denominator of a rational number is greater then its numerator by 6 . If
the numerator is decreased by 1 and the denominator is increased by 1, the
number is 1/3, find the rational number.
55
6. A two digit number is such that sum of its digits is 8. When we interchange
the digits new number formed is 36 more then the original number. Find the
number.
7. The average of 3 numbers is 39. If the first number is twice the second and
second is 4 times of the third. Find the number.
8. If 3m/5 + 5m/4 = 29/40, find m.
9. Solve: 5x – 3(2x-7) = 5(3x – 1) + 7/2
10. The measure of two sides of a parallelogram are in the ratio 3:2 and if the
perimeter of parallelogram is 180cm, find the measure of all sides.
11. Two adjacent angles of parallelogram are (3a + 10 )° and (3a - 4 )°. Find all
the angles of the parallelogram.
12. PQRS is trapezium such that PQ//SR .LP:LS = 7:2 , and LQ: LR = 4:5 , Find the
angles of trapezium.
13. Construct the quadrilateral MORE,where MO=5cm, OR=3.5cm, LM =600 ,
LO=1050, LR= 1050
14. Construct a rhombus ABCD in which diagonal AC =7.6cm,BD=7cm.
15. Draw a pie chart for the following data of expenditure pattern in a family:
Item Expenditure in percent
Rent 10%
Food 40%
Education 10%
Medicine 5%
Other 15%
16. Determine the square root of 2 by long division method till two places of
decimal.
17. Find: (a) The smallest 3-digit perfect square number.
(b) Find the largest 4-digit perfect square number.
18. Find Pythagorean triplet whose one of the number is 18.
19. Find the smallest square number that is divisible by 8,9 and 10.
20. √
=
, find the value of x.
21. Draw an appropriate graph to represent the given information.
Children who
prefer
School A School B School C
Football 40 55 15
56
cricket 45 25 35
22. When a die is thrown, find the probability of an event of getting:
(a) Even prime number
(b) Odd number greater then 4
(c) Even number less then 5
(d) Numbers multiple of 3
23. Find the cube of -23
24. Three numbers are in the ratio 1:2:3. The sum of their cubes is 36000. Find
the numbers.
25. If the area of a square is 57.76 sq cm, find the side of the square.
26. Arrange the following in ascending order:
,
,
,
27. A hall is a hollow cube and holds 74088 cu.m of air. Find the length of the
hall.
28. Find (
) +
– (
) +
29. Find the measure of interior angle of a regular polygon of 9 sides.
30. A father is six times as old as his son. After four years he will be only four
times as old as his son. What are their present ages.
ACTIVITY (CLASS - VIII)
TOPIC: ALGEBRIAC IDENTITIES
OBJECTIVE
By doing this activity the students will be able to verify the identity
(x+a) (x+b) = x2 +ax + bx + ab practically.
PRE-REQUISITE KNOWLEDGE
Students should be familiar with
(1) Areas of squares and rectangles
(2) Four basic operations of polynomials.
MATERIAL REQUIRED
Cartridge sheet
57
Crayons
Pair of scissors
Geometry box
PROCEDURE
(1) Draw a rectangle ABCD of sides (x+a) and (x+b) respectively.
Area of the rectangle ABCD = (x+a) (x+b)
(2) Draw a square AEFG (Color it Red) with sides x.
Area of Red Square = x. x = x2
(3) Produce EF to meet CD in H.
(4) We obtain a rectangle GFHD (II). Colour it blue with sides b and x.
Area of blue rectangle = b x x = bx.
(5) Produce GF to meet BC in I.
(6) We obtain two rectangles, rectangle EBIF (III), with sides x and a. Color this one yellow and a
rectangle FICH with sides a and b colour it green
(7) Area of yellow rectangle = ax and Area of green rectangle = ab.
Observation
It is observed from the figure area of the rectangle ABCD = sum of the area of four parts
(x + a)(x + b) = x2 + ax + bx + ab
PROBLEM SOLVING ASSESSMENT(CLASS -
VIII)
x + a
I
x2
x
II bx
III
ax
E A
x
G
b
D
x + b
ax IV
F F
B
x
I
b
C H
Figure 1
58
Quantitative Reasoning ( मात्रात्मक तकक )
Q 1.0.024÷0.0012=?
(A)2 (B)200 (C)20 (D)None of these
Q 2. Square root of 10 is :
(A)a rational number (B)an integer (C)a negative integer (D)none of these
Q 3.Find the value of 0.5x0.5+0.5÷5=
(A)0.15 (B)0.25 (C)0.35 (D)0.45
Q 4.A man saved Rs.600 in 30 days. The number of days needed by him to save Rs. 1160 is
(A)66 (B)72 (C)45 (D)58
Q 5.Cost of 17 dolls is Rs306. The number of dolls that can be bought for Rs.522 is
(A)29 (B)28 (C)27 (D)32
Q 6.Interest= …………………….. - Principal
(a) Rate (b)Amount
(c)time (d) none of these
Q 7.(a-b)2=……………..
(a) a2+2ab+b2 (b) a2-2ab+b2
(c) a2+b2 (d) a2-b2
Q 8. Ratio of 50paise to Rs 5 is
(a) 1:10 (b) 10:1
(c) 1:2 (d) 50:5
Q 9.The numerical coefficient on the algebraic expression -4x2y2z is
(a) 1 (b) 4
(c) 0 (d) -4
Q 10. The cube of 20 is
(a) 40 (b) 800 (c) 8000 (d)4000
QUIZ (CLASS - VIII)
1. What do you mean by Polyhedron?
59
2. What do you mean by Regular polyhedron? 3. What is the difference between Convex and Concave polyhedron? 4. What do you mean by Prism? 5. What do you mean by Pyramid? 6. What is the difference between prism and pyramid? 7. Give few example of prism and pyramid form our daily life 8. What is the Euler’s formula for polyhedrons? 9. How are prism and cylinder alike? 10. how are pyramid and cone alike?
MATH CROSSWORD PUZZLE CLASS 8
1 2 3
4 5
6
7 8
9 10
11 12
13
14
15
16
17
18
19
20
ACROSS DOWN
4. Answer to an addition problem 1. Answer to a division problem
9. Answer to a subtraction 2. Twelve
11. 3, 9, 37 and 131 are all ___numbers 3. Graph that uses pictures to show information
12. Bottom number of a fraction 5. Shape of a tennis ball
14. Polygon with five sides 6. Number added to another number to find a
sum
16. straight lines that never cross 7. Answer to a multiplication problem
17. Having the same size and shape 8. Shape of a cereal box
60
18. Shape of a soup can 10. Nine___ seven equals 63
19. Distance around a figure 13. 90 degree angle
20. Graph that uses bars to show information 15. Top number of a fraction
SUMMATIVE FORMATIVE ASSESSMENT
Section – A Question numbers from 1 to 8 are of one mark each.
