Category Archives: MATHS

CET 2011-MATHEMATICS SOLVED PAPER

DEAR STUDENTS

HERE IS   CET 2011 MATHEMATICS  PAPER  COMPLETELY SOLVED .

THIS WAS GIVEN BY OUR CONTRIBUTOR

SUCHINDRA D,  LECTURER IN MATHEMATICS,VIDYABHARATHI IND PU COLLEGE, SHIMOGA &

VASUDEVA KH, LECTURER IN MATHEMATCS, SAGAR

all are scanned copies and in jpeg format, HERE IS THE LINK

MATHEMATICS-MODEL PAPER -3

This model paper in II PUC MATHEMATICS  was contributed by

Shri Ganachari M , Lecturer in Mathematics

Thanks to shri GM

ದ್ವಿತೀಯ ಪಿ.ಯು.ಸಿ,  ಗಣಿತಶಾಸ್ತ್ರದ ಈ ಮಾದರಿ ಪತ್ರಿಕೆ -೩  ನ್ನು  ನೀಡಿದವರು

ಶ್ರೀ ಗಣಾಚಾರಿ ಎಂ. ಗಣಿತಶಾಸ್ತ್ರ ಉಪನ್ಯಾಸಕರು.

ಇವರಿಗೆ ವಂದನೆಗಳು

Here is the link/ಇಲ್ಲಿದೆ ಲಿಂಕ್:

MATHEMATICS-II PUC-HOT MODEL PAPER – 3

Ist year PUC-Maths-The Questions that one should never neglect.

ಪ್ರಿಯ ವಿದ್ಯಾರ್ಥಿಗಳೇ,
ಇಲ್ಲಿ ಪ್ರಥಮ ಪಿಯುಸಿ ವರ್ಷದ ಗಣಿತಕ್ಕೆ ಸಂಬಂದಿಸಿದ ಪ್ರಶ್ನೆಗಳ ಪಟ್ಟಿಯೊಂದಿದೆ.

ಇದನ್ನು ನೀಡಿದವರು: ಶ್ರೀ ಗಣೇಶ ಕಾಮತ್, ಶ್ರೀ ಸುಚೀಂದ್ರ, ಮತ್ತು ವಾಸುದೇವ ಕೆ.ಹೆಚ್.
ಕೆಳಗಿನ ಲಿಂಕ್ ಮೂಲಕ ಡೌನ್ ಲೋಡ್ ಮಾಡಿ..

 

I PUC MATHS-IMP QUESTIONS ONE SHOULD NEGLECT 2.pdf

MATHEMATICS- QUESTIONS ONE SHOULD NOT NEGLECT – PART ONE

Dear students

Here is  some Questions on Mathematics,   one should not neglect in preparing for coming Annual Examination 2011 .

This is part  One which covers : Algebra, Analytical Geometry, and Trigonometry.

HERE IS THE LINK:

II_PUC_MATHEMATICS_PART_1-IMP_QUESTIONS_PART_1

This was prepared  by

D. SUCHINDRA  AND

KHV

KARNATAKA CET ANSWER KEYS 2010: MATHEMATICS with solutions

Here is key answers with solutions for KARNATAKA COMMON ENTRANCE TEST -2010

in mathematics

SUGGESTIONS TAKEN FROM :

D. SUCHINDRA ,

KH VASUDEVA,

SHRI GANACHARI M,

SHRI SEETHARAM SHETTIGAR

DOWNLOAD:

KCET Maths 2010 solved paper

REVISING MATHEMATICS-LAST MINUTE PREPERATION-(II PUC)

THIS ARTICLE IS FOR THE STUDENTS WHO ARE IN LAST MINUTE PREPARATION.

It is very difficult to mention important questions  in mathematics. Because the direct questions what everybody list as important questions   in other subjects will not  appear in  mathematics.

But patron of the questions will be same as in previous year question papers.  practicing  problems of  previous year questions  is enough to prepare for Mathematics.

