Solution Key -- Class XII (Second Term Exam)

Hello All,

Hope the class XII students must have done well in their maths paper.

Here is the Question Paper.

Please check out the Solutions here.

(Right click the above link and choose the option "Save link/target as")

ALL THE BEST

Happy Birthday to Greatest Mathematician Ramanujan

The Indian mathematician Srinivasa Ramanujan Aiyangar (1887-1920) is best known for his work on hyper geometric series and continued fractions.
Srinivasa Ramanujan, born into a poor Brahmin family at Erode on Dec. 22, 1887, attended school in nearby Kumbakonam. By the time he was 13, he could solve unaided every problem in Loney's Trigonometry ,and at 14 he obtained the theorems for the sine and the cosine that had been anticipated by L. Euler.
Ramanujan became so absorbed in mathematics that when he entered the local government college in 1904 with a meritscholarship, he neglected his other subjects and lost the scholarship. Ramanujan married in 1909, and while working as a clerk he continued his mathematical investigations. In January 1913 Ramanujan sent some of his work to G. H. Hardy, Cayley lecturer in mathematics at Cambridge. Hardy noticed that Ramanujan had rediscovered, and gone far beyond, some of the latest conclusions of Western mathematicians.
In 1914 Ramanujan went to Cambridge. The university experience gave him considerable sophistication, but intuition still played a more important role than argument. In Hardy's opinion, if Ramanujan's gift had been recognized early, he could have become one of the greatest mathematicians of all time. His patience, memory, power of calculation, and intuition made him the greatest formalist of his day.
In 1918 Ramanujan was elected a fellow of the Royal Society and a Fellow of Trinity College, Cambridge. However, the story goes that , Ramanujan’s health deteriorated greatly while he was in England, and he eventually had to travel back to India in 1919. He died a year later, when he was only 33 years of age, although his work will be remembered for a long time. He dealt with Riemann series, the elliptic integrals, hyper geometric series, and functional equations of the zeta function. Hardy liked to rank mathematicians on a scale of 1 to 100, and he gave himself 25, Littlewood 30, David Hilbert 80, and Ramanujan 100, which shows just how great Ramanujan was.

Third Intra School Mathematics Olympiad - RESULT

Dear All,

The Third Intra School Mathematics Olympiad was held on 07 November 2012.

Hopefully, it was a great learning experience for all. It surely provided an extended platform for all the participating students and it is wished that it is utilized to its fullest.

Here are many young Ramanujan’s as well as Shakuntala Devi’s in our school who had performed very well in the exam.

Check out the result here:

III-V RANK HOLDERS

III-V  MERIT HOLDERS

VI-VIII RANK HOLDERS

IX-XII RANK HOLDERS   

VI-XII MERIT HOLDERS

Congratulations to all the rank and merit holders for their brilliant performance in the  Olympiad.

Third Intra School Mathematics Olympiad -------- Solution Key

Dear All

Mathematics, often called as language of nature has become an integral part of everyone’s life. In today's highly competitive world, one has to bear a lot of mental stress and also have to get involved in so many things in order to acquire knowledge. This is where co-scholastic activities play a very significant role. They provide the much needed exposure for a student.

CRPF Public School has fulfilled its motto of striving towards excellence by organizing and successfully completing its Third Intra School Mathematics Olympiad on 7^th November 2012. A large number of students enthusiastically participated in the Olympiad held in school premises.

Such Olympiads and events provide a great and extended platform for the students to nurture and showcase their ability and talent. It was a towering learning experience for the students of the school from class III to XII. To encourage students, merit certificates will be given to those scoring at least 60% along with the normal prizes for the top scorers.

The result would be declared on 30 November 2012 and would be available here.

Wishing you all the best!!!

