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FSc Part 2 (KPK Boards)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:42:52 +0000

FSc Part 2 (KPK Boards) [A Textbook of Mathematics For Class XII] 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.$y=x^n$$y=(ax+b)^n$

FSc Part 1 Mathematics Notes/Solutions

anonymous@undisclosed.example.com (Anonymous) — Sun, 20 Jul 2025 09:10:04 +0000

FSc Part 1 Mathematics Notes/Solutions This is an old book. Notes of new book are available at following link: [FSc Part1 PTB Book Cover] Notes (Solutions) of Textbook of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB) Lahore.

FSc/ICS Part 2 Solutions

anonymous@undisclosed.example.com (Anonymous) — Fri, 21 Mar 2025 18:12:01 +0000

FSc/ICS Part 2 Solutions [Calculus and Analytic Geometry, MATHEMATICS 12] Notes (Solutions) of Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc/ICS 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 Cr…

FSc Part 1 (KPK Boards)

anonymous@undisclosed.example.com (Anonymous) — Tue, 12 Dec 2023 17:30:33 +0000

FSc Part 1 (KPK Boards) These are the notes of old book. The notes of new book is AVAILABLE HERE [FSc Part 2 KPTP] Notes of FSc Part 1 of “A Textbook of Mathematics For Class XI” 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.$P(z)$$(\sum)$$\sum n$$\sum n^2$$\sum n^3$$n$$n$$$\frac{a}{a(a+d)}+\frac{a}{(a+d)(a+2d)}+...$$$^nP_r$$^nC_r=\left(\begin{smallm…

MCQs with Answers (FSc/ICS Part 1)

anonymous@undisclosed.example.com (Anonymous) — Thu, 02 May 2024 17:03:11 +0000

MCQs with Answers (FSc/ICS Part 1) [MCQs Choice] In this one PDF, MCQs of all chapters of FSc/ICS Part1 are given. There are seven chapters. Answers of MCQs is starting from page 71. SAMPLE MCQs * $i^{13}=$............. * (A) $i$ * (B) 1 * (C) -1 * (D) 2 * $S$$1, \omega, \omega^2$$-1, \omega, \omega^2$$-1, -\omega, -\omega^2$$1, -1, 2$$ax^2+bx+c=0$$a=0, b\neq 0$$a\neq 0$$a=b=0$$b=$$ax^2+bx+c=0$$a=0, b\neq 0$$a\neq 0$$a=b=0$$b=$$n!=n(n-1)(n-2)...3\cdot 2\cdot 1$$n$

Chapter 01: Number System

anonymous@undisclosed.example.com (Anonymous) — Sat, 03 Jun 2023 16:30:31 +0000

Chapter 01: Number System [Chapter 01: Number System] Notes (Solutions) of Chapter 01: Number System, Textbook of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary * Rational numbers and irrational numbers$\mathbb{C}$$(x+iy)^n$$\left(\frac{x_1+iy_1}{x_2+iy_2}\right)^n, x_2+iy_2\neq 0$$\sqrt{-1}=i$$\sqrt{-1}$$i$$-i$$i$$-i$$-1$$i^2=-1$$\sqrt{-1}=i$$\sqrt{-1}$

Chapter 02: Sets, Functions and Groups

anonymous@undisclosed.example.com (Anonymous) — Wed, 05 Apr 2023 12:54:57 +0000

Chapter 02: Sets, Functions and Groups Notes (Solutions) of Chapter 02: Sets, Functions and Groups, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. [Chapter 02: Sets, Functions and Groups] Contents & summary * Introduction$p\leftrightarrow q$

Chapter 05: Partial Fractions

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:29 +0000

Chapter 05: Partial Fractions [Chapter 05: Partial Fractions] Notes (Solutions) of Chapter 05: Partial Fractions, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary * Introduction * Rational Fraction$\frac {P(x)}{Q(x)}$

