Karnataka PUC Board (KSEEB) Maths Class 12 Question Paper 2016

Here, let us have a look at the important concepts of the PYQP of KSEEB Maths 2016.

• Relations and Functions

• Types of relations.

• Types of functions.

• Binary operations.

• Inverse Trigonometric Functions

• Definition, range, domain, principal value branches.

• Properties and proofs of inverse trigonometric functions.

• Conversion of one inverse trigonometric function to another with respect to the right-angled triangle.

• Matrices

• Types of matrices.

• Algebra of matrices.

• Symmetric and skew-symmetric matrices and their properties.

• Concept of elementary row and column operations.

• Determinants

• Determinant of a square matrix and its Definition, expansion.

• Properties of determinants.

• Minors and cofactors of determinants.

• Finding the area of a triangle by using applications of determinants.

• Adjoint and inverse of a square matrix.

• Definition of singular and non-singular matrices and their properties.

• System of linear equations - Consistency, inconsistency and number of solutions.

• Solving system of linear equations in two and three variables using the inverse of a matrix.

• Continuity and Differentiability

• Continuity Definition.

• Continuity of a function on a domain and at a point.

• Algebra of continuous functions.

• Continuity of a composite function.

• Differentiability Definition.

• Theorem connecting differentiability and continuity.

• Concepts of exponential and logarithmic functions.

• Defining logarithms and their properties.

• Derivative of composite functions using the chain rule.

• Derivatives of inverse trigonometric functions.

• Derivative of implicit functions.

• Derivative of logarithmic functions.

• Derivative of functions expressed in parametric forms.

• Second-order derivatives.

• Rolle’s and Lagrange’s Mean Value Theorems.

• Applications of Derivatives

• Tangents and normal.

• Derivative as a Rate of change.

• Increasing and decreasing functions.

• Maxima and minima.

•  Integrals

• Methods of Integration.

• Integration by partial fractions.

• Integrals of some particular functions.

• Integration by parts.

• Definite integrals.

• Applications of the Integrals

• The area under the curve.

• The area bounded two curves.

• Differential Equations

• Definition of the differential equation.

• Order and degree.

• General and particular solutions of a differential equation

• Formation of the differential equation.

• Solving the differential equations by the method of separation of variables.

• Solving the first order and first-degree Homogeneous differential equations.

• Solutions of linear differential equations.

• Vector Algebra

• Definition of Vectors and Scalars.

• Magnitude and direction of a vector.

• Direction cosines and ratios of vectors.

• Types of vectors.

• Components of a vector.

• Algebra of vectors.

• Scalar or dot product of vectors.

• Vector or cross product of vectors.

• Scalar triple product

• Three-Dimensional Geometry

• Straight lines in space.

• Cartesian and vector equation of a line.

• Coplanar and skew lines.

• Distance between two skew lines.

• Distance between two parallel lines.

• The angle between the two lines.

• Cartesian and vector equation of a plane in normal form.

• Equation of a plane that passes through the point and is perpendicular to the vector.

• Equation of a plane that passes through three non-collinear points.

• The equation of a plane and its intercept form.

• The angle between two planes.

• Equation of plane when passing through the intersection of two given planes.

• Finding the angle between line and plane.

• Condition for the coplanarity of two lines.

• Distance of a point from a plane.

• Linear Programming

• Introduction of L.P.P.

• Definition of constraints.

• Objective function.

• Optimization.

• Constraint equations.

• Non-negativity restrictions.

• Feasible and infeasible region.

• Feasible solutions.

• The mathematical formulation of L.P.P. 

• Different types of L.P.P.

• Diet and allocation problems with bounded feasible regions.

• Graphical solutions for the problem in two variables.

• Optimum feasible solution.

• Probability

• Conditional probability definition and their properties.

• Multiplication theorem.

• Independent events.

• Bayes theorem.

• The theorem of total probability.

• Definition of a random variable.

• Probability distribution of a random variable.

• Mean, the variance of a random variable.

PYQP of KSEEB Maths 2016

Let us look at the design of the KSEEB Previous Year Question Paper Class 12 Maths 2016.

The question types in the PYQP is classified based on three levels of difficulty. Easy questions carry 35% of the total weightage and moderate questions carry 55% and the remaining 10% of questions are of difficult level.

Now let us see the breakage of marks for each chapter.

• Relations and Functions - 11 marks

• Inverse Trigonometric Functions - 8 marks

• Matrices - 9 marks

• Determinants - 12 marks

• Continuity and Differentiability - 20 marks

• Applications of Derivatives - 10 marks

• Differential Equations - 10 marks

• Vector Algebra - 11 marks

• Three-Dimensional Geometry - 11 marks 

• Linear Programming - 7 marks

• Probability - 11 marks

Coming to the pattern of the PYQP of KSEEB Maths 2016 there will be five parts to the question paper.

• The first part called as ‘A’ part is a one mark question that has 10 questions and all are compulsory to be answered.

• The second part called as ‘B’ part is two mark questions that have 14 questions and all are compulsory to be answered. 

• The third part called the ‘C’ part is three mark questions that have 14 questions and all are compulsory to be answered.

• The fourth part called the ‘D’ part is five mark questions that have 10 questions and any of the six questions can be answered.

• The fifth part called the ‘E’ part is ten mark questions that have 2 questions and any of the one questions can be answered. This part has 2 subparts in which there will be two questions of 4 marks and 6 marks respectively.

KSEEB Previous Year Question Paper Class 12 Maths 2016 - Tips and Guidelines

In this section, we will discuss the examination preparation tips and guidelines by using the PYQP of KSEEB Maths 2016.

• Before attempting the questions of Class 12 revise all the basic concepts studied in Class 11 as most of the concepts are carried from Class 11 to Class 12.

• Make a list of all the important formulas that are useful in answering the questions of Class 12 Maths.

• When studying through the PYQP try to take a break after every chapter so that you can be refreshed and calm before attempting the new chapter.

• Make a timetable on when to study and how to study. Make a list of the topics of high priority to be revised as many times as possible as these topics carry a huge percentage of marks in exams.

• If you are fuzzy about some concepts make sure to clear all the doubts and revise as many times as possible before the exams.

• After studying, take a mock test using the KSEEB class 12 Maths 2016 PYQP and test your knowledge.

• Time management is one of the most important skills while attempting the KSEEB Previous Year Question Paper Class 12 Maths 2016. So make sure that you are preparing for exams in such a way that you can answer all the questions in a given amount of time.

Conclusion

The KSEEB class 12 Maths 2016 PYQP will help students to revise all the important concepts before their board exams in a quick way. The solutions to PYQP of KSEEB Maths 2016 are prepared by the experts in a detailed manner to help students to revise the concepts clearly without any doubts before their exams. The PDF of KSEEB Previous Year Question Paper Class 12 Maths 2016 is available completely free on the Vedantu platform which can be downloaded easily by the students to prepare for their exams.