It is hoped that all the participating students must have done well in the exam. To access your performance, check out the solution keys of the question papers below:-

Question papers:-

ClassIII      Class IV          Class V

ClassVI      Class VII     Class VIII

Class IX      Class X        Class XI       Class XII

Solutions keys:-

Class III-V      

ClassVI      Class VII     Class VIII

Class IX      Class X        Class XI       Class XII

Third Intra School Mathematics Olympiad

Dear all,

The Mathematics Department of CRPF Public School is back with the Third Intra-School Mathematics Olympiad, to be held on 07 November 2012 (Wednesday) in the school premises only. The last date for registration is 19 October 2012 (Friday), so hurry up. Go, get yourself registered!

To felicitate the efforts and intelligence of participants, the department has decided to award a certificate of merit to every participant this year scoring at least 60%, other than the regular prizes for top scorers.

Consult your Math teacher for other details or queries and check out the following links for the circular, sample papers and previous year’s Olympiad papers:

Here are the Sample Papers:

CLASS VI  CLASS VII CLA SS VIII
CLASS IX  CLASS X   CLASS XI   CLASS XII

Also check the previous year's Question Papers:

First Intra School Olympiad Papers with Solutions 

Second Intra School Olympiad papers with Solutions 

Wish you good luck already. Start quizzing your brain and get your mathematical quotient checked this November!

Amit Sir

International Mathematics Olympiad (IMO)

Dear All,

Science Olympiad Foundation (SOF) organize International Mathematics Olympiad (IMO) every year. This year the 6th IMO will held on 20 December 2012. Please note down all the details provided below.

kindly note that this information is provided for all the students stuydying in CRPF School, Rohini only.

Amit Sir

Class XII First Term Exam Mathematics - SOLUTIONS

Hello All,

Hope the class XII students must have done their maths paper well. Here is the Question Paper.

Please check out the Solutions here (8MB File)/ or here ( 500 kb - low quality).
(Right click the above link and choose the option "Save link/target as")

ALL THE BEST

I am conferred with the State Teacher's Award!

Dear All

I am feeling very happy to inform you all that I am conferred with the State Teacher's Award, on the occasion of Teacher’s Day. It was a token of sincere appreciation and recognition of contribution towards meritorious services rendered in educational field specially Mathematics Education. The award was conferred upon by Smt. Sheila Dikshit, Hon'ble Chief Minister of Delhi, in the presence of Prof. Kiran Walia, Hon'ble Education Minister of NCT; Sh. Amit Singla, IAS, Worthy Director of Education Delhi and Dr R P Malik, Chairman of the Federation of Public School.

Introduction of Value based questions in all major subjects in classes IX-XII w.e.f. session 2012-13.

Dear All

It is to bring to your notice that CBSE has decided to follow an interdisciplinary approach in value education where values are intermingled with the content of all the major subjects in classes IX to XII. The Board has also decided to assess students for 5 percent weighting in the major subjects through questions which will be integrated with the content of the subject and analyzed on the basis of the values it reflects.

The questions will be for 5 marks in a question paper of 100 marks and 3-4 marks in a question paper of 70-90 marks. This will be effective from the Summative Assessments-II 2012-2013 in classes IX, X. The Board Exam in 2013 for Classes X (Summative-II) and Class XII will also have such questions.

Sample Papers for Class XII: Mathematics 

Sample Papers for Class X:    Mathematics   

For other subjects and related circulars refer Circular numbers Acad-21/2012, 22/2012, 46/2012 and 47/2012 in CBSE new site http://www.cbseacademic.in/circulars.html

Math Exhibition held in CRPF School

Here are the videos presentation by the students . Students were not told earlier about it so few were not actually prepared for the same.

Maths Workshop at S. D. School, Pitam Pura

Dear All

It is a matter of pride and pleasure for Mathematics community that Government of India has declared the Year 2012 as National Year of Mathematics to commemorate the 125^th Birth Anniversary of eminent Mathematician ‘Sri Nivas Ramanujan’. To pay our homage to this great man, it is decided to start a series of programme in the year 2012 with the intention of making it a mass movement namely ‘Mathematics Movement’.

