CLASS XII MATHS ANSWER KEY

Hello All,

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

Here is the question paper.

Please check out the answer key of the paper.

ALL THE BEST

HAPPY BIRTHDAY TO GREATEST INDIAN MATHEMATICIAN -- SRINIVASA 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.

APNO GHAR TRIP ON 4 DEC 2010

Hello All,

I went for an educational trip (i know many of u r laughing) with XII C and D. Amarjeet and Beena madam were also there. It was really a wonderful n memorable experience... ( jitna socha tha ,usse to kam hi pereshaan kiya tha stuents ne..) finally, being a maths teacher.... i am giving marks to both the classes for their overall performance . class XII C scored 8/10 and class XII D got 7/10. not a bad score :)

here is a video upload by one of my dear student...

CLASS XI - ENRICHMENT ASSIGNMENT - I

Dear All

Here is an enrichment assignment- I for class XI students. It is not meant from examination point of view. But if you really love maths, you will surly enjoy doing this.

Happy learning...

Amit Sir

First Intra-School Maths Olympiad

Dear all

The school's Mathematics Department is organising the First Intra-School Mathematics Olympiad for all the classes (I - XII) on Tuesday, 9 November 2010 in the school.

All the students of classes I-XII who have scored at least 75% marks in mathematics in their previous class are eligible to participate in the Olympiad. (And all those students who are interested but do not satisfy the eligibility criteria may also participate, provided they submit a recommendation letter from their respective mathematics teacher.)

The questions may be expected from non-routine math of various topics of school mathematics. The question paper will only contain multiple choice questions.

THERE IS NO ENTRY/REGISTRATION FEE.

DATE OF EXAM: 09 NOVEMBER 2010 (Tuesday)

DURATION OF EXAM: 1 HOUR AND 30 MINUTES

LAST DATE TO APPLY: 30 OCTOBER 2010 (Saturday)

FOR OTHER DETAILS, CONTACT YOUR MATHEMATICS TEACHER.

Link to question papers,answer key and the result.

Amit Sir

Solve it - Question no. 15

Dear All

Try this one also :

well, 2 students have solved this correctly. well done!!!

Here is the solution:

Solve it - Question no. 14

Dear All

Solve the following question:

Here is the Solution:

PROUD TO BE A TEACHER

Hello All

Writing at my blog after a long time... My dear students and their love forced me to do so. Today 'Teachers Day' was celebrated in the school. I felt very good and honored by the love and affection shown by my students. Well, its not the cards or flowers which can ever make a good teacher but its the 'real' and unconditional love which do that. I thank to God to help me decide my career as a teacher. I am a teacher by choice and not by chance.

I THANK ALL MY DEAR STUDENTS TO MAKE ME FEEL PROUD BEING A TEACHER.

And yes, A token of love presented to me today by Aakash and Sasha, my dear students...

What is the best way to study mathematics

Dear All

Once open a time a lady wanted to hire a cook for her restaurant. She interviewed many candidates and finally she selected the one who impressed her in the interview. Lady was very impressed with his knowledge of cooking. He was like a cooking encyclopedia.

On his first day of the job, lady thought of taking his trial. She asked him to cook “Kadai Chicken“. She started eagerly waiting for the food. Food was served and she had her first bite. It was pathetic in taste. She could not swallow even a single bite of it. The lady was shocked and asked the man “It is so horrible in taste. Are you sure you can cook food?” He replied, “Madam, sorry for the food. Actually I have never done cooking before. I just had taken lessons on cooking from experts and during my training classes, I saw the instructor cooking. Also, I have read and learned all the recipes of making excellent food.”

Moral of the story is, there is a difference in knowing how to do things and actually being able to do things. By merely just knowing how to do things does not make you expert on actually doing it yourself.

Learning Mathematics is like learning the art of solving problems (actually doing) and not just knowing formulae and concepts (acquiring knowledge). So if you want to improve your mathematics, you need to focus more and more on problem solving instead of just reading theories, formulae, and solutions.

Following are some instructions/tips that would definitely help you learn mathematics better:

Always study Mathematics sitting on a study table with paper and pen to use: More you write, better you remember. Even if you are reading concepts and learning formulae, write it and learn it. Mathematics needs a higher level of concentration. Whether you are solving a problem or reading mathematical steps of a solution you need better concentration and focus. So my suggestion would be to sit on a table chair with no disturbance around. If your room is noisy, you can put cotton balls in your ears.

Spend more time on solve problem instead of reading solutions/theories/formulae: More you practice, better you would learn. It is very important that you solve problems to learn topics in mathematics. Just understanding concepts and learning formulae would not be sufficient to be able to solve questions in exam. In mathematics more than 50% of the knowledge comes through tricks/methods involved in solving problems. If you don’t practice questions, you don’t acquire this knowledge. In fact learning in Mathematics starts the day you start solving problems with pen and paper.

