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        <item>
            <title>FSc Part 1 (KPK Boards)</title>
            <link>https://www.mathcity.org/fsc/kpk_fsc_part_1</link>
            <description>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…</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Tue, 12 Dec 2023 17:30:33 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 04: Quadratic Equations</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_solutions/ch04</link>
            <description>Chapter 04: Quadratic Equations

[Chapter 04: Quadratic Equations]
Notes (Solutions) of Chapter 04: Quadratic Equations, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board, Lahore.

Contents &amp; summary

	*  Introduction
		*  Solutions of Quadratic Equations</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 04 Jun 2023 16:13:15 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 06: Sequences and Series</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_solutions/ch06</link>
            <description>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 &amp; 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 &amp;=  l(q-r)+m(r-p)+n(p-q)\\
&amp;= lq-lr+mr-mp+np-nq\\
&amp;=…</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:29 +0000</pubDate>
        </item>
        <item>
            <title>Unit 03: Integration</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_solutions/ch03</link>
            <description>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&#039;(x)$$[f(x)]^{-1}f&#039;(x)$</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sat, 03 Jun 2023 17:25:33 +0000</pubDate>
        </item>
        <item>
            <title>FSc Part 2 (KPK Boards)</title>
            <link>https://www.mathcity.org/fsc/kpk_fsc_part_2</link>
            <description>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$</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:42:52 +0000</pubDate>
        </item>
        <item>
            <title>Short Questions by Mr. Akhtar Abbas</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_mcqs/short_questions_by_mr._akhtar_abbas</link>
            <description>Short Questions by Mr. Akhtar Abbas

	*  We are very thankful to Mr. Akhtar Abbas for sharing these short questions.
	*  These short questions are selected from previous 5 years papers of different boards. Solve these at your own to perform well in annual exams.</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:09 +0000</pubDate>
        </item>
        <item>
            <title>MCQs by Muhammad Imran Qureshi</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_mcqs/mcqs_by_muhammad_imran_qureshi</link>
            <description>MCQs by Muhammad Imran Qureshi

MCQs of the Textbook of Algebra and Trigonometry Class XI is published by Punjab Textbook Board (PTB) Lahore, Pakistan. 

To see the keys of the MCQs, please see Key to MCQs by Muhammad Imran Qureshi.

	*  Chapter 01 | View Online  | Download PDF (166KB)

	*  Chapter 02 | View Online  | Download PDF (77KB)</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:06 +0000</pubDate>
        </item>
        <item>
            <title>MCQs by Nauman Idrees</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_mcqs/mcqs_by_nauman_idrees</link>
            <description>MCQs by Nauman Idrees

	*  Text Book of Algebra and Trigonometry, Class XI (Punjab Textbook Board, Lahore).

Chapter 01

View Online  | Download PDF (52KB)  | Ch 01: Key

Chapter 02

View Online  | Download PDF (68KB)  | Ch 02: Key

Chapter 03

View Online  | Download PDF (41KB)  | Ch 03: Key

Chapter 04

View Online  | Download PDF (43KB)  | Ch 04: Key

Chapter 05

View Online  | Download PDF (39KB)  |</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:06 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 03: Matrices and Determinants</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_solutions/ch03</link>
            <description>Chapter 03: Matrices and Determinants

[Chapter 03: Matrices and Determinants]

Notes (Solutions) of Chapter 03: Matrices and Determinants, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.

