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- FSc/ICS Part 2 (Mathematics): PTB
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- Unit 01: Functions and Limits
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Fulltext results:
- Short Term Preparation FSc/ICS 1 @fsc-part1-ptb
- t Term Preparation FSc/ICS 1 ====== {{tag>FSc FSc_Part1 M_Salman_Sherazi Important_Questions_FSc_1}} {{ :fsc-part1-ptb:short-term-preparation-fsc-1.jpg?nolink|Shor... and Long Questions of Mathematics HSSC-I (FSc/ICS Part 1) from the Textbook of Algebra and Trigonometry ... questions are also given. **Sample:** - $\sqrt{2}$ is a number - Rational - Irrational
- MCQs with Answers (FSc/ICS Part 1) @fsc:fsc_part_1_mcqs
- with Answers (FSc/ICS Part 1) ====== {{ :fsc:fsc_part_2_mcqs:testchoices.jpg?nolink|MCQs Choice}} In this one PDF, MCQs of all chapters of FSc/ICS Part1 are given. There are seven chapters. Answers of ... * (A) $i$ * (B) 1 * (C) -1 * (D) 2 * Set of all possible subsets of $S$ is called ... be root of unity are * (A) $1, \omega, \omega^2$ * (B) $-1, \omega, \omega^2$ * (C) $-1,
- FSc/ICS Part 2 Solutions @fsc
- ====== FSc/ICS Part 2 Solutions ====== {{ :fsc:fsc-math-part2.jpg?nolink|Calculus and Analytic Geometry, MATHEMATICS 12}} <lead>Notes (Solutions) of Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc/ICS Part 2 or HSSC-II), Punjab Text Book Board Lahore.</le... to view PDF on their smartphone. * **[[FSc:FSc Part 2 Solutions:ch01]]** * **[[FSc:FSc Part 2 Solu
- Important Questions: HSSC-II @fsc-part2-ptb
- book Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Textbook Board (PTB) Lahore... estions:unit-01-functions-and-limits]] * [[fsc-part2-ptb:important-questions:unit-02-differentiation ]] * [[fsc-part2-ptb:important-questions:unit-03-integration ]] * [[fsc-part2-ptb:important-questions:unit-04-introduction-to-
- FSc/ICS Part 2 (Mathematics): PTB
- ====== FSc/ICS Part 2 (Mathematics): PTB ====== {{ :fsc-part2-ptb.jpg?nolink|Calculus and Analytic Geometry, MATHEMATICS 12}} <lead>Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc/ICS Part 2 or HSSC-II), Punjab Textbook Board (PTB) Lahore... type="success" size="lg" block="true">**[[FSc:FSc Part 2 Solutions|Solutions (Notes)]]**</btn>\\ <btn type
- Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib @fsc-part1-ptb
- esponds to the horizontal axis, and the imaginary part \( y = 2 \) corresponds to the vertical axis. Thus, \( z \... would be plotted as a point at coordinates \( (3, 2) \) on the Argand diagram. ====Modulus of Comple... of its real and imaginary parts: \( |z| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \). Therefore, \( |z| = 5 \). =====Chapter 02: Set and Operat
- Definitions: FSc Part 1 (Mathematics): PTB @fsc-part1-ptb
- has only a finite number of digits in its decimal part, is called terminating decimal.\\ e.g. 0.33333... and 21.134134... is examples of terminating decimal. ... s called complex number. Here $x$ is called real part and $y$ is called imaginary part of $z$.\\ e.g. $2, 3+\sqrt{3}i, \frac{1}{2}+i$. * **Real plane or coordinate plane:** T... ted by $|x+iy|$ or $|(x,y)|$. ===== Chapter 02: Functions and groups ===== * **Set:** A set is... elements within brackets.\\ e.g. $\mathbb{N}=\{1,2,3,4,...\}$ * **Set-builder method:** In this f
- Unit 01: Complex Numbers (Solutions) @math-11-kpk:sol
- rs and $i=\sqrt{-1}$. * Recognize $a$ as real part of $z$ and $b$ as imaginary part of $z$. * Know condition for equality of complex numbers. * Ca... onjugate of $z=a+ib$. * Define $|z| = \sqrt{a^2+b^2}$ as the absolute value or modulus of a complex number $z=a+ib$ * Describe algebraic propert