Q1. Number of integers between -3/2 and 2/3
a) 1
b) 2
c) 0
d) Infinitely many Q2. X/3 – 5/2 = -1/6 then x=
a) 4
b) 5
c) 6
d) 7 Q3. The angle sum of a convex polygon with sides 10 is
a) 1800°
b) 1260°
c) 1440°
d) 1080°
Q4.The number of independent measurements required to construct a unique quadrilateral is a) 3
b) 4
c) 5
d) 6 Q5.Which of the following gives the relationship between the whole and its part of the given data? a) Pie chart
b) Pictograph
c) Bar graph
d) Histogram Q6.The area of a square plot is 2716 M2 . The side of the square plot is a) 43 m
b) 34 m
61
c) 53 m
d) 54 m Q7. The smallest number by which 351 is divided to make it a perfect cube is a) 2
b) 13
c) 6
d) 9 Q8. 2x/3 + 1 = 7x/15 – 3 then x = a) 20 b) -20 c) 10 d) -10
Section – B Question numbers from 9 to 13 are of two marks each Q9.Write five rational numbers that are greater then -2. Q10. How many sides does a regular polygon have if each of its interior angles is 150°? Q11.Find the least number which must be subtracted from 4000 so as to get a perfect square. Q12. Find the cube root of 91125. Q13. Factorize: x² -2xy + y² - z²
Section – C Question numbers from 14 to 19 are of three marks each Q14. Find five rational numbers between -5/3 and ¾. Q15. One of the two digits of a two digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number? Q16. Find the smallest square number that is divisible by each of the numbers 4, 9 and 10. Q17. Construct a rhombus whose diagonals are 5.2 cm and 6.4 cm long. Q18.The number of marks scored by a student in different subjects in an examination is given below. Display the data in a pie chart.
Subject Sanskrit Hindi English Mathema Science Social
62
tics Marks 70 60 80 95 90 85
Q19. In the parallelogram ABCD. Find the angles x, y and z.
Section – D Question numbers from 20 to 25 are of four marks each Q20.Deveshi has a total of Rs 590 as currency notes in the denominations of Rs 50, Rs20 and Rs 10. The ratio of the number of Rs 50 notes and Rs 20 notes is 3:5. If she has a total of 25 notes, how many notes of each denomination she has? Q21. One-half of Meera’s age two years from now plus one-third of her age three years ago is twenty years. Find how old is she now ?
Q22. A gardener has 1000 plants. He wants to plant these in such a way that the number
of rows and the number of columns remain same. Find the minimum number of plants he
needs more for this.
Q23. Construct a quadrilateral ABCD where AB=3.5cm BC=6.5 cm A=75° ,B=105° and C =120°. Q24.Factorize:
(a) 25 a² - 4b² +28bc -49c² (b) (x-y)⁴ -y⁴
Q25.Find x in the figure shown
63
VARAHMIHIR GROUP
MINIMUM LEVEL LEARNING (CLASS - IX)
Number system
1) Simplify( 27)1/3.(4)1/2
2) Express 1.050505......in the form of p/q
3) Which of the following is an irrational number?
(a) 3.14 (b) 3.14144144... (c) 3.1 ̅ (d)
3.141141114
4) Represent √ on number line
5) Find four rational numbers between
and
.
Polynomial
64
1) Find the degree of (x3-1)(x+1)
2) Expand (4a-b+2c)2
3) Factorise 6x2 + 5x – 6
4) Factorize 8a3 + b
3 + 12a
2b + 6ab
2 5) Without actual calculation, find the value of following using identity.
(a) 102 X 98 and (b) 992
6) Factorise: (p – q)3 + (q – r)
3 + (r – p)
3
Coordinate geometry
1)Write the coordinates of a point
(a) above x axis lying on y axis at a distance of 3 units.
(b) below x axis and on y axis at a distance of 8 units.
(c) right of origin and on x axis at a distance of 2 units.
2) Plot the points A (0,3), B (5,3), C(4,0) and D(-1,0) on the graph paper.
Geometry
1) If a point C lies between two points A and B such that AC=BC, prove that
AC=1/2 of AB
2) If AB is a straight line and OC is a ray in
The given fig., find x and y if x-y=800
3) In Δ PSR, If Q is a point on SR such that x y
PQ =PR show that PQ<PS A C B
4) Explain Euclid‟s 5th postulate.
Triangles
1)The perimeter of an equilateral triangle is 60 metres. Find the area of the triangle.
2) Prove that sum of interior angles of a triangle is 1800
3) Find the area of a triangle, two sides of which are 8cm and 6cm and the perimeter is 24cm
65
HIGHER ORDER THINKING SKILLS (CLASS - IX)
1. A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The
non-parallel sides are 14 m and 13 m. Find the area of the field.
2. Find the area of a triangle two sides of which are 18 cm and 10 cm and the
perimeter is 42 cm.
3. Give the equations of two lines passing through (2, 10). How many more such lines
are there, and why?
4. Two points with coordinates (2, 3) and (2, –1) lie on a line, parallel to which axis?
Justify your answer.
5. Simplify the following expression.
6. In a quadrilateral ABCD, AB = 9 cm, BC = 12 cm, CD = 5 cm, AD = 8 cm and ∠C = 90°. Find
the area Of triangle ABD.
7. The floor of a rectangular hall has a perimeter 150 m. If the cost of painting the
four walls at the rate of Rs 10 per m2 is Rs 9000, find the height of the hall.
8. Three coins are tossed simultaneously 200 times with the following frequencies of
different outcomes. compute the probability of getting
lessthen 3 tails.
9. The taxi fair in a city is as follows:
For the first kilometer, the fare is Rs 10 and for the subsequent distance it is Rs 6 per km. Taking
the
distance covered as x km and total fare as Rsy, write a linear equation for this information and
draw its
66
graph. From the graph, find the fare for travelling a distance of 4 km.
10. Prove that the angles opposite to equal sides of an isosceles triangle are equal.
Using the above, find ∠ B in a right triangle ABC, right angled at A with AB = AC.
11. Prove that the angle subtended by an arc at the centre is double the angle subtended by it at
any
point on the remaining part of the circle. Using the above result, find x in figure where O is
thecentre of the circle.
12. A dome of a building is in the form of a hollow hemisphere. From inside, it was white-washed
at the
cost of Rs 498.96. If the rate of white washing is Rs 2.00 per square meter, find the volume of air
inside the dome.
