Karnataka Board Class 12 Maths Syllabus
Karnataka PUC Board (KSEEB) Class 12 Mathematics Syllabus – Latest 2022-2023
Karnataka PUC Board releases KSEEB Class 12 Mathematics Syllabus for the students ready to enhance their knowledge in advanced topics in their stream of study. The education board regulates and designs the entire KSEEB syllabus and offers students a comprehensive learning experience. The syllabus covers essential aspects and provides the utmost details in easy-to-understand language. It is not easy to breeze through mathematically complex topics, but with our dedicated efforts to make learning easy, we provide students with the Karnataka PUC Board Class 12 Mathematics Syllabus.
Mathematics as a subject teaches students various topics. Some of the topics are – Number System, Algebra, Arithmetic, Geometry and Modern Mathematics. The syllabus contains all important mathematical concepts that help students in their exam preparations. The KSEEB Class 12 Mathematics Syllabus provides learning details through various sources such as the KSEEB syllabus, sample paper, and past year question papers. To prepare well for competitive exams, students should build a strong fundamental base and practice the previously known topics involving various theorems, formulas and equations .
KSEEB Class 12 Mathematics Syllabus will provide students with all the relevant information in the curriculum, which will prepare them for the upcoming exams. Just going through the syllabus will not be enough to score better marks in the exams. They are required to solve examples and problems based on the chapters. Therefore, students can refer to the KSEEB sample question papers and KSEEB past years’ question papers.
Karnataka Board (KSEEB) Mathematics Syllabus for Class 12 – Free PDF Download
KSEEB Class 12 Mathematics Syllabus is meant to cater to the specific need of higher education in Karnataka. The initial step is to provide a comprehensive learning experience of enhanced versions. The education board is committed to ensuring that students of Class 12 will get to understand more complex engineering and technology topics with ease.
The board wants to make sure that the students have all the necessary concepts for required education courses; a cursory glance at the Class 12 Mathematics syllabus shows that both pure and applied mathematics are given equal weightage. Mathematics is given a prime importance in the syllabus by employing different techniques to explain it. The board also insists on having two questions for mathematics as part of the general examination for each subject. This makes students acquainted with mathematical theories, concepts and methods used in various disciplines.
KSEEB Class 12 Mathematics syllabus comprises topics like Number System, Algebra, Trigonometry, Coordinate Geometry and Calculus of One Variable. It also covers topics such as the Approximate Solution of a Polynomial Equation etc. Further, the board gives equal importance to both topics and assigns the same number of marks. Mathematics is taught in a simplified manner which makes it easier for students to understand it.
Extramarks provides students a joyful learning experience and encourages them to be curious and look for answers themselves. Students would be able to glance through the syllabus quickly and know which new topics have been added and the ones which have been dropped. This will definitely help them to follow the systematic approach and regular practice to master the topic.To make sure that the syllabus for Mathematics for Class 12 is relevant and up-to-date, the education board has ensured that only topics already in practice are included. Therefore, students can directly access the course material by clicking on the link mentioned below:
Karnataka PUC Board (KSEEB) Mathematics Syllabus for Class 12
KSEEB Class 12 Mathematics Syllabus teaches students the basics of various subjects such as Geometry, Algebra and Trigonometry. The content also focuses on concepts related to Calculus, graphs and the study of trigonometric equations. KSEEB Mathematics Sample Paper helps candidates understand the format of the paper they will face in the exam. . Further, students learn the guidelines given by Karnataka Secondary Education Examination Board (KSEEB) to score good grades in the examination.
Karnataka SSLC Examination Board has released the Mathematics syllabus, sample papers, past year question papers and other relevant information. KSEEB Mathematics Sample Paper is available for students preparing for their Class 12 board exams in Mathematics planning to take the KSEEB exam. The syllabus will help them to score better in the exams and to build a strong foundation in the subject.
Mathematics is a scoring subject, and students must know the chapters in detail. Thus, the following is the list of the chapters and their topics given in detail:
|Chapter No.||Name of the Chapter|
|1||Relations and Functions|
|2||Inverse Trigonometric Functions|
|5||Continuity and Differentiability|
|6||Applications of Derivatives|
|8||Applications of the Integrals|
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|I. Relations and Function 1.1 to 1.3
(Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions.)
2. Inverse Trigonometric Functions 2.1
(Definition, range, domain, principal value branch.)
|3. Matrices 3.1 to 3.6|
|(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. Noncommutativity of multiplication of matrices, Invertible matrices; (Here all matrices will have real entries)
|4. Determinants 4.1, 4.2, 4.4 to 4.7|
|(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. Solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.)
|5.Continuity and Differentiability 5.1to 5.4
(Limits and Derivatives first PUC revision 2 hours)
(Continuity and differentiability, derivative of composite functions, chain rule, derivative of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions.)