Contents &amp; summary

	*  Introduction$2\times2$$2\times2$$2\times2$$n\geq 3$$n\geq 3$</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:27 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 09: Fundamentals of Trigonometry</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_solutions/ch09</link>
            <description>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&#039;S&#039;&#039;$$45^\circ , 30^\circ , 60^\circ$$0^\circ , 90^\circ , 180^\circ , 270^\circ , 36…</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 04 Jun 2023 16:03:04 +0000</pubDate>
        </item>
        <item>
            <title>Unit 01: Functions and Limits</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_solutions/ch01</link>
            <description>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{…</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sat, 03 Jun 2023 16:30:56 +0000</pubDate>
        </item>
        <item>
            <title>Unit 02: Differentiation</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_solutions/ch02</link>
            <description>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&#039;(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) &amp;= \frac{(x-1)\frac{d}{dx}(x…</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:47:05 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 12: Application of Trigonometry</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_solutions/ch12</link>
            <description>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 &amp; summary

	*  Introduction</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:34 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 02: Sets, Functions and Groups</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_solutions/ch02</link>
            <description>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 &amp; summary

	*  Introduction$p\leftrightarrow q$</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Wed, 05 Apr 2023 12:54:57 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 07: Permutation, Combination and Probability</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_solutions/ch07</link>
            <description>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 &amp; summary</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sat, 26 Mar 2022 16:28:40 +0000</pubDate>
        </item>
        <item>
            <title>Unit 06: Conic Section</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_solutions/ch06</link>
            <description>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.</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:47:08 +0000</pubDate>
        </item>
        <item>
            <title>Unit 07: Vectors</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_solutions/ch07</link>
            <description>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)$</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Thu, 25 Mar 2021 17:27:32 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 05: Partial Fractions</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_solutions/ch05</link>
            <description>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 &amp; summary

	*  Introduction
	*  Rational Fraction$\frac {P(x)}{Q(x)}$</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:29 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 10: Trigonometric Identities</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_solutions/ch10</link>
            <description>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.</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:32 +0000</pubDate>
        </item>
        <item>
            <title>MCQs by Muhammad Imran Qureshi</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_mcqs/mcqs_by_muhammad_imran_qureshi</link>
            <description>MCQs by Muhammad Imran Qureshi

	*  Calculus and Analytic Geometry, MATHEMATICS 12 (Punjab Textbook Board, Lahore)
 Unit 01  View Online   Download PDF (78KB)  Unit 01: Key  Unit 02 View Online   Download PDF (71KB)  Unit 02: Key  Unit 03  View Online   Download PDF (67KB)  Unit 03: Key  Unit 04  View Online   Download PDF (50KB)  Unit 04: Key  Unit 05  View Online   Download PDF (49KB)  Unit 05: Key  Unit 06  View Online   Download PDF (58KB)</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:42 +0000</pubDate>
        </item>
        <item>
            <title>MCQs by Nauman Idrees</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_mcqs/mcqs_by_nauman_idrees</link>
            <description>MCQs by Nauman Idrees

	*  Calculus and Analytic Geometry, MATHEMATICS 12 (Punjab Textbook Board, Lahore)
 ARW Unit 01  View Online   Download PDF (48KB)   Unit 01: Key   ARW Unit 02  View Online   Download PDF (62KB)  Unit 02: Key   ARW Unit 03  View Online   Download PDF (72KB)  Unit 03: Key   ARW Unit 04  View Online   Download PDF (48KB)  Unit 04: Key   ARW Unit 05  View Online   Download PDF (52KB)  Unit 05: Key   ARW</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:43 +0000</pubDate>
        </item>
        <item>
            <title>Unit 04: Introduction to Analytic Geometry</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_solutions/ch04</link>
            <description>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.$ax^2+ 2hxy+by^2=0$</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:47:07 +0000</pubDate>
        </item>
        <item>
            <title>Unit 05: Linear Inequalities and Linear Programming</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_solutions/ch05</link>
            <description>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.</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:47:08 +0000</pubDate>
        </item>
        <item>
            <title>FSc Part 1 Model Papers</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_model_papers</link>
            <description>FSc Part 1 Model Papers

Federal Board of Intermediate &amp; Secondary Education, Islamabad
 ARW Model Paper 2008   View Online  Download PDF (69KB)   ARW Official Model Paper (with solution)   View Online Download PDF (154KB)   ARW Model Paper 1 (Old)   View Online Download PDF (103KB)   ARW Model Paper 2 (Old)   View Online Download PDF (96KB)</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:42:38 +0000</pubDate>
        </item>
        <item>
            <title>Fill in the blanks by Rauf &amp; Nabeel</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_mcqs/fill_in_the_blanks_by_rauf_nabeel</link>
            <description>Fill in the blanks by Rauf &amp; Nabeel