Chapter 06: Sequences and Series

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:29 +0000

Chapter 06: Sequences and Series [Chapter 06: Sequences and Series] Notes (Solutions) of Chapter 06: Sequences and Series, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary * Introduction * Types of Sequences$l,m,n$$p$$q$$r$$$l(q-r)+m(r-p)+n(p-q)=0$$$a_1$$d$$$\begin{align}l=a_1+(p-1)d,\\ m=a_1+(q-1)d,\\ n=a_1+(r-1)d.\end{align}$$ Now $$\begin{align}L.H.S &= l(q-r)+m(r-p)+n(p-q)\\ &= lq-lr+mr-mp+np-nq\\ &=…

Chapter 07: Permutation, Combination and Probability

anonymous@undisclosed.example.com (Anonymous) — Sat, 26 Mar 2022 16:28:40 +0000

Chapter 07: Permutation, Combination and Probability [Chapter 07: Permutation , Combination and Probability] Notes (Solutions) of Chapter 07: Permutation , Combination and Probability, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary

Chapter 08: Mathematical Induction and Binomial Theorem

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:30 +0000

Chapter 08: Mathematical Induction and Binomial Theorem [Chapter 08 Mathematical Induction and Binomial Theorem] Notes (Solutions) of Chapter 08: Mathematical Induction and Binomial Theorem, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.$(a+x)^n$$(a+x)^n$

Chapter 09: Fundamentals of Trigonometry

anonymous@undisclosed.example.com (Anonymous) — Sun, 04 Jun 2023 16:03:04 +0000

Chapter 09: Fundamentals of Trigonometry [Chapter 09: Fundamentals of Trigonometry] Notes (Solutions) of Chapter 09: Fundamentals of Trigonometry, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. This chapter has four exercise and solutions of those exercises are given below which can be downloaded in PDF format or can be viewed online.$D^\circ M'S''$$45^\circ , 30^\circ , 60^\circ$$0^\circ , 90^\circ , 180^\circ , 270^\circ , 36…

Chapter 10: Trigonometric Identities

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:32 +0000

Chapter 10: Trigonometric Identities [Chapter 10: Trigonometric Identities] Notes (Solutions) of Chapter 10: Trigonometric Identities, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. There are four exercise in this chapter.

Chapter 11: Trigonometric Functions and their Graphs

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:34 +0000

Chapter 11: Trigonometric Functions and their Graphs [Chapter 11: Trigonometric Functions and their Graphs] Notes (Solutions) of Chapter 11: Trigonometric Functions and their Graphs, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary $ y = \sin x$$-2\pi \hbox{ to } 2\pi$$ y = \cos x$$-2\pi \hbox{ to } 2\pi$$ y = \tan x$$-\pi \hbox{ to } \pi$$ y = \cot x$$-2\pi \hbox{ to } \pi$$ y = \sec x$$-2\pi \hbox{ to } 2\pi…

Chapter 12: Application of Trigonometry

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:34 +0000

Chapter 12: Application of Trigonometry [Chapter 12: Application of Trigonometry] Notes (Solutions) of Chapter 12: Application of Trigonometry, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary * Introduction

Chapter 13: Inverse Trigonometric Functions

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:37 +0000

Chapter 13: Inverse Trigonometric Functions [Chapter 13: Inverse Trigonometric Functions] Notes (Solutions) of Chapter 13: Inverse Trigonometric Functions, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary * ${\sin ^{ - 1}}A + {\sin ^{ - 1}}B = {\sin ^{ - 1}}\left( {A\sqrt {1 - {B^2}} + B\sqrt {1 - {A^2}} } \right)$${\sin ^{ - 1}}A - {\sin ^{ - 1}}B = {\sin ^{ - 1}}\left( {A\sqrt {1 - {B^2}} - B\sqrt {1 - {…