If u are selecting, complete the following areas:

ALGEBRA

Matrices and determinants:

a)Solving the simultaneous equation by cramer’s rule and matrix method

b)Statement of cayley Hamilton theorem and finding inverse of matrix and verifying cayley Hamilton theorem

Vectors

a)Application of vectors like: proving sine rule, projection rule, cosine rule, compound angle formulae, angle in a semicircle is right angle by vector method

b)Problems on scalar triple product and vector triple product.(standard problems)

c)Find the projection of one vector to another vector , find the sine or cosine of angle between the vectors, unit vector in the direction of vector,

Groups

a)Proving a particular set forms an abelian group like Show that a*b=a+b-ab forms an abelian group, Show that G={5^n, (integral multiples of 5) } forms an abelian group etc  refer topic wise questions in mathematics in this website.

Elements of Number theory :

a)Finding GCD of two numbers and representing them as a linear combination of x and y and showing x and y is not unique

b)Find the number and sum of divisors

c)Finding the last digit or unit digit, solving linear congruence.

TRIGONOMETRY

INVERSE TRIGONOMETRIC FUNCTIONS:

a)problems on use of formula tan^-1 x + tan^1 y= tan^1(x+y/1-xy)  etc

GENEREAL SOLUTION OF TRIGONOMETRIC EQUATION

a)GS of trignometric equation of the form acosx+bsinx=c

b)GS  by using  FORMULA OF CONVERTING sum of trigonometric functions  into product or product into sum

COMPLEX NUMBERS

a)State and prove Demoivre’s theorem

b)problems on this,  see topic wise questions in this website.

CIRCLES

a)all derivations: equation of tangent, condition of orthogonality, finding length of tangent, condition for the line y=mx+c to be tangent to to circle x^2+y^2 =a^2

b)problems on orthoganal circles, and finding  equation of circle by finding g, f and c using conditions in the given problem.

CONIC SECTION:

a) all derivations: Derivation of parabola, ellipse and Hyperbola

b)problems on finding centre , focus, directrix and ends of Latus rectum of parabola , ellipse and Hyperbola,

c)Definition of rectangular hyperbola, director circle, auxilary circle and its equations

DIFFERENTIATION:

a)problems on differentiation from first principles: no need to solve differentiation of inverse trigonometric function by first principles and some problems like  root sinx, sinrootx etc.

b)problem on successive differentiation, logarithmic differentiation , parametric differentiation

implicit differentiation (refer topic wise questions- it contains limited number of questions).

APPLICATION OF DERIVATIVES

a)Problems on Derivative as a rate measure, problems on finding maxima and minima involving 2 dimensions figure only( Don’t go for problems on finding maxima and minima involving figures like , sphere, cylinder, etc)

b)Angle of intersection between two curves: like: If ax^2+by^2=1 and Ax^2+By^2=1 cut each other orthogonally , show that 1/a-1/b=1/A-1/B

INDEFINITE INTEGRAL:

a)problems on forms of integral, all types

DEFINITE INTEGRAL

Proving  some properties of definite integral, and problems using definite integral.

AREA UNDER A CURVE

See topic wise questions in this website.

DIFFERENTIAL EQUATION

a)Finding order and degree of Differential equation.

b)Solving Differential equations by variable separable method (see topic wise questions)

At last:

Finding GCD of two numbers, and representing them as linear combination  or finding sum and number of divisors                                                                                                    5 MARKS

Solving simultaneous linear equations by matrix method, cramer’s rule, finding inverse and verifying matrix by using cayley Hamilton theorem.                                  5 marks

Groups : Showing a set forms a group :                                                              5 marks

Definition of ellipse , hyperbola, parabola as a locus and Derivation of parabola, ellipse , hyperbola in standard form in  conic section (Important) or all derivations in conic section like  condition for the line y =mx+c to be tangent to parabola, ellipse, hyperbola  including problem etc                                                          6 marks

Problems on differentiation from first principles:                              3 marks

Complex numbers: problems on demovires theorem

and its proof :                                                           6 marks

Vectors: Application of vectors or problems                                       4 marks

Problems on Derivative as a rate measure , angle of intersection between two curves, maximal and minima (application of derivative problems)                        :                         6 marks

Finding Area under a curve                                                                     5 marks

Proving  some important properties of Definite integral and problem on this            6 marks

And so on……………………………………………………………………..