Step by Step learning:Learn theory and formulae first. Practice them in written. You should start reading solved-examples only after learning the concepts and formulae. This is must for easy understanding of the solved-examples as in every questions you use multiple formulae. If you don’t remember formulae well, you will take more time to understand the solution. After finishing examples, you need to solve level-1 (easy-to-average level) problems.

How to decide level? If you are not able to solve, go through solution. If you can understand the solution by just glancing it (as a hint), then it is level-1 (easy-to-difficult) problem. If you have to go through complete solution step by step and then finally you can understand the solution, then it is a level-2 (average-to-difficult) problem. If you find it hard to understand solution, it means it is level-3 (difficult-to-very difficult) problem. These levels are relative as every student has his own potential.

Once you have solved 30-40 level-1 problems and have thoroughly revised them to a level that you remember the ideas of most of them, you can then move to level-2 problems. Practice at least 30-40 level-2 problems. Don’t solve level-3 problems. They are not important and you can confidently leave them. Trying to solve them can be negative as they can break your confidence in the topic.

Revision and Re-Learning: Generally when you are not able to solve problems, you see their solutions. But you do nothing after that. In 1-2 weeks time you forget the solution. I am sure if you face that question again, you would not be able to solve it. So what is the point spending time on the question at first stage.

I suggest after reading the solution, you try to solve it yourself with paper and pen. Don’t worry if you know the solution now as you have read the solution. Mind will retain only if you do it with your hands. Then, mark the level of the question for future revision. After few week, try all questions again which are level -1 and Level-2. Do them like a test. Shortlist 50 such questions and take a 2-hours test. Even before exam, when you are confused what to revise, take out Level-1 and Level-2 (or just level-2) problems and revise them. If you don’t mark them, you cannot revise them.

Don’t refer solutions without trying problems: With all the books and study material around, most students have a tendency to read a question and immediately jump to see the solution. This is totally wrong and if you continue this for a long time, you will become dependent on solutions and you develop a bad habit of surrendering. Where as in mathematics, you need a fighting attitude. Try hard to crack the trick. I know you don’t have too much time to spend on each question but at least in each 60-70% questions you should attempt yourself first (spend 10-15 minutes average time on each question) and then refer solution. It is very important to try first as your brain develops only when you put stress on it.

Generate your Interest to perform better: No doubt, People who like mathematics perform better than others. As it involves applying tricks (like in puzzles and games) to solve problems, you perform better if you are liking what you are doing. You need to do problem solving when you are willing to do it. Feel proud if you are able to solve a question, feel thrilled rather than feeling frustrated when you take help of solutions (or help of others) to solve the problems. As I suggested in “Revision and Re-Learning”, those questions which you are able to solve through solutions, solve them again. When you are able to solve them again, you will feel good and that will help in generating interest.

Make Flash Cards for better learning: To learn formulae and even tricks involved in problem solving, make paper based card (paper sheets) and keep them with you. You can memorize them even when you are not at your desk, may be when you in a car/bus, in school, while walking, etc. This helps in building your knowledge, generates interest and above all you are utilizing your non productive time.

Help others if you get chance: If somebody needs your help in solving a problem and you know how to solve it, never miss the opportunity to help her. This generates confidence in you as well as your interest would also go up. More confident you are, better you can think.

By: Manmohan Gupta

(HOD Mathematics, VMC)
Mathematics is Fun

MATH FUN

Dear All

Let me take only a minute

Just do the following multiplication :

13837 x Your Age x 73 = ? ? ?

You get very interesting resut, let me know.


You get the same result if you multiply 10001 * your age * 101

How is that?

INTERSTING NUMBER 37

NUMBER 37 IS AN INTERESTING NUMBER:

SEE THE PATTERN:
111/(1+1+1)=37
222/(2+2+2)=37
333/(3+3+3)=37
444/(4+4+4)=37
555/5+5+5=37
666/(6+6+6)=37
777/(7+7+7)=37
888/(8+8+8)=37
999/(9+9+9)=37

hope you like it...

do you have other number patterns to share... do write in comment section.

Nature by Numbers

CBSE 2010 TOPPERS

Setting Goals after Board Results

Setting Goals after Board Results

There are certain basic fundas that you need to know while setting your goals :

A) Write down all your goals separately. Writing is described as the act of inscribing characters or shapes on a surface to convey thoughts and ideas. Have you ever wondered why this symbolic, mechanical act is considered so important in the goal-achievement process?

It is important because putting pen to paper gives body to our thoughts. It transfers non-verbal cues into tangible, concrete expressions. The writing becomes your signed testimonial. You can look at it, physically from a distance and it will remind you of what you promised yourself a year ago.

