7th EDITION YEAR 2021-22

ISBN SYLLABUS COVERED

"978-93-5550-469-2"

DEPARTMENT OF PRE UNIVERSITY DEPARTMENT, KARNATAKA

PUBLISHED BY OSWAAL BOOKS & LEARNING PVT. LTD.

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D ISCL AIMER Oswaal Books has exercised due care and caution in collecting all the data before publishing this book. In spite of this, if any omission, inaccuracy or printing error occurs with regard to the data contained in this book, Oswaal Books will not be held responsible or liable. Oswaal Books will be grateful if you could point out any such error or offer your suggestions which will be of great help for other readers. Printed at Repro India Ltd. ( ii )

( iv )

CONTENTS

l Syllabus & Blueprint vii l II PUC Solved Paper 2020 with Scheme of Valuation xxvi l II PUC Toppers’ Answers 2019 3 l II PUC Solved Paper 2019 with Scheme of Valuation 28 l II PUC Model Paper –1 (Issued by PUE Board in Sep. 2018) 66 l II PUC Model Paper –2 (Issued by PUE Board in Sep. 2018) 78 l II PUC Model Paper –3 (Issued by PUE Board in Sep. 2018) 90 l Toppers’ Answers, March-2018 104 l Solved Paper –July 2017 129 q On Tips Notes q Sample Question Papers (Solved)

1 - 32

Sample Question Paper - 1 (Examination Paper, March 2017) with Scheme of Valuation 2017 Sample Question Paper - 2 (Examination Paper, March 2016) with Toppers’ Answers Sample Question Paper - 3 (Issued by Department of PUE Karnataka) Sample Question Paper - 4 (Issued by Department of PUE Karnataka) Sample Question Paper - 5 (Issued by Department of PUE Karnataka)

q Sample Question Papers (Self Assessment) Sample Question Paper - 6 Sample Question Paper - 7 Sample Question Paper - 8 Sample Question Paper - 9 Sample Question Paper - 10

33 - 54 55 - 80 81 - 84 85 - 87 88 - 91 92 - 95 96 - 99 100 - 102 103 - 106 107 - 110

q Solutions

Sample Question Paper - 3 Sample Question Paper - 4 Sample Question Paper - 5

111 - 122 123 - 132 133 - 144

 

For Solved Paper Physics

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(v)

( vi )

( vii )

06-May-18 7-May-18

08-May-18

9-May-18 10-May-18

11-May-18

12-May-18 13-May-18 14-May-18

DAY 7

DAY 8 DAY 9

DAY 10

DAY 11 DAY 12 DAY 13

04-May-18

DAY 3

DAY 5 DAY 6

3-May-18

DAY 2

5-May-18

DATE 02-May-18

DAY DAY 1

DAY 4

Column2 CLASS II PUC

Column1 SUBJECT MATHEMATICS

SATURDAY SUNDAY MONDAY

FRIDAY

WEDNESDAY THURSDAY

TUESDAY

SUNDAY MONDAY

SATURDAY

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THURSDAY

DAY WEDNESDAY

Column3 CODE 35

Column42

Composite functions definition gof, fog and properties Invertible functions definition and properties

Functions definitions and types of functions one-one, on-to, in-to, many-one and bijective functions along with number of examples and digramatic representation

CHAPTER 1 : RELATIONS AND FUNCTIONS : Recapitulation of I PU Sets Relations and Functions Types of Relations Definitions along with examples Reflexive, Symmetric, Transitive and Equivalence Relations Definitions along with examples

Problems on invertible functions carrying 5 marks.

Problems on types of relations carrying 1, 2 and 3 marks.

Problems on Equivalence relations and others carrying 1, 2 and 3 marks.

PUC (4 THEORY + 2 PROBLEM PROBLEM CLASSES/ CLASSES A WEEK) PRACTICE SESSIONS

Column4 DEPARTMENT OF P U EDUCATION

Column5 ACADEMIC PROGRAM

(Issued by Department of PUE, Karnataka) BLOW UP SYLLABUS II PUC MATHEMATICS - Code No. 35

Latest Syllabus

Column6

( viii )

15-May-18

16-May-18

17-May-18

18-May-18

19-May-18

20-May-18 21-May-18

22-May-18

23-May-18

24-May-18

25-May-18

26-May-18

27-May-18 28-May-18

29-May-18

30-May-18

DAY 14

DAY 15

DAY 16

DAY 17

DAY 18

DAY 19 DAY 20

DAY 21

DAY 22

DAY 23

DAY 24

DAY 25

DAY 26 DAY 27

DAY 28

DAY 29

WEDNESDAY

TUESDAY

SUNDAY MONDAY

SATURDAY

FRIDAY

THURSDAY

WEDNESDAY

TUESDAY

SUNDAY MONDAY

SATURDAY

FRIDAY

THURSDAY

WEDNESDAY

TUESDAY

Properties of addition and multiplication of matrices

Types of matrices, operation on matrices Addition and Subtraction Multiplication of matrices

CHAPTER 3 : MATRICES : Introduction and definition a brief biographical information may be given about the mathematicians like Cayley, J J Sylvester, Hamilton and others may be given

± Standard results like tan–1(x) tan–1(y)=tan–1 (x ± y/1 – xy) and others Solving inverse trigonometric equations involving tan–1, sin–1 and cos–1.

