Notes of FSc Part 2 of 'A Textbook of Mathematics For Class XII' published by Khyber Pakhtunkhwa Textbook Board, Peshawar. We are posting the notes chapter-wise. These notes are shared as open educational resources. This page will be continuously updated.
Key Features of our 2nd Year Math Notes We uploaded the best quality FA / FSC Part 2 Math notes that cover the requirements of the new syllabus of all Punjab boards. As these notes are in the best format so that you can print them and prepare yourself for exams. 2nd Year All Subjects Notes in PDF. In this online lecture,Muhammad Naveed Jaffar explains FSC part 2 Mathematics Chapter 1 Functions and Limits.The topic being discussed is Topic Exercise 1.1.
Author: | Muhammad Ashfaq |
---|---|
Type: | Solutions only |
Sender: | Muhammad Marwan |
Format: | PDF Scanned (Handwritten) |
Unit 01: Functions and Limits
Objectives
After reading this unit the students will be able to:
- identify the domain and range of a functions through graphs.
- draw the graph of modulus function and identify its domain and range.
- recognize the composition of a function and then to find out the composition of two functions.
- describe the inverse of a function and then to find out the inverse of composition of two functions.
- recognize the algebraic and transcendental functions as well as the concepts of explicit, implicit and parametric functions.
- display graphically the explicit, implicit and parametric functions as well as the compound functions.
- introduce the limit of a function with respect to real number intervals on the real number line, the open and closed intervals and its location on a real number line.
- explain the meaning of x tends to zero, x tends to a and x tends to infinity
- define the limit of a sequence when the limit of a sequence with nth term is given.
- define the limit of a function and the statement of theorems on limits of sum, difference, product and quotient of functions.
- evaluate the limits of a function in case of some special functions.
- evaluate the limit of algebraic, exponential and trigonometric functions.
- introduce the continuous and discontinuous functions.
- recognize the left hand and right hand limits through examples.
- define the continuity of a function at a point and in an interval.
- test the continuity and discontinuity of a function a point and in an interval.
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Unit 02: Differentiation
Objectives
After reading this unit the students will be able to:
- distinguish between independent and dependent variables.
- estimate the change in the dependent variable, when the independent variable is incremented or decremented.
- define the derivative of a function as an instantaneous rate of change of variable with respect to another variable.
- define derivative or differential coefficient of a function.
- differentiate $y=x^n$ and $y=(ax+b)^n$ by first principle rule.
- introduce the theorems of differentiation, such as the derivative of a constant function, the derivative of any constant multiple of a function, the derivative of a sum or difference of two functions, the derivative of the product of two functions and the derivative of a quotient of two functions.
- apply theorems of differentiation in solving problems.
- introduce chain rule of differentiation in different situations.
- introduce implicit differentiation of a function.
- introduce differentiation of trigonometric and inverse trigonometric functions.
- introduce differentiation of exponential and logarithmic functions.
- introduce the differentiation of hyperbolic and inverse hyperbolic functions.
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Unit 03: Higher Order Derivative and Application
Objectives
After reading this unit the students will be able to:
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Unit 04: Differentiation of Vector Functions
Objectives
After reading this unit the students will be able to:
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Unit 05: Integration
Objectives
After reading this unit the students will be able to:
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Unit 09: Integration
Objectives
This unit tells us, how to:
- define the differential equation, its order, degree, general and particular solutions, and its identification as linear and nonlinear ordinary differential equations.
- demonstrate the concept in forming a differential equation.
- solve the first order linear and nonlinear ordinary differential equations by separable variable form, and homogenuous form and then how to reduce differential equations in standard form of homogenuous.
- solve the real life problems related to differential equations.
- define the orthogonal trajectories and then how to show the orthogonal trajectories of the two families of curve.