This act of using your eye in co-ordination with your hand, while holding a pen, will make a firm impression on your mind, so while you are reading or re-reading a particular phrase, a sentence or a book section, this impression consolidates and slips deeper into our subconscious.

B) Define goals in terms of specific activities and specific processes. Without specifics, the whole exercise is futile and meaningless. So split your goals in terms of specific actions and prioritise those actions.

C) Prioritise and re-prioritise your goals. This will help you make the maximum use of your time resource, so that nothing important gets left out.

D) Identify your obstacles. These could be internal, as well as external. Decide what additional knowledge you need to gather before you can set out to achieve your goals.

E) Define your goals and start working backwards from those goals. Affirmative commands are excellent for time management. Keep repeating to yourself, “I am always punctual”, “I am well-organised”, “I use my time productively.” Repeat these commands in your spare time. Act or pretend as if you have already begun to follow these commands.
In short, fake it until you make it.

To solve a problem or to reach a goal, you...don't need to know all the

answers in advance. But you must have a clear idea of the problem or

the goal you want to reach.

source: www.icbse.com

DIFFERENT KINDS OF NUMBERS NUMBERS

Deficient number -number whose proper divisors add up to less than itself. For example, 16 is a deficient number as sum of its proper divisors {1, 2, 4, 8} = 15.

Abundant number -number whose proper divisors add up to more than the number itself. For example, 18 is a abundant number as 1+2 +3 +6 +9 = 21. Can you find the smallest abundant number?

Happy number -number for which the sum of the squares of the digits eventually equals 1.For example, 203 is happy because 2² +0² +3² = 13; 1² +3² = 10; 1² +0² = 1

Can you think of another happy number? An unhappy number?

Solve it - Question 14

Dear All


Solve the following question:

well, we have a quick respose by Prabhat. Well done!

I will appriciate if you could give your responses in the comment section of the post. Anyways, here is the solution:

DIFFERENT KINDS OF NUMBERS NUMBERS

Dear All

Do you know any perfect human being! May be NO... But, in mathematics there are the numbers which are perfect. Let us consider the following definition:
Perfect number -number whose divisors (except itself) add up to itself. For example,. 28 is a perfect number. Its proper divisors are {1, 2, 4, 7, 14} and 1 +2 +4 +7 +14 = 28.
Well, Can you find the smallest perfect number?
All perfect numbers less than 500.
Is 360 a perfect number?
Find out more about perfect numbers and explore the beautiful world of numbers!

Math Joke

A math major studied hard in the university library all evening. On his way home, he felt very
hungry so he stopped at a nearby pizza place and ordered a large pizza. When it was ready, the pizza guy asked him if he wanted it cut into six or eight pieces. The Math major replied, “Cut it
into six—I don’t think I could eat eight pieces.”

SOLVE IT - QUESTION 13

Dear All


Today, I am posting a very interesting problem. Waiting for your responses...


QUESTION:

Two women Mrs. X and Mrs. Y met each other in a park.

Mrs. X : ‘‘Hi, how are you? How are your children? You have three children if I remember correctly. But how old are they now?’’

Mrs. Y : ‘‘Yes, I have three children. The product of their ages is equal to 36. The sum of their ages is equal to number of chairs lying in a park.’’

Mrs. X counted the number of chairs, thought for a while and said, ‘‘ I still can’t figure out the ages of your children.’’

Mrs. Y : ‘‘ My eldest son will definitely won math olympiad this year.’’

What are the ages of the three children?

(Assume whole number for ages)

Well, Here is the answer:

Solve it - Question 12

Dear All

A simple question for you all:

Solve it - Question 11

Dear All

One more very interesting question for all of you:

In trapezium ABCD with bases AB and CD, AB = 52 , BC = 12, CD = 39, and DA = 5. Find the area of ABCD.

Here is the Solution:

Solve it - Question 10

Dear All

Writing after so long... I was busy doing many other assignments.

So, here is a question for you :)

Question :

Twenty matchsticks of equal length are placed to form a triangle. Find the total number of different triangles that can be made with a perimeter of 20 matchsticks?

ANSWER:

HAPPY NEW YEAR 2010

Dear All

I wish Happy New Year 2010 to all of you. May God fulfill your dreams of life to be true and keep you healthy, give you wealth, family prosperity, happiness, free from all worries, achieve your goal, and other good wishes.

New day, new blessings. Don’t let yesterday’s failures ruin the beauty of today. Blessings of God are new every morning. Today has its own promise of love, forgiveness, joy and success.

As our world grows another year older… Here’s wishing that you get the biggest slice of happiness and good luck to fill your heart and home today and the whole year through. Happy New Year!!!