Chapter 14: Solutions of Trigonometric Equation

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:37 +0000

Chapter 14: Solutions of Trigonometric Equation [Chapter 14: Solutions of Trigonometric Equation] Notes (Solutions) of Chapter 14: Solutions of Trigonometric Equation, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary ${\sin ^{ - 1}}A + {\sin ^{ - 1}}B = {\sin ^{ - 1}}\left( {A\sqrt {1 - {B^2}} + B\sqrt {1 - {A^2}} } \right)$${\sin ^{ - 1}}A - {\sin ^{ - 1}}B = {\sin ^{ - 1}}\left( {A\sqrt {1 - {B^2}} - B\sqr…

MCQs with key

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:44 +0000

MCQs with key [MCQs Choice] In this one PDF, MCQs of all chapters of FSc Part2 are given. There are seven chapters. Keys of MCQs is starting from page 51. SAMPLE MCQs * A function $I(x)=x$ is called * (A) A linear function * (B) An identity function * (C) A quadratic function$\frac{d}{dx} \tan 3x =$$3\sec^2 3x$$\frac{1}{3}\sec^2 3x$$\cot 3x$$\sec^2 x$$y=f(x)$$y$$dy=f'(x)$$dy=f'(x) dx$$dy=f(x)$$\frac{dy}{dx}$$x<0$$y<0$$P(x,y)$$ax+by

Objective Mathematics 12th by Muhammad Shahbaz

anonymous@undisclosed.example.com (Anonymous) — Fri, 21 Mar 2025 15:20:30 +0000

Objective Mathematics 12th by Muhammad Shahbaz [Objective Mathematics 12th by Muhammad Shahbaz] These notes are sent by Muhammad Shahbaz. We are very thankful to him for send this booklet. This booklet is very helpful to cover the following things for Mathematics 12 (Mathematics for Intermediate) * Summary

Unit 01: Functions and Limits

anonymous@undisclosed.example.com (Anonymous) — Sat, 03 Jun 2023 16:30:56 +0000

Unit 01: Functions and Limits [Unit 01: Functions and Limits] Notes (Solutions) of Unit 01: Functions and Limits, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. There are five exercises in this chapter. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from $\lim_{x\to a}\frac{x^n-a^n}{x-a} = na^{n-1}$$\lim_{x\to0}\frac{\sqrt{x+a} - \sqrt{a}}{x} = \frac{…

Unit 02: Differentiation

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:05 +0000

Unit 02: Differentiation [Unit 02: Differentiation] Notes (Solutions) of Unit 02: Differentiation, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Software section.$f'(x)$$x^n$$n \in \mathbb{Z}$$\frac{x+1}{x-1}$$x$$$ \begin{aligned} \frac{d}{dx}\left(\frac{x+1}{x-1}\right) &= \frac{(x-1)\frac{d}{dx}(x…

Unit 03: Integration

anonymous@undisclosed.example.com (Anonymous) — Sat, 03 Jun 2023 17:25:33 +0000

Unit 03: Integration [Unit 03: Integration] Notes (Solutions) of Unit 03: Integration, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Software section.$dy$$\delta{y}$$[f(x)]^n f'(x)$$[f(x)]^{-1}f'(x)$

Unit 04: Introduction to Analytic Geometry

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:07 +0000

Unit 04: Introduction to Analytic Geometry [Unit 01: Functions and Limits] Notes (Solutions) of Unit 04: Introduction to Analytic Geometry, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Software section.$ax^2+ 2hxy+by^2=0$

Unit 05: Linear Inequalities and Linear Programming

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:08 +0000

Unit 05: Linear Inequalities and Linear Programming [Unit 05: Linear Inequalities and Linear Programming] Notes (Solutions) of Unit 05: Linear Inequalities and Linear Programming, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Software section.

Unit 06: Conic Section

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:47:08 +0000

Unit 06: Conic Section [Unit 06: Conic Section] Notes (Solutions) of Unit 06: Conic Section, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Software section.

Unit 07: Vectors

anonymous@undisclosed.example.com (Anonymous) — Thu, 25 Mar 2021 17:27:32 +0000

Unit 07: Vectors [Unit 07: Vectors] Notes (Solutions) of Unit 07: Vectors, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Software section.$u\cdot v$$u\times v$$u\cdot(v\times w)$