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https://beta.mathcity.org/_media/logo.pngtext/html2025-01-21T16:13:56+00:00Anonymous (anonymous@undisclosed.example.com)FSc Part 1 (KPK Boards)
https://beta.mathcity.org/fsc/kpk_fsc_part_1?rev=1737476036&do=diff
FSc Part 1 (KPK Boards)
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$$^nC_r=\left(\begin{smallmatrix}n\\ r\end{smallmatrix} \right)=\frac{n!}{r!(n-r)!}$$P(…text/html2025-01-21T16:13:56+00:00Anonymous (anonymous@undisclosed.example.com)FSc Part 2 (KPK Boards)
https://beta.mathcity.org/fsc/kpk_fsc_part_2?rev=1737476036&do=diff
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$$y=(ax+b)^n$text/html2025-01-21T16:13:55+00:00Anonymous (anonymous@undisclosed.example.com)Chapter 04: Quadratic Equations
https://beta.mathcity.org/fsc/fsc_part_1_solutions/ch04?rev=1737476035&do=diff
Chapter 04: Quadratic Equations
[Chapter 04: Quadratic Equations]
Notes (Solutions) of Chapter 04: Quadratic Equations, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board, Lahore.
Contents & summary
* Introduction
* Solutions of Quadratic Equationstext/html2025-01-21T16:13:55+00:00Anonymous (anonymous@undisclosed.example.com)Chapter 03: Matrices and Determinants
https://beta.mathcity.org/fsc/fsc_part_1_solutions/ch03?rev=1737476035&do=diff
Chapter 03: Matrices and Determinants
[Chapter 03: Matrices and Determinants]
Notes (Solutions) of Chapter 03: Matrices and Determinants, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.
Contents & summary
* Introduction$2\times2$$2\times2$$2\times2$$n\geq 3$$n\geq 3$text/html2025-01-21T16:13:55+00:00Anonymous (anonymous@undisclosed.example.com)Chapter 06: Sequences and Series
https://beta.mathcity.org/fsc/fsc_part_1_solutions/ch06?rev=1737476035&do=diff
Chapter 06: Sequences and Series
[Chapter 06: Sequences and Series]
Notes (Solutions) of Chapter 06: Sequences and Series, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.
Contents & summary
* Introduction
* Types of Sequences$l,m,n$$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\\
&=…text/html2025-01-21T16:13:56+00:00Anonymous (anonymous@undisclosed.example.com)Chapter 09: Fundamentals of Trigonometry
https://beta.mathcity.org/fsc/fsc_part_1_solutions/ch09?rev=1737476036&do=diff
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…text/html2025-01-21T16:13:56+00:00Anonymous (anonymous@undisclosed.example.com)Unit 01: Functions and Limits
https://beta.mathcity.org/fsc/fsc_part_2_solutions/ch01?rev=1737476036&do=diff
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}$$\lim_{x\to0}\frac{\sqrt{x+a} - \sqrt{a}}{x} = \frac{…text/html2025-01-21T16:13:56+00:00Anonymous (anonymous@undisclosed.example.com)Unit 03: Integration
https://beta.mathcity.org/fsc/fsc_part_2_solutions/ch03?rev=1737476036&do=diff
Unit 03: Integration
[Unit 03: Integration]
Notes (Solutions) of Unit 03: Integration, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Software section.$dy$$\delta{y}$$[f(x)]^n f'(x)$$[f(x)]^{-1}f'(x)$text/html2025-01-21T16:13:55+00:00Anonymous (anonymous@undisclosed.example.com)Chapter 01: Number System
https://beta.mathcity.org/fsc/fsc_part_1_solutions/ch01?rev=1737476035&do=diff
Chapter 01: Number System
[Chapter 01: Number System]
Notes (Solutions) of Chapter 01: Number System, Textbook of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.