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|5. Continuity and Differentiability 5.5, 5.6 and 5.7
(Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives)
6. Applications of Derivatives 6.3 to 6.6
(increasing/decreasing functions, tangents and normals, 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 reallife situations)
7. Integrals 7.1 to 7.6
(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
1 1 1 1 1 1
types∫ 𝑑𝑥, ∫ 𝑑𝑥, ∫ 𝑑𝑥, ∫ 𝑑𝑥, ∫ 𝑑𝑥, ∫ 𝑑𝑥,
𝑎2+ 𝑥2 𝑎2−𝑥2 𝑥2−𝑎2 √𝑥2−𝑎2 √𝑥2+𝑎2 √𝑎2−𝑥2
and problems based on them. )
12. Linear Programming
(Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems. Graphical method of solution for problems in two variables, feasible and infeasible regions (bounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).
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|7. Integrals 7.7 to 7.10
Fundamental Theorem of Calculus (without proof).Basic properties of definite integrals and evaluation of definite integrals.
8. Applications of the Integrals 8.1
|Applications in finding the area under simple curves, especially lines,
parabolas; area of circles /ellipses (in standard form only) (the region should be clearly identifiable)
|9. Differential Equations 9.1 ot 9.3,9.5|
|(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 differential equations of first order and first degree of the type: 𝑑𝑦/𝑑𝑥 = f(y/x). Solutions of linear differential equation of the type: dy/ dx + py = q, where p and q are functions of x or constant.)
|10. Vector 10.110.6|
|(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)
|11. Three – dimensional Geometry|
|(Direction cosines and direction ratios of a line joining two points. Cartesian
equation and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane.
Distance of a point from a plane.)
|(Conditional probability, multiplication theorem on probability, independent
events, total probability, Bayes’ theorem, Random variable and its probability distribution.)
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|1. Relations and Functions
(Composite functions, Invertible functions and Binary operations)
2. Inverse Trigonometric Functions
(Properties of Inverse trigonometric functions and problems)
(Inverse of a matrix by elementary operations)
(Properties of Determinants and problems)
5. Continuity and Differentiability
(Mean Value Theorem andRolle’s Theorem)
6. Application of Derivatives
(Rate of change of quantities and Approximation) 7.Integration
( Definite integral as alimit of a sum)
8. Application of Integrals
(Area bounded by curve and line Area between two curves) 9.Differential Equation
(Formation of a Differential Equation whose General Solution is given. Solution of Linear differential equation of the type dx/dy +py=q)
(Scalar triple product of three vectors and problems)
11. Three Dimensional Geometry
(Angle between two lines, Angle between two planes and Angle between line and planes)
(Mean and Variance of a Random variable. Bernoulli Trials an Binomial Distribution)
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FAQs (Frequently Asked Questions)
1. What is the overall KSEEB Class 12 Mathematics Syllabus?
KSEEB Class 12 Mathematics Syllabus includes Arithmetics, Modern Mathematics, Algebra, and Geometry. It allows students to explore from Vedic to commercial Mathematics. Students are required to practise regularly and revise the concepts. In the syllabus, there will be a lot of different types of numerical and derivations that will be difficult to understand. Further, students can get the KSEEB sample papers and KSEEB past years question papers.
2. Where can I access the complete Mathematics syllabus for Class 12?
KSEEB Class 12 Mathematics Syllabus covers Algebra, Algebraic Operations on Numbers, Systematic Arithmetic Progression, Ratio and Proportion, HCF and LCM of Numbers, Histogram and Frequency Table. Mathematics Syllabus also covers the concepts of Functions in Differential Calculus – Limits & Derivatives. By visiting our website, students can get more information about the KSEEB Syllabus. Therefore the students need to go through each chapter and concept. So it’s important to get hold of the syllabus and prepare for the board examinations accordingly.
3. How to score better marks in Mathematics?
In Mathematics, students should have a clear understanding of the concepts. They should understand each and every topic in Mathematics. They should also start solving the examples which are provided on our website. It will help them to solve questions with varying levels of difficulty. This way, they can solve any questions asked in the examination confidently. KSEEB Class 12 Mathematics syllabus covers three main sections: Pure Mathematics, Algebra and Calculus & Trigonometry. Further, students can refer to the past years’ question papers and sample papers. In case students require any assistance or support, they can always visit Extramarks website to download the latest syllabus and also explore the repository of study material available at Extramarks to step up their preparation and create their own milestones in the process.