Merging man & maths https://www.mathcity.org/ Fri, 05 Jun 2026 13:31:12 +0000 FeedCreator 1.8 https://www.mathcity.org/_media/logo.svg https://www.mathcity.org/ https://www.mathcity.org/fsc-part1-ptb/bise-papers 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… anonymous@undisclosed.example.com (Anonymous) Mon, 07 Feb 2022 13:46:14 +0000 https://www.mathcity.org/fsc-part1-ptb/bise-papers/view 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. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:33 +0000 https://www.mathcity.org/conferences Mathematics Conferences This page will no longer be updated. To spread the scope of this page, it has been merged with Mathematics Events. Conferences can be ideal places to meet with professionals and present our work to live audience to get engage with them. It might be best place to find collaborators from with in country and outside of the country. On this page we have posted mathematics conferences occurring all over the country (PAKISTAN). anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:39:21 +0000 https://www.mathcity.org/conferences/14th-rammma-2019-lahore Recent Advances in Mathematical Methods, Models & Applications, LSC Lahore, Pakistan (April 13-14, 2019) [RAMMMA LSE Lahore] New mathematical ideas may help in improving modeling of real problems, in deriving innovative and efficient numerical methods, and in developing approximate models which are amenable to mathematical analysis. There exists a non-trivial interplay between mathematics, mathematical modeling of complex systems and mathematical and computer methods oriented towards the quali… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:41:39 +0000 https://www.mathcity.org/khuram Khuram Ali Khan Khuram Ali Khan, PhD Associate Professor Department of Mathematics University of Sargodha Sargodha - PAKISTAN. Email: <khuram@MathCity.org> Field of Research: Difference and functional equations, Real functions, Mathematical inequalities involving convex functions, Time Scales Calculus, Soft Sets anonymous@undisclosed.example.com (Anonymous) Fri, 13 Jun 2025 12:03:59 +0000 https://www.mathcity.org/fsc/fsc_part_2_old_papers Old Papers (FSc Part 2) Federal Board of Intermediate & 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 & 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) anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:42:49 +0000 https://www.mathcity.org/fsc-part1-ptb/important-questions/ch08-mathematical-induction-and-binomial-theorem 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) * Use binomial theorem to show that $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$$(x-\frac{2}{x})^{10}$$… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:43 +0000 https://www.mathcity.org/conferences/conference_on_recent_advances_in_mathematical_methods_models_and_applications_lums Conference on Recent Advances in Mathematical Methods, Models and Applications, LUMS, Lahore (17-18 April 2010) [Main Building LUMS, Lahore] * Name of conference: Conference on Recent Advances in Mathematical Methods, Models and Applications * Palace: Lahore University of Management Sciences (LUMS), Lahore - PAKISTAN. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:41:46 +0000 https://www.mathcity.org/conferences/differential_equations_and_applications_may_26-28_2016_lums_lahore International Conference on Differential Equations and Applications, LUMS Lahore (May 26-28 2016) [Main Building LUMS, Lahore] * Name of conference: Differential Equations and Applications * Palace: Lahore University of Management Sciences (LUMS), Lahore - PAKISTAN. * Date: anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:41:47 +0000 https://www.mathcity.org/conferences/summer_conference_in_mathematics_2010_lums_lahore Summer Conference in Mathematics 2010, LUMS Lahore (July 26-27, 2010) [Main Building LUMS, Lahore] * Name of conference: Summer Conference in Mathematics 2010 * Palace: Lahore University of Management Sciences (LUMS), Lahore - PAKISTAN. * Date: 26-27 July 2010 (Monday and Tuesday) anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:42:12 +0000 https://www.mathcity.org/conferences/winter_conference_in_mathematics_2010_lums_lahore Winter Conference in Mathematics 2010, LUMS Lahore (January 11-12 2010) [Main Building LUMS, Lahore] * Name of conference: Winter Conference in Mathematics 2010 * Palace: Lahore University of Management Sciences (LUMS), Lahore - PAKISTAN. * Date: 11-12 January 2010 (Monday and Tuesday) anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:42:18 +0000 https://www.mathcity.org/conferences/winter_conference_in_mathematics_lums_lahore Winter Conference in Mathematics, LUMS Lahore (December 30-31, 2010) [Main Building LUMS, Lahore] * Name of conference: Winter Conference in Mathematics * Palace: Lahore University of Management Sciences (LUMS), Lahore - PAKISTAN. * Date: 30-31 December 2010 (Thursday and Friday) anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:42:18 +0000 https://www.mathcity.org/fsc/fsc_part_1_mcqs MCQs/Objective: HSSC-I Short Questions by Mr. Akhtar Abbas NEW Short Questions without answers by Mr. Akhtar Abbas for FSc Part 1. MCQs-Short Questions by Mr Parvez Khan MCQs and Short Question by Mr. Parvez Khan composed by Momin Ali: Text Book of Algebra and Trigonometry Class XI (Punjab Textbook Board, Lahore) MCQs by Nauman Idrees anonymous@undisclosed.example.com (Anonymous) Thu, 02 May 2024 17:05:13 +0000 https://www.mathcity.org/bsc/paper_pattern/sargodha_university/a-course_of_mathematics A-Course of Mathematics (Paper A & B) This subject is consists of two papers of 100 marks each. One is called “Paper A” and other is called “Paper B”. This page is updated on February 15, 2015. This syllabus is for 1st Annual 2015 and onward organized by University of Sargodha, Sargodha. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:54 +0000 https://www.mathcity.org/bsc/paper_pattern/sargodha_university/general_mathematics General Mathematics (Paper A & B) This subject is consists of two papers of 100 marks each. One is called “Paper A” and other is called “Paper B”. This syllabus is for 1st Annual 2015 and onward organized by University of Sargodha (UoS), Sargodha. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:55 +0000 https://www.mathcity.org/bsc/paper_pattern/sargodha_university/pure_mathematics Pure Mathematics (Paper A & B) This paper consist of two papers of 100 marks each. One paper is called “Paper A” and the other is called “Paper B”. Paper A * NOTE: attempt two questions from each section. SECTION-I (4/12: 17,17,17,17) anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:59 +0000 https://www.mathcity.org/papers Papers If you have any paper, which you think are also useful for others. you can send us (soft copy by email or hard copy by post) to publish on this page. Read more about here Old Papers of M.Phil. University of Sargodha Previous papers of MPhil (Mathematics) University of Sargodha, Sargodha. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:39:38 +0000 https://www.mathcity.org/conferences/5th-uicpam-2019-lahore 5th UMT International Conference on Pure and Applied Mathematics, Lahore (March 29th to 31st, 2019) [5th UICPAM-2019] UMT International Conference on Pure and Applied Mathematics (UICPAM) was successfully held for last four years. The support and participation of our membership and scholar promote it possible for UICPAM continuely to be held in University of Management and Technology, Lahore during March 29-31, 2019. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:41:44 +0000 https://www.mathcity.org/conferences/conference_on_general_relativity_and_gravitation_2010_pu_lahore Conference on General Relativity and Gravitation, PU Lahore (11-13 February 2010) University of the Punjab, Lahore is organizing the conference on General Relativity and Gravitation on February 11-13, 2010 [Old Campus, University of the Punjab, Lahore] * Conference Name: Conference on General Relativity and Gravitation anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:41:46 +0000 https://www.mathcity.org/conferences/icma-gcul-2017 International Conference on Mathematics and Its Applications GCU Lahore, Pakistan (November 13-15, 2017) [ICMA GCU Lahore] * Conference Name: International Conference on Mathematics and Its Applications * Registration Deadline: September 30, 2017 * Contact Dr. Shahid Ahmad ( anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:41:49 +0000 https://www.mathcity.org/conferences/international_conference_on_recent_advances_in_applied_mathematics_ciit_lahore International Conference on Recent Advances in Applied Mathematics, CIIT, Lahore (Dec 17-18, 2015) [CIIT Lahore] * Name of conference: International Conference on Recent Advances in Applied Mathematics * Palace: COMSATS Institute of Information Technology, Lahore - PAKISTAN. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:41:52 +0000 https://www.mathcity.org/conferences/wmaag-2015 Workshop on Modern Aspects of Algebra and Graph Theory, CIIT Lahore (March 27-28, 2015) * Name of conference: Workshop on Modern Aspects of Algebra and Graph Theory * Palace: COMSATS Institute of Information Technology (CIIT), Lahore - PAKISTAN. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:42:21 +0000 https://www.mathcity.org/fsc/fsc_part_2_mcqs MCQs/Objective: HSSC-II On this page, MCQ/Objective for FSc-II (HSSC-II) or FSc Part 2 are given. * Objective Mathematics 12th by Muhammad Shahbaz NEW * Short Questions without answers by Mr. Akhtar Abbas for FSc Part 2. * Short Questions by Mr. Akhtar Abbas * Short Questions without answers by Mr. Akhtar Abbas for FSc Part 2. anonymous@undisclosed.example.com (Anonymous) Fri, 21 Mar 2025 15:21:10 +0000 https://www.mathcity.org/fsc-part1-ptb/important-questions/ch03-matrices-and-determinants Ch 03: Matrices and Determinants * Fin $x$ and $y$ if $ \left[ {\begin{array}{c} x+3&1\\ -3& 3y-4 \end{array}} \right]= \left[ {\begin{array}{c} 2&1\\ -3&2 \end{array}} \right]$ --- BISE Gujrawala(2015) * Solve for matrix $A$ if $\left[ {\begin{array}{c}4&3\\ 2&2 \end{array}} \right]A-\left[ {\begin{array}{c} 2&3\\ -1&-2 \end{array}} \right]= \left[ {\begin{array}{c} -1&-4\\ 3&6 \end{array}} \right]$ --- BISE Gujrawala(2015) * Prove without expansion $ \left[ {\begin{array}{c} 6&7&… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:39 +0000 https://www.mathcity.org/fsc-part1-ptb/important-questions/ch07-permutation-combination-and-probablity 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 $400,000$ and $430,000$? ---$``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}{9}$… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:42 +0000 https://www.mathcity.org/bsc/paper_pattern/punjab_university/b.sc._paper_pattern_for_a_and_b_course_of_mathematics Syllabus & Paper Pattern for A and B Course of Mathematics This is a new page created to discuss the syllabus or course outline of PU splitted into two part. It will take some time to complete this page. Please stay in touch with this page to be updated. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:18 +0000 https://www.mathcity.org/bsc/paper_pattern/punjab_university/b.sc._paper_pattern_for_general_mathematics_split_program Syllabus & Paper Pattern for General Mathematics (Split Program) There was one examination after two years for BA/BSc Program from University of Punjab (PU), Lahore but from this year (2016), PU has made changes in its examination policies for the said program. The BA/BSc Program has been split into two parts. Syllabus is break into two part year wise. After the each year of the program candidate has to appeared in examination instead of appearing after two year. In this regards syllabus of Gen… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:21 +0000 https://www.mathcity.org/bsc/paper_pattern/sargodha_university/applied_mathematics Applied Mathematics (Paper A & B) This paper consista of two papers of 100 marks each. One paper is called “Paper A” and other is called “Paper B”. Paper A * NOTE: attempt two questions from each section. SECTION-I (4/12: 17,17,17,17) $(\lambda ,\mu )$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:46 +0000 https://www.mathcity.org/bsc/paper_pattern/sargodha_university/b-course_of_mathematics B-Course of Mathematics (Paper A & B) This subject is consists of two papers of 100 marks each. One is called “Paper A” and other is called “Paper B”. This page is updated on February 15, 2015. This syllabus is for 1st Annual 2015 and onward organized by University of Sargodha, Sargodha.$(\lambda ,\mu )$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:55 +0000 https://www.mathcity.org/conferences/1st-lgu-ncpam 1st LGU National Conference on Pure and Applied Mathematics (17-18 May 2017) [Lahore Garrison University] * Conference Name: 1st LGU National Conference on Pure and Applied Mathematics * Venue: Lahore Garrison University, DHA Phase IV, Lahore-PAKISTAN. * Conference Date: anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:41:41 +0000 https://www.mathcity.org/conferences/mathematical_inequalities_and_applications_2010_assms International Conference on Mathematical Inequalities and Application 2010, ASSMS, Lahore (7-13 March 2010) [ASSMS, old building in New Muslim Town, Lahore-PAKISTAN] * Conference Name: International Conference on Mathematical Inequalities and Application 2010 * Registration Deadline: January 30, 2010 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:41:52 +0000 https://www.mathcity.org/fsc-part1-kpk/important-questions Important Questions This page will be updated soon. * Prove that (without calculator) $\sin 10^{\circ}\sin 30^{\circ}\sin 50^{\circ}\sin 70^{\circ}=\frac{1}{16}$ --- BISE Gujrawala(2015) * Prove that $\sin(\frac{\pi}{4}-\theta)\sin(\frac{\pi}{4}+\theta)=\frac{1}{2}\csc^2\theta$ --- BISE Gujrawala(2017) * Prove that $\sin(\theta+\frac{\pi}{6})=\cos\theta$ --- BISE Gujrawala(2017) * Using without table or calculator find $tan(1110^{\circ})$ --- BISE Sargodha(2015), BISE Gujrawala(201… anonymous@undisclosed.example.com (Anonymous) Mon, 28 Aug 2023 17:06:07 +0000 https://www.mathcity.org/math-11-kpk/important-questions Important Questions This page will be updated soon. * Prove that (without calculator) $\sin 10^{\circ}\sin 30^{\circ}\sin 50^{\circ}\sin 70^{\circ}=\frac{1}{16}$ --- BISE Gujrawala(2015) * Prove that $\sin(\frac{\pi}{4}-\theta)\sin(\frac{\pi}{4}+\theta)=\frac{1}{2}\csc^2\theta$ --- BISE Gujrawala(2017) * Prove that $\sin(\theta+\frac{\pi}{6})=\cos\theta$ --- BISE Gujrawala(2017) * Using without table or calculator find $tan(1110^{\circ})$ --- BISE Sargodha(2015), BISE Gujrawala(201… anonymous@undisclosed.example.com (Anonymous) Tue, 05 Dec 2023 02:44:42 +0000 https://www.mathcity.org/people/kaushef Kaushef Salamat [Kaushef Salamat] [Solved Paper by Kaushef Salamat] We are very thankful to Ms. Kaushef Salamat for providing us notes. The author has done MPhil in Mathematics from Lahore Garrison University with Gold Medal. She is a lecturer in Queen Mary College Lahore. She also works as an online tutor for O Level and A Level Students. anonymous@undisclosed.example.com (Anonymous) Fri, 20 Jan 2023 17:40:22 +0000 https://www.mathcity.org/bsc/paper_pattern/punjab_university Syllabus/Model Papers for Punjab University Syllabus & Paper Pattern for General Mathematics (Split Program) NEW New syllabus and paper pattern for BSc General Mathematics for University of the Punjab for 1st year only Syllabus & Paper Pattern for A and B Course of Mathematics NEW New syllabus and paper pattern for BSc Double Mathematics for University of the Punjab for 1st year only anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:02 +0000 https://www.mathcity.org/fsc-part1-ptb/important-questions/ch01-number-systems 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}}$ --- BISE Sargodha(2015)$(\sqrt{2}, -\sqrt{5})$$\{0,-1\}$$a \div ib$$(-1)^\frac{-21}{2}$$(0,1)$$\{1,-1\}$$|z_… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:38 +0000 https://www.mathcity.org/fsc-part1-ptb/important-questions/ch04-quadratic-equations Ch 04: Quadratic Equations * Reduce $x^{-2}-10=3x^{-1}$ to quadratic form --- BISE Gujrawala(2015) * Show that $x^3-y^3=(x-y)(x-wy)(x-w^2y)$ --- BISE Gujrawala(2015) * If $n$ is an odd integer, is $(x+a)$ factor of $(x^n+a^n)$? --- BISE Gujrawala(2015) * If the roots of $px^2+qx+q=0$ are $\alpha$, $\beta$,then prove that $$\sqrt {\frac{\alpha}{\beta}}+\sqrt {\frac{\beta}{\alpha}}+\sqrt{\frac{p}{q}}=0$$ --- BISE Gujrawala(2017),BISE Sagodha(2017$${\begin{array}{c} x^2-5xy+6y^2=0\\x^2… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:40 +0000 https://www.mathcity.org/fsc-part1-ptb/important-questions/ch09-fundamentals-of-trigonometry Ch 09: Fundamental of Trigonometry * Find the value of the remaining trigonometric functions of $\theta$, If $cos \theta=\frac{12}{13}$ and the terminal side of the angle is not in the $I$ Quadrant. --- BISE Gujrawala(2015) * Express in radian $120'40''$ --- BISE Gujrawala(2017) * Verify $2 $ $\sin 45^{\circ} +\frac{1}{2}\cos 45^{\circ}=\frac{3}{\sqrt{2}}$$cosce \theta+tan\theta sec \theta=cosec \theta sec^2 \theta$$(tan\theta+cot\theta)^2=sec^2\theta cosec^2\theta$$150^{\circ}$$\theta$$l… anonymous@undisclosed.example.com (Anonymous) Sun, 28 Nov 2021 18:19:36 +0000 https://www.mathcity.org/fsc-part1-ptb/important-questions/ch10-trigonometric-identities Ch 10: Trigonometric Identities * Prove that (without calculator) $\sin 10^{\circ}\sin 30^{\circ}\sin 50^{\circ}\sin 70^{\circ}=\frac{1}{16}$ --- BISE Gujrawala(2015) * Prove that $\sin(\frac{\pi}{4}-\theta)\sin(\frac{\pi}{4}+\theta)=\frac{1}{2}\csc^2\theta$ --- BISE Gujrawala(2017) * Prove that $\sin(\theta+\frac{\pi}{6})=\cos\theta$ --- BISE Gujrawala(2017) * Using without table or calculator find $tan(1110^{\circ})$ --- BISE Sargodha(2015), BISE Gujrawala(2017)$sin(180^{\circ}+\a… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:44 +0000 https://www.mathcity.org/fsc-part1-ptb/important-questions/ch12-application-of-trigonometry Ch 12: Applications of Trigonometry * Find the value of $tan\frac{\alpha}{2}$ in term of $s$ --- BISE Gujrawala(2015) * Solve $\triangle ABC$ if $b=125$, $r=53^{\circ}$, $\alpha=47^{\circ}$ --- BISE Gujrawala(2015) * Show that $r_1=stan\frac{\alpha}{2}$ --- BISE Gujrawala(2015) * Define an escribed circle.--- BISE Gujrawala(2015) * With usual notation prove that $r_1+r_2+r_3-r=4R$$\triangle ABC$$r=90^{\circ}$$\alpha=62^{\circ}40'$$b=796$$\beta$$a$$\triangle ABC$$a=18$$b=24$$c=30$$\fra… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:46 +0000 https://www.mathcity.org/bsc/paper_pattern/sargodha_university/applied_mathematics_chapterwise Applied Mathematics Paper pattern for Applied Mathematics chapter-wise for University of Sargodha is given on this page. This pattern is extracted from syllabus, so use your own risk. Syllabus of Applied Mathematics can be seen here. Applied Mathematics is consists of two papers of 100 marks each. One is called “Paper A” and other is called “Paper B”. In every paper there are three sections with four questions each. A student have to attempt two questions from each section. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:54 +0000 https://www.mathcity.org/bsc/paper_pattern/sargodha_university/general_mathematics_chapterwise General Mathematics Paper pattern for General Mathematics chapter-wise for University of Sargodha is given on this page. This pattern is provided by Muhammad Siraj (+92-345-5365318). Syllabus of General Mathematics can be seen here. General Mathematics is consists of two papers of 100 marks each. One is called “Paper A” and other is called “Paper B”. In every paper there are three sections with four questions. A student have to attempt two questions from each section. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:58 +0000 https://www.mathcity.org/ppsc ~~DISCUSSION~~ PPSC General Information, Syllabus, Paper Pattern [PPSC] Our aim is to give general information, syllabus and paper pattern of paper couducted by Punjab Public Service Commission (PPSC) for the post of Lecturer in Mathematics. This page might be helpful for other jobs as subject specialist or for public service commission of other provinces. anonymous@undisclosed.example.com (Anonymous) Sun, 24 May 2026 17:45:57 +0000 https://www.mathcity.org/conferences/1st_uncpam-2015 1st UMT National Conference on Pure and Applied Mathematics, Lahore (7-8 March, 2015) * Name of conference: 1st UMT National Conference on Pure and Applied Mathematics * Palace: University of Management and Technology, Lahore - PAKISTAN. * anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:41:42 +0000 https://www.mathcity.org/conferences/5th_world_conference_on_21st_century_mathematics_2011_assms_lahore 5th World Conference on 21st Century Mathematics 2011, ASSMS, Lahore (9-13 February 2011) * Conference Name: 5th World Conference on 21st Century Mathematics 2011 * Registration Deadline: December 15, 2010 * Conference Date: February 9-13, 2011 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:41:44 +0000 https://www.mathcity.org/conferences/6th_world_conferences_on_21st_century_mathematics_lahore 6th World Conference on 21st Century Mathematics 2013, ASSMS, Lahore (6-9 March 2013) * Conference Name: 6th World Conference on 21st Century Mathematics 2013 * Registration Deadline: December 31, 2012 * Conference Date: March 6-9, 2013 * anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:41:45 +0000 https://www.mathcity.org/conferences/an_encounter_of_algebra_and_geometry_assms_lahore An Encounter of Algebra and Geometry, ASSMS, Lahore (19-22 November 2011) A Sharing and Learning Conference (Conference dedicated to Barbu Berceanu for his 60th birthday) * Conference Name: An Encounter of Algebra and Geometry * Registration Deadline: anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:41:45 +0000 https://www.mathcity.org/fsc-part1-ptb/important-questions 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,… anonymous@undisclosed.example.com (Anonymous) Thu, 18 Apr 2024 08:01:02 +0000 https://www.mathcity.org/fsc/fsc_part_1_model_papers FSc Part 1 Model Papers Federal Board of Intermediate & 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) anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:42:38 +0000 https://www.mathcity.org/fsc/fsc_part_2_model_papers FSc Part 2 Model Papers Federal Board of Intermediate & 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 & Secondary Education. All the boards in Punjab expect Federal Board have the same paper pattern. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:42:48 +0000 https://www.mathcity.org/papers/old_admission_test_of_assms_for_ph.d._mathematics Old admission test of ASSMS for Ph.D. Mathematics Abdus Salam School of Mathematical Sciences (ASSMS) was established by the Government of Punjab under the aegis of GC University Lahore. Goal of the School is to become a Centre of Excellence for research and advanced studies in Mathematical Sciences. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:43:59 +0000 https://www.mathcity.org/papers/old_papers_for_bsc_mathematics Old papers for BSc (Mathematics only) Previous/Past old papers of the University of the Punjab, Lahore and University of Sargodha for General Mathematics, Mathematics A Course and Mathematics B Course. * University of the Punjab, Lahore (Old Papers) Previous/Past old papers of General Mathematics, A-Course of Mathematics and B-Course of Mathematics for the University of the Punjab, Lahore - PAKISTAN. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:43:59 +0000 https://www.mathcity.org/papers/old_papers_for_msc_mathematics Old papers for MSc Mathematics * Previous/Past papers of University of the Punjab, Lahore and University of Sargodha. If you have any paper to share with us, you can send us a soft copy or a hard copy. Visit <http://www.mathcity.org/participate> for more info. * University of Sargodha, Sargodha (Old Papers) Previous/Past papers of University of Sargodha, Sargodha. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:44:02 +0000 https://www.mathcity.org/people/m-irfan-dogar Prof Muhammad Irfan Dogar [Mr. Muhammad Irfan Dogar] Prof Muhammad Irfan Dogar is a dedicated Mathematics Lecturer and a highly skilled Entry Test expert. He specializes in IGCSE and O/A-Level Mathematics, guiding students with clarity and confidence. Residing on Ravi Road, Lahore, he is admired for his commitment to education. anonymous@undisclosed.example.com (Anonymous) Mon, 01 Dec 2025 15:21:19 +0000 https://www.mathcity.org/fsc-part1-ptb/important-questions/ch02-functions-and-groups 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\}$$C=\{5,6,7,9,… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:39 +0000 https://www.mathcity.org/fsc-part1-ptb/important-questions/ch05-partial-fractions Ch 05: Partial Fraction * Resolve $\frac{1}{(x^2+1)(x+1)}$ into partial fraction --- BISE Gujrawala(2015) * Resolve the following into partial fractions $\frac{2x^4}{(x-3)(x+2)^2}$ --- BISE Gujrawala(2017) * Resolve $\frac{x^2+1}{(x+1)(x-1)}$ into partial fraction --- BISE Sargodha(2015),BISE Sargodha(2017) * Resolve $\frac{9}{(x+2)^2(x-1)}$$\frac{1}{(x-1)^2+(x+1)}$$\frac{x^2+1}{(x^3+1)}$$\frac{1}{(x-1)^2(x^2+2)}$$\frac{1}{x^2-1}$$\frac{x^2}{(x-2)(x-1)^2}$$\frac{3x-1}{(x^2+1)(x+3)}… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:40 +0000 https://www.mathcity.org/fsc-part1-ptb/important-questions/ch06-sequence-and-series Ch 06: Sequences and Series * If $\frac{1}{a}$, $\frac{1}{b}$ and $\frac{1}{c}$ are in $G.P$. Show that $r=\pm \sqrt{\frac{a}{c}}$ --- BISE Gujranwala(2015),BISE Sargodha(2015), BISE Sargodha(2017),BISE Lahore(2017) * With usual notation show that $AH=G^2$ --- BISE Gujrawala(2015) * Find $n$, so that $\frac{a^n+b^n}{a^{n-1}+b^{n-1}}$ maybe $A.M$ between $a$ and $b$$y=1+\frac{x}{2}+\frac{x^4}{4}+...$$x=2(\frac{y-1}{y})$$9th$$\frac{1}{3}, \frac{1}{5}, \frac{1}{7},...$$a=-2$$b=-6$$A.G$$\f… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:42 +0000 https://www.mathcity.org/fsc-part1-ptb/important-questions/ch13-inverse-trigonometry-functions Ch 13: Inverse Trigonometry Functions * Find the value of $cos^{-1}(\frac{1}{2})$ --- BISE Gujrawala(2015) * Prove that $2tan^{-1}(\frac{1}{3})+tan^{-1}(\frac{1}{7})=\frac{\pi}{4}$ --- BISE Gujrawala(2015), FBISE(2016) * Prove that $sin^{-1}(\frac{1}{\sqrt{5}})+cot^{-1}(3)=\frac{\pi}{4}$--- BISE Sargodha(2015), BISE Sargodha(2016), BISE Gujrawala(2017) * Prove that $cos^{-1}(-x)=\pi-cos^{-1}x$--- BISE Gujrawala(2017), FBISE(2017) $cos^{-1}(\frac{12}{13})=sin^{-1}(\frac{5}{13})$$cos(sin… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:46 +0000 https://www.mathcity.org/fsc/fsc_part_1_mcqs/mcqs-short_questions_by_mr._parvez_khan 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 $180^{\circ}$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:05 +0000 https://www.mathcity.org/msc/syllabus/pu Syllabus for PU Syllabus and scheme of studies for Regular/Private students doing MSc Mathematics from University of the Punjab, Lahore. 2 years M.Sc Mathematics programme consists of two parts namely Part-I and Part II. The regulation, Syllabi and Courses of Reading for the M.Sc. (Mathematics) Part-I and Part-II (Regular Scheme) are given below. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:50:16 +0000 https://www.mathcity.org/papers/old_papers_for_bsc_mathematics/punjab_university University of the Punjab, Lahore (Old Papers) [Old paper PU] Old papers for BSc (Mathematics), University of the Punjab, Lahore. From 2016, BSc has been split in to two parts. There will be exam after each year. Syllabus and chapter-wise paper pattern for Mathematics A & B courses is available anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:50:34 +0000 https://www.mathcity.org/papers/old_papers_for_msc_mathematics/punjab_university University of the Punjab, Lahore (Old Papers) Old papers for MSc (Mathematics), University of the Punjab, Lahore. Hopefully this will help students to understand the pattern. . Notes of different subject are available in MSc Notes section of this website. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:50:42 +0000 https://www.mathcity.org/bsc/paper_pattern/sargodha_university/pure_mathematics_chapterwise Pure Mathematics Paper pattern for Pure Mathematics chapter-wise for University of Sargodha is given on this page. This pattern is extracted from syllabus, so use your own risk. Syllabus of Pure Mathematics can be seen here. Pure Mathematics is consists of two papers of 100 marks each. One is called “Paper A” and other is called “Paper B”. In every paper there are three sections with four questions each. A student have to attempt two questions from each section. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:56:03 +0000 https://www.mathcity.org/fsc-part1-ptb/sol/ch01/ex1-1 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 MathCity.org $\{0… anonymous@undisclosed.example.com (Anonymous) Thu, 13 Apr 2023 09:34:48 +0000 https://www.mathcity.org/fsc-part1-ptb/sol/ch02/ex2-8 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 \\ \hline 1 & 1 & … anonymous@undisclosed.example.com (Anonymous) Wed, 05 Apr 2023 12:55:15 +0000 https://www.mathcity.org/fsc FSc Notes (Solutions), MCQs/Objective type questions, model papers and old/previous papers (of FBISE and BISE) given here, are useful for FSc Part 1 and Part 2 (HSSC). Text Book of Algebra and Trigonometry Class XI and Calculus and Analytic Geometry, MATHEMATICS 12, Punjab Text Book Board Lahore anonymous@undisclosed.example.com (Anonymous) Fri, 26 May 2023 06:29:22 +0000 https://www.mathcity.org/fsc-part1-ptb FSc/ICS Part 1 (Mathematics): PTB This is an old book. Notes of new book are available at following URL: <https://www.mathcity.org/math-11-pectaa> [Textbook of Algebra and Trigonometry Class XI] Textbook of Algebra and Trigonometry Class XI is published by Punjab Textbook Board (PTB) Lahore, Pakistan. The book has total of 14 chapters. anonymous@undisclosed.example.com (Anonymous) Sat, 19 Jul 2025 17:19:20 +0000 https://www.mathcity.org/fsc-part2-ptb FSc/ICS Part 2 (Mathematics): PTB [Calculus and Analytic Geometry, MATHEMATICS 12] Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc/ICS Part 2 or HSSC-II), Punjab Textbook Board (PTB) Lahore, Pakistan. There are total seven (7) units in this book. One this page we have posted Notes (Solutions), MCQs, short question, sample papers and old papers related to this subject. This book has wide scope and it is part of syllabus of Mathematics in FSc/ICS from all board (Board of Intermedi… anonymous@undisclosed.example.com (Anonymous) Sun, 22 Sep 2024 08:59:48 +0000 https://www.mathcity.org/math-9th-pctb Mathematics 9th for Matric (PCTB) [Mathematics 9th for Matric (PCTB)] Mathematics 9 is published by Punjab Curriculum and Textbook Board (PCTB), Lahore, Pakistan. This is a textbook for all the boards of Punjab for matriculation. The book has total of thirteen (13) chapters. The book is written by Muhammad Akhtar Shirani (Senior Subject Specialist, Mathematics), Madiha Mehmood, (Subject Specialist, Statistics) and Ghulam Murtaza (Subject Specialist, Mathematics). anonymous@undisclosed.example.com (Anonymous) Mon, 04 May 2026 16:19:23 +0000 https://www.mathcity.org/math-11-pectaa Mathematics 11 (PECTAA) [Mathematics 11 for FSc and ICS (PECTAA)] Mathematics 11 is is based on Updated/Revised National Curriculum of Pakistan 2023 and has been approved by the Punjab Education, Curriculum, Training and Assessment Authority (PECTAA) previously known as Punjab Textbook Board (PTB). This is a textbook for all the boards of Punjab for 11th class (FSc or ICS Part 1 or HSSC-I). The book has total of fourteen (14) units. anonymous@undisclosed.example.com (Anonymous) Sun, 20 Jul 2025 06:50:20 +0000 https://www.mathcity.org/participate Participate If you have written notes, then why not share on MathCity.org with others. This is your help to mathematics students and teachers (یہ صدقہ جاریہ ہے). For further details, please contact webmaster for more information. * The material given on MathCity.org is free and publish to help the students to learn Mathematics. It will take a lot of time to manage this website and prepare new material to publish on this website. anonymous@undisclosed.example.com (Anonymous) Sun, 31 May 2026 09:56:03 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry Notes of Calculus with Analytic Geometry [Calculus with Analytic Geometry by Dr. S. M. Yusuf and Prof. Muhammad Amin] Calculus with Analytic Geometry by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore-Pakistan is one of the books studied widely in Bachelor and undergraduate classes inclduing different engineering programs. There are total of ten chapters. Solutions of the books are given in the chapters listed below. The only aim to publish the soltuions is to pro… anonymous@undisclosed.example.com (Anonymous) Mon, 30 May 2022 17:44:37 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method Notes of Mathematical Method [BSc Mathematical Method] Notes of the Mathematical Method written by by S.M. Yusuf, A. Majeed and M. Amin and published by Ilmi Kitab Khana, Lahore. This is an old and good book of mathematical method. The notes given here are provided by awesome peoples, who dare to help others. Some of the notes are send by the authors of these notes and other are send by people who didn't write but share these notes as Open Educational Resources (OER). We are thankful to anonymous@undisclosed.example.com (Anonymous) Sun, 02 Jul 2023 07:49:56 +0000 https://www.mathcity.org/bsc/paper_pattern Syllabus and paper pattern In Pakistan, BSc is a 2 year programme after FSc or FA. One can choose either a one course of mathematics known as “General Mathematics” or two courses of mathematics, in University of the Punjab, Lahore these are known as anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:41:06 +0000 https://www.mathcity.org/fsc-part1-ptb/definitions 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… anonymous@undisclosed.example.com (Anonymous) Sun, 22 Sep 2024 17:12:21 +0000 https://www.mathcity.org/fsc-part1-ptb/definitions-and-review 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. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:42:56 +0000 https://www.mathcity.org/fsc-part1-ptb/definitions-aurang-zaib 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 \( \dfrac{p}{q} \)\( p, q \in \mathbb{Z} \)\( q \neq 0 \)\( \dfrac{3}{4} \)\( \dfrac{7}{2} \)\( \sqrt{2} \)\( \pi \)\( \mathbb{R} \)\( 0.25 \)\( 3.75 \)\( 0.3333... \)\( 1.234234... \)\( \pi \)\( 3.1415... \)\( \sqrt{2} \)\(… anonymous@undisclosed.example.com (Anonymous) Sat, 30 Mar 2024 16:48:20 +0000 https://www.mathcity.org/fsc-part1-ptb/definitions-muzzammil-subhan 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)$ anonymous@undisclosed.example.com (Anonymous) Sun, 22 Sep 2024 17:24:14 +0000 https://www.mathcity.org/fsc-part1-ptb/fbise-papers 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 anonymous@undisclosed.example.com (Anonymous) Mon, 11 Dec 2023 13:01:04 +0000 https://www.mathcity.org/fsc-part1-ptb/mcq-bank 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. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:43:02 +0000 https://www.mathcity.org/fsc-part1-ptb/mcqs 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}$$\forall a, b, c \in R$$a<b \wedge c>0\Rightarrow ac\geq bc$$a<b \wedge c>0\Rightarrow ac> bc$$a<b \wedge… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:43:03 +0000 https://www.mathcity.org/fsc-part1-ptb/sol 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 under a Cre… anonymous@undisclosed.example.com (Anonymous) Tue, 08 Aug 2023 17:59:03 +0000 https://www.mathcity.org/fsc-part1-ptb/solution-and-area-of-oblique-triangle Solution and Area of Oblique Triangle These are the common formulas used in Chapter 12 of Textbook of Algebra and Trigonometry Class XI, Punjab Textbook 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 and a word file is also given if you wish to modify the contents or credit as you need.$a^2=b^2+c^2-2bc\cos \alpha$$b^2=c^2+a^2-2ca\cos \bet… anonymous@undisclosed.example.com (Anonymous) Mon, 25 Sep 2023 15:48:59 +0000 https://www.mathcity.org/fsc-part1-ptb/trigonometric-formulas Trigonometric Formulas These are the common formulas used in Chapter 9 to 14 of Textbook of Algebra and Trigonometry Class XI, Punjab Textbook Board Lahore. This handout is very helpful to remember the formulas. All these formulas are given for real valued and defined trigonometric functions. A PDF file can be downloaded for high quality printing and a word file is also given if you wish to modify the contents or credit as you need.${{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1$$1+{{\tan }^{2}}\t… anonymous@undisclosed.example.com (Anonymous) Thu, 25 May 2023 02:59:50 +0000 https://www.mathcity.org/fsc-part2-ptb/definitions Definitions: FSc Part 2 (Mathematics): PTB On this page, all the definitions of “Calculus and Analytic Geometry, MATHEMATICS 12” (Mathematics FSc Part 2 or HSSC-II), Punjab Textbook Board (PTB) Lahore, Pakistan are given. We are very thankful to $A=x^2$$f:X\to Y$$X$$f:X\to Y$$y$$Y$$y=ax+b$$x$$y$$f(x)=2x-6$$p(x) = {a_n}{x^n} + {a_{n - 1}}{x^{n - 1}} + {a_{n - 2}}{x^{n - 2}} + ... + {a_1}x + {a_0}$${a_0},\,{a_1},\,{a_2},...,{a_n}$$f(x)=ax+b$$X$$I:X\to X$$X$$Y$$C:X \rightarrow Y$$C(x)=a$$x \in X$$… anonymous@undisclosed.example.com (Anonymous) Sun, 20 Oct 2024 18:16:52 +0000 https://www.mathcity.org/fsc-part2-ptb/definitions-muzzammil-subhan Definitions: Mathematics 12: PTB by Muzzammil Subhan Definitions from Calculus and Analytic Geometry, MATHEMATICS 12, 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$P(x)=a_0 x^0+a_1 x^1+a_2 x^2+\ldots . .+a_{n-1} x^{n-1}+a_n x^n$$n \in W$$a_0, a_1, a_2, \ldots, a_n \in R$$f(x)=a x+b$$a, b \in R$$a \neq 0$$f(x)=x$$f(x)=c$$c \in R$$\frac{P(x)}{Q(x)}$… anonymous@undisclosed.example.com (Anonymous) Sun, 20 Oct 2024 18:16:28 +0000 https://www.mathcity.org/fsc-part2-ptb/fbise-papers Old Question Papers/Model Papers HSSC-II (FSc-II): FBISE Old (past) question papers and model papers of mathematics (math) for HSSC-II (FSc Part 2) conducted by Federal Board of Intermediate and Secondary Education (FBISE), Islamabad. Paper Pattern anonymous@undisclosed.example.com (Anonymous) Sun, 02 Jan 2022 18:31:48 +0000 https://www.mathcity.org/fsc-part2-ptb/important-questions Important Questions: HSSC-II These questions are taken from old papers for the book Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Textbook Board (PTB) Lahore, Pakistan. * Unit 01: Functions and Limits * Unit 02: Differentiation * Unit 03: Integration * Unit 04: Introduction to Analytic Geometry * Unit 05: Linear Inequalities and Linear Programming * anonymous@undisclosed.example.com (Anonymous) Thu, 18 Apr 2024 08:02:52 +0000 https://www.mathcity.org/fsc-part2-ptb/subjective-mathematics-m-shahbaz Subjective Mathematics 12th by Muhammad Shahbaz [Subjective Mathematics 12th by Muhammad Shahbaz] These handwritten notes are sent by Muhammad Shahbaz. We are very thankful to him for sending these notes. These notes are based on the book “Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc/ICS Part 2 or HSSC-II), Punjab Textbook Board (PTB) Lahore, Pakistan.'' There are total seven (7) units in this book. anonymous@undisclosed.example.com (Anonymous) Tue, 23 Sep 2025 19:59:04 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions FSc Part 1 Mathematics Notes/Solutions This is an old book. Notes of new book are available at following link: <https://www.mathcity.org/math-11-pectaa> [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. anonymous@undisclosed.example.com (Anonymous) Sun, 20 Jul 2025 09:10:04 +0000 https://www.mathcity.org/fsc/fsc_part_1_trigonometric_review 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 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:42:42 +0000 https://www.mathcity.org/fsc/fsc_part_2_solutions 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… anonymous@undisclosed.example.com (Anonymous) Fri, 21 Mar 2025 18:12:01 +0000 https://www.mathcity.org/math-9th-pctb/mcqs MCQS of Mathematics 9 (PCTB) Mathematics 9 is published by Punjab Curriculum and Textbook Board (PCTB), Lahore, Pakistan. This is a textbook for all the boards of Punjab for matriculation. The book has total of thirteen (13) chapters. The book is written by Muhammad Akhtar Shirani (Senior Subject Specialist, Mathematics), Madiha Mehmood, (Subject Specialist, Statistics) and Ghulam Murtaza (Subject Specialist, Mathematics). anonymous@undisclosed.example.com (Anonymous) Tue, 18 Nov 2025 17:29:59 +0000 https://www.mathcity.org/math-9th-pctb/sol Solutions: Math 9th PCTB [Solutions of Mathematics 9th PCTB] Notes (Solutions) of Mathematics 9 (Mathematics for Matric), Punjab Curriculum and Textbook Board (PCTB) Lahore. Our aim here is to provides clear and step-by-step solutions for mathematical concepts, including real numbers, logarithms, algebra, trigonometry, and probability. we will try our best to complete the solutions as soon as possible for teachers and students. To download a book, please anonymous@undisclosed.example.com (Anonymous) Mon, 04 May 2026 16:21:21 +0000 https://www.mathcity.org/math-11-pectaa/mcqs Multiple Choice Questions (MCQs) [FSC ICS Part 1 Math MCQs (11th Class) – Punjab Textbook Board] FSC or ICS Part 1 Math Multiple Choice Questions (MCQs) (11th Class). Mathematics 11 (FSc or ICS Part 1, HSSC-I) is published by Punjab Education, Curriculum, Training and Assessment Authority (PECTAA) Lahore - Pakistan formally know as Punjab Textbook Board (PTB) anonymous@undisclosed.example.com (Anonymous) Tue, 26 Aug 2025 11:48:11 +0000 https://www.mathcity.org/math-11-pectaa/sol FSC/ICS Part 1 Math Solution (11th Class) – Punjab Board Solved Exercises [FSC ICS Part 1 Math Solution (11th Class) – Punjab Board Solved Exercises] FSC or ICS Part 1 Math Solution (11th Class), Punjab Board Solved Exercises. Mathematics 11 (FSc or ICS Part 1, HSSC-I) is published by Punjab Education, Curriculum, Training and Assessment Authority (PECTAA) Lahore - Pakistan formally know as Punjab Textbook Board (PTB) anonymous@undisclosed.example.com (Anonymous) Sun, 24 May 2026 10:06:29 +0000 https://www.mathcity.org/matric/9th_general General Mathematics 9 [General Mathematics 9th Class] There are ten chapters in General Mathematics 9 for Punjab Textbook Board, Lahore. Solutions of all the chapters are given below. One can download the PDF file of the notes. Please remember that, to view these notes one must have PDF reader installed in their system. We will try our best to add online view of the notes very soon. anonymous@undisclosed.example.com (Anonymous) Mon, 15 Dec 2025 16:49:07 +0000 https://www.mathcity.org/matric/9th_science Mathematics 9 (Science Group) [Mathematics 9 (Science Group)] Mathematics 9 is written by Dr. Karamat H. Dar and Prof. Irfan-ul-Haq and this book is published by Carvan Book House, Lahore, Pakistan. This book consist of 302 pages and there are 17 units. Notes of Unit 1 and 3 are provided by $ka + kb + kc$$ac + ad + bc + bd$$a^2 + 2ab + b^2$$a^2 – b^2$$a^2 + 2ab + b^2 – c^2$$a^4 + a^2b^2 + b^4$$a^4 + 4b^4$$x^2 + px + q$$ax^2 + bx + c$$(ax^2 + bx + c) (ax2 + bx + d) + k$$(x + a) (x + b) (x + c) … anonymous@undisclosed.example.com (Anonymous) Wed, 08 Mar 2023 18:04:36 +0000 https://www.mathcity.org/matric/10th_science Mathematics 10 (Science Group) [Matric Science 10th Book Cover] The notes/solutions, definitions, MCQs and important question for Mathematics 10 (Science Group), published by Ilmi Kitab Khana, Urdu Bazar, Lahore, Pakistan are available on this page. Whenever we found the notes we will update this page and will upload notes here. If you wish to contribute and send us the notes please contact us via our $(b^2-4ac)$$ax^2+bx+c$$\mathbb{N}$$\mathbb{W}$$\mathbb{Z}$$E$$O$$P$$\mathbb{Q}$$\cup$$\cap$$\s… anonymous@undisclosed.example.com (Anonymous) Wed, 24 Jul 2024 18:33:10 +0000 https://www.mathcity.org/notes/analysis Notes of Analysis advanced-analysis-handwritten-notes Advanced Analysis: Handwritten Notes A handwritten notes of Advanced Analysis provided by Mr. Anwar Khan. We are really very thankful to Mr. Anwar Khan for providing these notes of 260 pages. Advanced-Analysis-iqra-liaqat Advance Analysis by Ms. Iqra Liaqat A handwritten notes of Advanced Analysis provided by Ms. Iqra Liaqat. Summary and contents are given on the page of notes. anonymous@undisclosed.example.com (Anonymous) Fri, 18 Aug 2023 15:15:07 +0000 https://www.mathcity.org/notes/fundamental-of-complex-analysis-prof-m-saleem Fundamental of Complex Analysis (Solutions of Some Exercises) [Fundamental of Complex Analysis, Solutions of Some Exercises] Complex analysis is the study of functions that exist in the complex plane, that is, functions with complex arguments and complex outputs. With roots in the 18th century and the years just before, it is one of the classical branches of mathematics. In the 20th century, significant figures in mathematics who are connected to complex numbers include Euler, Gauss, Riemann, … anonymous@undisclosed.example.com (Anonymous) Sat, 15 Apr 2023 18:26:12 +0000 https://www.mathcity.org/notes/topology-and-functional-analysis-solved-pu Topology and Functional Analysis Solved Paper by Noman Khalid These solved papers are written and provided by Mr. noman-khalid. We