Contents & summary
* Rational numbers and irrational numbers$\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}$text/html2025-01-21T16:13:55+00:00Anonymous (anonymous@undisclosed.example.com)Chapter 02: Sets, Functions and Groups
https://beta.mathcity.org/fsc/fsc_part_1_solutions/ch02?rev=1737476035&do=diff
Chapter 02: Sets, Functions and Groups
Notes (Solutions) of Chapter 02: Sets, Functions and Groups, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.
[Chapter 02: Sets, Functions and Groups]
Contents & summary
* Introduction$p\leftrightarrow q$text/html2025-01-21T16:13:55+00:00Anonymous (anonymous@undisclosed.example.com)Chapter 05: Partial Fractions
https://beta.mathcity.org/fsc/fsc_part_1_solutions/ch05?rev=1737476035&do=diff
Chapter 05: Partial Fractions
[Chapter 05: Partial Fractions]
Notes (Solutions) of Chapter 05: Partial Fractions, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.
Contents & summary
* Introduction
* Rational Fraction$\frac {P(x)}{Q(x)}$text/html2025-01-21T16:13:55+00:00Anonymous (anonymous@undisclosed.example.com)Chapter 07: Permutation, Combination and Probability
https://beta.mathcity.org/fsc/fsc_part_1_solutions/ch07?rev=1737476035&do=diff
Chapter 07: Permutation, Combination and Probability
[Chapter 07: Permutation , Combination and Probability]
Notes (Solutions) of Chapter 07: Permutation , Combination and Probability, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.
Contents & summarytext/html2025-01-21T16:13:56+00:00Anonymous (anonymous@undisclosed.example.com)Chapter 08: Mathematical Induction and Binomial Theorem
https://beta.mathcity.org/fsc/fsc_part_1_solutions/ch08?rev=1737476036&do=diff
Chapter 08: Mathematical Induction and Binomial Theorem
[Chapter 08 Mathematical Induction and Binomial Theorem]
Notes (Solutions) of Chapter 08: Mathematical Induction and Binomial Theorem, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.$(a+x)^n$$(a+x)^n$text/html2025-01-21T16:13:56+00:00Anonymous (anonymous@undisclosed.example.com)Chapter 10: Trigonometric Identities
https://beta.mathcity.org/fsc/fsc_part_1_solutions/ch10?rev=1737476036&do=diff
Chapter 10: Trigonometric Identities
[Chapter 10: Trigonometric Identities]
Notes (Solutions) of Chapter 10: Trigonometric Identities, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. There are four exercise in this chapter.text/html2025-01-21T16:13:56+00:00Anonymous (anonymous@undisclosed.example.com)Chapter 11: Trigonometric Functions and their Graphs
https://beta.mathcity.org/fsc/fsc_part_1_solutions/ch11?rev=1737476036&do=diff
Chapter 11: Trigonometric Functions and their Graphs
[Chapter 11: Trigonometric Functions and their Graphs]
Notes (Solutions) of Chapter 11: Trigonometric Functions and their Graphs, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.
Contents & summary
$ y = \sin x$$-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…text/html2025-01-21T16:13:56+00:00Anonymous (anonymous@undisclosed.example.com)Chapter 12: Application of Trigonometry
https://beta.mathcity.org/fsc/fsc_part_1_solutions/ch12?rev=1737476036&do=diff
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
* Introductiontext/html2025-01-21T16:13:56+00:00Anonymous (anonymous@undisclosed.example.com)Chapter 13: Inverse Trigonometric Functions
https://beta.mathcity.org/fsc/fsc_part_1_solutions/ch13?rev=1737476036&do=diff
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)$${\sin ^{ - 1}}A - {\sin ^{ - 1}}B = {\sin ^{ - 1}}\left( {A\sqrt {1 - {B^2}} - B\sqrt {1 - {…text/html2025-01-21T16:13:56+00:00Anonymous (anonymous@undisclosed.example.com)Chapter 14: Solutions of Trigonometric Equation
https://beta.mathcity.org/fsc/fsc_part_1_solutions/ch14?rev=1737476036&do=diff
Chapter 14: Solutions of Trigonometric Equation
[Chapter 14: Solutions of Trigonometric Equation]
Notes (Solutions) of Chapter 14: Solutions of Trigonometric Equation, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.
