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Definitions: FSc Part 1 (Mathematics): PTB

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00

Definitions: FSc Part 1 (Mathematics): PTB On this page, all the definitions of “Textbook of Algebra and Trigonometry Class XI, published by Punjab Textbook Board (PTB) Lahore, Pakistan are given. We are very thankful to Muhammad Waqas Sulaiman for his valuable contribution.$\frac{p}{q}$$p,q \in \mathbb{Z}$$q\neq 0$$\frac{p}{q}$$p,q \in \mathbb{Z}$$q\neq 0$$\mathbb{R}$$0.3333....,21.134134$$\pi = 3.1415...$$\divideontimes$$z=x+iy$$x,y \in \mathbb{R}, i = \sqrt{-1}$$x$$y$$z$$2, 3+\sqrt{3}i, \fra…

MCQs: Ch 04 Quadratic Equations

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00

MCQs: Ch 04 Quadratic Equations High quality MCQs of Chapter 01 Number System of Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. The answers are given at the end of the page. MCQs $ax^2+bx+c=0$$ax^2+bx+c=0$$b \neq 0$$c \neq 0$$a \neq 0$$x$$ax^2+bx+c$$ax^2+bx+c=0$$\{a,b\}$$ax^2+bx+c=0$$a\neq 0$$x= \frac{b \pm \sqrt{b^2-4ac}}{a}$$x= \frac{-b \pm \sqrt{b^2+4ac}}{2a}$$x= \frac{-b \pm \sqrt{4ac-b^2}}{2a}$$x= \frac{-b \pm \sqrt{b^2-…

Exercise 2.8 (Solutions)

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00

Exercise 2.8 (Solutions) Notes (Solutions) of Exercise 2.8: Textbook of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB) Lahore. The main topic of this exercise are binary operation, semi-group, monoid, groups and abelian groups. These notes are based on the new Student Learning Outcomes (SLOs). Version: 4.1, Available at MathCity.org $\oplus$$G=\{0,1\}$\[ \begin{array}{|c|c|c|} \hline \oplus & 0 & 1 \\ \hline 0 & 1 & 1 \\ \hl…

Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00

Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib Definitions from Textbook of Algebra and Trigonometry Class XI, published by Punjab Textbook Board (PTB) Lahore, Pakistan. We are very thankful to Aurang Zaib for his valuable contribution. Chapter 01: Number System $ \dfrac{p}{q} $$ p, q \in \mathbb{Z} $$ q \neq 0 $$ \dfrac{3}{4} $$ \dfrac{7}{2} $$ \sqrt{2} $$ \pi $$ \mathbb{R} $$ 0.25 $$ 3.75 $$ 0.3333... $$ 1.234234... $$ \pi $$ 3.1415... $$ \sqrt{2} $\(…

MCQs: Ch 02 Sets, Functions and Groups

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00

MCQs: Ch 02 Sets, Functions and Groups High quality MCQs of Chapter 02 Sets, Functions and Groups of Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. The answers are given at the end of the page.$\forall$$\wedge$$<$$\in$$A$$B$$A\cap B=\phi$$A=B$$B\subseteq A$$A \subseteq B$$A$$B$$A-B \neq \phi$$A=B$$A \subseteq B$$B\subseteq A$$A$$B$$A\cap B=A$$B \subseteq A$$A\cap B=\phi$$A\subseteq B$$B\subseteq A$$A=\phi$$A \cup B=A$$A \cap B=…

Exercise 1.1 (Solutions)

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00

Exercise 1.1 (Solutions) Notes (Solutions) of Exercise 1.1: Textbook of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB) Lahore. The main topics of this exercise are properties of real numbers, binary operation, addition and multiplication law, properties of equality, properties of inequality (order properties), field, rule of fractions. These notes are based on the new Student Learning Outcomes (SLOs). Version: 4.0, Available at Ma…

Ch 04: Quadratic Equations

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00

Ch 04: Quadratic Equations * Reduce $x^{-2}-10=3x^{-1}$ to quadratic form --- BISE Gujrawala(2015) * Show that $x^3-y^3=(x-y)(x-wy)(x-w^2y)$ --- BISE Gujrawala(2015) * If $n$ is an odd integer, is $(x+a)$ factor of $(x^n+a^n)$? --- BISE Gujrawala(2015) * If the roots of $px^2+qx+q=0$ are $\alpha$, $\beta$,then prove that $$\sqrt {\frac{\alpha}{\beta}}+\sqrt {\frac{\beta}{\alpha}}+\sqrt{\frac{p}{q}}=0$$$${\begin{array}{c} x^2-5xy+6y^2=0\\x^2+y^2=45\end{array}}$$$4x^2+7x-…