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Mathematics 1st Year All Chapter Notes | Math FSc Part 1
'Class 11 Mathematics Notes'
Mathematics-XI (Punjab Text Book Board, Lahore)
These Mathematics-XI FSc Part 1 (1st year) Notes are according to 'Punjab Text Book Board, Lahore'. Very helpful notes for the students of 1st year to prepare their paper of Maths according to syllabus given by Federal Board of Intermediate and Secondary Education (FBISE), Faisalabad Board, Multan Board, Sargodha Board, DG Khan Board, Gujranwala Board, Rawalpindi Board or others board of Punjab, Pakistan. These 11 Class Math Notes are obtained from mathcity.org.
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2nd Year Chemistry Notes
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Chapter # 1 Numbers Systems
Exercise 1.1 (Handwritten) | View Online | Download PDF |
Exercise 1.2 (Handwritten) | View Online | Download PDF |
Exercise 1.3 (Handwritten) | View Online | Download PDF |
Chapter # 2 Sets, Functions and Groups
Exercise 2.1 | Added soon | |
Exercise 2.2 (Handwritten) | View Online | Download PDF |
Exercise 2.3 (Handwritten) | View Online | Download PDF |
Exercise 2.4 | View Online | Download PDF |
Exercise 2.5 | View Online | Download PDF |
Exercise 2.6 (Handwritten) | View Online | Download PDF |
Exercise 2.7 (Handwritten) | View Online | Download PDF |
Exercise 2.8 | View Online | Download PDF |
Chapter # 3 Matrices and Determinants
Exercise 3.1 | View Online | Download PDF |
Exercise 3.2 | View Online | Download PDF |
Exercise 3.3 (Handwritten) | View Online | Download PDF |
Exercise 3.4 (Handwritten) | View Online | Download PDF |
Exercise 3.5 (Handwritten) | View Online | Download PDF |
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Chapter # 4 Quadratic Equations
Exercise 4.1 (Handwritten) | View Online | Download PDF |
Exercise 4.2 (Handwritten) | View Online | Download PDF |
Exercise 4.3 (Handwritten) | View Online | Download PDF |
Exercise 4.4 | View Online | Download PDF |
Exercise 4.5 (Handwritten) | View Online | Download PDF |
Exercise 4.6 (Handwritten) | View Online | Download PDF |
Exercise 4.7 | View Online | Download PDF |
Exercise 4.8 (Handwritten) | View Online | Download PDF |
Exercise 4.9 (Handwritten) | View Online | Download PDF |
Exercise 4.10 (Handwritten) | View Online | Download PDF |
Chapter # 5 Partial Fractions
Exercise 5.1 | View Online | Download PDF |
Exercise 5.2 (Handwritten) | View Online | Download PDF |
Exercise 5.3 | View Online | Download PDF |
Exercise 5.4 (Handwritten) | View Online | Download PDF |
Chapter # 6 Sequences and Series
Exercise 6.1 | View Online | Download PDF |
Exercise 6.2 (Handwritten) | View Online | Download PDF |
Exercise 6.3 (Handwritten) | View Online | Download PDF |
Exercise 6.4 (Handwritten) | View Online | Download PDF |
Exercise 6.5 (Handwritten) | View Online | Download PDF |
Exercise 6.6 (Handwritten) | View Online | Download PDF |
Exercise 6.7 (Handwritten) | View Online | Download PDF |
Exercise 6.8 (Handwritten) | View Online | Download PDF |
Exercise 6.9 | View Online | Download PDF |
Exercise 6.10 | View Online | Download PDF |
Exercise 6.11 | View Online | Download PDF |
Chapter # 7 Permutation, Combination and Probability
Exercise 7.1 | View Online | Download PDF |