Count the marks  you will get more than 35 marks

So it is easy to prepare for mathematics examination .

Excuse for spelling and grammatical mistakes

so

BEST OF LUCK .

FROM

VASUDEVA KH

VYBHAV G.R.

ಗಣಿತ ಪರೀಕ್ಷೆಯ ಸಂದರ್ಭದಲ್ಲಿ ಸಮಯ ನಿರ್ವಹಣೆ :

TIME MANAGEMENT IN MATHS EXAM}

Sun, 02/28/2010 – 23:56 |  aravind

TIME MANAGEMENT IN MATHS EXAM

“I knew answer for all questions but I did not get sufficient time to answer”. These are the words students usually utter once they come out of the exam hall! Some students even say “ I knew every thing but i had written only for 80-90 marks” . Some students may write only for 50-60marks, even if they are prepared very well. Why this happens ? how this happens ? can it be avoided?

YES!

These can be avoided (100%) just by proper time management and by selecting the proper questions

Scoring in exam depends not only on your preparation but also on your mind set, time management, proper selection of questions and precise answering.

Now here are some advice to students

DURING THE EXAM DAY:

Arrive at the exam center 30 minutes early. Find your register number, the allotted room .Compose yourself. Consciously relax and take a few deep breaths. Think of your reward after the EXAM is completed. Be confident! Think positively

1. Remember ,,, P.U. Department has given an opportunity to select proper questions with out wasting your 180 minutes, by providing extra 15 min for reading the question paper. In this 15 min of time go through the question paper and gauze or identify the easy questions which can be solved in lesser time . .while doing this don’t write or mark anything on the question paper except your register number.

2. Start looking at the question paper from question no 1. DECIDE the question IN WHICH U R CONFIDENT OF ANSWERING AND also decide about the questions which  you cannot answer. Solve the problems for which you know the answers partially at the end.

3. Here I have given average time for attending each question but you may follow other known methods also. But the questions in which you are confident should be solved in less time ( say for attending 5 mark question u may need 5-6 min but it should be solved with in 4 min) so, remaining time can be utilized to try some lengthy or known questions

PART A: (1 MARK): MAX TIME: 15-20MINUTES(TEN QUESTIONS)

PART B: (2 MARK): MAX TIME: 40 MINUTES(ANY TEN QUESTIONS)

PART C: (5 MARK): MAX TIME: 56 MINUTES( EIGHT QUESTIONS)

PART D: (10 MARK): MAX TIME: 26 MINUTES(ANY TWO)

PART E: (10 MARK): MAX TIME: 18 MINUTES (ANY ONE)

TOTAL: MAX TIME: 160 MINUTES OUT OF 180 MINUTES

So you have 20 -30 minutes left if you complete problems in the above method. After finishing answering of all required known questions, go through it rapidly. then in the remaining time you can attend extra questions either in part B or in Part C (where you have doubts) or other wise you can revise and recheck the answered one,  once again.

There are many students who will able to complete all prescribed questions within two hour.

7. It always better to attend questions on proof( provided you know well), in sub groups, circles, conics , complex number, vectors,) and It is better to avoid questions which is having figure in circles and conics to save time . Remember your sketch should be clear. You will get ZERO if u don’t write the correct figure especially in derivations in conic section and circles.