13. Verify that:
14. Find the value of K if ( K – 2 ) is a factor of 4x3 + 3x2 – 4x + k.
15. Write the quadrant in which each of the following points lie :
(i) (–3, –5)
(ii) (2, –5)
(iii) (–3, 5)
Also, verify by locating them on the cartesian plane.
16. In Figure 3, ABC and ABD are two triangles on the same base AB.If the line segment CD is
bisected
by AB at O, then show that: Area (
67
C B
A D
17. The surface area of a sphere of radius 5 cm is five times the
area of the curved surface of a cone of radius 4 cm. Find the height and the volume of
the cone (taking 22/7)
18 The radius of a sphere is increased by 10%. Prove that the volume will be increased by 33.1%
approximately.
19 A shopkeeper has one spherical laddoo of radius 5cm. With the same amount of material, how
many laddoos of radius 2.5 cm can be made?
20 Rain water which falls on a flat rectangular surface of length 6 m and breadth 4 m is
transferred into a cylindrical vessel of internal radius 20 cm. What will be the height of water
in the cylindrical vessel if the rain fall is 1 cm. Give your answer to the nearest integer. (Take
21 A cube of side 4 cm contains a sphere touching its sides. Find the volume of the gap in
between.
22. The perimeter of a triangular field is 420 m and its sides are in the ratio 6 : 7 : 8. Find the area
of
the triangular field.
23. Find the area of the trapezium PQRS with height PQ given in Fig.
68
24. The perimeter of a triangle is 50 cm. One side of a triangle is 4 cm longer then the smaller side
and the third side is 6 cm less then twice the smaller side. Find the area of the triangle.
25. Find the value of x in the adjoining figure if AB||CD.
26. Without finding the cubes, factorize and find the value of (
) (
) (
)
27. Q.31 In the given figure and PS bisects ∠ If ∠ and ∠ find
∠
28. Plot the points P (1, 0), Q (4, 0) and S (1, 3). Find the coordinates of the point R such that PQRS
is a square.
29. Find the value of m so that 2x – 1 be a factor of 8x4 + 4x3 – 16x2 + 10x + m.
30. If x + 2a is a factor of x5 – 4a2 x3 + 2x + 2a + 3, find a.
ACTIVITY (CLASS - IX)
OBJECTIVE
To verify that sum of all the interior angles of a quadrilateral is 360C
69
PRE-REQUISITE KNOWLEDGE
(1) Knowledge of interior angles of a quadrilateral.
(2) Sum of all the angles at a point in a plane is 360°.
MATERIAL REQUIRED
• Drawing sheet
• Sketch pens
• A pair of scissors
• Glue stick
PROCEDURE
(1) Draw a quadrilateral ABCD on a drawing sheet, see Figure 1.
(2) Label the interior angles of the quadrilateral as ∠l, ∠2, ∠3 and ∠4 as shown in Figure
1.
(3) Mark these angles with sketch pens of different colours.
(4) Mark a point P on the drawing sheet.
(5) Cut ∠l, ∠2, ∠3 and ∠4 as shown in Figure 2 and arrange them at the point P as shown
in Figure 3.
A B
C D
1 2
4 3
70
OBSERVATION
It is observe that arms coincide with each other. And there is no gap in-between them.
This means they are angles at a point in the plane.
CONCLUSION:
Since, some of all the angles at a point is 3600.
Therefore, ∠1 + ∠2 +∠3 +∠4= 3600.
PROBLEM SOLVING ASSESSMENT
(CLASS - IX)
Q1: If Rekha can type a page in 'm' minutes, what piece of the page she can do it in 10 minutes? (a) 10/m
A B
C D
1 2
4 3
FIGURE 2.
1
P
3 4
2
FIGURE 3
71
(b) m - 10 (c) M + 10 (d) m/10 Q2: If sum of t and t+3 is greater then 20, what is a possible value of m? (a) -9 (b) -6 (c) -2 (d) 10 Q3: How many times between 3 O'clock and 6 O'clock will hands of a clock coincide? (a) 5 times (b) 2 times (c) 4 times (d) 3 times Q4: Find the missing number:
(a) 1 (b) 14 (c) 17 (d) 16 Q5: How many parallelograms are there in the given figure?
(a) 14 (b) 15 (c) 18 (d) 16 Q6: Find the value of 'x' in the given triangle.
http://2.bp.blogspot.com/-NqF9YySG2PM/UJoYJCDnVxI/AAAAAAAAD2I/5z8ktmnKO8E/s1600/cl9MathsPSA1Fig1.jpg
http://1.bp.blogspot.com/-8NirGi4Yk1k/UJoZJHdY5uI/AAAAAAAAD2Q/OS-ZJaU9GVY/s1600/cl9MathsPSA1Fig2.jpg
72
(a) 80° (b) 70° (c) 55° (d) 50° Q7: Mahesh walks 20m North then he returns right and walks 30m. Now he turns right and walks 35m. After turning left, he walks 15m. Again he turns left and moves 15m. In which direction and how far is he from his original position? (a) 15m east (b) 45m east (c) 15m west (d) none of these Q8: One half of the difference between the number of degrees in a rectangle and the number of degrees in a triangle is (a) 360° (b) 240° (c) 180° (d) 90° Q9: Where does the line y = x - 3 cross the y-axis? (a) (2, 3) (b) (0, -3) (c) (-3, 2) (d) (-3, 3) Q10: The value of 3(x
2y
-4z)
4x
3y is equal to
(a) 81x
-1y
-4z
4
(b) 81x11
y-15
z4
(c) 3x11
y-15
z4
(d) 3x9y
1z
4
Q11: The mean of 10 numbers is 20. If 5 is subtracted from every number, what will be the new mean? (a) 15 (b) 20 (c) 25 (d) none of these Q12: There are 24 birds on a tree. A hunter fired a gun and 20 fall down on ground. How many birds left on the tree ? (a) 4 (b) 7 (c) 24 (d) none
73
Q13: In the following sequence find the missing number (?). 01 : 08 : : (?) : 125 (a) 10 (b) 12 (c) 15 (d) 16 Q14: In the group of 26 girls Anna's Position is 7th from the bottom. What is the position of Anna from the top of the group ? (a) 20th (b) 21st (c) 22nd (d) 17th Q15: Jyoti is 2 years older than Sindhu. Aarti is 4 years older than Sindhu. Which of the following show relation between Jyoti”s and Aarti”s age?
a) Jyotia”s age = Aarti”s age -2 b) Jyotia”s age = Aarti”s age +2 c) Jyotia”s age = Aarti”s age +6 d) Jyotia”s age = Aarti”s age -6
Q16: If Sunita can read 25 pages of a novel of 250 pages in x days. Which of the following equation would give the number of days she can read half the novel?
a) 5 X b) 5+X c) 10+X d) 10X
Q17: Read the given statements: I. 20% of the doctors are surgeons. II. The remaining are physicians. III. 10% of the physicians are neurologists
What percent of the doctors are neurologists? a) 8 b) 10 c) 20 d) 2
Q18: When Udar purchased an item online from Australia for AUD 350.00, the exchange rate was 1000 INR for AUD 17.50. (AUD =Australian Dollar). Udar’s bank charged him 1.5% for the transaction. The total cost for the item was
a) 23,300 INR b) 30,000 INR c) 20,015 INR d) 20,525 INR
Q19:Haima”s internet plan allows 20 Gb of downloads per calendar month without any excess charges. (1 Gb=1000 Mb ). By the end of june24
th ,Haima has used 15800 Mb.