Exercise 7.2 | View Online | Download PDF |
Exercise 7.3 | View Online | Download PDF |
Exercise 7.4 | View Online | Download PDF |
Exercise 7.5 | View Online | Download PDF |
Exercise 7.6 | View Online | Download PDF |
Exercise 7.7 | View Online | Download PDF |
Exercise 7.8 | View Online | Download PDF |
Math Notes 2nd Year Fsc 2.1
![Fsc Fsc](https://1.bp.blogspot.com/-1cg2PIKpydE/Xp7VNN9ii8I/AAAAAAAAACw/T_OOUOSHM2InrvK1KayKQDZAfvSXO22jACLcBGAsYHQ/s1600/12th%2BMath-min.png)
Chapter # 8 Mathematics Inductions and Binomial Theorem
Exercise 8.1 | View Online | Download PDF |
Exercise 8.2 | View Online | Download PDF |
Exercise 8.3 | View Online | Download PDF |
Chapter # 9 Fundamentals of Trigonometry
Fsc 2nd Year Math Notes Youtube Chapter No 6
Exercise 9.1 | View Online | Download PDF |
Exercise 9.2 | View Online | Download PDF |
Exercise 9.3 | View Online | Download PDF |
Exercise 9.4 (Handwritten) | View Online | Download PDF |
Chapter # 10 Trigonometric Identities Sum and Difference of Angles
Exercise 10.1 | View Online | Download PDF |
Exercise 10.2 | View Online | Download PDF |
Exercise 10.3 | View Online | Download PDF |
Exercise 10.4 | View Online | Download PDF |
Math City 2nd Year
Chapter # 11 Trigonometric Functions and Their Graph
Math Notes 2nd Year Fsc 1.3
Exercise 11.1 (Handwritten) | View Online | Download PDF |
Exercise 11.2 (Handwritten) | View Online | Download PDF |
Chapter # 12 Application of Trigonometry
Exercise 12.1 | View Online | Download PDF |
Exercise 12.2 (Handwritten) | View Online | Download PDF |
Exercise 12.3 (Handwritten) | View Online | Download PDF |
Exercise 12.4 | View Online | Download PDF |
Exercise 12.5 | View Online | Download PDF |
Exercise 12.6 (Handwritten) | View Online | Download PDF |
Exercise 12.7 (Handwritten) | View Online | Download PDF |
Exercise 12.8 | View Online | Download PDF |
2nd Year Math Problems
Chapter # 13 Inverse Trigonometric Functions
Exercise 13.1 | View Online | Download PDF |
Exercise 13.2 | View Online | Download PDF |
You Can Easily View or Download These Notes For PC. To view PDF files, there must be PDF Reader (Viewer) installed on your computer. Click Here to Download PDF Viewer and other Softwares.
Chapter # 1 Numbers Systems
Exercise 1.1 (Handwritten) | View Online | Download PDF |
Exercise 1.2 (Handwritten) | View Online | Download PDF |
Exercise 1.3 (Handwritten) | View Online | Download PDF |
Chapter # 2 Sets, Functions and Groups
Exercise 2.1 | Added soon | |
Exercise 2.2 (Handwritten) | View Online | Download PDF |
Exercise 2.3 (Handwritten) | View Online | Download PDF |
Exercise 2.4 | View Online | Download PDF |
Exercise 2.5 | View Online | Download PDF |
Exercise 2.6 (Handwritten) | View Online | Download PDF |
Exercise 2.7 (Handwritten) | View Online | Download PDF |
Exercise 2.8 | View Online | Download PDF |
Chapter # 3 Matrices and Determinants
Exercise 3.1 | View Online | Download PDF |
Exercise 3.2 | View Online | Download PDF |
Exercise 3.3 (Handwritten) | View Online | Download PDF |
Exercise 3.4 (Handwritten) | View Online | Download PDF |
Exercise 3.5 (Handwritten) | View Online | Download PDF |
Chapter # 4 Quadratic Equations
Exercise 4.1 (Handwritten) | View Online | Download PDF |
Exercise 4.2 (Handwritten) | View Online | Download PDF |