A three day workshop at S. D. Public School was scheduled from 26^th July to 28^th July, 2012. It is a matter for pride for me that I was invited there as a Resource Person to take different sessions on the topic “Solving Real Life Problems using Mathematics’”. (click here for the solutions). I was there to take interactive sessions on 27-28 July with the students. It was really a great learning experience. I thank Ms. Anita Sharma, Principal S. D. School for having trust on me and Sh. H. R. Sharma Sir , Principal from my school for allowing me to be a part of this workshop.
Amit Bajaj

Workshop by Prof. M. M. Pant

Dear All

On 28 June , I (along with whole staff of CRPF School) attended a workshop by renowned Physicist and Educationist Prof. M. M. Pant. It was a great learning experience.

The two things which inspired me the most are as follows:

A. A famous quote about IsidorIsaac Rabi (born American physicist and Nobel laureate recognized in 1944 for his discovery of nuclear magnetic resonance )

“My mother made me a scientist without ever intending to. Every other Jewish mother in Brooklyn would ask her child after school: So? Did you learn anything today? But not my mother. "Izzy," she would say, "did you ask a good question today?" That difference--asking good questions--made me become a scientist.”

So, one should always ask questions and seek for the answers.

B. Harvard University’s list of skills that make an “educated person”:

1.      The ability to define problems without a guide.

2.      The ability to ask hard questions which challenge prevailing assumptions.

3.      The ability to quickly assimilate needed data from masses of irrelevant information.

4.      The ability to work in teams without guidance.

5.      The ability to work absolutely alone.

6.      The ability to persuade others that your course is the right one.

7.      The ability to conceptualize and reorganize information into new patterns.

8.      The ability to discuss ideas with an eye toward application.

9.      The ability to think inductively, deductively and dialectically.

10. The ability to attack problems heuristically.

So, it’s not only subjective knowledge which makes an "educated man", the above skills are needed for the same.

Fail. Fall. Cry. But DON’T GIVE UP!

Dear All

Heartiest congratulations to all class XII students who have successfully passed their board exams.

Also, there may be few who did not make it this time, may be compartment or a failure.

"I was crying for having no shoes until I saw a man without feet.”

 Take this world as a challenge. And believe me you may not be successful in an exam only and it’s not the end. Fail. Fall. Cry. But DON’T GIVE UP!

You all must read this article.

In case of any guidance in Mathematics I am available not only for those to whom I teach but to any student who needs any sort of help.

I intend to provide special assignments and papers in Mathematics. You just have to provide me with your email id (email to me or just mention in the comment section here).
Click the following links to download relevant material.
1    2    3    4     5     6     7  
8    9   10   11   12   13   14
NCERT TEXTBOOK MOST IMPORTANT QUESTIONS:
Book 1    Book 2
NCERT BOOK SOLUTIONS

I assure you that you will surly secure good marks if you study with dedication and sincerity. Have a short term goal now. A good goal is SMART: specific, measurable, attainable, realistic, and time-bound. Believe in yourself.

You may write to me at amitbajajcrpf@gmail.com or call me at 9891644454 for any question, guidance and help.

Regards

Amit Sir

2012 - National Mathematics Year

Celebrations at CRPF Public School, Rohini

Dear All,

Indian Prime Minister Manmohan Singh paid tribute to Indian Mathematician Srinivasa Ramanujan (1887- 1920), on the occasion of 125th birth anniversary. He announced that his birthday - Dec. 22 - would henceforth be a National Mathematics Day and 2012 would be the National Mathematical Year. We at CRPF Public School will be celebrating this special year as Mathematics Year in collaboration with www.ganitgurooz.com .

