CBSE Question Bank Class 12 Mathematics Book Based On Latest Board Sample Paper Released On 16th Sep 2022 (For 2023 Exam)

397 Pages·2022·53.271 MB·English

by  Oswaal Editorial Board

MATHEMATICS
(INCLUDES COMPETENCY BASED QUESTIONS)
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18th EDITION
YEAR 2022-23

I S B N

“978-93-5595-564-7”

CENTRAL BOARD OF
SYLLABUS
SECONDARY EDUCATION
COVERED
DELHI
PUBLISHED BY
OSWAAL BOOKS &
LEARNING PVT. LTD.
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TABLE OF CONTENTS
g Latest CBSE Circular released on 20th May 2022 for Academic Year 2022-2023
(CBSE Cir. No. Acad 57/2022) 7 - 7
g Latest CBSE Syllabus released on 21st April 2022 for Academic Year 2022-2023
(CBSE Cir. No. Acad 48/2022) 8 - 11
g CBSE Solved Board Papers 2022 Term-II Examination 14 - 32
(To download Solved paper for Term-I 2021-22 & Latest Topper’s Answers 2020, scan the QR Code

given on Page 32)

UNIT-I : RELATIONS & FUNCTIONS
1. Relations and Functions 1 - 22
Topic - 1 : Relations
Topic - 2 : Functions
2. Inverse Trigonometric Functions 23 - 41
 Self Assessment Paper- 1 42 - 43
UNIT-II : ALGEBRA
3. Matrices 44 - 66
Topic - 1 : Matrices and Operations
Topic - 2 : Symmetric, Skew Symmetric and Invertible Matrices
4. Determinants 67 - 87
Topic - 1 : Determinants, Minors & Co-factors
Topic - 2 : Solutions of System of Linear Equations
 Self Assessment Paper- 2 88 - 90
UNIT-III : CALCULUS
5. Continuity & Differentiability 91 - 115
Topic - 1 : Continuity
Topic - 2 : Differentiability
6. Applications of Derivatives 116 - 145
Topic - 1 : Rate of Change of Bodies
Topic - 2 : Increasing/Decreasing Functions
Topic - 3 : Maxima and Minima
7. Integrals 146 - 185
Topic - 1 : Indefinite Integral
Topic - 2 : Definite Integral
8. Applications of the Integrals 186 - 207
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TABLE OF CONTENTS
9. Differential Equations 208 - 237
Topic - 1 : Basic Differential Equations
Topic - 2 : Variable Separable Methods
Topic - 3 : Linear Differential Equations
Topic - 4 : Homogeneous Differential Equations
 Self Assessment Paper- 3 238 - 240
UNIT-IV : VECTORS & THREE DIMENSIONAL GEOMETRY
10. Vectors 241 - 268
Topic - 1 : Basic Algebra of Vectors
Topic - 2 : Dot Product of Vectors
Topic - 3 : Cross Product
11. Three Dimensional Geometry 269 - 290
Topic - 1 : Direction Ratios and Direction Cosines
Topic - 2 : Lines & Its Equations in Different forms
 Self Assessment Paper- 4 291 - 293
UNIT-V : LINEAR PROGRAMMING
12. Linear Programming 294 - 314
 Self Assessment Paper- 5 315 - 317
UNIT-VI : PROBABILITY
13. Probability 318 - 348
Topic - 1 : Conditional Probability and Multiplication Theorem on Probability
Topic - 2 : Bayes’ Theorem
Topic - 3 : Random Variable and its Probability Distributions
 Self Assessment Paper- 6 349 - 350
 Practice Paper- 1 351 - 354
 Practice Paper- 2 355 - 359
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PREFACE
Who is this book for?
We are delighted to present the updated edition of the CBSE Questions Banks for the 2022-23 academic
session for Class 10. This edition is based on the latest CBSE Syllabus and Scheme of Assessment and
Evaluation Practices of the Board for the Session 2022-23. National Education Policy 2020 has affirmed
the need to move from rote to competency based learning. The Board has taken multiple steps towards
the implementation of Competency Based Education (CBE) to equip the learning to meet 21st Century
challanges proactively.
Why is this book different?
The structural changes in Education that are being brought in by
the latest Syllabus and the new National Educational Policy (NEP)
resonate with our approach of focusing on deeper understanding The new way of learning;
instead of rote learning. Available for all subjects, these books Blended Learning
have been designed to help students achieve high scores in their
Board Examinations. Prepared by the Editorial Board of Oswaal The pandemic introduced us
Books, comprising leading subject matter experts, it consists of all to a phenomenon -
CBE pedagogical features such as Multiple Choice Questions, Case
Blended Learning.
based Questions, Source based Integrated Questions alongwith
In no time e-learning has
Objective Types, Short & Long Answer Types Questions - all of
become mainstream.
which reinforce learning and improve conceptual understanding.
Oswaal Books identified this
To make these books 100% exam-centric, we've also included-
like an opportunity and thus,
 Latest Board Exam Papers (all sets of Delhi & Outside Delhi) of we decided to introduce
CBSE Term-II 2022
