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OSWAAL BOOKS“Oswaal House” 1/11, Sahitya Kunj, M.G. Road,
AGRA-282002Ph.: 0562-2857671, 2527781, Fax : 0562-2854582,
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email : [email protected], website :
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Published by :
Class 12
SampleQuestion
Papers
Mathematics
Strictly Based on Latest Syllabus Issued by CBSEfor 2015
Examination
*Solutions for SQP 6-10 can be downloaded
from www.oswaalbooks.com
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Our Distributors
© PublisherTypeset by : Jhalak ComputersPrinted by : Aadhya
Printers
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CONTENTS
Modified Syllabus-2014-15 5 - 10
Sample Question Paper (Issued by CBSE) 11 - 18
Kindly ignore the pattern of the SQP as it has been revised
now.
The SQP's in the following pages follow the revised latest CBSE
syllabus for March 2015 Examination.
On Tips Notes 19 - 49
1. Sample Question Papers (Solved)
Sample Question Paper 1 51 - 53
Sample Question Paper 2 54 - 56
Sample Question Paper 3 57 - 59
Sample Question Paper 4 60 - 62
Sample Question Paper 5 63 - 65
2. Self Assesment Papers (Unsolved)
Sample Question Paper 6 66 - 68
Sample Question Paper 7 69 - 71
Sample Question Paper 8 72 - 74
Sample Question Paper 9 75 - 77
Sample Question Paper 10 78 - 80
3. Solutions
Sample Question Paper 1 81 - 91
Sample Question Paper 2 92 - 103
Sample Question Paper 3 104 - 115
Sample Question Paper 4 116 - 124
Sample Question Paper 5 125 - 135
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Believe in YourselfThis is the foremost barrier to be crossed
for scoring high marks in exams. One needs to believe in his /
her
ability to learn, memorize and reproduce what has been learnt.
Exams are nothing but the test of our faith,confidence and
knowledge.
Follow a Time – TableA well set time table allotting specific
durations for studying, sleeping, playing/surfing the net and
eating
can help every student a lot. Every above quoted thing has to be
done every day. A proper schedule can help astudent beat
examination stress.
Set Every Day GoalsPreparations should be done every day to
excel at the day of exams without depending upon any miracle
capsule to bail you out at the last moment. By setting everyday
targets and goals, one can achieve incredibleresults in terms of
efficiency and performance.
Take care of your HealthHealth is wealth. This adage never
fails. Only a sound body and sound mind can work effectively
towards
achieving any objective. Thus to sum up, healthy body is a
mandate for rigorous mental exercise that comes upduring
examinations.
Practice DailyWe eat daily, we sleep daily, so why not study
daily?
Regular practice in every subject will keep students close to a
subject. If one avoids any subject for more than three days in a
go, he/she is bound to lose interest in it.
1.TIPS N How to Score
2.
3.
OSWAAL
Your Elixir of Positivity & ConfidencePositivity and
confidence can do wonders to your grades,
far more than you can think. By studying from Oswaal
SampleQuestion papers, you develop confidence in yourself which
makesyou positive and hence gives you the winners advantage!!
Abunch of important questions along with their
systematicpresentation helps you tremendously in studying
effectively.
OSWAAL - Your Planner
For Examination PreparationsYou must make a schedule for your
studies followed by
strict implementation of that schedule. Oswaal SQP's give
youquestions on the important topics or topics which need
morepractice or time. Oswaal SQP's include last year examquestions
as well as sample papers for the proper schedule ofyour study. You
may also study with your friends and make theentire learning
process fun!!
OSWAAL - Your Confidence Booster
Just before the ExamOne should never try to read, study or cram
anything new
just before the beginning of your exam. You can just open
yourOswaal SQP's and read through the answers highlighted by youa
night before for the last time and then put away all yourbooks.
This gives you a new wave of confidence just before thecommencement
of your exam!
4.
5.
High in your Examination?
How to get6.
7.
8.
9.
10.
1.
2.
3.
Play GamesPlaying games – both the indoors and
outdoors, help in inculcating a practical approachtowards
dealing with a problem along withbeating the examination
stress.
PresentationTill now we have discussed the pre-exam tips.