She doesn’t want to pay an excess for june. What is the average download she can make per day for the remainder of june?
a) 700Mb b) 4200 Mb c) 600 Mb d) 840 Mb
Q20: In Jain”s school average score of two unit tests is considered the final score. First test is marked out of 40 and second test out of 60. Jian scored 80% in the first test and in second test he scored 90% . What is Jian”s final score? a )40 b) 45 c) 85 d) 80
74
QUIZ (CLASS - IX)
(1) Number system QUIZ Q.1 What is a rational number? Q.2 What is an irrational number? Q.3 What type of decimal representation do rational numbers have? Q.4 Why do we calculate the approximate value of an irrational number? Q.5 State whether is an irrational or a rational number? ORAL Q.1 All rational and irrational number is _____________? Q.2 Is 3.1010010001………………a rational number? Q.3 Is negative or positive? Q.4 The smallest composite number is …………..? Q.5 The decimal expansion of is non-terminatingnon recurring or non-terminating recurring. (2) POLYNOMIALS QUIZ Q.1 What is the degree of a quadratic polynomial? Q.2 How can you decide that is a factor of a polynomial Q.3 How many variables can be there in a polynomial? Q.4 What is a linear polynomial? Q.5 A cubic polynomial has how many zeroes? ORAL Q.1 A polynomial / expression with two terms is called ……………..? Q.2 An example of a monomial of degree 7 is. Q.3 If a + b + c = 0, then what is the value of is equal to ______? Q.4 Complete this identity = Q.5 The zeroes of polynomial are ………………? (3) COORDINATE GEOMETRY QUIZ Q.1 In which quadrant does the point (-4,-5) lie? Q.2 What are the coordinates of origin? Q.3 What is the abscissa of all the point on the y-axis? Q.4 What is the ordinate of all point on the x-axis? Q.5 Point (2,0) lies on which axis. ORAL Q.1 The perpendicular distance of the point (5,3) from the x-axis is ………….. Q.2 Point (-4,3) lies in the ……………..quadrant. Q.3 The points in which abscissa and ordinate have same signs will lie in ……….. Q.4 Is the point (5,-2) is same as the point (-2,5) or not. Q.5 The ordinate of the point (1,9) is ……………….. (4) INTRODUCTION TO EUCLID'S GEOMETRY QUIZ Q.1 Name the part of a line which has only one end point. Q.2 What was the name of the famous book of Euclid? Q.3 How many lines can pass through a given point? Q.4 How many common points can two distinct lines have?
75
Q.5 How many dimensions, a point has? ORAL Q.1 The side faced of a pyramid are ……………….. Q.2 Part of the line with two end points is called ………………… Q.3 To which country does Euclid belong? Q.4 Axioms are assumed to be ………………. Q.5 The things which are double of the same thing are ……………….. (5) LINES AND ANGLES QUIZ Q.1 What is the sum of the angles of triangle. Q.2 What is the sum of two opposite angles of cyclic quadrilateral? Q.3 Define Reflex angle. Q.4 What is the complement of 450? Q.5 What is the difference between a line and line segment? ORAL Q.1 400 and 500 are example of compliment angles or not? Q.2 In a triangle with a right angle, the other two angles are ……………. Q.3 A line with two end points is called ……………………. Q.4 Through a point infinite number of ……………..can be drawn. Q.5 An angle of measure greater than 900 but less than 1800 is called …………. (6) TRIANGLES QUIZ Q.1 In right angled triangle which side is the longest side? Q.2 What do you mean by congruence of two figures? Q.3 What are the various parts of a triangle? Q.4 Classify triangles on the basis of their sides? Q.5 Classify triangles on the basis of their angles. ORAL Q.1 Angle opposite to greater side of a triangle is ……………….. Q.2 The sum of any two sides of a triangle is greater than ……………… Q.3 Each angle of an ………………….triangle is 600. Q.4 If all angles of a triangle are equal, then all of its …………… are also equal. Q.5 Can a triangle have two right angles? (7) HERON'S FORMULAE QUIZ Q.1 What is semi perimeter of a triangle? Q.2 What does the letter 's' used in Heron's formula denotes? Q.3 Who gave the famous formula for calculating the area of a triangle in terms of its three sides? Q.4 Triangle with no two side equal is called? Q.5 What is the area of an equilateral triangle with side x units? ORAL Q.1 The area of a rhombus can be obtained by the measure of its two ……… Q.2 What is the formula to find area of a triangle? Q.3 In a triangle, side opposite to the ………………. angle is longer. Q.4 the sum of any two sides of a triangle is greater than ………………… Q.5 Name all the criterions for congruency of triangles.
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PUZZLE(CLASS - IX)
ACROSS DOWN
2. Another word for inclination. 1. Height of a triangle
3. The way a point moves 4. Abbreviation of greatest commondivisor
5. A cube numbered 1, 2, 3, 4 , 5, and 6 6. Adot on a piece of a paper
on the faces 8.Geometrical shape 7. A solid having six identical faces
9. The longest chord of a circle 10. Consider as equal or equivalent
12. Part of circumference of a circle 11. A another measure of central tendency
14.Numbers divisible by 2 are called 13. Information can be used in statistics as
1 2 4
3 7
6 5
8 10
9 11 13
12
14
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SUMMATIVE ASSESSMENT – 1
CLASS – IX (MATHEMATICS)
Time allowed:3:00Hrs Max. Marks :90
General Instructions:
(i)All questions are compulsory. (ii)The question paper consists of 31 questions divided into 4 sections. A, B, C and D. Section -A comprises of 4 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 11 questions of 4 marks each. (iii)Question numbers 1 to 4 in section-A are multiple choice questions where you are to select one correct option out of the given four. (iv)Use of calculator is not permitted. Section –A(1 mark questions)
Q1. Which of the following can be expressed in the form of p/q ,where p & q are
integers,q≠0.
a) 0.3454454445….. b) 0.045045604567……c) 0.234523452345
d)0.6326324124359…..