are very thankful to him for providing these notes to publish on MathCity.org. Topology and Functional Analysis is considered as one the tough subject in BS/MSc Mathematics in different universities. Here solved paper for the said subject is given for the University of the Punjab (PU), Lahore. anonymous@undisclosed.example.com (Anonymous) Sun, 11 Feb 2024 12:38:09 +0000 https://www.mathcity.org/papers/old_ppsc_written_tests_for_lecturer_mathematics Old PPSC Written tests for Lecturer (Mathematics) * Previous Written tests (papers) of Punjab Public Service Commission, Lahore for Lecturer in Mathematics. * From now the PPSC will conduct a MCQs test for this post. * We have created a page to give information to students. This page is anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:44:09 +0000 https://www.mathcity.org/people/bahadar-ali-khan Bahadar Ali Khan [Bahadar Ali Khan] We are very thankful to Mr. Bahadar Ali Khan for contributing to this website. * Email: <bahadarkhan639@yahoo.com> * Cell: +92-305-8069878 * Civil Engineer from University of Engineering & Technology Lahore (Narowal Campus) Contribution: bahadar_ali_khan-contributor anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:44:39 +0000 https://www.mathcity.org/people/bilal-mehand Bilal Mehand We are very thankful to Mr. Bilal Mehand for his contribution to the website. [Bilal Mehand] Mr. Bilal Mehand belongs to a nearby village (Vinni) of District Hafizabad. He has done MSc in Mathematics from University of the Punjab, Lahore. Now, he wants to do PhD after MPhil. He wishes every student to be a good mathematician. anonymous@undisclosed.example.com (Anonymous) Wed, 16 Apr 2025 17:15:20 +0000 https://www.mathcity.org/people/moin Engr. Moin Latif We are very thankful to Engr. Moin Latif for his contribution to the website. [Moin Latif] * Email: <moinlatif@gmail.com> * Cell: +92-342-7673137 * Qualification: B.E (UET Lahore, Pakistan) * Currently working as Assistant Manager at Millat Tractors Limited. anonymous@undisclosed.example.com (Anonymous) Sun, 17 Dec 2023 16:55:22 +0000 https://www.mathcity.org/people/saleem-shahzad Sheikh Muhammad Saleem Shahzad “Mr. Saleem, an accomplished mathematician with an M.Phil in Processor Optimization through Memoryless Computations from the University of Sargodha, currently serves as a dedicated Mathematics Lecturer at Government Graduate College Jauharabad. His teaching experience includes a role as a Visiting Lecturer at the University of Education, Lahore, where he instructed courses such as Calculus, Set Theory, Real Analysis, Group Theory, and Linear Algebra. Additionally,… anonymous@undisclosed.example.com (Anonymous) Sat, 23 Dec 2023 13:41:25 +0000 https://www.mathcity.org/ppsc/ppsc-maths-2021 PPSC Paper 2021 (Lecturer in Mathematics) [PPSC Paper 2011 (Lecturer in Mathematics)] On this page, we have given question from old (past) paper of Lecturer in Mathematics conducted in year 2021. This is a MCQs paper and answers are given at the end of the paper. At the end of the PDF is also given to download. This paper is provided by Ms. \(2018\)$4$\(6\)$8$$10$\(X\)\(Y\)\(X\times Y\)\(\parallel (x,y) \parallel=\parallel x\parallel+\parallel y\parallel, \,\forall \, (x,y)\in X \times Y\)\(f(… anonymous@undisclosed.example.com (Anonymous) Tue, 23 Aug 2022 17:04:49 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch01_real_numbers_limits_and_continuity Chapter 01: Real Numbers, Limits and Continuity [Chapter 01 of Calculus with Analytic Geometry] Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. The notes of this chapter is written by Prof. $\mathbb{R}$$\mathbb{R}$$\mathbb{R}$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:28 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch02_derivatives Chapter 02: The Derivative [Chapter 02: The Derivative BSc Calculus] Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Here are few online resource, which are very helpful to find derivative. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:28 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch06_plane_curves_i Chapter 06: Plane Curves I Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. [Conic section] Contents and summary * Conic sections * The parabola * The ellipse anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:31 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch07_plane_curves_ii Chapter 07: Plane Curves II Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. [Asymptote] Contents and summary * Asymptotes: A straight line $l$ is called an asymptote for a curve $C$$l$$C$$l$$l$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:32 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch08_analytic_geometry_of_three_dimensions Chapter 08: Analytic Geometry of Three Dimensions Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Contents & Summary * Distance between two points$\mathbb{R}^3$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:33 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch01_complex_numbers Chapter 01: Complex Numbers [Chapter 01 Complex Numbers Methods] Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. A complex number is an element $(x,y)$ of the set $$ \mathbb{R}^2=\{(x,y): x,y \in \mathbb{R}\} $$ obeying the following rules of addition and multiplication.$z_1=(x_1,y_1)$$z_2=(x_2,y_2)$$z_1+z_2= (x_1+x_2, y_1+y_2)$$z_1 z_2 = (x_1 x_2 - y_1 y_2, x_1 y_2+y_1 x_2)$$\mathbb{R}^2$$\mathbb{C}$ anonymous@undisclosed.example.com (Anonymous) Mon, 11 Dec 2023 12:59:57 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch02_groups Chapter 02: Groups [Chapter 02: Groups] Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Contents and summary * Definition (axioms of group) * Definition ( commutative group ) * anonymous@undisclosed.example.com (Anonymous) Mon, 11 Dec 2023 13:00:23 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch03_matrices Chapter 03: Matrices Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. The difficulty level of this chapter is very low. Most of the questions involve calculations. This chapter is wide range of applications in Linear Algebra. In many universities teachers include this chapter in the syllabus of Linear Algebra for BS students of mathematics and other subjects. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:44 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch04_system_of_linear_equations Chapter 04: System of Linear Equations Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. The difficulty level of this chapter is low. Most of the questions involve calculations. This chapter is wide range of applications in Linear Algebra and Operations Research. In many universities teachers include this chapter in the syllabus of Linear Algebra and Operations Research for BS students of mathematics and other … anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:45 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch06_vector_spaces Chapter 06: Vector Spaces Notes of Chapter 06 Vector Spaces of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Contents and summary * Subspaces * Linear combinations and spanning sets anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:47 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch07_inner_product_spaces Chapter 07: Inner Product Spaces Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Inner product spaces form and important topic of Functional Analysis. These are simply vector space over the field of real or complex numbers and with an inner product defined on them. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:48 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch08_infinite_series Chapter 08: Infinite Series Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Infinite series are of great importance in both pure and applied mathematics. They play a significant role in Physics and engineering. In fact many functions can be represented by infinite series. The theory of infinite series is developed through the use of special kind of function called sequence. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:49 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch09_first_order_differential_equations Chapter 09: First Order Differential Equations Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Contents and summary * D.E and their classification * Formation of differential equation anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:50 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch10_higher_order_linear_differential_equations Chapter 10: Higher Order Linear Differential Equations Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Contents and summary * Higher order linear differential equations anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:51 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch11_the_laplace_transform Chapter 11: The Laplace Transform Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin. This book is published by Ilmi Kitab Khana, Lahore - PAKISTAN. Solutions of Chapter 11: The Laplace Transform are given here in pdf form. $f$$[0,\infty)$$f$$\mathcal{L}(f)$$F$$ provided the above improper integral converges. We have $ anonymous@undisclosed.example.com (Anonymous) Sun, 29 May 2022 17:43:26 +0000 https://www.mathcity.org/fsc-part1-ptb/important-questions/ch11-trigonometric-functions-and-their-graphs Ch 11: Trigonometric Functions and Their Graphs * Find the period of $\sin 4x$ --- BISE Gujrawala(2015) * Find the period of $\tan 4x$ --- BISE Gujrawala(2017) * Find the period of $\sin\frac{x}{5}$ --- BISE Sargodha(2015), BISE Sargodha(2016) * Find the period of $cosec10x$ --- BISE Sargodha(2015)$\cot\frac{x}{2}$$\sin x$$2\pi$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:44 +0000 https://www.mathcity.org/fsc-part1-ptb/important-questions/ch14-solutions-of-trigonometric-equation Ch 14: Solutions of Trigonometric Equation * Solve $cose^2\theta=\frac{4}{3}$ in $[0,2\pi]$--- BISE Gujrawala(2015), BISE Sargodha(2016), BISE Gujrawala(2017) * Solve $sinx=\frac{1}{2}$ in $[0,2\pi]$--- BISE Gujrawala(2015) * Solve $cot\theta = \frac{1}{\sqrt{3}}$, $\theta \in [0,2\pi]$--- BISE Gujrawala(2017), BISE Sargodha(2016) * Solve $sec^2\theta=\frac{4}{3}$ in $[0,2\pi]$--- BISE Sargodha(2015)$4cos^2x-3=0$$x \in [0,2\pi]$$secx=-2$$x \in [0,2\pi]$$cosec\theta=2$$[0,2\pi]$$tanx=-1… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:46 +0000 https://www.mathcity.org/fsc-part1-ptb/mcq-bank/ch01 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}})$$(\displaystyle{\frac{1}{10}},-\display… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:49 +0000 https://www.mathcity.org/fsc-part1-ptb/mcq-bank/ch02 MCQs: Ch 02 Sets, Functions and Groups High quality MCQs of Chapter 02 Sets, Functions and Groups of Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. The answers are given at the end of the page.