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- yed-gul-shah|read more for download]] * | [[fsc-part1-ptb|FSc-I (PTB)]] | Online version of solutions of the Exercise 1.2 of FSc Part 1 (PTB) has been updated... [[fsc-part1-ptb/sol/ch01/ex1-2|click here to see]] * | [[fsc-part1-ptb|FSc-I (PTB)]] | Online version of solutions of th... s:ring_notes|read more for download]] * | [[fsc-part1-ptb|FSc-I (PTB)]] | Online version of solutions of the Exercise 2.8 of FSc Part 1 (PTB) has been updated... [[fsc-part1-ptb/sol/ch02/ex2-8|click here to see]] ====Solutions of Books==== <grid> <col lg="4"> <well> [[:matric
- FSc Part 1 (KPK Boards) @fsc
- math-11-kpk|AVAILABLE HERE]] </text> {{ :fsc:fsc-part-1-kptb.jpg?nolink&600x315|FSc Part 2 KPTP}} Notes of FSc Part 1 of "A Textbook of Math... success" icon="fa fa-download"> **{{:fsc:kpk_fsc_part_1:ch02-matrices-and-determinants-fsc1-kpk.pdf|Download PDF}}** | **[[:fsc:kpk fsc part 1:chapter 02 matrices and determinants|View Online]]** </callo... "success" icon="fa fa-download"> **{{:fsc:kpk_fsc_part_1:ch12-graph-of-trigonometric-and-inverse-trigonometric-
- Old Question Papers/Model Papers HSSC-I (FSc-I): FBISE @fsc-part1-ptb
- arks}} ===== Old or Past Papers ===== * [[:fsc-part1-ptb:fbise-papers:view?f=mathematics-hssc-i-annual-2019-fbise|Mathematics I (Annual 2019)]] NEW * [[:fsc-part1-ptb:fbise-papers:view?f=mathematics-hssc-i-annual-2018-gp1-fbise|Mathematics I (Annual 2018) - Group 1]] NEW * [[:fsc-part1-ptb:fbise-papers:view?f=mathematics-hssc-i-annual-2018-gp2-fbise|Mathematics I (Annual 2018) - Group 2]] NEW * [[:fsc-part1-ptb:fbise-papers:view?f=mathematics-hssc-i-annual-2017-fbise|Mathematics I (Annual 2017) with Solutio
- Question 8, Exercise 1.2 @math-11-kpk:sol:unit01
- ====== Question 8, Exercise 1.2 ====== Solutions of Question 8 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of A Textbo... ====Question 8(i)===== Show that $z+\overline{z}=2\operatorname{Re}\left( z \right)$. ====Solution==... ib \right)\\ &=a+ib+a-ib\\ &=2a\\ z+\overline{z}&=2\operatorname{Re}\left( z \right)\end{align} ====
- Question 7, Exercise 1.2 @math-11-kpk:sol:unit01
- =&\dfrac{4}{29}+\dfrac{19}{29}i \end{align} Real part $=\dfrac{4}{29}$\\ Imaginary part $=\dfrac{19}{29}$ =====Question 7(ii)===== Separate into real and imaginary parts $\dfrac{{{\left... \ =&\dfrac{-3}{2}-\dfrac{1}{2}i\end{align} Real part $=\dfrac{-3}{2}$ \\ Imaginary part $=-\dfrac{1}{2}$ =====Question 7(iii)===== Separate into real and imaginary parts $\dfrac{1-i}{{{
- Unit 02: Matrices and Determinants (Solutions) @math-11-kpk:sol
- ===== Unit 02: Matrices and Determinants (Solutions) ===== This is a second unit of the book Mathema... bers and $i=\sqrt{-1}$. * Recognize $a$ as real part of $z$ and $b$ as imaginary part of $z$. * Know condition for equality of complex numbers. * Carry ... conjugate of $z=a+ib$. * Define $|z| = \sqrt{a^2+b^2}$ as the absolute value or modulus of a compl
- Definitions: FSc Part1 KPK @math-11-kpk
- ====== Definitions: FSc Part1 KPK ====== A Textbook of Mathematics for Class XI is published by Khybar P... eshawar, Pakistan. The book has total of twelve (12) chapters. Definition of the book provide the qu... equal parts in length, the angle subtended by one part at the center of the circle is called a degree. ... e $90^{\circ} \pm \theta, 180^{\circ} \pm \theta, 270^{\circ} \pm \theta, 360^{\circ} \pm \theta$ are
- Ch 07: Permutation, Combination and Probability: Mathematics FSc Part 1 @fsc:fsc_part_1_solutions:ch07
- Unit 05: Linear Inequalities and Linear Programming: Mathematics FSc part 2 @fsc:fsc_part_2_solutions:ch05
- Ch 08: Mathematical Induction and Binomial Theorem: Mathematics FSc Part 1 @fsc:fsc_part_1_solutions:ch08