 Topic-wise/Concept wise segregation of chapters Oswaal360 -
 Important Keywords for quick recall of concepts A platform that simplifies
 Fundamental Facts to enhance knowledge learning with Chapter-wise
 Practice Questions within the chapters for better practice e-assessments articulated
 Reflection to ask about your learnings for students to crack Board
 Self-Assessment Tests & Practice Papers for Self-Evaluation Exams.
 Art Integration for Experiential learning
Other Important features of this book such as-Art Integrated
activities, Mind Maps, Concept Videos and Academically Important
(AI) Questions make it an indispensable resource for students
desiring to secure top marks in the examination.
How to use this book?
You should use this book to supplement your learning and test your conceptual understanding. The rich
instructive pedagogy encourages critical thinking and reflection and acts as a handy resource for students to
learn, course correct, and test their knowledge.
Making this book a part of your day-to-day exam preparation routine will help you sharpen your conceptual
understanding, enhance your application to exam questions, and help you improve your test-taking abilities.
We wish you great success for your Board Examinations in 2023 and hope this book helps
you achieve exemplary success.
Team Oswaal Books
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CBSE CIRCULAR 2022-23
dsUæh; ek/;fed f'k{kk cksMZ
CENTRAL BOARD OF SECONDARY EDUCATION
CBSE/DIR(ACAD)/2022/ Dated: 20.05.2022
Circular No. ACAD-57/2022
All Heads of schools affiliated to CBSE
Subject : Assessment and Evaluation Practices of the Board for the Session 2022-23
National Education Policy 2020 has affirmed the need to move from rote to competency-based learning. This will
equip the learners with key competencies to meet the challenges of the 21st century proactively. Accordingly, the
Board has taken multiple steps towards the implementation of Competency Based Education (CBE) in schools.
These range from aligning assessment to CBE, development of exemplar resources for teachers and students on
CBE pedagogy and assessment and continued teacher capacity building.
In this context the Board has released Circular No. Acad-05/2019 dated 18.01.2019; Circular No. Acad-11/2019 dated
06.03.2019; Circular No. Acad-18/2020 dated 16.03.2020; Circular No. Acad-32/2020 dated 14.05.2020 and Circular
No. Acad-31/2020 dated 22.04.2021. In continuation to these circulars, the Board is initiating further corresponding
changes in the Examination and Assessment practices for the year 2022-23 to align assessment to Competency
Based Education. Therefore, in the forthcoming sessions a greater number of Competency Based Questions or
questions that assess application of concepts in real-life/ unfamiliar situations will be part of the question paper.
The changes for classes IX-XII (2022-23) internal year-end/Board Examination are as detailed:
(Classes IX-X)
Year End (2021-22) (2022-23)
Examina- Existing Modified
tion/ Board (As per Special Scheme of Assessment for (Annual Scheme)
Examination Board Examination – Circular No. Acad-
(Theory) 51/2021 dated 05.07.2021)
Composition • Term I – Multiple Choice Question includ- • Competency Based Questions would be
ing case based and assertion reasoning type minimum 40%
MCQs – 100% (30% questions competency These can be in the form of Multiple Choice
based) Questions, Case based Questions, Source based
• Term II – Case based/ Situation based, Integrated Questions or any other types.
Open Ended- short answer/long answer • Objective Type Questions will be 20%
questions (30% questions competency based) • Remaining 40% short
Composition • Term I – Multiple Choice Question includ- • Competency Based Questions would be
ing case based and assertion reasoning type minimum 40%
MCQs – 100% (30% questions competency These can be in the form of Multiple Choice
based) Questions, Case based Questions, Source based
• Term II – Case based/ Situation based, Integrated Questions or any other types.
Open Ended- short answer/long answer • Objective Type Questions will be 20%
questions (30% questions competency based) • Remaining 40% short answer/long answer
questions (as per existing pattern)
Internal Assessment : No change Internal Assessment: End of year examination = 20:80
Year End Examination/ Board Examination (Theory)
Curriculum document released by the Board vide circular No.Acad-50/2022 dated 28th April, 2022 and
the forthcoming Sample Question Papers may be referred for the details of changes in the QP design
of individual subjects.