Ch 08: Mathematical Induction and Binomial Theorem

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00

Ch 08: Mathematical Induction and Binomial Theorem * Using binomial theorem,expand $\left(\frac{x}{2}-\frac{2}{x^2}\right)$ --- BISE Gujranwala(2015) * Find the $6$th term in the expansion of $\left( x^2-\frac{3}{2x}\right)$ --- BISE Gujranwala(2015) * Expand $\left( 8-2x\right)^{-1}$ up to two terms. --- BISE Gujranwala(2015)$1+\frac{1}{4}+\frac{1.3}{4.8}+\frac{1.3.5}{4.8.12},...=\sqrt{2}$$(1.03)^{\frac{1}{3}}$$(a+x)$$n$$x$$(x-\frac{2}{x})^{10}$$n^3-n$$6$$n=2,3$$4^n>3^n+…

Definitions: Mathematics 11: PTB by Muzzammil Subhan

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00

Definitions: Mathematics 11: PTB by Muzzammil Subhan Definitions from Textbook of Algebra and Trigonometry Class XI, published by Punjab Textbook Board (PTB) Lahore, Pakistan. We are very thankful to Muzzammil Subhan for his valuable contribution. Download or view PDF for all definitions. Samples is given below$y=2^x$$y=e^x$$f(x)=\log_a x$$f(x)=\log_e x$$y$$x$$y$$y=x^2+3x$$x^2+xy+y^2=4$$f(-x)=f(x)$$f(-x)=-f(x)$

Definitions and Review

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00

Definitions and Review Textbook of Algebra and Trigonometry Class XI is published by Punjab Textbook Board (PTB) Lahore, Pakistan. The book has total of 14 chapters. On this page, we have posted material related to definitions, reviews and quick reviews.

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

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00

Old Question Papers/Model Papers HSSC-I (FSc-I): FBISE [FBISE Paper Papers HSSC-I] Old (past) question papers and model papers of mathematics for HSSC-I (FSc Part 1) conducted by Federal Board of Intermediate and Secondary Education (FBISE), Islamabad. Paper Pattern The recommended book for the mathematics paper is

Important Questions: HSSC-I

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00

Important Questions: HSSC-I [Important Questions FSc/ICS Part 1] These are the important questions for “Textbook of Algebra and Trigonometry Class XI” published by Punjab Textbook Board (PTB) Lahore, Pakistan. These questions are taken from old papers. These are very helpful to understand the types of questions which may asked final paper of mathematics for FSc/ICS (HSSC) Part 1. Lot of energy has been put to collect and write these questions. These are taken from old papers of FBISE Islamabad,…

Short Term Preparation FSc/ICS 1

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00

Short Term Preparation FSc/ICS 1 fsc fsc_part1 m_salman_sherazi important_questions_fsc_1 [Short Term Preparation by M Salman Sherazi] This document contains all the important MCQs, Short Questions and Long Questions of Mathematics HSSC-I (FSc/ICS Part 1) from the Textbook of Algebra and Trigonometry for Class XI. It has been done to help the students and teachers at no cost by $\sqrt{2}$

FSc Part 1 Mathematics Notes/Solutions

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00

FSc Part 1 Mathematics Notes/Solutions [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. There are fourteen chapters in this book and we have work hard to make easy and suitable solution for students and teachers so that it help them learn things quickly and easily. Please click on a desire chapter to view the solution of any particular exercise. This work is licensed…

Ch 01: Number Systems

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00

Ch 01: Number Systems * Simplify $(i)^{19}$ --- BISE Gujrawala(2015) * If $z$ be a complex number then prove that $\overline{z_1 + z_2}=\overline z_1 +\overline z_2$ --- BISE Sargodha(2015) * Simplify $\frac{2}{\sqrt{5}+\sqrt{-8}}$ in the form of $a+ib$ --- BISE Sargodha(2015) * Simplify by justify each step $\frac{\frac{1}{a}-\frac{1}{b}}{1-\frac{1}{a}\frac{1}{b}}$ --- $(\sqrt{2}, -\sqrt{5})$$\{0,-1\}$$a \div ib$$(-1)^\frac{-21}{2}$$(0,1)$$\{1,-1\}$$|z_1z_2|=…

Ch 02: Functions and Groups

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00

Ch 02: Functions and Groups The important questions of Chapter 2 of Textbook of Algebra and Trigonometry Class XI is published by Punjab Textbook Board (PTB) Lahore, Pakistan has been given on this page. These questions are selected from old papers. $(2,4)$$\{a,\{b,c\}\}$$A-B=A \cup B^c$$p \longrightarrow q$$\{(1,2),(2,5),(3,7),(4,9),(5,11)\}$$\{a,b \}$$\{\{a,b\}\}$$~(p \longrightarrow q) \longrightarrow p$$A \cap(B \cup C)=(A \cap B)\cup(A \cap C)$$A=\{1,2,3,4\}$$B=\{3,4,5,6,7,8\}$…