CHAPTER 2 : INVERSE TRIGONOMETRIC FUNCTIONS : recapitulation of range and domain of trigonometric functions. Inverse Trigonometric functions definition range and domain of inverse trigonometric functions with their graphs Properties of inverse trigonometric functions like sin-1(x)+ cos–1(x) = p/2 and sin–1 (1/x) = cosec–1 (1/x) and others—

Binary operation definition and properties like commutative, associative, identity and inverse

Harder types of problems on expressing inverse trigonometric functions into simplest form Miscellaneous problems on Inverse trigonometric functions

Problems on principal value and properties carrying 1, 2 and 3 marks

Problems on binary operation carrying 1, 2, and 3 marks.

DAY 36

DAY 35

DAY 34

DAY 33

DAY 32

DAY 31

DAY 30

6-Jun-18

05-Jun-18

4-Jun-18

03-Jun-18

2-Jun-18

01-Jun-18

31-May-18

THURSDAY

WEDNESDAY

TUESDAY

MONDAY

SUNDAY

SATURDAY

FRIDAY

THURSDAY

FRIDAY

07-Jun-18

8-Jun-18

DAY 37

DAY 38

SUNDAY

SATURDAY

10-Jun-18

MONDAY

09-Jun-18

DAY 40 11-Jun-18

DAY 39

DAY 41

TUESDAY WEDNESDAY

12-Jun-18 13-Jun-18

DAY 42 DAY 43

Invertible matrix and finding inverse by elementary row and column operations Symmetric and Skew symmetric matricesdefinition, theorems and related problems carrying 1, 2 and 3 marks CHAPTER-4 : DETERMINANTS : Definition of 2nd and 3rd order determinant and some simple problems to understand the definition Verification of the properties of determinants for third order determinant-first 4 Verification of the properties of determinants for third order determinant - 5 and 6 and simple problems to illustrate the properties

Applications of determinants: Area of triangle and finding the equation of the line passing through two points and related problems (carrying 2 marks) Minors and cofactors, adjoint of a matrix and verification of A.adj A = adj A.A = |A| for both 2×2 and 3×3 matrices Theorems on inverse of a square matrix - 1, 2 and 3 statement only, Theorem-4 statement and proof

Problems on order of a matrix, operations on matrices and types of matrices carrying 1, 2 and 3 marks Problems carrying 5 marks on algebra of matrices

problems on properties of determinants carrying 1, 2 and 4 marks

Problems on finding the inverse, |adjA|, |A-1| carrying 1, 2 and 3 marks

( ix )

(x)

27-Jun-18

28-Jun-18

29-Jun-18

DAY 57

DAY 58

DAY 59

22-Jun-18

DAY 52

26-Jun-18

21-Jun-18

DAY 51

DAY 56

20-Jun-18

DAY 50

25-Jun-18

19-Jun-18

DAY 49

24-Jun-18

18-Jun-18

DAY 48

DAY 55

17-Jun-18

DAY 47

DAY 54

16-Jun-18

DAY 46

23-Jun-18

15-Jun-18

DAY 45

DAY 53

14-Jun-18

DAY 44

FRIDAY

THURSDAY

WEDNESDAY

TUESDAY

MONDAY

SUNDAY

SATURDAY

FRIDAY

THURSDAY

WEDNESDAY

TUESDAY

MONDAY

SUNDAY

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Differentiability : Definition and theorem on differentiability statement and proof

Continuity of greatest integer function, signum function, modulus function along with graph Algebra of continuous functions and continuity of composite functions

CHAPTER-5 : CONTINUITY AND DIFFERENTIABILITY : Recapitulation of limit of a function along with some simple problems Continuity : Definitions (at a point, in an interval and in the domain of a function) along with graphical representation of continuity of a function

RAMZAN

Solving the system of linear equations by matrix method in two and three unknowns, by checking the consistancy.

