Merging man & maths https://www.mathcity.org/ Thu, 04 Jun 2026 15:41:09 +0000 FeedCreator 1.8 https://www.mathcity.org/_media/logo.svg https://www.mathcity.org/ 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/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/short-term-preparation-salman-sherazi Short Term Preparation FSc 2 fsc fsc_part2 m_salman_sherazi important_questions_fsc_2 [Short Term Preparation Guide FSc 2] This document contains all the important MCQs, Short Questions and Long Questions of Mathematics HSSC-II (FSc Part 2) from the Calculus and Analytic Geometry, MATHEMATICS 12. It has been done to help the students and teachers at no cost by M Salman Sherazi. This work (pdf) is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0. It has been done to… anonymous@undisclosed.example.com (Anonymous) Sun, 28 Nov 2021 18:17:44 +0000 https://www.mathcity.org/fsc-part2-ptb/important-questions/unit-01-functions-and-limits Unit 01: Functions and Limits Here is the list of important questions. * Evaluate $\lim\limits_{\theta \to 0}\frac{1-\cos \theta}{\sin^3\theta}$ --- FBSIC (2016) * Graph the curve of the following parametric equations $x=\sec \theta$, $y=\tan\theta$ where $\theta$ is a parameter.--- FBSIC (2016) * Evaluate $\lim\limits_{x \to 2}\frac{\sqrt{x}-\sqrt{2}}{x-2}$ --- BSIC Rawalpendi(2016), BSIC Rawalpendi(2017)$f(x)=x^3+x$$\lim\limits_{\theta \to 0}\frac{\tan \theta-\sin \theta}{\sin^3\t… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:54 +0000 https://www.mathcity.org/fsc-part2-ptb/important-questions/unit-02-differentiation Unit 02: Differentiation Here is the list of important questions. * Differentiate $\frac{(x^2+1)^2}{x^2-1}$ $w.r.t.x$. --- BSIC Gujranwala (2016) * If $x=at^2$, $y=2at$. Find $\frac{dy}{dx}$ --- BSIC Gujranwala (2016) * Differentiate $x^2-\frac{1}{x^2}$ $w.r.t.x^2$. --- BSIC Gujranwala (2016) * Prove that $\frac{d}{dx}(tan^{-1}x)=\frac{1}{1+x^2}$ --- BSIC Gujranwala (2016)$\frac{d}{dx}(sinh^{-1}x)=\frac{1}{\sqrt{1+x^2}}$$y=x^2ln(\frac{1}{x})$$\frac{dy}{dx}$$x=sin\theta$$y=sin m\t… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:54 +0000 https://www.mathcity.org/fsc-part2-ptb/important-questions/unit-03-integration Unit 03: Integration Here is the list of important questions. * Evaluate $\int \frac{1}{\sqrt{x}(\sqrt{x}+1)}dx$ --- BSIC Gujranwala (2016) * Find $\int \frac{1}{1+ cosx}dx$ --- BSIC Gujranwala (2016) * Evaluate $\int \frac{1}{x \ln x}dx$ --- BSIC Gujranwala (2016) * Find $\int x \ln x dx$ --- BSIC Gujranwala (2016) * Evaluate $\int e^{2x}(-sinx+2cosx)dx$ --- BSIC Gujranwala (2016)$\int^2_1(x^2+1)dx$$\int^{\frac{\pi}{4}}_0 \sec x(\sec x+\tan x)dx$$\sin y cosec x \frac{dy}{d… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:55 +0000 https://www.mathcity.org/fsc-part2-ptb/important-questions/unit-04-introduction-to-analytic-geometry Unit 04: Introduction to Analytic Geometry Here is the list of important questions. * Find the area between $x-axis$ and the curve $y=4x-x^2$ --- BSIC Gujranwala (2016) * Find $h$ if $A(-1,h)$, $B(3,2)$, $C(7,3)$ are collinear --- BSIC Gujranwala (2016) * Find the point three fifth of the way along the line segment from $A(-5,8)$$B(5,3)$$2$$y-intercept$$5$$5x-12y+39=0$$2x^2+3xy-5y^2=0$$x-y-4=0$$7x+y+20=0$$6x+y-14=0$$5x-12y+39=0$$(4,6)$$(4,8)$$x-2y+1=0$$2x-y+2=0$$A(2,-5)$$B(-4,-3)$$C(-1… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:56 +0000 https://www.mathcity.org/fsc-part2-ptb/important-questions/unit-05-linear-inequalities-and-linear-programming Unit 05: Linear Inequalities and Linear Programming Here is the list of important questions. * Graph the solution region of $2x+y \geq 2$ --- BSIC Gujranwala (2016) * Graph the feasible region subject to the following constraint: --- BSIC Gujranwala (2016)$2x-3y \leq 6$$2x+3y \leq 12$$x \geq 0$$y \geq 0$$2x+y\geq 2$$x+2y\leq10$$x\geq0,y\geq0$$2x+3y\leq 12$$z=x+3y$$2x+5y\leq30$$5x+4y\leq20$$x\geq0$$y\geq0$$x+2y\leq 14$$3x+4y\leq 36$$2x+y\leq 10$$x\geq0, y\geq0$$f(x)=2x+5y$$-x\leq8$$-y\leq… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:57 +0000 https://www.mathcity.org/fsc-part2-ptb/important-questions/unit-06-conic-section Unit 06: Conic section Here is the list of important questions. * Find the centre and radius of the circle given by the equation $4x^2+4y^2-8x+12y-25=0$ --- BSIC Gujranwala (2016) * Find equation of tangent to the circle $x^2+y^2=2$ parallel to the line $x-2y+1=0$ --- BSIC Gujranwala (2016)$x^2=-16y$$(0,\pm5)$$\frac{3}{5}$$ABC$$a^2=b^2+c^2-2bc \cos A$$A(4,5)$$B(-4,-3)$$C(8,-3)$$9x^2-18x+4y^2+8y-23=0$$x^2+y^2-6x+4y+13=0$$x^2+y^2=25$$(4,3)$$(-3,1)$$x=3$$(0,0)$$(6,0)$$(4,0)$$x^2-4x-8y+4=… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:57 +0000 https://www.mathcity.org/fsc-part2-ptb/important-questions/unit-07-vectors Unit 07: Vectors Here is the list of important questions. * Find position vector of a point which divide the join of $P$ and $Q$ with position vectors $2\underline i-3 \underline j$ and $3\underline i+2\underline j$ in ratio $4:3$. --- BSIC Gujranwala (2016) * Find $a$ and $b$ so that the vectors $3\underline i-\underline j+4\underline k$ and $a\underline i+b\underline j+2\underline k$ are parallel. $\cos$$u.v$$u=3\underline i+\underline j-\underline k$$v=2\underline i-\underline j-\un… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:47:57 +0000