Contents & summary
${\sin ^{ - 1}}A + {\sin ^{ - 1}}B = {\sin ^{ - 1}}\left( {A\sqrt {1 - {B^2}} + B\sqrt {1 - {A^2}} } \right)$${\sin ^{ - 1}}A - {\sin ^{ - 1}}B = {\sin ^{ - 1}}\left( {A\sqrt {1 - {B^2}} - B\sqr…text/html2025-01-21T16:13:56+00:00Anonymous (anonymous@undisclosed.example.com)Unit 02: Differentiation
https://beta.mathcity.org/fsc/fsc_part_2_solutions/ch02?rev=1737476036&do=diff
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$$$
\begin{aligned}
\frac{d}{dx}\left(\frac{x+1}{x-1}\right) &= \frac{(x-1)\frac{d}{dx}(x…text/html2025-01-21T16:13:56+00:00Anonymous (anonymous@undisclosed.example.com)Unit 07: Vectors
https://beta.mathcity.org/fsc/fsc_part_2_solutions/ch07?rev=1737476036&do=diff
Unit 07: Vectors
[Unit 07: Vectors]
Notes (Solutions) of Unit 07: Vectors, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Software section.$u\cdot v$$u\times v$$u\cdot(v\times w)$text/html2025-01-21T16:13:55+00:00Anonymous (anonymous@undisclosed.example.com)MCQs with Answers (FSc/ICS Part 1)
https://beta.mathcity.org/fsc/fsc_part_1_mcqs/mcqs_with_answers?rev=1737476035&do=diff
MCQs with Answers (FSc/ICS Part 1)
[MCQs Choice]
In this one PDF, MCQs of all chapters of FSc/ICS Part1 are given. There are seven chapters. Answers of MCQs is starting from page 71.
SAMPLE MCQs
* $i^{13}=$.............
* (A) $i$
* (B) 1
* (C) -1
* (D) 2
$S$$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$$n$text/html2025-01-21T16:13:56+00:00Anonymous (anonymous@undisclosed.example.com)Short Questions by Mr. Akhtar Abbas
https://beta.mathcity.org/fsc/fsc_part_2_mcqs/short_questions_by_mr._akhtar_abbas?rev=1737476036&do=diff
Short Questions by Mr. Akhtar Abbas
* We are very thankful to Mr. Akhtar Abbas for sharing these short questions.
* These short questions are selected from previous 5 years papers of different boards. Solve these at your own to perform well in annual exams.$\sqrt{x^2-4}$$f(x)=\frac{2x}{x-2}$$x=2$$x^{100}$text/html2025-01-21T16:13:56+00:00Anonymous (anonymous@undisclosed.example.com)Unit 04: Introduction to Analytic Geometry
https://beta.mathcity.org/fsc/fsc_part_2_solutions/ch04?rev=1737476036&do=diff
Unit 04: Introduction to Analytic Geometry
[Unit 01: Functions and Limits]
Notes (Solutions) of Unit 04: Introduction to Analytic Geometry, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Software section.$ax^2+ 2hxy+by^2=0$text/html2025-01-21T16:13:56+00:00Anonymous (anonymous@undisclosed.example.com)Unit 05: Linear Inequalities and Linear Programming
https://beta.mathcity.org/fsc/fsc_part_2_solutions/ch05?rev=1737476036&do=diff
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.text/html2025-01-21T16:13:56+00:00Anonymous (anonymous@undisclosed.example.com)Unit 06: Conic Section
https://beta.mathcity.org/fsc/fsc_part_2_solutions/ch06?rev=1737476036&do=diff
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.