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- Exercise 1.1 (Solutions) @fsc-part1-ptb:sol:ch01
- of inequality (order properties), field, rule of fractions. These notes are based on the new Student Le... mmutative property w.r.t. '+'. ---- (ii) $(a+1)+ \frac{3}{4}= a+(1+\frac{3}{4})$ **Property:** Associative property w.r.t. '+'. ---- (iii) $(\sqrt{3}+\sqrt{... cative property. ---- (v) $a>b \quad \Rightarrow \frac{1}{a}<\frac{1}{b}$. **Property:** Multiplicative
- MCQs: Ch 04 Quadratic Equations @fsc-part1-ptb:mcq-bank
- ormula for $ax^2+bx+c=0$, $a\neq 0$ is - $x= \frac{b \pm \sqrt{b^2-4ac}}{a}$ - $x= \frac{-b \pm \sqrt{b^2+4ac}}{2a}$ - $x= \frac{-b \pm \sqrt{4ac-b^2}}{2a}$ - $x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ - A quadratic equation which
- MCQs: Ch 01 Number Systems @fsc-part1-ptb:mcq-bank
- $z=(1,3)$ then $z^{-1}= $ - $(\displaystyle{\frac{1}{10}},\displaystyle{\frac{3}{10}})$ - $(-\displaystyle{\frac{1}{10}},\displaystyle{\frac{3}{10}})$ - $(\displaystyle{\frac{1}{10}},-\displaystyle{\frac{3}{10}})
- Definitions: FSc Part 1 (Mathematics): PTB
- ** A number which can be written in the form of $\frac{p}{q}$, where $p,q \in \mathbb{Z}$, $q\neq 0$, is... l number which cannot be written in the form of $\frac{p}{q}$, where $p,q \in \mathbb{Z}$, $q\neq 0$, i... al number because it can be converted into common fraction. * **Non-terminating decimal or non-recurr... g. it is not possible to convert it into a common fraction. Thus non-terminating, non-recurring decimals
- Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
- tion 4(iv)** Simplify: $\displaystyle {{(-1)}^{-\frac{21}{2}}}$ **Solution** \begin{align} (-1)^{-\frac{21}{2}}&=\frac{1}{(-1)^\frac{21}{2}}=\frac{1}{[(-1)^\frac{1}{2}]^{21}}\\ &= \frac{1}{i^{21}}=\frac{1}{(i^2)^{10}\cdot
- Ch 10: Trigonometric Identities @fsc-part1-ptb:important-questions
- rc}\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+\fra
- Ch 08: Mathematical Induction and Binomial Theorem @fsc-part1-ptb:important-questions
- -group> * 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)// *... 2015)// * Use binomial theorem to show that $1+\frac{1}{4}+\frac{1.3}{4.8}+\frac{1.3.5}{4.8.12},...=\s
- Ch 06: Sequences and Series @fsc-part1-ptb:important-questions
- Sequences and Series ====== <list-group> * 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(20
- Multiple Choice Questions (MCQs)
- * integer * none of these - Golden rule of fractions is that for $K \neq o, \frac{a}{b}=$ * $\frac{ab}{k}$ * $\frac{k}{ab}$ * $\frac{kb}{ka}$ * $\frac{ka}{kb}$ - Geometrically, the modulu
- Ch 05: Partial Fraction @fsc-part1-ptb:important-questions
- ====== Ch 05: Partial Fraction ====== <list-group> * 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 Gu
- Ch 12: Applications of Trigonometry @fsc-part1-ptb:important-questions
- ry ====== <list-group> * Find the value of $tan\frac{\alpha}{2}$ in term of $s$ --- //BISE Gujrawala(2... //BISE Gujrawala(2015)// * Show that $r_1=stan\frac{\alpha}{2}$ --- //BISE Gujrawala(2015)// * Defi... 30$ --- //BISE Gujrawala(2017)// * Prove that $\frac{1}{r^2}+\frac{1}{{r_1}^2}+\frac{1}{{r_2}^2}+\frac{1}{{r_3}^2}=\frac{a^2+b^2+c^2}{\triangle^2}$ --- //BI
- Ch 13: Inverse Trigonometry Functions @fsc-part1-ptb:important-questions
- === <list-group> * 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 $sin^{-1}(\frac{1}{\sqrt
- Trigonometric Formulas
- }}\theta }$ </col><col sm="6"> * ${{\sin }^{2}}\frac{\theta }{2}=\dfrac{1-\cos \theta }{2}$ * ${{\cos }^{2}}\frac{\theta }{2}=\dfrac{1+\cos \theta }{2}$ * ${{\tan }^{2}}\frac{\theta }{2}=\dfrac{1-\cos \theta }{1+\cos \theta ... col sm="6"> * $\sin \theta +\sin \phi \,=2\sin \frac{\theta +\phi }{2}\,\,\cos \frac{\theta -\phi }{2}
- Ch 09: Fundamental of Trigonometry @fsc-part1-ptb:important-questions
- gonometric functions of $\theta$, If $cos \theta=\frac{12}{13}$ and the terminal side of the angle is no... rawala(2017)// * Verify $2 $ $\sin 45^{\circ} +\frac{1}{2}\cos 45^{\circ}=\frac{3}{\sqrt{2}}$ --- //BISE Gujrawala(2017), BISE Sargodha(2017)// * Prove th... 5cm$ --- //BISE Sargodha(2015)// * Prove that $\frac{cos\theta+sin\theta}{cos\theta-sin\theta}+\frac{c
- Ch 01: Number Systems @fsc-part1-ptb:important-questions
- _2$ --- // BISE Sargodha(2015)// * Simplify $\frac{2}{\sqrt{5}+\sqrt{-8}}$ in the form of $a+ib$ ... godha(2015)// * Simplify by justify each step $\frac{\frac{1}{a}-\frac{1}{b}}{1-\frac{1}{a}\frac{1}{b}}$ --- // BISE Sargodha(2015)// * Find multiplicative