# WELCOME TO THE EXCITING WORLD OF MATHEMATICS

### XII CLASS PRE-BOARD - II JAN 2016 MATHEMATICS PAPER SOLUTION KEY

Dear class XII Students,

Hope this time all of you must have performed well
in the exam.

I am providing you with the question paper and the
solution key.

Here is the Sample Paper released by CBSE for 2016
exam.

Link for most important questions:

Click here for the sample papers of the other
subjects.

You may also check my Previous Posts where reference
material, assignments, book by DOE (govt. Schools) etc.

All the best for your board examination.

Amit Sir

### XII CLASS MATHS MOST IMPORTANT QUESTIONS

### XII CLASS PRE-BOARD - 1 2015 MATHEMATICS PAPER SOLUTION KEY

Dear class XII Students,

Hope this time all of you must have performed well in the
exam.

I am providing you with the question paper and the solution
key.

Here is the Sample Paper released by CBSE for 2016 exam.

Click here for the sample papers of the other subjects.

You may also check my

You may also check my

**Previous Posts**where reference material, assignments, book by DOE(govt. Schools) etc.
All the best for your board examination.

Amit Sir

### HAPPY BIRTHDAY TO GREAT INDIAN MATHEMATICIAN - RAMANUJAN

Dear Reader,

Srinivasa Ramanujan (22 December 1887 – 26 April 1920) was an Indian mathematician, who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. Ramanujan independently compiled nearly 3900 results (mostly identities and equations). His work continues to inspire mathematicians even today!

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 merit scholarship, 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.
### PRIZE WINNERS - SIXTH INTRA SCHOOL MATHEMATICS OLYMPIAD

Dear Reader,

CRPF Public School has fulfilled its motto of striving towards excellence by organizing and successfully completing its Sixth

Intra School Mathematics Olympiad on 6 November 2015. Around 250 students enthusiastically participated in the Olympiad held in school premises.

Intra School Mathematics Olympiad on 6 November 2015. Around 250 students enthusiastically participated in the Olympiad held in school premises.

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.

Check out the result here:

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

You may again like to see the question papers and their solution

### 5 Reasons Why Math Matters

Dear Reader,

Math
is important. It really is.

Despite
how you felt about algebra class or geometry class or even basic addition and
subtraction, math is a life skill that applies to everyone, not just
accountants and engineers. It is the language of many fields, some of which may
surprise you. But math matters, in more ways than one. And while numbers and
equations are a necessary evil to some and pure enjoyment to others, we need
math to live.

Below
are five reasons why math is worth knowing. Starting with…

Building
Stuff: Balancing a cheque-book? Dividing rent among four roommates? Determining
your share of the electric bill? How about taxes and student loans? Paying
bills is the worst, no doubt about it. But you need to know some math in order
to stay on top of your finances, balance your budget, and avoid all those
overdrafts.

**Cooking:**Surprised? Baking cupcakes and roasting a chicken requires math skills. You need to measure the ingredients in terms of teaspoon, tablespoon, ounces, grams, kilograms, etc. And what if you what to cut a recipe in half? This is serious business. Unless you’re a pro at eyeballing the “this much salt” and “that much flour,” you need math in the kitchen.

**Travel:**Planning to jump the pond for a backpacking adventure? If so, better prepare yourself for currency confusion, especially if your currency converter is not a physical device. Knowledge of currency conversion is essential when traveling to a foreign country. Your iPhone may not be able to save you, but your math skills sure can.

**Building Stuff:**There will come a time when you need to assemble a desk, a shelving unit, or perhaps a crib. And you’ll thank your math teacher for helping you become the hero that you are once that desk sits proudly constructed by the window. Putting stuff together requires math aptitude in order to avoid a safety hazard.

**Career Readiness:**Are you thinking of becoming a nurse? How about a marketing manager or a lawyer? Nurses use math to calculate medication dosages, marketing managers use math to determine profit margin and pricing strategies, and lawyers use math to determine settlements and statistical evidence. Even sports agents and high school English teachers use math on a regular basis.

Think
about it. Math really is everywhere. From the kitchen to the courtroom,
numbers, graphs, and measurements are all around us. Knowing how to calculate a
tip at a restaurant or your fantasy football score is important business!
Mortgage payments, caloric intake, and retail discounts are a big part of our
everyday lives. And we can’t always rely on our phones to do the work for us
when it comes to math. Your brain is a much better, and more reliable tool.

**Source:**http://onlinemathdegrees.org/

### Believe it or not in Mathematics

**1.**Russian King Peter the Great announced that no member of the Royal Family should marry until they pass in arithmetic, geometry and navigation.

**2.**There is no equilateral triangle, the coordinates of whose vertices are all integers.

**3.**There are only five Heronian triangles (triangles having integer sides) such that the perimeter is equal to the area. They are: (5, 12, 13) , (6, 8, 10) , (6, 25, 29) , (7, 15, 20) and (9, 10, 17). The first two triangles are right triangles also.

**4.**A plane can be filled with squares, equilateral triangles and regular hexagons. No other regular polygons can fill the plane without gaps.

**5.**Three legged stool is more stable than any other stool. The principle underlying is this fact is we can draw only one circle through three given points which are not collinear. That is why old people walk with the assistance of a stick (third leg) , or even think of tripod.

**6.**An angle of 3 degrees is the only constructible angle of prime measure.

**7.**The average human body contains about 10^27 atoms whereas the number of atoms in the whole universe is 10^73.

**8.**There are certainly at least two peoples in the world with exactly the same number of hairs on their heads! (There are more people than the hairs on any one head).

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