Exercise 4.3 (Handwritten) | View Online | Download PDF |
Exercise 4.4 | View Online | Download PDF |
Exercise 4.5 (Handwritten) | View Online | Download PDF |
Exercise 4.6 (Handwritten) | View Online | Download PDF |
Exercise 4.7 | View Online | Download PDF |
Exercise 4.8 (Handwritten) | View Online | Download PDF |
Exercise 4.9 (Handwritten) | View Online | Download PDF |
Exercise 4.10 (Handwritten) | View Online | Download PDF |
Chapter # 5 Partial Fractions
Exercise 5.1 | View Online | Download PDF |
Exercise 5.2 (Handwritten) | View Online | Download PDF |
Exercise 5.3 | View Online | Download PDF |
Exercise 5.4 (Handwritten) | View Online | Download PDF |
Chapter # 6 Sequences and Series
Exercise 6.1 | View Online | Download PDF |
Exercise 6.2 (Handwritten) | View Online | Download PDF |
Exercise 6.3 (Handwritten) | View Online | Download PDF |
Exercise 6.4 (Handwritten) | View Online | Download PDF |
Exercise 6.5 (Handwritten) | View Online | Download PDF |
Exercise 6.6 (Handwritten) | View Online | Download PDF |
Exercise 6.7 (Handwritten) | View Online | Download PDF |
Exercise 6.8 (Handwritten) | View Online | Download PDF |
Exercise 6.9 | View Online | Download PDF |
Exercise 6.10 | View Online | Download PDF |
Exercise 6.11 | View Online | Download PDF |
Chapter # 7 Permutation, Combination and Probability
Exercise 7.1 | View Online | Download PDF |
Exercise 7.2 | View Online | Download PDF |
Exercise 7.3 | View Online | Download PDF |
Exercise 7.4 | View Online | Download PDF |
Exercise 7.5 | View Online | Download PDF |
Exercise 7.6 | View Online | Download PDF |
Exercise 7.7 | View Online | Download PDF |
Exercise 7.8 | View Online | Download PDF |
Math Notes 2nd Year Fsc 2.1
Chapter # 8 Mathematics Inductions and Binomial Theorem
Exercise 8.1 | View Online | Download PDF |
Exercise 8.2 | View Online | Download PDF |
Exercise 8.3 | View Online | Download PDF |
Chapter # 9 Fundamentals of Trigonometry
Fsc 2nd Year Math Notes Youtube Chapter No 6
Exercise 9.1 | View Online | Download PDF |
Exercise 9.2 | View Online | Download PDF |
Exercise 9.3 | View Online | Download PDF |
Exercise 9.4 (Handwritten) | View Online | Download PDF |
Chapter # 10 Trigonometric Identities Sum and Difference of Angles
Exercise 10.1 | View Online | Download PDF |
Exercise 10.2 | View Online | Download PDF |
Exercise 10.3 | View Online | Download PDF |
Exercise 10.4 | View Online | Download PDF |
Math City 2nd Year
Chapter # 11 Trigonometric Functions and Their Graph
Math Notes 2nd Year Fsc 1.3
Exercise 11.1 (Handwritten) | View Online | Download PDF |
Exercise 11.2 (Handwritten) | View Online | Download PDF |
Chapter # 12 Application of Trigonometry
Exercise 12.1 | View Online | Download PDF |
Exercise 12.2 (Handwritten) | View Online | Download PDF |
Exercise 12.3 (Handwritten) | View Online | Download PDF |
Exercise 12.4 | View Online | Download PDF |
Exercise 12.5 | View Online | Download PDF |
Exercise 12.6 (Handwritten) | View Online | Download PDF |
Exercise 12.7 (Handwritten) | View Online | Download PDF |
Exercise 12.8 | View Online | Download PDF |
2nd Year Math Problems
Chapter # 13 Inverse Trigonometric Functions
Exercise 13.1 | View Online | Download PDF |
Exercise 13.2 | View Online | Download PDF |