This is a crucial tip while writing theexaminations. A
systematic and neat display ofanswers can boost your chances of
scoring high.
Time ManagementYou need to manage time not only during
exam preparations, but also at the time of solvingthe Question
paper. Carrying a wrist watchduring exams is an excellent way to
manage timewell. You should also try to save some time at the end
of the paper to recheck the answers.
Sleep WellA sound sleep a night before exam helps us
relax and rejuvenates our mind. The tired brainneeds and we need
to understand the needs of ourbrain, only then we will be able to
make the mostout of it especially during examinations.
Relax YourselfThis is last but not the least. Relaxing is
like
meditating. When we are relaxedwe are the most efficient
inreproducing what we havelearnt.
The 'OSWAAL' Advantage?
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Syllabus | 5
SYLLABUS
CLASS -XII(2014-15)
MATHEMATICS (Code No. 041)The Syllabus in the subject of
Mathematics has undergone changes from time to time in accordance
with growth of the subject and emerging needs of the society.
Senior Secondary stage is a launching stage from where the students
go either for higher academic education in Mathematics or for
professional courses like engineering, physical and Bioscience,
commerce or computer applications. The present revised syllabus has
been designed in accordance with National Curriculum Frame work
2005 and as per guidelines given in Focus Group on Teaching of
Mathematics 2005 which is to meet the emerging needs of all
categories of students. Motivating the topics from real life
situations and other subject areas, greater emphasis has been laid
on application of various concepts.
Objectives
The broad objectives of teaching Mathematics at senior school
stage intend to help the pupil :
to acquire knowledge and critical understanding, particularly by
way of motivation and visualization, of basic concepts, terms,
principles, symbols and mastery of underlying processes and
skills.
to apply the knowledge and skills acquired to solve problems and
wherever possible, by more than one method.
to develop positive attitude to think, analyze and articulate
logically.
to develop interest in the subject by participating in related
competitions.
to acquaint students with different aspects of mathematics used
in daily life.
to develop an interest in students to study mathematics as a
discipline.
to develop awareness of the need for national integration,
protection of environment, observance of small family norms,
removal of social barriers, elimination of sex biases.
to develop reverence and respect towards great Mathematicians
for their contributions to the
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6 | Oswaal CBSE (Sample Question Paper) Mathematics
Class-XII
Class XIIOne Paper Time : Three Hours Marks : 100
Unit Marks
I. RELATIONS AND FUNCTIONS 10
II. ALGEBRA 13
III. CALCULUS 44
IV. VECTORS AND THREE - DIMENSIONAL GEOMETRY 17
V. LINEAR PROGRAMMING 16
VI. PROBABILITY
Total 100
The Question Paper will include Value Based Question(s) to the
extent of 3 – 5 marks
Unit I : Relations and Functions
1. Relations and Functions : (15 Periods)
and onto functions, composite functions, inverse of a function.
Binary operations.
2. Inverse Trigonometric Functions : (15 Periods)
Elementary properties of inverse trigonometric functions.
Unit II : Algebra
3. Matrices : (25 Periods)
Concept, notation, order, equality, types of matrices, zero
matrix, transpose of a matrix, symmetric and skew symmetric
matrices. Addition, multiplication and scalar multiplication of
matrices, simple properties of addition, multiplication and scalar
multiplication. Non-commutativity of multiplication of matrices and
existence of non-zero matrices whose product is the zero matrix
(restrict to square matrices of order 2). Concept of elementary row
and column operations. Invertible matrices and proof of the
uniqueness of inverse, if it exists; (Here all matrices will have
real entries).
4. Determinants : (25 Periods)
Determinant of a square matrix (upto 3 × 3 matrices), properties
of determinants, minors,
inverse of a square matrix. Consistency, inconsistency and
number of solutions of system of linear equations by examples,
solving system of linear equations in two or three variables
(having unique solution) using inverse of a matrix.
-
Syllabus | 7
Unit III : Calculus
5. Continuity and Differentiability : (20 Periods)Continuity and
differentiability, derivative of composite functions, chain rule,
derivatives of inverse trigonometric functions, derivative of
implicit function. Concept of exponential and logarithmic function.