	*  Fill in the blanks, provided by Adil Rauf &amp; Muhammad Nabil (F.Sc. Part I, Session: 2003-05, FAZMIC Sargodha)
	*  Text Book of Algebra and Trigonometry Class XI (Punjab Textbook Board, Lahore)
 Chapter 02   Download PDF (93KB)</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:06 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 01: Number System</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_solutions/ch01</link>
            <description>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 &amp; 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}$</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sat, 03 Jun 2023 16:30:31 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 08: Mathematical Induction and Binomial Theorem</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_solutions/ch08</link>
            <description>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$</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:30 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 13: Inverse Trigonometric Functions</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_solutions/ch13</link>
            <description>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 &amp; 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 - {…</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:37 +0000</pubDate>
        </item>
        <item>
            <title>FSc Part 2 Model Papers</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_model_papers</link>
            <description>FSc Part 2 Model Papers

Federal Board of Intermediate &amp; Secondary Education, Islamabad
 ARW 1st Model Paper 2009   View Online  Download PDF (84KB)   ARW Official Model Paper (with solution)   Download PDF (233KB)  
Board of Intermediate &amp; Secondary Education.

All the boards in Punjab expect Federal Board have the same paper pattern.</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:42:48 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 11: Trigonometric Functions and their Graphs</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_solutions/ch11</link>
            <description>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 &amp; 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…</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:34 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 14: Solutions of Trigonometric Equation</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_solutions/ch14</link>
            <description>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 &amp; 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…</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:37 +0000</pubDate>
        </item>
        <item>
            <title>MCQs with Answers (FSc/ICS Part 1)</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_mcqs/mcqs_with_answers</link>
            <description>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$</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Thu, 02 May 2024 17:03:11 +0000</pubDate>
        </item>
        <item>
            <title>FBISE Annual 2009</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_old_papers/fbise_annual_2009</link>
            <description>FBISE Annual 2009

	*  FSc part 1 (HSSC-I) mathematics paper conducted by Federal Board of Intermediate and Secondary Education (FBISE), Islamabad has been analyse on this web page with the help of chart. Three type of chart are given in which one includes bar chart between chapters and marks, 2nd one include relation between algebraic and trigonometric portion and 3rd one contains pie chart which show the portion of questions from exercises to non-exercise question from book a</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:16 +0000</pubDate>
        </item>
        <item>
            <title>FBISE Annual 2011</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_old_papers/fbise_annual_2011</link>
            <description>FBISE Annual 2011

	*  FSc part 1 (HSSC-I) mathematics paper conducted by Federal Board of Intermediate and Secondary Education (FBISE), Islamabad has been analyse on this web page with the help of chart. Three type of chart are given in which one includes bar chart between chapters and marks, 2nd one include relation between algebraic and trigonometric portion and 3rd one contains pie chart which show the portion of questions from exercises to non-exercise question from book a</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:18 +0000</pubDate>
        </item>
        <item>
            <title>FBISE Annual 2012</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_old_papers/fbise_annual_2012</link>
            <description>FBISE Annual 2012

	*  FSc part 1 (HSSC-I) mathematics paper conducted by Federal Board of Intermediate and Secondary Education (FBISE), Islamabad has been analyse on this web page with the help of chart. Three type of chart are given in which one includes bar chart between chapters and marks, 2nd one include relation between algebraic and trigonometric portion and 3rd one contains pie chart which show the portion of questions from exercises to non-exercise question from book a</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:18 +0000</pubDate>
        </item>
        <item>
            <title>Objective Mathematics 12th by Muhammad Shahbaz</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_mcqs/objective-mathematics-12th-by-m-shahbaz</link>
            <description>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</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Fri, 21 Mar 2025 15:20:30 +0000</pubDate>
        </item>
        <item>
            <title>Solution &amp; Area of Oblique Triangle</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_solution_area_of_oblique_triangle</link>
            <description>Solution &amp; Area of Oblique Triangle