We intend to hold following events in the School (as a part of inter-house events or otherwise):

1. MENTAL MATHEMATICS INTERSCHOOL COMPETITION (Class VI-VIII and IX-X)

                One of the most exciting events conducted by Ganit Gurooz is the Mental Math Competition for students. This powerpoint based, timed mental math test requires students to compute numeric expressions and simplify algebraic expressions and equations mentally. MMC is the best test of speed and accuracy for students’ mental math abilities. Each test has 90 questions that have to be attempted in 60 minutes. Every student will get a certificate of participation. The First Round will be held tentatively in the month of September 2012. The examination fee is Rs. 100 per student. Students who will be selected for the inter-school round (to be held in November 2012) are not required to pay additionally.

2. INTERSCHOOL T-SHIRT DESIGNING COMPETITION (Class VIII - XII)

                Students love to wear T-shirts with slogans. Ganit Gurooz will provide a chance to up to 25 students to make their T-shirt design a reality. The material on the T-shirt design can be a problem, graffiti, a message, a quotation, an expression of feeling, a math concept or a mathematician. Ideally, this will be a summer project to be done during summer vacations. Top 10 designs will be selected (in July 2012) and will be submitted to Ganit Gurooz for the inter-school event. If a student’s design is chosen by panel of experts, it will be launch as a T-shirt with the Name of the student printed on it. Guidelines for this event will be intimated soon.

 3. POSTER COMPETITION (Class VI - X)

                A Poster is a communication tool that depicts information visually. As students develop a poster on any topic, they learn various things about that topic. This will be a summer project to be done during summer vacations. This activity will appeal to students who are “Right-brained” or “Creative”. These students usually shy away from mathematics as they find it very procedural. Here is a chance for us to get them involved in loving mathematics. The size of the Poster will be a half pastel sheet. Best Poster from each class will be selected and the students will get prize and a certificate. Guidelines for this event will be intimated soon.            

INTERSCHOOL POSTER COMPETITION (Optional):

A maximum of 10 posters per school across all classes can be submitted for the interschool poster competition. All submissions will be displayed at a public exhibition for           couple of days. During this time, online polling of votes will also be conducted. All participants will receive a Certificate of Participation and a mention on Ganit Gurooz website. Prizes will be given to the top 3 entries. Participation fee will be informed soon.

4. PARENT WORKSHOPS (Class VI - XII)

                Math education is highly influenced by parents as most of them pay special attention to their child’s performance in mathematics. However, there are several parents who do not know how they can contribute to a better math education of their child. Ganit Gurooz plans to educate parents on the aspects that are of concern to them.

“Helping your child with Math” is a series of interactive lectures delivered by experts. Separate sessions will be conducted for parents of primary, middle and senior school students.

Some of the topics which will be covered during these lectures are:

1. Math Phobia: What can parents do?        2. Why does your child not get a 100? 

3. Engaging children in math activities at home    4. Handling the Math Stress

Participation Fee and the date will be informed soon.

5. THIRD INTRA SCHOOL MATHEMATICS OLYMPIAD (Class VI - XII)

                The main objectives of the Olympiad is to arouse students’ interest and enthusiasm for mathematical problem solving, develop mathematical intuition, reasoning and logical thinking,  as well as creative and critical thinking.

                The Olympiad will held in the month of November 2012. Other detail with Sample Papers and Last Year Paper’s is available at School’s Blog http://crpfpsrohini.blogspot.in/ .

                This Olympiad is meant only for those students who have scored A Grade in Mathematics in their previous class.

6. SCHOOL MATH PROJECT (Class IX – XII)

                 A School Math Project is a serious task carried out by a team with members across different classes. It could involve either investigation of a mathematical concept, or building something that represent mathematics. It is a serious attempt at bringing math to life or diving deeper into the subject.

Ganit Gurooz will provide a list of school projects. Schools will then select one project and build a team of students as per the guidelines provided. The team will be guided by 2 teachers from the school and a member of the Ganit Gurooz Editorial Board to complete the project. The projects will be screened by a panel of mathematicians to select the top 15 projects.Each team will then be invited to present its project to a panel of math teachers and mathematicians for a final evaluation. The awards to the top 3 school projects will be announced in the Ganit Gurooz National Conference on Quality of Math Education on December 22nd, 2012.