Q2. Which of the following expressions is a polynomial in one variable ?
a) 4x2 – 3x + 7 b) y
-2 + 2 c)3√t t√2 d) y +
Q3. Which among the following is true for a Δ ABC?
a) AB+BC CA B) BC+CA =AB C) CA+AB BC d) All of the given
Q4. The area of an equilateral triangle whose perimeter is 36√ cm. Is
a) 36√ cm2 b)72 √ cm2 c)108 √ cm2 d)98√ cm2
Section –B(2 marks questions)
Q5. Simplify: (27)1/6
x (27)1/2
78
Q6.Find the remainder when 2x3-5x2-7 is divided by x-2.
Q7. In the fig..x= 300, find the value of y .
2x3y
Q8. Find the angle whose measure is 180 less than its complement.
Q9.Two adjacent angles on a straight line are (3x - 2)0 and (2x + 7)
0.Find the value
of x and measure of each angle.
Q10. Find the value of x and y.
Section -C
Q11. Find three rational numbers between
&
Q 12.Rationalize the denominator of √
√
Q13. Evaluate the following using identities:
(i) 103 × 107 (ii) (104)2
Q14. Without actually calculating the cubes, find the value of each of the following:
(–12)3 + (7)
3 + (5)
3
Q15. If a point C lies between two points A and B such that AC = BC, then prove
that
AC =
AB. Explain by drawing the figure.
Q16. In Fig, lines AB and CD intersect at O. If
˪AOC + ˪BOE = 70° and ˪BOD = 40°, find
79
˪BOE and reflex ˪COE.
Q17.In fig, find the values of x and y and then
show that AB || CD.
Q18.In fig. , ˪PQR = ˪PRQ, then prove that ˪PQS = PRT .
.
Q19.Write the answer of each of the following questions:
(i) What is the name of horizontal and the vertical lines drawn to determine the
position of any point in the Cartesian plane?
(ii) What is the name of each part of the plane formed by these two lines?
(iii) Write the name of the point where these two lines intersect.
Q20.In which quadrant or on which axis do each of the points (3, – 1), (– 1, 0),
(1, 2) and (– 3, – 5) lie? Verify your answer by locating them on the Cartesian
plane.
SECTION D
Q21. Represent √ on the number line.
Q22. Simplify: (
)-3/4x [(
)-3/2 ÷ (
)-3]
Q 23 Using factor theorem factorise the polynomial :x3 – 23x
2 + 142x – 120.
80
Q24. Expand each of the following, using suitable identities
i) (2x – y + z)2 ii) (2x + 1)
3
Q25. Verify that x3 + y
3 + z
3 – 3xyz =
(x + y + z) [(x-y)
2+(y-z
)2+(z-x)
2]
Q26.Find the remainder when x3 – 4 x
2 – 11x + 33 is divided by x-3 by long division
method.Verify the result using remainder theorem.
Q27.In fig., the side QR of ΔPQR is produced to a point S. If the bisectors of
˪PQR and
˪PRS meet at point T, then prove that ˪QTR =
˪QPR
Q28.In fig. if PQ PS, PQ || SR, SQR = 28° and QRT = 65°, then find the
valuesofx and y.
Q29..In quadrilateral ACBD,
AC = AD and AB bisects ˪A(see Fig.). Show that ΔABC ΔABD.What can you
say
about BC and BD?
Q30.AB is a line segment and P is its mid-point. D and
81
E are points on the same side of AB such that˪BAD = ˪ABE and ˪EPA = ˪DPB
(see Fig.). Show that
(i) ΔDAP ΔEBP
(ii) AD = BE
Q31. Two sides of a triangle with perimeter 112 cm are 50 cm and 48 cm. Find the
area of the triangle.Also, find the length of the altitude corresponding to the side of
length 50 cm.
BHASKARACHARYA GROUP
MINIMUM LEVEL LEARNING (CLASS - X)
TOPIC:- REAL NUMBER
1 Say Whether 7× 11 ×13 +13 is prime or composite.
2 what is the H.C.F of 475, 495.
3 State Euclid division Lemma.
4 State Fundamental theorem of Arithmetic.
Level -2 (2 marks)
1 H.C.F(306, 657)= 9. Find L.C.M (306, 657)
2 Use Euclid‟s Division Algorithm to find H.C.F of 867 & 255.
3 The decimal expansion of rational number
will terminate after how many places of
decimal.
4 Show that 6n does not end with zero
TOPIC: POLYNOMIALS
Level-1 (1 mark)
82
1 The graph of the polynomial f(x)= 2x−5 is a straight line which intersect the axis exactly at
one point namely.
2 If 2 is the zero of the polynomial p(x)= px2−3(p−1)x−1, then the value of p is
3 If the roots of the quadratic equation ax2+bx+c=0 are equal, then find its sum of zeroes and
product of zeroes.
4 Find out the quadratic polynomial with the sum & the product of zeros as −1,
respectively.
Level-2 ( 2marks)
1 If α & β are the zeroes of the polynomial 4x2+3x+7 then find
α&
β .
2 If the zeroes of the polynomial x3−3x
2+x+1 are a-b, a,a+b then find out the value of a & b.
3 Find the quadratic polynomial whose zeroes are 2+√ and 2−√ .
4 If α & β are the zeroes of p(x)=kx2−5x+3k and α + β=αβ, then find the value k.
Pair of linear Equation in two variables
Level-1 (1 mark)
1. The graph of linear equation in one variable in two variable is
a) a parallel line
b) a curve
c) a straight line
d) a pair of parallel lines
2. The value of k for which the system of equation kx+3y = k-3 and 12x+ky = y , has no
solution is
a) k =4
b) k =-6
c) k =6
d) k =8
3. 3x+4y = 4 have
a) One solution
b) Two solution
c) Three solutions
d) Infinitely many solutions
Level-2 ( 2marks)
4. Solve the following system of linear equation by substitution method
3x+2y =7
4x+5y = 3
5. If the lines are given by 3x+2ky = 2 and 2x+5y+1= 0 are parallel, then find the value of k.
6. Draw the graph of the following pair of linear equation
83
X+3y = 6
2x-3y = 12
Hence find the area of the region bounded by the lines x=0, y= 0 and 2x-3y = 12
Geometry (Similar Triangle)
1. 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.
2. The ratio of areas of the similar triangles is equal to the squares of the ratio of their
corresponding sides.
3. In a right triangle the square of hypotenuse is equal to the sum of the squares of the other
two sides.