$\forall$$\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=… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:49 +0000 https://www.mathcity.org/fsc-part1-ptb/mcq-bank/ch04 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-… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:50 +0000 https://www.mathcity.org/fsc/fsc_part_1_mcqs/fill_in_the_blanks_by_rauf_nabeel Fill in the blanks by Rauf & Nabeel * Fill in the blanks, provided by Adil Rauf & 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) anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:06 +0000 https://www.mathcity.org/fsc/fsc_part_1_mcqs/mcqs_by_muhammad_imran_qureshi 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) anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:06 +0000 https://www.mathcity.org/fsc/fsc_part_1_mcqs/mcqs_by_nauman_idrees 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) | anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:06 +0000 https://www.mathcity.org/fsc/fsc_part_1_mcqs/short_questions_by_mr._akhtar_abbas 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. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:09 +0000 https://www.mathcity.org/fsc/fsc_part_1_old_papers/fbise_annual_2009 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 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:16 +0000 https://www.mathcity.org/fsc/fsc_part_1_old_papers/fbise_annual_2011 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 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:18 +0000 https://www.mathcity.org/fsc/fsc_part_1_old_papers/fbise_annual_2012 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 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:18 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch01 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}$ anonymous@undisclosed.example.com (Anonymous) Sat, 03 Jun 2023 16:30:31 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch02 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$p\leftrightarrow q$ anonymous@undisclosed.example.com (Anonymous) Wed, 05 Apr 2023 12:54:57 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch03 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$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:27 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch04 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 Equations anonymous@undisclosed.example.com (Anonymous) Sun, 04 Jun 2023 16:13:15 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch05 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$\frac {P(x)}{Q(x)}$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:29 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch06 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 $$\begin{align}L.H.S &= l(q-r)+m(r-p)+n(p-q)\\ &= lq-lr+mr-mp+np-nq\\ &=… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:29 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch07 Chapter 07: Permutation, Combination and Probability [Chapter 07: Permutation , Combination and Probability] Notes (Solutions) of Chapter 07: Permutation , Combination and Probability, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary anonymous@undisclosed.example.com (Anonymous) Sat, 26 Mar 2022 16:28:40 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch08 Chapter 08: Mathematical Induction and Binomial Theorem [Chapter 08 Mathematical Induction and Binomial Theorem] Notes (Solutions) of Chapter 08: Mathematical Induction and Binomial Theorem, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.$(a+x)^n$$(a+x)^n$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:30 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch09 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… anonymous@undisclosed.example.com (Anonymous) Sun, 04 Jun 2023 16:03:04 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch10 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. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:32 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch11 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$$-2\pi \hbox{ to } 2\pi… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:34 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch12 Chapter 12: Application of Trigonometry [Chapter 12: Application of Trigonometry] Notes (Solutions) of Chapter 12: Application of Trigonometry, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary * Introduction anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:34 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch13 Chapter 13: Inverse Trigonometric Functions [Chapter 13: Inverse Trigonometric Functions] Notes (Solutions) of Chapter 13: Inverse Trigonometric Functions, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. Contents & summary * ${\sin ^{ - 1}}A + {\sin ^{ - 1}}B = {\sin ^{ - 1}}\left( {A\sqrt {1 - {B^2}} + B\sqrt {1 - {A^2}} } \right)$${\sin ^{ - 1}}A - {\sin ^{ - 1}}B = {\sin ^{ - 1}}\left( {A\sqrt {1 - {B^2}} - B\sqrt {1 - {… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:37 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch14 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… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:37 +0000 https://www.mathcity.org/fsc/fsc_part_2_mcqs/mcqs_by_muhammad_imran_qureshi 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) anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:42 +0000 https://www.mathcity.org/fsc/fsc_part_2_mcqs/mcqs_by_nauman_idrees 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 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:43 +0000 https://www.mathcity.org/fsc/fsc_part_2_mcqs/mcqs-short_questions_by_mr._parvez_khan 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. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:42 +0000 https://www.mathcity.org/fsc/fsc_part_2_mcqs/short_questions_by_mr._akhtar_abbas 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}$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:46:47 +0000 https://www.mathcity.org/fsc/fsc_part_2_solutions/ch01 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}$$\lim_{x\to0}\frac{\sqrt{x+a} - \sqrt{a}}{x} = \frac{… anonymous@undisclosed.example.com (Anonymous) Sat, 03 Jun 2023 16:30:56 +0000 https://www.mathcity.org/fsc/fsc_part_2_solutions/ch02 Unit 02: Differentiation [Unit 02: Differentiation] Notes (Solutions) of Unit 02: Differentiation, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Software section.$f'(x)$$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… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:05 +0000 https://www.mathcity.org/fsc/fsc_part_2_solutions/ch03 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)$ anonymous@undisclosed.example.com (Anonymous) Sat, 03 Jun 2023 17:25:33 +0000 https://www.mathcity.org/fsc/fsc_part_2_solutions/ch04 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$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:07 +0000 https://www.mathcity.org/fsc/fsc_part_2_solutions/ch05 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. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:08 +0000 https://www.mathcity.org/fsc/fsc_part_2_solutions/ch06 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. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:08 +0000 https://www.mathcity.org/fsc/fsc_part_2_solutions/ch07 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$$u\cdot(v\times w)$ anonymous@undisclosed.example.com (Anonymous) Thu, 25 Mar 2021 17:27:32 +0000 https://www.mathcity.org/matric/9th_science/ex-4-1 Exercise 4.1 On the following page we have given the solution of Exercise 4.1 of Mathematics 9 (Science) published by Caravan Book House, Lahore. We have created this page and it will be updated to add new solutions occasionally. Please stay in touch with this page.$3x^2+\frac{1}{x}-5$$3x^3-4x^2-x\sqrt{x}+3$$x^2-3x+\sqrt{2}$$\frac{3x}{2x-1}+8$$3x^2+\frac{1}{x}-5$$No (Reason:\frac{1}{x})$$3x^3-4x^2-x\sqrt{x}+3$$No (Reasons \sqrt{x})$$x^2-3x+\sqrt{2}$$Yes$$\frac{3x}{2x-1}+8$$No (Reason:\frac{1}… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:48:06 +0000 https://www.mathcity.org/matric/9th_science/ex-6-1 Exercise 6.1 On the following page we have given the solution of Exercise 6.1 of Mathematics 9 (Science) published by Caravan Book House, Lahore. We have created this page and it will be updated to add new solutions occasionally. Please stay in touch with this page.$39x^7y^3z$$91x^5y^6 z^7$$102xy^2z$$85x^2yz$$187xyz^2$$39x^7y^3z=13\times 3\times x^7 y^3 z$$91x^5y^6 z^7=13\times 7\times x^5 y^6 z^7$$13 x^5y^3z$$102xy^2z=2\times 3\times 17 xy^2z$$85x^2yz=3\times 17 x^2 y z$$187xyz^2 = 11\times 1… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:48:08 +0000 https://www.mathcity.org/matric/9th_science/ex-6-2 Exercise 6.2 On the following page we have given the solution of Exercise 6.2 of Mathematics 9 (Science) published by Caravan Book House, Lahore. We have created this page and it will be updated to add new solutions occasionally. Please stay in touch with this page.$\frac{x^2-x-6}{x^2-9}+\frac{x^2+2x-24}{x^2-x-12}$\begin{align} \frac{x^2-x-6}{x^2-9}&+\frac{x^2+2x-24}{x^2-x-12}\\ &=\frac{x^2-3x+2x-6}{(x)^2-(3)^2}+\frac{x^2+6x-4x-24}{x^2-4x+3x-12}\\&= \frac{x(x-3)+2(x-3)}{(x-3)(x+3)}+\frac{x(x+6… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:48:08 +0000 https://www.mathcity.org/matric/9th_science/ex-6-3 Exercise 6.3 On the following page we have given the solution of Exercise 6.3 of Mathematics 9 (Science) published by Caravan Book House, Lahore. We have created this page and it will be updated to add new solutions occasionally. Please stay in touch with this page.$4x^2-12xy +9y^2$$x^2-1+\frac{1}{4x^2}, (x\neq 0)$$\frac{1}{16}x^2-\frac{1}{12}xy+ \frac{1}{36}y^2$$4(a+b)^2-12(a^2-b^2)+9(a-b)^2$$\frac{4x^6-12x^3y^3+9y^6}{9x^4-24x^2y^2+16y^4},(x \neq 0)$$\left( x+\frac{1}{x}\right)^2-4\left( x-\f… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:48:09 +0000 https://www.mathcity.org/matric/9th_science/review_exercise Review exercise On the following page we have given the solution of Review exercise of Mathematics 9 (Science) published by Caravan Book House, Lahore. We have created this page and it will be updated to add new solutions occasionally. Please stay in touch with this page.$x-2$$x^2+x-6$$x^2+x-6$$x+3$$x-2$$x+2$$c$$a^3+b^3$$a^2-ab+b^2$$a+b$$a^2-ab+b^2$$(a-b)^2$$a^2+b^2$$c$$x^2-5x+6$$x^2-x-6$$x-3$$x+2$$x^2-4$$x-2$$a$$a^2-b^2$$a^3-b^3$$a-b$$a+b$$a^2+ab+b^2$$a^2-ab+b^2$$a$$x^2+3x+2$$x^2+4x+3$$x^2+5x… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:48:10 +0000 https://www.mathcity.org/matric/10th_science/unit01-view Unit 01: Quadratic Equations: Online View On this page the solutions of Unit 01: Quadratic Equations, Mathematics 10 (Science Group), published by Ilmi Kitab Khana, Urdu Bazar, Lahore, Pakistan. List of all exercise of Unit 01 * Exercise 1.1 * Exercise 1.2 * Exercise 1.3 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:48:01 +0000 https://www.mathcity.org/matric/10th_science/unit02-view Unit 02: Theory of Quadratic Equations: Online View On this page the solutions of Unit 02: Theory of Quadratic Equations, Mathematics 10 (Science Group), published by Ilmi Kitab Khana, Urdu Bazar, Lahore, Pakistan. List of all exercise of Unit 02 anonymous@undisclosed.example.com (Anonymous) Wed, 24 Jul 2024 18:33:41 +0000 https://www.mathcity.org/matric/10th_science/unit03-view Unit 03: Variations: Online View On this page the solutions of Unit 03: Variations, Mathematics 10 (Science Group), published by Ilmi Kitab Khana, Urdu Bazar, Lahore, Pakistan. List of all exercise of Unit 03 * Exercise 3.1 * Exercise 3.2 * Exercise 3.3 * Exercise 3.4 * Exercise 3.5 * Exercise 3.6 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:48:02 +0000 https://www.mathcity.org/matric/10th_science/unit04-view Unit 04: Partial Fractions: Online View On this page the solutions of Unit 04: Partial Fractions, Mathematics 10 (Science Group), published by Ilmi Kitab Khana, Urdu Bazar, Lahore, Pakistan. List of all exercise of Unit 04 * Exercise 4.1 * Exercise 4.2 * Exercise 4.3 * anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:48:03 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch01_real_numbers_limits_and_continuity/viewer Chapter 01: Viewer Notes of “Chapter 01: Real numbers, limits and continuity” of Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. You can also download a PDF file of respective exercise from this page. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:51:44 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch02_derivatives/viewer Chapter 02: Viewer Notes of Chapter 02: The Derivatives of Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. You can also download a PDF file of respective exercise from this page. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:51:47 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch03_general_theorem_intermediate_forms/viewer Chapter 03: PDF Viewer Notes of the Chapter 03: General Theorem, Intermediate Forms with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. There are three exercises in this chapter. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:51:57 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch04_techniques_of_integration/viewer Chapter 04: PDF Viewer Notes of the Chapter 04: Techniques of integration written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. There are three exercises in this chapter. List of all exercise of chapter 04 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:51:58 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch05_the_definite_integral/viewer Chapter 05: PDF Viewer Notes of the Chapter 05: The Definite Integral, Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. There are three exercises in this chapter. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:52:05 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch06_plane_curves_i/viewer Chapter 06: PDF Viewer Notes of the Chapter 06: Plane Curves I, Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. There are three exercises in this chapter. List of all resources of chapter 06 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:52:10 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch07_plane_curves_ii/viewer Chapter 07: Viewer Notes of “Chapter 07: Plane Curve II” of Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. You can also download a PDF file of respective exercise from this page. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:52:14 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch08_analytic_geometry_of_three_dimensions/viewer Chapter 08: PDF Viewer Notes of the Chapter 08: Analytic Geometry of Three Dimensions of Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. There are thirteen exercises in this chapter. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:52:18 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch09_functions_of_several_variables/viewer Chapter 09: PDF Viewer Notes of the Chapter 09: Functions of Several Variables of Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. There are thirteen exercises in this chapter. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:52:23 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch01_complex_numbers/viewer Viewer: Ch 01 Complex Numbers Notes of Chapter 01: Complex Numbers of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page. anonymous@undisclosed.example.com (Anonymous) Wed, 09 Mar 2022 19:08:50 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch02_groups/viewer Chapter 02: Viewer Notes of Chapter 02: Groups of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page. Here is the list of all available exercises of Chapter 02 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:52:36 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch03_matrices/viewer Chapter 03: Viewer Notes of Chapter 03: Matrices of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page. Here is the list of all available exercise of Chapter 03 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:53:09 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch04_system_of_linear_equations/viewer Chapter 04: Viewer Notes of Chapter 04: System of linear equations of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:53:51 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch04system_of_linear_equations/viewer Chapter 04: Viewer Notes of Chapter 04: System of linear equations of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:53:27 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch05_determinants/viewer Chapter 05: Viewer Notes of Chapter 05: Determinants of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page. Notes of two exercises are given here. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:53:54 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch06_vector_spaces/viewer Chapter 06: Viewer Notes of Chapter 06: Vector space of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page. Here is the list of all available exercises of Chapter 06 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:54:03 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch07_inner_product_spaces/viewer Chapter 07: Viewer Notes of Chapter 07: Inner Product Spaces of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page. Here is the list of all available exercise of Chapter 07 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:54:11 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch08_infinite_series/viewer Chapter 08: Viewer Notes of Chapter 08: Infinite Series of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page. Here is the list of all available exercise of Chapter 08 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:54:31 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch09_first_order_differential_equations/viewer Chapter 09: Viewer Notes of Chapter 09: First Order Partial Differential Equations of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:54:45 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch10_higher_order_linear_differential_equations/viewer Chapter 10: Viewer Notes of Chapter 10: Higher Order Linear Differential Equations of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:54:54 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch11_the_laplace_transform/viewer Chapter 11: Viewer Notes of Chapter 11: The Laplace Transform of Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. PDF file of respective exercise can be downloaded from this page. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:02 +0000 https://www.mathcity.org/bsc/paper_pattern/punjab_university/b.sc._paper_pattern_for_general_mathematics Paper Pattern for General Mathematics Paper pattern for General Mathematics chapter-wise for University of the Punjab, Lahore is given on this page. This pattern is extracted from syllabus and old papers, so use at your own risk. This pattern is made by Prof. Muhammad Farooq. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:17 +0000 https://www.mathcity.org/bsc/paper_pattern/punjab_university/b.sc._paper_pattern_for_mathematics_a_course Paper Pattern for A-Course of Mathematics Paper pattern for A-Course of Mathematics, chapter-wise for University of the Punjab, Lahore is given on this page. This pattern is extracted from syllabus and old papers, so use at your own risk. * Download PDF ~ BSC_maths_paper_pattern_farooq.pdf bsc punjab_university paper_pattern syllabus anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:23 +0000 https://www.mathcity.org/bsc/paper_pattern/punjab_university/b.sc._paper_pattern_for_mathematics_b_course Paper Pattern for B-Course of Mathematics Paper pattern for B-Course of Mathematics chapter-wise for University of the Punjab, Lahore is given on this page. This pattern is extracted from syllabus and old papers, so use at your own risk. This pattern is made by Prof. Muhammad Farooq. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:29 +0000 https://www.mathcity.org/fsc-part1-ptb/sol/ch01/ex1-2 Exercise 1.2 (Solutions) Notes (Solutions) of Exercise 1.2: 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 complex numbers, real part and imaginary part of complex numbers, properties of the fundamental operation on complex numbers, complex number as ordered pair of real numbers and special subset of complex numbers. These notes are based on the new Student Learning Outcomes (SLOs). Versio… anonymous@undisclosed.example.com (Anonymous) Sun, 09 Apr 2023 07:32:53 +0000 https://www.mathcity.org/fsc/fsc_part_1_mcqs/short_questions_by_mr._akhtar_abbas/view View * We are very thankful to Mr. Akhtar Abbas for sharing these short questions. These short questions are selected from previous five years papers of different boards. Solve these at your own to perform well in annual examination. Recommended book for these short questions is “Text Book of Algebra and Trigonometry Class XI (Punjab Textbook Board, Lahore)”. But any student Mathematics can get benefit from it. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:57:20 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch01/view Ch 01: Number System: Mathematics FSc Part 1 Notes (Solutions) of Chapter 01: Number System, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB), Lahore. There are three exercises in this chapter. Please see the main page of this chapter for MCQs and important question at anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:57:21 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch02/view Ch 02: Sets, Functions and Groups: Mathematics FSc Part 1 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 Textbook Board (PTB), Lahore. There are eight exercises in this chapter. Please see the main page of this chapter for MCQs and important question at anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:57:28 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch04/view 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. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:57:41 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch05/view Ch 05: Partial Fractions: Mathematics FSc Part 1 Notes (Solutions) of Chapter 05: Partial Fractions, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB), Lahore. There are four exercises in this chapter. Please see the main page of this chapter for MCQs and important question at anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:57:45 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch06/view Ch 06: Sequences and Series: Mathematics FSc Part 1 Notes (Solutions) of Chapter 06: Sequences and Series, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB), Lahore. There are eleven exercises in this chapter. Please see the main page of this chapter for MCQs and important question at anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:57:49 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch07/view Ch 07: Permutation, Combination and Probability: Mathematics FSc Part 1 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 Textbook Board (PTB), Lahore. There are eight exercises in this chapter. Please see the main page of this chapter for MCQs and important question at anonymous@undisclosed.example.com (Anonymous) Sat, 26 Mar 2022 16:27:34 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch07/viewer View Online (Solutions of Chapter 07) 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. Here is the list of all exercises of Chapter 07 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:57:56 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch08/view Ch 08: Mathematical Induction and Binomial Theorem: Mathematics FSc Part 1 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 Textbook Board (PTB), Lahore. There are three exercises in this chapter. Please see the main page of this chapter for MCQs and important question at anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:58:09 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch09/view Ch 09: Fundamentals of Trigonometry: Mathematics FSc Part 1 Notes (Solutions) of Chapter 09: Fundamentals of Trigonometry, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB), Lahore. There are four exercises in this chapter. Please see the main page of this chapter for MCQs and important question at anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:58:21 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch10/view Ch 10: Trigonometric Identities: Mathematics FSc Part 1 Notes (Solutions) of Chapter 10: Trigonometric Identities, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB), Lahore. There are four exercises in this chapter. Please see the main page of this chapter for MCQs and important question at anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:58:44 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch10/viewer View Online (Solutions of Chapter 10) 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 total of four exercise in this chapter. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:58:43 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch11/viewer View Online (Solutions of Chapter 11) 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. There are two exercise in this chapter. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:58:56 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch12/view Ch 12: Application of Trigonometry: Mathematics FSc Part 1 Notes (Solutions) of Chapter 12: Application of Trigonometry, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB), Lahore. There are four exercises in this chapter. Please see the main page of this chapter for MCQs and important question at anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:58:56 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch12/viewer View Online (Solutions of Chapter 12) 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. There are eight exercises in this chapter. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:58:57 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch13/view Ch 13: Inverse Trigonometric Functions: Mathematics FSc Part 1 Notes (Solutions) of Chapter 10: Inverse Trigonometric Functions, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB), Lahore. There are two exercises in this chapter. Please see the main page of this chapter for MCQs and important question at anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:59:03 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch13/viewer View Online (Solutions of Chapter 13) 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. In this chpater, there are two exercise. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:59:03 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch14/view Ch 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 Textbook Board (PTB), Lahore. There are four exercises in this chapter. Please see the main page of this chapter for MCQs and important question at anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:59:08 +0000 https://www.mathcity.org/fsc/fsc_part_1_solutions/ch14/viewer View Online (Solutions of Chapter 14) Notes (Solutions) of Chapter 14: Solutions of Trigonometric Equation of Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. In this chapter there is only one exercise. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:59:08 +0000 https://www.mathcity.org/fsc/fsc_part_2_solutions/ch02/view Unit 02: Differentiation: Mathematics FSc part 2 Notes (Solutions) of Unit 02: Differentiation, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. There are ten exercises in this chapter. Please see the main page of this chapter for MCQs and important question anonymous@undisclosed.example.com (Anonymous) Wed, 20 Sep 2023 13:53:02 +0000 https://www.mathcity.org/fsc/fsc_part_2_solutions/ch03/view Unit 03: Differentiation: Mathematics FSc part 2 Notes (Solutions) of Unit 03: Integration, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. There are eight exercises in this chapter. Please see the main page of this chapter for MCQs and important question anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 17:00:14 +0000 https://www.mathcity.org/fsc/fsc_part_2_solutions/ch03/viewer View Online (Solutions of Unit 03) Notes (Solutions) of Unit 03: Integration, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. In this chapter, integration is defined and basic techniques of integration are given. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 17:00:14 +0000 https://www.mathcity.org/fsc/fsc_part_2_solutions/ch04/view Unit 04: Introduction to Analytic Geometry: Mathematics FSc part 2 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. There are five exercises in this chapter. Please see the main page of this chapter for MCQs and important question anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 17:00:17 +0000 https://www.mathcity.org/fsc/fsc_part_2_solutions/ch04/viewer View Online (Solutions of Unit 04) 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. This chapter have only five exercises but it covers lot of topics of analytic geometry in the plane. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 17:00:17 +0000 https://www.mathcity.org/fsc/fsc_part_2_solutions/ch05/view Unit 05: Linear Inequalities and Linear Programming: Mathematics FSc part 2 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. There are three exercises in this chapter. Please see the main page of this chapter for MCQs and important question anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 17:00:20 +0000 https://www.mathcity.org/fsc/fsc_part_2_solutions/ch06/view Unit 06: Conic Section: Mathematics FSc part 2 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. There are nine exercises in this chapter. Please see the main page of this chapter for MCQs and important question anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 17:00:23 +0000 https://www.mathcity.org/fsc/fsc_part_2_solutions/ch06/viewer 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. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 17:00:22 +0000 https://www.mathcity.org/fsc/fsc_part_2_solutions/ch07/view Unit 07: Vectors: Mathematics FSc part 2 Notes (Solutions) of Unit 07: Vectors, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. There are three exercises in this chapter. Please see the main page of this chapter for MCQs and important question anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 17:00:25 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-2 Exercise 6.2 (Solutions) The solutions of the Exercise 6.1 of book “Model Textbook of Mathematics for Class XI” published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan are given on this page. This exercise consists of the question related to factorial function.$n!$$$ n!=\left\{\begin{array}{l} n(n-1)(n-2)\cdot \ldots \cdot 3 \cdot 2 \cdot 1 \text{ if } n\geq 1,\\ 1 \text{ if } n=0. \end{array} \right. $$$n \in \mathbb{N}$${ }^n P_r=\frac{n!}{(n-r)!}$$\quad{ }^… anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 08:59:59 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-2-p13 Question 22 and 23, Exercise 6.2 Solutions of Question 22 and 23 of Exercise 6.2 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $(3\quad 4\quad 6\quad 1\quad 5\quad2)$$1$$2$$L=1, A=2, H=3, O=4, R=5, E=6$$(3,4,6,1,5,2)=$$(4\quad 6\quad 3\quad 2\quad 1\quad5)$$(4,6,3,2,1,5)$$4^{\text {th }}$$2^{\text {nd }}$$6^{\text {th }}$$3^{\text {rd }}$$3^{\text {rd… anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 08:59:46 +0000 https://www.mathcity.org/matric/10th_science/unit01/viewer Unit 01: Quadratic Equations: Online View On this page the solutions of Unit 01: Quadratic Equations, Mathematics 10 (Science Group), published by Ilmi Kitab Khana, Urdu Bazar, Lahore, Pakistan. List of all exercise of Unit 01 * Exercise 1.1 * Exercise 1.2 * Exercise 1.3 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 17:00:28 +0000 https://www.mathcity.org/matric/10th_science/unit02/viewer Unit 02: Theory of Quadratic Equations: Online View On this page the solutions of Unit 02: Theory of Quadratic Equations, Mathematics 10 (Science Group), published by Ilmi Kitab Khana, Urdu Bazar, Lahore, Pakistan. List of all exercise of Unit 02 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 17:00:28 +0000 https://www.mathcity.org/matric/10th_science/unit03/viewer Unit 03: Variations: Online View On this page the solutions of Unit 03: Variations, Mathematics 10 (Science Group), published by Ilmi Kitab Khana, Urdu Bazar, Lahore, Pakistan. List of all exercise of Unit 03 * Exercise 3.1 * Exercise 3.2 * Exercise 3.3 * Exercise 3.4 * Exercise 3.5 * Exercise 3.6 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 17:00:30 +0000 https://www.mathcity.org/matric/10th_science/unit04/viewer Unit 04: Partial Fractions: Online View On this page the solutions of Unit 04: Partial Fractions, Mathematics 10 (Science Group), published by Ilmi Kitab Khana, Urdu Bazar, Lahore, Pakistan. List of all exercise of Unit 04 * Exercise 4.1 * Exercise 4.2 * Exercise 4.3 * anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 17:00:31 +0000 https://www.mathcity.org/matric/10th_science/unit05/viewer Unit 05: Sets and Functions: Online View On this page the solutions of Unit 05: Sets and Functions, Mathematics 10 (Science Group), published by Ilmi Kitab Khana, Urdu Bazar, Lahore, Pakistan are given. List of all exercise of Unit 05 * Exercise 5.1 * anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 17:00:33 +0000 https://www.mathcity.org/matric/10th_science/unit06/viewer Unit 06: Basic Statistics: Online View On this page the solutions of Unit 06: Basic Statistics, Mathematics 10 (Science Group), published by Ilmi Kitab Khana, Urdu Bazar, Lahore, Pakistan are given. List of all exercise of Unit 06 * Exercise 6.1 * Exercise 6.2 * anonymous@undisclosed.example.com (Anonymous) Sun, 21 Feb 2021 17:29:34 +0000 https://www.mathcity.org/msc/notes/fundamental_of_complex_analysis/viewer Fundamental of Complex Analysis: Viewer Solutions of some exercises from Fundamental of Complex Analysis written by Dr. M. Iqbal and published by Ilmi Kitab Khana, Lahore- PAKISTAN. These are handwritten notes by Prof.(Rtd) Muhammad Saleem. You can also download PDF of solutions from this page. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 17:00:41 +0000 https://www.mathcity.org/papers/old_papers_for_bsc_mathematics/punjab_university/view View Online (PU) * Old/previous papers of BSc (only mathematics), University of the Punjab, Lahore. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 17:00:44 +0000