Problems on Algebra of continuous functions and continuity of composite functions carrying 1, 2 and 3 marks Problems on continuity of a function carrying 4 marks

Problems on proving continuity of split functions, an algebraic function, trigonometric functions

Problems on properties of determinants harder cases Miscellaneous exercise problems Miscellaneous exercise problems

Problems on matrix method carrying 5 marks along with word problems

( xi )

14-Jul-18

15-Jul-18

DAY 75

09-Jul-18

DAY 69

DAY 74

8-Jul-18

DAY 68

13-Jul-18

07-Jul-18

DAY 67

DAY 73

6-Jul-18

DAY 66

12-Jul-18

05-Jul-18

DAY 65

DAY 72

4-Jul-18

DAY 64

11-Jul-18

03-Jul-18

DAY 63

DAY 71

2-Jul-18

DAY 62

10-Jul-18

01-Jul-18

DAY 61

DAY 70

30-Jun-18

DAY 60

SUNDAY

SATURDAY

FRIDAY

THURSDAY

WEDNESDAY

TUESDAY

MONDAY

SUNDAY

SATURDAY

FRIDAY

THURSDAY

WEDNESDAY

TUESDAY

MONDAY

SUNDAY

SATURDAY

CHAPTER-6 : APPLICATION DERIVATIVES : Introduction derivative as a rate measure recapitulation of areas and volumes 3-D figures

OF and and 2-D,

Rolles theorem and Mean value theorem statement, geometrical interpretation and problems

Derivative of implicit functions and related problems Derivative of inverse trigonometric functions and related problems Derivative of parametric functions and related problems Exponential and Logarithnic functions domain, range and their graphs, Laws of Logarithms Logarithmic differentiation and related problems Second order derivatives introduction and simple problems

Derivative of composite functions by chain rule and related problems

Cone problem, ladder problem, shadow problem and other problems relate to rate measure carrying 5 marks

Derivative of a determinant, proving sin (x + y) using derivatives Miscellaneous exercise problems on continuity differentiation

Standard problems and harder cases on second order derivatives carrying 5 marks

( xii )

30-Jul-18

31-Jul-18

1-Aug-18

02-Aug-18

DAY 91

DAY 92

DAY 93

25-Jul-18

DAY 85

DAY 90

24-Jul-18

DAY 84

29-Jul-18

23-Jul-18

DAY 83

DAY 89

22-Jul-18

DAY 82

28-Jul-18

21-Jul-18

DAY 81

DAY 88

20-Jul-18

DAY 80

27-Jul-18

19-Jul-18

DAY 79

DAY 87

18-Jul-18

DAY 78

26-Jul-18

17-Jul-18

DAY 77

DAY 86

16-Jul-18

DAY 76

THURSDAY

WEDNESDAY

TUESDAY

MONDAY

SUNDAY

SATURDAY

FRIDAY

THURSDAY

WEDNESDAY

TUESDAY

MONDAY

SUNDAY

SATURDAY

FRIDAY

THURSDAY

WEDNESDAY

TUESDAY

MONDAY

Methods of Integration : Substitution, Using trigonometric identities

Comparision of Integration and differentiation and some problems carrying 1 and 2 marks

Tangents and Normals, Angle between the curves and related problems Errors and Approximations and problems carrying 2 and 3 marks Maxima and Minima introduction and problems carrying 2 and 3 marks Global maximum and Global minimum and problems carrying 2 and 3 marks CHAPTER-7 : INTEGRALS : Integration is the Inverse process of differentiation, arbitrary constant, symbol and integral constant List of standard integrals, properties of indefinite integrals and geometrical interpretation of integrals

1st test

1st test

1st test

Increasing and Decreasing functions : definitions and illustrations along with graphical representations Theorem on Increasing and Decreasing functions statement and proof

Problems on substitution carrying 1, 2 and 3 marks

Problems on standard integrals carrying 1, 2 and 3 marks

Varieties of problems on Increasing and Decreasing functions carrying 2 and 3 marks 1 TEST

( xiii )

3-Aug-18

04-Aug-18

5-Aug-18

06-Aug-18

7-Aug-18

08-Aug-18

9-Aug-18

10-Aug-18

11-Aug-18

12-Aug-18

13-Aug-18

14-Aug-18

15-Aug-18

16-Aug-18

17-Aug-18

18-Aug-18

19-Aug-18

20-Aug-18

DAY 94

DAY 95

DAY 96

DAY 97

DAY 98

DAY 99

DAY 100

DAY 101

DAY 102

DAY 103

DAY 104

DAY 105

DAY 106

DAY 107

DAY 108

DAY 109

DAY 110

DAY 111

MONDAY

SUNDAY

SATURDAY

FRIDAY

THURSDAY

WEDNESDAY

TUESDAY

MONDAY

SUNDAY

SATURDAY

FRIDAY

THURSDAY

WEDNESDAY

TUESDAY

MONDAY

SUNDAY

SATURDAY

FRIDAY

Properties of definite Integals : P0, P1, P2, P3 statement and proof P4, P5, P6, P7 statement and proof