4. In a triangle of square of one side is equal to the sum of the squares of the other two sides
then angle opposite the first side is right angle.
TOPIC: TRIGONOMETRY
Level-1 (1 mark)
1 If Sin𝜃=
, find 2cot
2𝜃 +2
2 If cos(400 + A) = Sin30
0, find the value of A.
3 In fig, find tanP− cotR
4 Express cot850+cos65
0 in terms of trigonometric ratios of angles between 0 & 45
0.
5 Evaluate
Level-2 (2 marks)
1 Evaluate tan350tan40
0tan45
0tan50
0tan55
0
2 In a ∆ABC rt angled at B, AB=24cm, BC=7cm, determine sinA, cosA
STATISTICS
QUESTIONS CARRY ONE MARKS :
Q.No.1: In the formula x = a+h (
), then Ui is
Q.No.2: What is the relationship between Mean ,Median ,Mode?
13 cm
P
12 cm
R Q
84
Q.NO.3:- The formula for finding the Mode of grouped data:-
Q.NO.4:-What is the formula for finding the Median for the grouped data:-
HIGHER ORDER THINKING SKILLS (CLASS -
X)
REAL NUMBERS
1. Use Euclid‟s division algorithm to fin the HCF of 135 and 225.
2. Show that any positive odd integer is of the form 6 q + 1 or 6 q + 3 or 6 q + 5, where q is
some integer.
3. Find the LCM and HCF of 12,15 and 21 by applying the prime factorisation method.
4. Given that HCF of 306 & 657 is 9. Find LCM of these numbers.
5. Prove that 2 is irrational.
POLYNOMIALS 1. Find the zeroes of the given quadratic polynomial and verify the relationship between the
zeroes and the coefficients- 3 x2- x - 4.
2. Find the quadratic polynomial with 4 as the sum and 1 as the product of its zeroes.
3. Divide 2x2
+ 3 x + 1 by x + 2
4. Obtain all other zeroes of 3 x4
+ 6x3- 2x
2-10x - 5, if two of its zeroes are
3
5and
3
5
5. If the zeroes of the polynomial x3- 3 x
2+ x + 1 area-b, a, a+b, find a and b
TRIANGLES
1. Sides of two similar triangles are in the ratio 4:9. What is the ratio of areas of these
triangles?
2. In ∆ABC, AB=6 3 cm, Ac = 12 cm and BC= 6cm. What is the measure of ?B
3. ∆ABC ∆DEF and their areas are 64 cm2 and 121 cm
2 respectively. If EF=15.4 cm,
find BC.
4. Give an example of each:-
(a) Similar figures (b) congruent figures
5. In the figure, DE ǁ BC. Find EC.
INTRODUCTION TO TRIGONOIMETRY
85
1. Express sec 72˚ in terms of trigonometric ratio of angle between 0˚ to 30˚.
2. Evaluate tan 32˚.sin 65˚ - cos 25˚. Cot 58˚
3. If sin B =5
3, then calculate cos B and tan B. Also draw the right triangle for it and do the
labeling of sides as base, height and hypotenuse.
4. Prove that 1cos
1cos
coscot
coscot
ecA
ecA
AA
AA
5. Evaluate
45cot60cos30sec
60cos45tan30sin ec
STATISTICS
1. If the mean of distribution is 25 and mode is 40, then find the median of that distribution.
2. Complete the Cumulative frequency table and draw a less than type cumulative frequency
curve for following data.
Marks of children Number of
children
Cumulative
frequency Less than equal to 30
Less than equal to 40
Less than equal to 50
Less than equal to 60
Less than equal to 70
Less than equal to 80
Less than equal to 90
Less than equal to 100
3
5
12
15
6
5
3
3
3
8
20
35
41
47
50
3. Find the median for the following data.
Class 20-40 40-60 60-80 80-100
Frequency 15 10 5 20
4. Calculate mean for the following data.
x 21 56 20 8 10
f 15 10 5 20 10
5. In the following distribution find the median class, mode class and mode.
Class Frequency(f) Cumulative frequency(cf)
100-200
200-300
300-400
400-500
500-600
600-700
11
12
10
13
20
14
11
23
33
46
66
86
80
QUIZ (CLASS - X)
Question:1. What 3 positive numbers give the same result when multiplied and added together?
Answer: 1, 2, and 3
Question:2. If you randomly choose one of the following answers to this question, what is your
chance of getting it right?
Answer: 0%. No matter which answer you choose you are incorrect. All of the answers create a
logic loop.
Question:3. What number do you get when you multiply all of the numbers on a telephone's
number pad?
Ans 0.
Question:4 There are several books on a bookshelf. If one book is the 4th from the left and 6th
from the right, how many books are on the shelf?
ANS-9
Question:5. John has been hired to paint the numbers 1 through 100 on 100 apartments.
How many times with he have to paint 8?
ANS-20
Question:6. What's the angle between minute hand and hour hand at a quarter past three?
Answer: 7.5 degrees.
Question: 7. As I was going to St. Ives,
I met a man with seven wives,
Each wife had seven sacks,
Each sack had seven cats,
Each cat had seven kits:
Kits, cats, sacks, and wives,
How many were there going to St. Ives?
Answer: 1
Question:8. Mr. Smith has 4 daughters. Each of his daughters has a brother.
How many children does Mr. Smith have?
Answer: He has 5 children, all of the daughters have the same 1 brother.
Question:9. What is 1/2 of 2/3 of 3/4 of 4/5 of 5/6 of 6/7 of 7/8 of 8/9 of 9/10 of 10,000?
Answer: 1000
Question:10. If 1+9+8=1, what is 2+8+9?
87
Answer: 10
Question:11. What is 40 divided by 1/2, plus 15?
Answer: 95
Question:12. How can you add 8 8's to make 1000?
Answer: 888 + 88 + 8 + 8 + 8 = 1000.
Question:13. You have found a mutant algae that doubles in size every hour. It takes 18 hours for
one algae plant to take up half of a certain lake.
How long would it take for two of these plants to take up half of the same lake?
Answer:14. 17 hours. At 17 hours the one plant will take up 1/4 of the lake (1/2 of 1/2). At 17
hours the two plants would be double the size of the one plant and double 1/4 is one half.
Question:15. You have a cube made of 10 x 10 x 10 smaller cubes, for a total of 1000 smaller
cubes. If you take off 1 layer of cubes, how many remain?
Answer:. The remaining cube will be 8 x 8 x 8. This will be 512. A layer is take from all sides of
the cube, so it would reduce the dimensions be two, not one.
Question: 16 When is 1500 plus 20 and 1600 minus 40 the same thing?
Answer: Military time
Question:17. Which triangle will have a larger perimeter : 3,4,5 or 3,4,7 ?
