2nd Year Math Notes Mathematics 2nd Year All Chapter Notes-If you are a 2nd-year student and looking for 2nd Year Math Notes then you are at right place. These Mathematics-XII FSc Part 2 (2nd year) Notes are according to “Punjab Text Book Board, Lahore”.
Get NCERT solutions for Class 12 Maths free with videos. Solutions of all exercise questions, examples, miscellaneous exercise, supplementary exercise are given in an easy to understand way
- Home Easy Notes & MCQS Bsc Math Notes “Calculus” Solved Exercises. Easy Notes & MCQS; BSC & MSC Notes; Mathematics Notes; Bsc Math Notes “Calculus” Solved Exercises. Saweel ur Raheem. 2nd Year Complete Notes Chemistry with Solved Exercises.
- Mathematics Notes for 2nd Year for Federal Board (FBISE) Islamabad & Punjab Boards. A Complete Key Book in PDF Format for Class 12 (XII) / HSSC / Intermediate. These Notes Key Book, Guide & Handouts with solved exercises are as per latest syllabus.
The chapters and the topics in them are
- Chapter 1 Relation and Functions – Types of Relation - Reflexive, Symmetric, Transitive & Equivalence relation, Type of functions - One-one (injective), Onto (surjective) & Bijective, Composition of functions and Inverse of a function, Binary Operation - Commutative, Associative, Identity and Inverse.
- Chapter 2 Inverse Trigonometric Functions – Finding principle value, solving identities using properties
- Chapter 3 Matrices – Order of matrix, Types of matrices - Column matrix, Row matrix, Square matrix, Diagnol matrix, Scalar Matrix, Identity matrix, Equal matrices, Addition, Subtraction and Multiplication of matrices, Transpose of a Matrix, Symmetric, Skew Symmetric Matrices, Finding inverse of matrix by elementary operations
- Chapter 4 Determinants – Evaluating 2 x 2, 3 x 3 Determinant, Properties of Determinant, Area of triangle, Minors and Cofactors, Adjoint and inverse of matrix, Solution of system of linear equations using matrix method
- Chapter 5 Continuity and Differentiability – Finding whether function is continuous, composition of continuous functions is continuous, Finding Derivative using chain rules, logarithmic and exponential differentiation, Mean value of theorem, Rolle's Theorem.
- Chapter 6 Application of Derivatives – Finding rate of change, Increasing & decreasing functions, Point of Inflexion, Finding slope of tangent and normal, Finding approximate of functions and numbers, Finding maxima & minima using first derivative & second derivative test and Finding absolute maxima and minima
- Chapter 7 Integrals – Finding integration by substitution, trigonometric identities, Partial Fractions & using special formulas. Finding definite integrals as Limit as a Sum, Finding definite integral using indefinite integral and finding Definite Integral using properties
- Chapter 8 Application of Integrals – Finding area of region of simple curve, curve and line. Finding area between two curves.
- Chapter 9 Differential Equations – Degree and order of differential equations, General & Particular Solutions of Differential Equation, Forming differential equation when general solution is equation, Solving by variable separating, solving homogeneous differential equations, Linear Differential Equation
- Chapter 10 Vector Algebra – What is vector, Difference between vector and scalar, Types of vector - Unit vector, Equal vector, Addition of vectors, Components of vector, Scalar(Dot) product of vectors, Projection of vector on line, Vector (Cross) product of vectors, Finding area of parallelogram
- Chapter 11 Three Dimensional Geometry – Direction Ratio & Direction cosines of line, Finding equation of line - given point & parallel vector, though two points, Angle between two lines, Distance between two skew lines, Distance between two parallel lines, Finding equation of plane - normal form, perpendicular to given vector & passing through point, through 3 non-collinear points, intercept form, through two planes. Coplanarity of two planes, Angle between two planes, Distance between point and plane, Angle between Line & Plane
- Chapter 12 Linear Programming – Finding maximum or minimum value of Z using bounded or unbounded region of graphical inequality. Solving Diet, Manufacturing & Transport problems.
- Chapter 13 Probability – Conditional Probability, Multiplication Theorem of Probability, Independent events, Bayes Theorem, Random Variable & its Probability Distributions, Mean & Variance of Random Variable, Bernoulli Trials & Binomial Distribution
Each chapter is divided into two parts - Serial Order Wise and Concept Wise.
- In Serial Order Wise, the chapter is taught according to the NCERT Book with exercises, examples and miscellaneous. You should follow this when you are searching for a particular question
- In Concept Wise, we have divided the Chapter into topics. Concept is explained first, and then questions are ordered from easy to difficult. You should always follow this method to do the chapter. This is the Teachoo (टीचू) way of doing a chapter.
In addition to that, Important Questions are marked for your reference.
And, we have also solved Past Year Papers, and Sample Papers with step by step marking as well
Money pro: personal finance 2 0 1. Click on a Chapter below to begin
Notes (Solutions) of Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore.
There are seven units in this book and we have work hard to make easy and suitable solutions for students and teachers so that it help them learn things quickly and easily. Please click on a desire unit to view the solution of any particular exercise. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License or stated otherwise. To view PDF files, there must be PDF Reader (Viewer) installed on your PC or mobile or smartphone. It can be downloaded from Software section or a user viewing on Android Smartphone may consider EBookDroid to view PDF on their smartphone.
Formula pages
2nd Year Math
- Important Formulas Derivatives (by Ali Nawaz Bajwa (MS(Math), M.Ed.))
- Important Formulas Integration (by Ali Nawaz Bajwa (MS(Math), M.Ed.))