It is hoped that by offering such competitions and contests, we can challenge and inspire students to learn and enjoy Mathematics. Your help and support will not only make your child more successful in Mathematics but will instill good study habits that will last a lifetime.

Please don’t hesitate to contact me at 9891644454 or amitbajajcrpf@gmail.com if you have any questions, suggestions or concerns during the year. Do visit www.ganitgurooz.com for further details.

Sincerely,

Amit Bajaj

HOD (Mathematics)

CRPF Public School, Rohini

Solve it - Question no. 18

Dear All,

I am posting a problem after a long time. Try this out and post your answer in the comment section.

QUESTION:

A mother has four children, each with a di erent age. The product of their ages is 17 280. The sum of the ages of the three oldest children is 40 and the sum of the ages of the three youngest children is 32. Determine the ages of the four children.

All the best!

Making Mathematics Simpler! NCERT class XII Solutions

Dear Students Of Class XII

It is observed that many a times, after teachers have explained certain topics and have discussed certain questions from the related exercise, not all the questions of the exercise are being solved/attempted by the students. It is practically impossible and undesirable for the teacher to solve each and every question in the class itself. The remaining questions are supposed to be attempted by the student at home. However, it is very much possible that the student is unable to successfully solve all of them.

After discussing this issue with the students, I have decided to make the NCERT textbook solutions available at my blog. The solutions are taken from www.meritnation.com. You can directly visit this website but you will first need to register there and the solution of only one question can be seen at a time. This might be a cumbersome process while you are checking your answers. Therefore, to  save the student’s time and to make those solutions available to all the unregistered students as well, I have decided to upload the solutions here from time to time. 

At the same time, I would want that the students do not check the solutions before they have tried the questions themselves. Hence, I’ll be uploading the solutions here only after the exercise has been covered in the class.

Note: Check this post frequently to get the latest updates and keep doing mathematics!

CHAPTER 1 (RELATIONS AND FUNCTIONS)

EX. 1.1        EX.1.2       EX. 1.3      EX. 1.4      MISC. EX.

CHAPTER 2 (INVERSE TRIGONOMETRY)

EX. 2.1     EX 2.2    MISC. EX.   Presentation

CHAPTER 3 (MATRICES)

EX. 3.1     EX. 3.2     EX. 3.3      EX. 3.4      MISC. EX.

CHAPTER 4 (DETERMINANTS)

EX. 4.1     EX.4.2       EX. 4.3      EX. 4.4
EX. 4.5     EX. 4.6      MISC. EX.  

CHAPTER 5 (CONTINUITY AND DIFFERENTIABILITY)
EX 5.1        EX 5.2      EX. 5.3      EX. 5.4      EX. 5.5    

Happy learning... 

All the best...

Amit Sir        

Addition in Mathematics syllabus (class XI and XII)

Dear All,

Please check the following additions in class XI and class XII Mathematics syllabus (CBSE). Remember that these are provided by CBSE in the form of supplementary books and not given in main NCERT textbook. Get the supplementary book (quite difficult to arrange) or take out print out of the attached files. Also, do inform your Maths teacher to teach following subtopics (in case they are not aware).

Infact there are certain additions in other subjects too. Please check the following link from CBSE site to know the same.

Amit Sir

OATH FOR STUDENTS

OATH FOR STUDENTS

☼ I will pursue my education with dedication and I will excel in it.

☼ I will plant at least five saplings and shall ensure their growth through constant care.

☼ I will constantly endeavour to remove the pain of my suffering brethren.

☼ I will work for becoming an enlightened citizen and make my family righteous.

☼ I will always be a friend of the mentally and physically challenged and will work hard to make them feel normal, like the rest of us.