Derivatives of logarithmic and exponential functions. Logarithmic
differentiation, derivative of functions expressed in parametric
forms. Second order derivatives. Rolle’s and Lagrange’s Mean Value
Theorems (without proof) and their geometric interpretations.
6. Applications of Derivatives : (10 Periods)Applications of
derivatives : rate of change of bodies, increasing/decreasing
functions,
derivative test motivated geometrically and second derivative
test given as a provable tool). Simple problems (that illustrate
basic principles and understanding of the subject as well as
real-life situations).
7. Integrals : (20 Periods)Integration as inverse process of
differentiation. Integration of a variety of functions by
substitution, by partial fractions and by parts, Evaluation of
simple integrals of the following type and problems based on them
:
8. Applications of the Integrals : (15 Periods)
parabolas/ellipses (in standard form only), area between any of
the two above said curves
9. Differential Equations : (15 Periods)
Formation of differential equation whose general solution is
given. Solution of differential
differential equations. Solutions of linear differential
equation of the form.
, where p and q are functions of x or constant.
, where p and q are functions of y or constant.
Unit IV : Vectors and Three-Dimensional Geometry
10. Vectors : (15 Periods)
Vectors and scalars, magnitude and direction of a vector.
Direction cosines and direction ratios of a vector. Types of
vectors (equal, unit, zero, parallel and collinear vectors),
position vector of a point, negative of a vector, components of a
vector, addition of vectors,
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8 | Oswaal CBSE (Sample Question Paper) Mathematics
Class-XII
multiplication of a vector by a scalar, position vector of a
point dividing a line segment in a given ratio.
of vectors, vector (cross) product of vectors, scalar triple
product of vectors projection of a vector on a line.
11. Three-Dimensional Geometry : (15 Periods)
Direction cosines and direction ratio of a line joining two
points. Cartesian and vector equation of a line, coplanar and skew
lines, shortest distance between two lines. Cartesian and vector
equation of a plane. Angle between (i) two lines, (ii) two planes,
(iii) a line and a plane. Distance of a point from a plane.
Unit V : Linear Programming
12. Linear Programming : (20 Periods)
Introduction, related terminology such as constraints, objective
function, optimization. Different types of linear programming
(L.P.) problems, mathematical formulation of L.P. problems,
graphical method of solution for problems in two variables,
feasible and infeasible regions, feasible and infeasible solutions,
optional feasible solutions (upto three non-trivial
constraints).
Unit VI : Probability
13. Probability : (30 Periods)
Conditional probability, Multiplication theorem on probability,
independent events, total probability, Baye’s theorem, Random
variable and its probability distribution, mean and variance of
Random variable. Repeated independent (Bernoulli) trials and
Binomial distribution.
Prescribed Books : 1. Mathematics Part I – Textbook for Class
XI, NCERT Publication 2. Mathematics Part II – Textbook for Class
XII, NCERT Publication 3. Laboratory Manual Mathematics (Higher
Secondary Stage) NCERT Publication
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Syllabus | 9
(Issued By Board)
MATHEMATICSCLASS-XII (2014-15)
Duration — 3 hrs. Marks — 100
Weightage and distribution of marks over different dimensions of
the question paper shall be follows :
S. Typology of Question Learning Very Short Long Long Marks %
No. Outcomes Answer Answer I Answer II Weightage and Testing (1
marks) (4 marks) (6 marks) Competencies
1. Remembering— • Reasoning 2 3 1 20 20% (Knowledge based •
Analytical Simple recall questions Skill
• Critical terms, concepts, thinking principles, or theories, •
Derivative
recite, information)
2. Understanding— 2 2 1 16 16% (Comprehension to be familiar
with meaning and to understand conceptually, interpret, compare,
contrast, explain, paraphrase information)
3. Application (Use 1 3 2 25 25% abstract information in
concrete situation, to apply knowledge to new situations, Use given
content to interpret a Situation, Provide an example, or solve a
problem)
4. High Order Thinking 1 2 2 21 21% Skill (Analysis &
Synthesis— Classify, compare, contrast, or differentiate between
different pieces of information, Organize and/or integrate unique
pieces of information from a variety of sources)
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