Answer: 3,4,5...... A triangle of sides of 3,4,7 is impossible to construct
Question:18. what are the next two letters in this sequence: A, E, F, H, I, K, L, M,
Answer: N, T
Question: 19.When I was 2 years old, my brother was half my age. Now I am 100 years old, how
old is my brother?
Answer 99
Question: 20. What digit is the most frequent between the numbers 1 and 1,000 (inclusive)? To
solve this riddle you don't want to manually do all of the math but rather try to figure out a pattern.
Answer - The most common digit is '1.'
PROBLEM SOLVING ASSESSMENT(CLASS - X) Q.1.H.C.F. of two consecutive even natural numbers is :
(A) 0 (B) 1 (C) 2 (D)4
Q.2.The graph of y=p(x) is given below. The numbers of zeroes of p(x)are:
88
(A) 3 (B) 2 (C) 1 (D) 4
Q.3.Which of the following is not defined?
(A) Cos00 (B) tan 45
0 (C) tan90
0 (D)tan0
0
Q.4.Which measure of central tendency is given by the x co-ordinate of the point of intersection of the more than ogive and less than ogive?
(A) mean (B) median (C) mode (D) all of these
Q.5 If the lines l1and l2 are parallel then they have
(A) Unique Solution (B)No Solution
(C)Infinitely Many Solutions (D) None of the above
Q.6 If ∆ ABC ~ ∆ DEF, BC = 3 cm EF =4 cm and area of ∆ ABC = 54 cm2
then the area of ∆ DEF is
(A) 96 cm2 (B) 94 cm
2 (C)48 cm
2 (D) 42 cm
2
Q.7 The zeros of polynomial X2 – 2X – 8 are:
(A) 4,-2 (B) -4, 2 (C) 3, 5 (D) none of these
Q8 A ladder 10 m long reaches a window 8 m above the ground. The distance of the
foot of the ladder from base of the wall is :
(A)5m (B) 12m (C) 7m (D) 6m
Q.9.The number 7 x 11 x 13 + 13+13 x 2 is
(A) multiple of 7 (B) Neither prime nor composite
(C) Prime (D) Composite
Q.10 If ▲ ABC ~ ▲DEF, BC= 3 cm, EF=4cm and area ABC= 54 cm2
then the area of DEF is
(A) 96 cm2
(B) 94 cm2
(C) 48 cm2 (D) 42 cm
2
Q11. Which of the following is rational
(A) √6 + √9 (B) √2+ √4 (C) √4+√ 9 (D) √3+√5
Q12. If sinθ = cosθ , then the value of θ is
( A) 0° (B) 450
(C) 60° (D)30°
89
Q13 A Rational Number inserted between two rational number R and S is given by –
(A)
(B)
(C)
(D) None of these
Q14 The number of circle(s) passing through three Non-collinear points is
(A) One (B)Two (C) Three (D) None of these
Q15. The volume of a right circular cone is 100π cm3 and its height is 12cm.
Then its curved surface area is
(A) 62π cm2 (B) 64π cm
2 (C) 65π cm
2 (D) 67π cm
2
Q18. The length of altitude of an equilateral triangle is 15√3 cm, then the length of its side is
(A) 30 cm (B) 15√3 cm (C) 60 cm (D) none of these
Q.19.. If k-1, k + 1 and 2k + 3 are in AP, then the value of „k‟ is
(A) – 2 (D) 0 (C) 2 (D) 4.
Q. 20. Area of triangular surface is calculated as
x altitude x base. If the altitude of a triangle is
increased by 5% and base of the triangle is increased by 7%. What percent would the area of the
triangle increased?
(A) 12.35% (B) 12% (C) 6% (D) 3.33
SUMMATIVE ASSESSMENT – 1
CLASS X
MATHEMATICS
Time allowed: 3 hours Max.Marks:
90
General Instructions: All Questions are compulsory
The question paper consists of 31questions divided into four sections A,B,C,D
Section-A comprises of 4 multiple choice 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
Section-D comprises of 11questions of 4 marks each.
Use of calculator is not permitted.
SECTION A (Q. No. 1 -4 each of 1mark)
1. The zeros of polynomial X2 – 2X – 8 are:
(A) 4,-2 (B) -4, 2 (C) 3, 5 (D) none of these 2. A ladder 10 m long reaches a window 8 m above the ground. The distance of the
90
foot of the ladder from base of the wall is :
(A)5m (B) 12m (C) 7m (D) 6m 3. The value of sin30 is
(A) ½ (B) 0 (C) 1 (D) 2 4. The class mark of 15.5 – 20.5 is
(A) 15.5 (B) 20.5 (C) 18 (D) 5
SECTION B (Q. No. 5 -10 each of 2marks)
5. If α and β are zeros of the Polynomial 3x2+5x+2, Find the value of
α
β
6. For what value of k,will the following system of equations have no solution
3x + y =1
(2k -1)x + (k-1)y = 2k + 1 7. let ABC DEF and their areas be respectively 64 cm
2 and 121 cm
2.If EF = 15.4 cm,
Find BC. 8. If tanA = cotB , prove that A + B = 90 9. Convert the following frequency distribution table into a less than type cumulative
frequency distribution table:
Marks No of Students
0-5 4
5-10 7
10-15 12
15-20 18
20-25 6
25-30 3
10. Evaluate cos48 – sin42
SECTION C (Q. No. 11 -20 each of 3 marks)
11. Find the LCM and HCF of 26 and 91 Also verify that HCF X HCF = product of the two
numbers. 12. Find the zeros of the quadratic polynomial 6x
2 – 7x – 3 and verify the relationship
between the zeros and the coefficients. 13. Solve: 3x – 5y =4
9x – 2y = 7 14. If the areas of two similar triangles are equal then show that the triangles are congruent 15. ABC is an isosceles triangle right angled at C Prove that AB
2 = 2AC
2
16. Prove that
(sinA + cosecA)2 + (cosA + secA)
2 = 7 + tan
2A + cot
2A
17. Without using t-tables evaluate the following
3cos68 cosec22 - ½ tan43 tan47 tan12 tan60 tan78 18. If tan(A + B) =√3 and tan(A – B) = 1/√3. Find A and B 19. Find the median of the following distribution
Class frequency
0-10 4
10-20 4
20-30 8
30-40 10
40-50 12
50-60 8
60-70 4
91
20. If the mean of the following distribution is 6 , find the value of p
X 2 4 6 10 P+5
F 3 2 3 1 2
SECTION D(Q. No. 21 -31 each of 4 marks)
21. Prove that √5 is irrational. 22 Find all the zeros of the polynomial 2x
4 + 7x
3 – 19x
2 - 14x + 30 if two of its zeros are
√2 and - √2 23. 8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys
can finish it in 14 days.Find the time taken by one man and by one boy alone to finish the
Work.What value is depicted ? 24. If tan A = 2 Evaluate sec A sin A + tan
2A – cosec A
25. The marks obtained by 30 students of class X of certain school in Mathematics paper
Consisting of 100 marks are presented in the table below. Find the mode of this data
Class
Interval 10-25 25-40 40-55 55-70 70-85 85-100
Number of
Students 2 3 7 6 6 6
26. In an equilateral triangle ABC , D is a point on side BC such that BD = 1/3 BC
Prove that 9 AD2 = 7 AB
2
27 Prove that the ratios of the areas of two similar triangles is equal to the square of the
ratio of their corresponding sides.