For example: In part D if u have questions on a) derivation in conic section b)problem on application of differentiation c) problem on complex numbers , It is better to choose ‘b’ and ‘c’ instead ‘ a’

8.If they asked the questions of type differentiate cosecx, secx, tan^-1x, cot^-1 x, and other inverse trigonometric  functions (IN MY VIEW , ACTUALLY QUESTIONS on DIFFERENTIATING INVERSE FUNCTIONS FROM FIRST PRINCIPLES SHOULD NOT BE ASKED AS PER RECENT SYLLABUS, STILL SOME ARE ASKING ABOUT SUCH QUESTIONS FOR JUST 3 MARKS ,) In that case it is better to leave differentiate from First principle , attempt some other question( from choice,if u know) as it time is consuming, if don’t know any other then u have to attend it.

9. Now take up the questions u know how to do but it take little time to think and solve ,attempt those questions now and if u don’t get the exact solutions just think for 1 min and leave that question and attend other question. don’t waste your valuable time in solving single unknown problem

10. Don’t change your plan at any cost that to in exam hall, which may lead you to confusion

11.If possible , Day before the exam take 2-3 question paper ( take 2march, 1July supplementary exam)and allot 15 min of time and select the questions as stated above (no need to solve the paper just to practice).

12.On the exam day after u wake up imagine u r self as a good math teacher and say with confidence that , in exam i will solve the questions that i have studied.

TRY TO FOLLOW ABOVE METHOD IF U LIKE

WISH U A HAPPY PROBLEM SOLVING

FROM

VASUDEVA KH

VYBHAV G.R.

2ND PUC MODEL PAPER IN MATHEMATICS-(LEVEL: AVERAGE, NOT EASY)

THIS MODEL PAPER IN  2ND PUC MATHEMATICS IS  FOR THOSE WHO ARE ABOVE AVERAGE in studies.

LEVEL: AVERAGE NOT EASY

Download link:

2nd PUC -MATHEMATICS-MODEL PAPER -above average

QUESTIONS ABOUT DEFINITIONS IN MATHS FOR SECOND PUC

Dear students

Certain students asked

the important definitions required to learn for one mark.

One student sudhamshu mitra wrote :

“I’m a 2nd puc student studying in bangalore. Can you tell me the important definitions required to learn? Because I have observed in many question papers and found out that we can lose one marks many a times, which should not happen while we are aiming for 100. It will be a great help to all the students here!!”

For many of such students, Here is the little effort

Download the following link:

important-definitions-in-maths

Groups: Math error done by student

For proving the questions on Groups many students commits mistakes on the following questions.
1. If Q1 is the set of rationall numbers other than 1 with binary operation * defined by a*b=a+b-ab for all a,b εQ1, Show that (Q1,*) is an abelian group and solve 5*x=3 in Q1.
2.If Q-1 is the set of all rational numbers except -1 and * is a binary operation defined on Q-1 by a*b= a+b+ab, Prove that Q-1 is an abelian group.
For verifying closure law for the above the problems, many students simply do in the following way
Wrong approach:
Closure law: a*b=a+b-ab is again a rational number and hence closure law is true.
However Here student did not verified a*b is a rational number except 1. Hence it is very necessary to show that a*b is a rational numbr other than 1 . Other wise 1Mark will be reduced in the valuation. In april 2002, the 1 Mark is reduced for the students who did not verified the closure law correctly.
The correct approach is as follows:
For question number 1:
Let a, b Q1 such that a #1, b#1 a+b-ab is also a rational number and it cannot be equal to 1
Because If a+b-ab=1, then a+b-ab-1=0
then (a-1)(b-1)=0
thereofore a=1 or b=1 which is not true as a#1 and b#1. a*b belongs to Q1
therefore Q1 is closed w.r.t * (GIVING REASONS IS IMP)
Similarly for verfying closure for 2 question
Closure law: or Q-1 a*b=a+b-ab is again a rational number and hence closure law is true.
Let a, b Q-1such that a # -1 b#-1 a+b+ab is also a rational number and it cannot be equal to -1
Because If a+b+ab=-1, then a+b+ab+1=0
therefore (a+1)(b+1)=0
Hence a= -1 or b= -1 which is not true as a# -1 and b# -1. a*b belongs to Q-1
Q-1 is closed w.r.t * (GIVING REASONS IS IMP)

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