Question Paper/Model Paper/Paper Pattern HSSC-I: BISE

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00

Question Paper/Model Paper/Paper Pattern HSSC-I: BISE On this page, we have discussed the paper pattern of the HSSC-I or FSc Part 1 paper pattern of the mathematics subject. All the boards follow the same pattern. Old (past) question papers and model papers of mathematics for HSSC-I (FSc Part 1) conducted by Board of Intermediate and Secondary Education (BISE) in Punjab. There are lot of boards (e.g. Multan Board, Faisalabad Board, Sargodha Board, Gujranwala Board, DG Khan Board, Rawalpindi Boa…

MCQs Bank: FSc-I

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00

MCQs Bank: FSc-I Lot of high quality MCQs covering Textbook of Algebra and Trigonometry Class XI are available here. There are fourteen (14) chapters in this book, therefore MCQs of each chapters are given on separate page. This book was published by Punjab Textbook Board (PTB) Lahore, Pakistan. These MCQs are not only helpful for this book but can be considered for students of Higher Secondary Schools. Answer are also given on the same page.

Multiple Choice Questions (MCQs)

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00

Multiple Choice Questions (MCQs) Textbook of Algebra and Trigonometry Class XI is published by Punjab Textbook Board (PTB) Lahore, Pakistan. The book has total of 14 chapters. Our plan is to give lot of Multiple Choice Questions (MCQs) for the above mentioned book. MCQs are very important because most of entry tests, admission tests and job tests consists of only MCQs.$\sqrt{3}$$n$$\sqrt{n}$$\forall a, b, c \in R$$a0\Rightarrow ac\geq bc$$a0\Rightarrow ac>…

Trigonometric Formulas (New Edition)

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00
fsc fsc_part1 formula_pages muzzammil_subhan Trigonometric Formulas (New Edition) This page contains all the important trigonometric formulas used in chapter 9 to 14 of FSc Part 1. This page was sent by Muzzammil Subhan. [Trigonometric Formulas] [Download PDF]

Papers (Old/Past/Model): BISE

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00
Papers (Old/Past/Model): BISE Old (or Past) Papers or Model Papers help the students and teachers to get an idea about the paper pattern and distribution of syllabus. This page is created to view or download the old or model papers. Please remember, only old papers or model papers of Mathematics FSc Part 1 (HSSC-I) conducted by Board of Intermediate and Secondary Education (BISE) of different cities of the Punjab are given on this page. List of papers is given below.

Papers (Old/Past/Model): FBISE

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00
Papers (Old/Past/Model): FBISE Old (or Past) Papers or Model Papers help the students and teachers to get an idea about the paper pattern and distribution of syllabus. This page is created to view or download the old or model papers. Please remember, only old papers or model papers of Mathematics FSc Part 1 (HSSC-I) conducted by Federal Board of Intermediate and Secondary Education (FBISE) are given on this page. List of papers is given below.

Ch 07: Permutation, Combination and Probability

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00
Ch 07: Permutation, Combination and Probability * Find $n$ when ${^nC_{12}}={^nC_6}$ --- BISE Gujranwala(2015) * Evaluate ${^{20}C_{17}}$ without calculator --- BISE Gujranwala(2015) * How many $6-digit$ numbers can be formed from the digits $2,2,3,3,4,4$? How many of them with lie between $400,000$$430,000$$``PLANE"$$^nC_4=^nC_{n-r}$$6-digits$$n^3-n$$6$$n=2,3$$n$$^nP_2=30$$6-dided$$n$$^nC_{12}=^nC_6$$^{n-1}C_r+^{n-1}C_{r-1}=^nC_r$$\frac{a_5}{a_3}=\frac{4}{9}$$a_2=\frac{4}{…

MCQs: Ch 01 Number Systems

Anonymous (anonymous@undisclosed.example.com) — 2025-01-21T16:13:57+00:00
MCQs: Ch 01 Number Systems High quality MCQs of Chapter 01 Number System of Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. The answers are given at the end of the page. MCQs * If $*$$A$$a, b \in A$$a+b \in A$$a-b \in A$$a \times b \in A$$a * b \in A$$z=(1,3)$$z^{-1}= $$(\displaystyle{\frac{1}{10}},\displaystyle{\frac{3}{10}})$$(-\displaystyle{\frac{1}{10}},\displaystyle{\frac{3}{10}})$$(\displaystyle{\frac{1}{10}},-\display…