Here is the list of all the formulas used in Chapter 12 of FSc Part 1. If there is difficulty to remember these formulas then take a print of this page and see formula from this page while solving the question. After a while you will learn all formulas by heart. To download the PDF of this page see below.</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:42:41 +0000</pubDate>
        </item>
        <item>
            <title>Important Derivatives &amp; Integrals</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_important_derivatives_integrals</link>
            <description>Important Derivatives &amp; Integrals</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:42:44 +0000</pubDate>
        </item>
        <item>
            <title>Old Papers (FSc Part 2)</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_old_papers</link>
            <description>Old Papers (FSc Part 2)

Federal Board of Intermediate &amp; Secondary Education, Islamabad

The special page has been created for Federal Board:

	*  Old Question Papers/Model Papers HSSC-II (FSc-II): FBISE

Board of Intermediate &amp; Secondary Education.

(All the boards have same paper pattern in Punjab excluding Federal Board)
These papers can be used as a model paper for other board (e.g. Multan Board, Faisalabad Board, Sargodha Board, Gujranwala Board, DG Khan Board, Rawalpindi Board etc)</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:42:49 +0000</pubDate>
        </item>
        <item>
            <title>MCQs with key</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_mcqs/mcqs_with_key</link>
            <description>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$$dy=f&#039;(x)$$dy=f&#039;(x) dx$$dy=f(x)$$\frac{dy}{dx}$$x&lt;0$$y&lt;0$$P(x,y)$$ax+by&lt;c$$1$</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:44 +0000</pubDate>
        </item>
        <item>
            <title>Short Questions by Mr. Akhtar Abbas</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_mcqs/short_questions_by_mr._akhtar_abbas</link>
            <description>Short Questions by Mr. Akhtar Abbas

	*  We are very thankful to Mr. Akhtar Abbas for sharing these short questions.
	*  These short questions are selected from previous 5 years papers of different boards. Solve these at your own to perform well in annual exams.$\sqrt{x^2-4}$$f(x)=\frac{2x}{x-2}$$x=2$$x^{100}$</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:47 +0000</pubDate>
        </item>
        <item>
            <title>Important Trigonometric Formulae</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_important_trigonometric_formulae</link>
            <description>Important Trigonometric Formulae

These two pages contains all the important trigonometric formulae used in Chapter 09 to Chapter 14. These notes are provide by Ali Nawaz Bajwa  (MS(Math), M.Ed.). It is necessary for student to remembers these values by heart.</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:42:38 +0000</pubDate>
        </item>
        <item>
            <title>Trigonometric Review</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_trigonometric_review</link>
            <description>Trigonometric Review

Here the review of the formulas are given, which are used in Chapter 9 to 14 of Text Book of Algebra and Trigonometry Class XI, Punjab Text Book Board Lahore. This handout is very helpful to remember the formulas. All these formulas are given for real valued and defined trigonometric functions. A PDF file can be downloaded for high quality printing. We are very thankful to</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:42:42 +0000</pubDate>
        </item>
        <item>
            <title>Chap 04: Formulas Introduction to Analytics Geometry</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_formulas_introduction_to_analytics_geometry</link>
            <description>Chap 04: Formulas Introduction to Analytics Geometry

On these four pages, one can find all the formulas used in Chapter 04: Formulas Introduction to Analytics Geometry of FSc Part 2. There are five exercises in chapter 04 with lot of questions. These basic things help to solve the questions easily without going to the depth of each concept.</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:42:43 +0000</pubDate>
        </item>
        <item>
            <title>Important Formulas Derivatives</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_important_formulas_derivatives</link>
            <description>Important Formulas Derivatives

This page contains all the important derivatives used in chapter 2 and 3 of FSc Part 2. This page is send by Ali Nawaz Bajwa  (MS(Math), M.Ed.). It is very helpful to remember thes formulas.