☼ I promise that I will work hard with honesty to transform my country into a developed country.

- Dr. A.P.J. Abdul Kalam

Mathematics Workshop at Mahavir Sr. Model school

Dear All

I have attended a one day workshop at Mahavir Senior Model School today. It was organised by www.ganitgurooz.com . The main theme was to share few interesting ideas to celebrate 2012 as a Mathematics Year. Visit here to know more about 2102 MY . 

Well, I was surprised to see my blog on the presentation by Dr. Atul Nishal, Founder and Chairperson of Ganitgurooz.com . He shared my blog address with all the teacher who were present there (about 100) from different schools. He also invited me to share my experience about blogging. It was really a great learning experience.

 

 I recommend all the mathematics teachers and students to visit www.ganitgurooz.com and enjoy the great math stuff available there.

Regards,

Amit Bajaj

 

Top 10 Reasons Why I love Maths

Dear All,

You must watch this video...

Hope you like it!

Amit Bajaj

HAPPY PI DAY

Dear All

Pi Day is held to celebrate the mathematical constant π (pi). Pi Day is observed on March 14 (3/14) ,due to π being roughly equal to 3.14.

Pi Minute is also sometimes celebrated on March 14 at 1:59 p.m. If π is truncated to seven decimal places, it becomes 3.1415926, making March 14 at 1:59:26 p.m., Pi Second (or sometimes March 14, 1592 at 6:53:58 a.m.).

The Pi Day celebration includes public marching, consuming fruit pies and playing pi games... The founder of Pi Day was Larry Shaw,a now retired physicist at the Exploratorium who still helps out with the celebrations.

HAPPY PI DAY :)

Success Mantra for Students - Tips to Manage your TIME

Dear All

Studying is a big commitment and needs time to work on it. Managing time is the best way for students to succeed. By managing your time, other commitments can be fulfilled and you can study without distractions.  You need to balance time. If you are bad at balancing things make a personal timetable. Even if you do not stick to it, you will have an idea what you should be doing each day. This is better than trying to do everything each day and, at the end of the week, not achieve anything.

Choose a degree you are generally interested in rather than studying for the sake of having a degree. You will learn more because you are interested in the subject.

Always look at your assignments as a challenge rather than saying "it is too hard". A task thought of as too hard can slow you down to a standstill. The same task thought of as a challenge can spur you on.

It is best to keep up with your work. A timetable should be arranged each week, to ensure that you do not fall behind.

You should be aware of all your assignments and deadlines from the earliest stages of each Class/Semester. You can make a calendar for each module, stick on the wall in your room, where you can refer to it as and when the need arises.

If you organise your studies around the important outside commitments you have, such as work and family, you will find that you can cope quite well with what is expected of you.

Here are some tips to improve your study, but they will only work if you manage your time to get the best out of study.

Do not leave your course work to the last minute

Make sure you understand the lecture before you leave the classroom.

Be prepared to ask questions.

Read your text books and lecture notes again and again as you get new information.

You should be prepared to spend at least 3 to 4 hours every day reading lecture notes and text books, and gathering information.

Balancing study and other aspects of your life

Manage your time well for each module, but also make sure you get a good balance between work and social life. That is vital for life in general.

Set aside time specifically for each subject. Try to study one subject a day.

PRIORITIZE. Give each item a number or letter as to how important it is and according to when it needs to be completed.

GET REAL. You may want to list that Biology assignment as a C task but if your marks slip, don't see many Cricket Matches or Big Boss in your future. Keep yourself honest and get the studying done first so you can fun later on.

Stay FOCUSED. The key to a managing your time with a calendar or planner is to stick with it. If it sits in your dresser drawer and never is used, it isn't serving its purpose very well. Make sure to keep at it and keep it up to date. Cross off tasks.

If you do this SUCCESS IS YOURS!

Source: http://www.successcds.net