(Dr. Joseph Emmanuel)
Director (Academics)
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SYLLABUS
Latest Syllabus issued by CBSE for Academic Year 2022-23
MATHEMATICS (Code No. 041)
CLASS–XII
One Paper Max Marks : 80
No. Units No. of Periods Marks
I. Relations and Functions 30 08
II. Algebra 50 10
III. Calculus 80 35
IV. Vectors and Three - Dimensional Geometry 30 14
V. Linear Programming 20 05
VI. Probability 30 08
Total 240 80
Internal Assessment 20
Unit I : Relations and Functions
1. Relations and Functions : 15 Periods
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto
functions.
2. Inverse Trigonometric Functions 15 Periods
Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions.
Unit II : Algebra
1. Matrices 25 Periods
Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix,
symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and
multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication.
Oncommutativity of multiplication of matrices, and existence of non-zero matrices whose product is
the zero matrix (restrict to square matrices of order 2). Invertible matrices and proof of the uniqueness
of inverse, if it exists; (Here all matrices will have real entries).
2. Determinants 25 Periods
Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors and applications of determinants
in finding the area of a triangle. Adjoint and 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.
Unit III : Calculus
1. Continuity and Differentiability : 20 Periods
Continuity and differentiability, chain rule, derivative of inverse trigonometric functions, like sin–1 x,
cos–1 x and tan–1 x, derivative of implicit functions. Concept of exponential and logarithmic functions.
Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of
functions expressed in parametric forms. Second order derivatives.
2. Applications of Derivatives 10 Periods
Applications of derivatives: rate of change of bodies, increasing/decreasing functions, maxima and
minima (first 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).
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SYLLABUS
3. 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 types and problems based
on them.
dx dx dx dx dx
∫ ∫ ,∫ ,∫ ,∫
x2±a2 x2±a2 a2−x2 ax2+bx+c ax2+bx+c

px+q px+q
∫ dx, ∫ dx,∫ a2 ±x2dx,∫ x2 −a2dx
ax2 +bx+c ax2 +bx+c

∫ ax2 +bx+cdx,

Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation
of definite integrals.
4. Applications of the Integrals 15 Periods
Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in
standard form only).
5. Differential Equations 15 Periods
Definition, order and degree, general and particular solutions of a differential equation. Solution of
differential equations by method of separation of variables, solutions of homogeneous d ifferential
equations of first order and first degree. Solutions of linear differential equation of the type:
dy
+py=q, where p and q are functions of x or constants.
dx
dx
+px=q, where p and q are functions of y or constants.
dy
Unit-IV: Vectors and Three-Dimensional Geometry
1. 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, multiplication of a vector by a scalar,
position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation,
properties and application of scalar (dot) product of vectors, vector (cross) product of vectors.
2. Three - dimensional Geometry 15 Periods
Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector
equation of a line, skew lines, shortest distance between two lines. Angle between two lines.
Unit-V: Linear Programming
1. Linear Programming 20 Periods
Introduction, related terminology such as constraints, objective function, optimization, graphical method
of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded),
feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).
Unit-VI: Probability
1. Probability 30 Periods
Conditional probability, multiplication theorem on probability, independent events, total probability,
Bayes’ theorem, Random variable and its probability distribution, mean of random variable.
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