[Download PDF]</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:42:45 +0000</pubDate>
        </item>
        <item>
            <title>Important Formulas Integration</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_important_formulas_integration</link>
            <description>Important Formulas Integration

This page contains all the important integration used in chapter 3 of FSc Part 2. This page is send by Ali Nawaz Bajwa  (MS(Math), M.Ed.). This page helps to remember important formulas of integration.



[Download PDF]</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:42:46 +0000</pubDate>
        </item>
        <item>
            <title>MCQs Made by Nauman Idrees</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_mcqs/mcqs_made_by_nauman_idrees</link>
            <description>MCQs Made by Nauman Idrees
 Chapter 01  View Online      Download PDF (43KB)    
	*  Online View</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:08 +0000</pubDate>
        </item>
        <item>
            <title>MCQs-Short Questions by Mr Parvez Khan</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_mcqs/mcqs-short_questions_by_mr._parvez_khan</link>
            <description>MCQs-Short Questions by Mr Parvez Khan

	*  MCQs and Short Question written by Mr. Parvez Khan, composed by Mr. Momin Ali from Text Book of Algebra and Trigonometry Class XI (Punjab Textbook Board, Lahore)
	*  Key to the MCQs is given at page 57.

Erratum
$180^{\circ}$</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:05 +0000</pubDate>
        </item>
        <item>
            <title>MCQs-Short Questions by Mr. Parvez Khan</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_mcqs/mcqs-short_questions_by_mr._parvez_khan</link>
            <description>MCQs-Short Questions by Mr. Parvez Khan

	*  MCQs and Short Question by Mr. Parvez Khan composed by Momin Ali: Calculus and Analytic Geometry, MATHEMATICS 12 (Punjab Textbook Board, Lahore). Answers are given at page 32.</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:46:42 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 01: Complex Numbers</title>
            <link>https://www.mathcity.org/fsc/kpk_fsc_part_1/chapter_01_complex_numbers</link>
            <description>Chapter 01: Complex Numbers

Notes of Chapter 01: Complex Numbers of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources.



[Download PDF ~ ch01-complex-numbers-fsc1-kpk.pdf]

fsc kpk_fsc_part1</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:47:20 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 02: Matrices and Determinants</title>
            <link>https://www.mathcity.org/fsc/kpk_fsc_part_1/chapter_02_matrices_and_determinants</link>
            <description>Chapter 02: Matrices and Determinants

Notes of Chapter 02: Matrices and Determinants of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources.</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:47:20 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 03: Vectors</title>
            <link>https://www.mathcity.org/fsc/kpk_fsc_part_1/chapter_03_vectors</link>
            <description>Chapter 03: Vectors

Notes of Chapter 03: Vectors of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources.



[Download PDF ~ ch03-vectors-fsc1-kpk.pdf]

fsc kpk_fsc_part1</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:47:21 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 04: Sequences</title>
            <link>https://www.mathcity.org/fsc/kpk_fsc_part_1/chapter_04_sequences</link>
            <description>Chapter 04: Sequences

Notes of Chapter 04: Sequences of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources.



[Download PDF ~ ch04-sequences-fsc1-kpk.pdf]

fsc kpk_fsc_part1</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:47:21 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 05: Miscellaneous Series</title>
            <link>https://www.mathcity.org/fsc/kpk_fsc_part_1/chapter_05_miscellaneous_series</link>
            <description>Chapter 05: Miscellaneous Series

Notes of Chapter 05: Miscellaneous Series of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources.