Integrals of the form ex [f(x) + f1(x)] and relate problems, Definite integrals as limit of sum and related problems Definite integrals : Definition and related problems to illustrate this INDEPENDENCE DAY

Integration by partial fractions and related problems carrying 2 and 3 marks Integration by parts and three standard derivations

Integration by completing squares and integrals of the form Px + Q/ax2 + bx + c or square root of ax2 + bx + c

Integration by using standard substitutions all the six derivations

Miscellaneous exercise problems on chapter-7 carrying 1, 2, 3 and 6 marks

Problems on properties of carrying 2, 3 and 6 marks

Problems on integration by parts and standard derivations involving the proof of the derivations, carrying 5 marks

Problems on the two methods carrying 2 and 3 marks

Problems on standard substitutions involving the proof of the derivations, carrying 5 marks

Problems on trigonometric identities carrying 1, 2 and 3 marks

( xiv )

21-Aug-18

22-Aug-18

23-Aug-18

24-Aug-18

25-Aug-18

26-Aug-18

27-Aug-18

28-Aug-18

29-Aug-18

30-Aug-18

31-Aug-18

01-Sep-18

2-Sep-18

03-Sep-18

4-Sep-18

DAY 112

DAY 113

DAY 114

DAY 115

DAY 116

DAY 117

DAY 118

DAY 119

DAY 120

DAY 121

DAY 122

DAY 123

DAY 124

DAY 125

DAY 126

TUESDAY

MONDAY

SUNDAY

SATURDAY

FRIDAY

THURSDAY

WEDNESDAY

TUESDAY

MONDAY

SUNDAY

SATURDAY

FRIDAY

THURSDAY

WEDNESDAY

TUESDAY

Formation of a differential Equation : i) when the solution is given ii) Word problems, carrying 2 and 3 marks Methods of solving a differential equation : First order, first Degree : variable seperable form carrying 3 and 5 marks

CHAPTER-9 : DIFFERENTIAL EQUATIONS : Introduction, Definition, Basic concepts, Types of differential equations, Order and Degree of a differential equation and related problems carrying 1, 2 and 3 marks Solution of a differential equation : General and particular solution and problems on verifying the solution of the differential equation carrying 1 and 2 marks

Area between two curves iii) circle and a circle carrying 5 marks Area of a triangle carrying 5 marks

Area bounded i) by a curve and a line and related problems carrying 3 and 5 marks Area bounded by ii) a circle iii) an ellipse, Area between two curves i) parabola and a parabola carrying 5 marks Area between two curves ii) circle and a parabola carrying 5 marks

CHAPTER-8: APPLICATION ON INTEGRATION : Fundamental theorems of Calculus 1 and 2 statement only and definite integral as area under the curve introduction and problems to illustrate this BAKRID

Miscellaneous exercise problems carrying 3 and 5 marks Problems involving inequalities carrying 5 marks

( xv )

12-Sep-18

13-Sep-18

14-Sep-18

15-Sep-18

16-Sep-18

17-Sep-18

18-Sep-18

19-Sep-18

20-Sep-18

21-Sep-18

22-Sep-18

23-Sep-18

24-Sep-18

DAY 134

DAY 135

DAY 136

DAY 137

DAY 138

DAY 139

DAY 140

DAY 141

DAY 142

DAY 143

DAY 144

DAY 145

DAY 146

09-Sep-18

DAY 131

11-Sep-18

8-Sep-18

DAY 130

DAY 133

07-Sep-18

DAY 129

10-Sep-18

6-Sep-18

DAY 128

DAY 132

05-Sep-18

DAY 127

MONDAY

SUNDAY

SATURDAY

FRIDAY

THURSDAY

WEDNESDAY

TUESDAY

MONDAY

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WEDNESDAY

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MONDAY

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WEDNESDAY

LAST DAY OF MOHARRUM

MID TERM EXAMINATION

MID TERM EXAMINATION

MID TERM EXAMINATION

MID TERM EXAMINATION

MID TERM EXAMINATION

MID TERM EXAMINATION

GANESH CHATURTHI

MID TERM EXAMINATION

MID TERM EXAMINATION

MID TERM EXAMINATION

Linear differential equations : (i) dy/dx + Py = Q (ii) dx/dy + P1 = Q1, finding the integrating factor and solution; Finding the general and particular solution of linear differential equations (in two forms) carrying 5 marks

Homegeneous differential equations : Definition, problems on solution of homegeneous differential equations (in two forms) carrying 3 marks

Word problems, miscellaneous exercise problems on LDE

Word problems, miscellaneous exercise problems on LDE

Finding the general and particular solution of homogeneous differential equations (in two forms)

Harder cases of finding the general and particular solution of first order, first degree differential equations in variable seperable form

MID TERM