28. Divide : 2t
4 + 3t
3 -2t
2 – 9t -12 by t
2 – 3
29. The median of the following data is 525 Find the values of x and y if the total
Frequency is 100
Class interval Frequency
0-100 2
100-200 5
200-300 x
300-400 12
400-500 17
500-600 20
600-700 y
700-800 9
800-900 7
900-1000 4
30. Prove that
–
–
31. For a morning walk three persons step off together. There steps measure 80cm, 85cm, and
90cm respectively. What is the minimum distance each should walk so that they can cover
the distance in complete steps?
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Quotations on Mathematics
1 "Mathematics is the Queen of the Sciences." Carl Friedrich Gauss.
2 "Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to
us by human agency." Descartes.
3 "The essence of mathematics is not to make simple things complicated, but to make complicated things
simple." S. Gudder
4."People who don't count won't count." - Anatole France.
5."Pure mathematics is, in its way, the poetry of logical ideas." Albert Einstein
6."The advancement and perfection of mathematics are intimately connected with the prosperity of the
state." Napoleon
7. "Geometry existed before creation." Plato
8.“Algebra is the intellectual instrument which has been created for rendering clear the quantitative
aspects of the world." Alfred North Whitehead
9 The science of Pure Mathematics, in its modern developments, may claim to be the most original
creation of the human spirit. Alfred North Whitehead
10. The best math teacher is not the one who knows most, but the one who is most capable of reducing
knowledge to that simple compound of the obvious and wonderful applets. H.L. Mencken
11. The Good Lord made all the integers; the rest is man's doing." Leopold Kronecker
93
12 “ Whenever you can, count." Sir Francis Galton
11 “Life is good for only two things: discovering mathematics and teaching mathematics." - Simeon
Poisson
14 “A man is like a fraction whose numerator is what he is and whose denominator is what he thinks of
himself. The larger the denominator, the smaller the fraction." Tolstoy
15. In most sciences one generation tear down what another has build. In mathematics alone each
generation build new story to the old structures. Hermans
l6. Nature’s good book is written in mathematical symbols. Galileo
LIST OF USEFUL WEBSITES
1. www.studyweb.com
2. www.mathsforum.com
3. www.cut-the-knot.org
4. www.enhantedlearning.com
S. www.cyberbee.com
6. www.exploratorium.com
7. www.discovery.com
8. www.mathleague.com
9. www.askdrmath.com
10. www.ithihass.com
11. www.teachervision.com
12. www.sciencepage.com
13. www.lessionplan.com
14. www.education-world.com
15. www.mathematicshelgcentral.com
16. www.wikipedia.com
94
17. www.goldenmeangauge.com.
18. www.goldennumber.net
19. www.mathsfun.com
20. www.aglusmaths.com
21. www.k111.k12.il.us/kingt/math.htm
22. www.ies-co.jin/maths/java
23. www.walth-tendt.de/wiue/
24 www.woodlands-junior.kent.such.ulc/maths
25.www.mathgoodins.com
List of Reference Book
1. Fascinating world of mathematical science By J .N. Kapoor, Publish -Book depot. 2. Suggested experiments for a mathematical laboratory By J .N. Kapoor mathematical Science trust Society 3. Junior Mathematics Laboratort , By J .N. Kapoor(M.S.T.S) 4. Project of enrich School Mathematics By L. Sachs (M.S.T.S) 5. Vedic Mathematics for school By J .T. Glover. Motilal Bonarsides Pub. Delhi 6. Olympiad Mathematics by M.K.Singhal - Pitambar Publication 7. Mastering Mathematics Olympiad by V. Seshan - F ranksons Pub. 8. College Aigebra -Schaum’outlines 9. Vedic Geometry by S.K.Kapoor Pitambar Pub. 10.Activities Handbook for teaching the metric system by Bitter Gurg (Allyn$Banco Pub.) 1 1.Discovering meanings in Elementary School Mathematics By- Grossnickle. E.Foster 12.Guiding Children’s learning of Mathematics by Kennedy Leonard M. Wadworth Pub. 13.Teaching elementary School Mathematics for understanding By- Maru John L..Mc. Graw Hill Book Company New York. I I 14.Guiding Discovery in elementary School Mathematics By -Riedesel C. Alan Appleton Centre Crafts (New York) 15.Exce12000 - BPB Publication 16.office2000-BPB Publication l7.Numbers rational and irrational : Ivan Niven ,New Mathematics Library , New York, Random House, Inc 18.Calculus and analytical Geometry by Thomas Finacy Narosa publishing house Delhi 19. An Excursion in Mathematics by Bhaskaracharya Group Pratishthan , Pune. l. 20. Higher Algebra by S. Banard and J .M. Child, Macmillan and Co. London 21. The theory of equations by S. Chand and Co. Delhi. 22. Modern Geometry, by Macmillan and Co. London 23. Challenges and Thrills of Pre- College Mathematics By K. Krishnamurthy , K.N. Raganathan 24. Triangle, Construction and Inequalities by A. Subraamnian and S. Murlidharan 25. An Introduction to the Theory of Numbers, L.Niven and HS. Zuckerman. 26. Challenging Mathematical problems with Elementary Solutions- A.M. aglom and 1M. Yaglom
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27. Mathematical circles By Dimitri Fomin 28. Problem Solving Strategies, Aurther Engel. SOME USEFUL MATHEMATICAL PERIODICALS l. Bona Mathematica, by Bhaskaracharya Group Pratishthan , Pune. 2. Crux Mathematricorum, Canadian Mathematical society 3. Mathematics Magazine, Mathematical Association of America., USA 4. Samasya, The Secretary, Leelavati Trust Banglore. 5. The American Mathematical Monthly, Mathematical Association of America, USA 6. Mathematics Magazine, Mathematical Association of America, USA 7. The Mathematics Teacher, The Association of Mathematics Teachers of India.
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