[Download PDF ~ ch05-miscellaneous-series-fsc1-kpk.pdf]

fsc kpk_fsc_part1</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:47:22 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 06: Permutation, Combination and Probability</title>
            <link>https://www.mathcity.org/fsc/kpk_fsc_part_1/chapter_06_permutation_combination_and_probability</link>
            <description>Chapter 06: Permutation, Combination and Probability

Notes of Chapter 06: Permutation, Combination and Probability of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources.</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:47:22 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 07: Mathematical Induction and Binomial Theorem</title>
            <link>https://www.mathcity.org/fsc/kpk_fsc_part_1/chapter_07_mathematical_induction_and_binomial_theorem</link>
            <description>Chapter 07: Mathematical Induction and Binomial Theorem

Notes of Chapter 07: Mathematical Induction and Binomial Theorem of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources.</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:47:23 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 08: Function and Graphs</title>
            <link>https://www.mathcity.org/fsc/kpk_fsc_part_1/chapter_08_functions_and_graphs</link>
            <description>Chapter 08: Function and Graphs

Notes of Chapter 08: Function and Graphs of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources.



[Download PDF ~ ch08-functions-and-graphs-fsc1-kpk.pdf]

fsc kpk_fsc_part1</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:47:23 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 09: Linear Programming</title>
            <link>https://www.mathcity.org/fsc/kpk_fsc_part_1/chapter_09_linear_programming</link>
            <description>Chapter 09: Linear Programming

Notes of Chapter 09: Linear Programming of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources.



[Download PDF ~ ch09-linear-programming-fsc1-kpk.pdf]

fsc kpk_fsc_part1</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:47:24 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 10: Trigonometric Identities of Sum and Difference of Angles</title>
            <link>https://www.mathcity.org/fsc/kpk_fsc_part_1/chapter_10_trigonometric_identities_of_sum_and_difference_of_angles</link>
            <description>Chapter 10: Trigonometric Identities of Sum and Difference of Angles

Notes of Chapter 10: Trigonometric Identities of Sum and Difference of Angles of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources.</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:47:25 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 11: Application of Trigonometry</title>
            <link>https://www.mathcity.org/fsc/kpk_fsc_part_1/chapter_11_application_of_trigonometry</link>
            <description>Chapter 11: Application of Trigonometry

Notes of Chapter 11: Application of Trigonometry of “A Textbook of Mathematics for Class XI” published by Khyber Pakhtunkhwa (KPK) Textbook Board, Pesharwar. These notes are shared as open educational resources.</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:47:26 +0000</pubDate>
        </item>
        <item>
            <title>Chapter 12: Graph of Trigonometric and Inverse Trigonometric Functions and Solutions of ...</title>
            <link>https://www.mathcity.org/fsc/kpk_fsc_part_1/chapter_12_graph_of_trigonometric_and_inverse_trigonometric_functions_and_solutions_of_trigonometric_equations</link>
            <description>Chapter 12: Graph of Trigonometric and Inverse Trigonometric Functions and Solutions of Trigonometric Equations

Notes of Chapter 12: Graph of Trigonometric and Inverse Trigonometric Functions and Solutions of Trigonometric Equations of “A Textbook of Mathematics for Class XI</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:47:26 +0000</pubDate>
        </item>
        <item>
            <title>View Online (Notes of Chapter 04)</title>
            <link>https://www.mathcity.org/fsc/fsc_part_1_solutions/ch04/view</link>
            <description>View Online (Notes of Chapter 04)

Notes (Solutions) of Chapter 04: Quadratic Equations, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board, Lahore. 

These notes are provided by M. Shahid Nadeem, Lecturer in Mathematics, Punjab College Wah Cantt. One can also download PDF of the notes from this page.</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 16:57:41 +0000</pubDate>
        </item>
        <item>
            <title>View Online (Solutions of Unit 06)</title>
            <link>https://www.mathcity.org/fsc/fsc_part_2_solutions/ch06/viewer</link>
            <description>View Online (Solutions of Unit 06)

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. From this page, you can also download PDF of the notes.</description>
            <author>anonymous@undisclosed.example.com (Anonymous)</author>
            <pubDate>Sun, 07 Feb 2021 17:00:22 +0000</pubDate>
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