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- Definitions: FSc Part 1 (Mathematics): PTB
- ===== * **Rational number:** A number which can be written in the form of $\frac{p}{q}$, where $p,q ... **Irrational number:** A real number which cannot be written in the form of $\frac{p}{q}$, where $p,q... rring decimal is a rational number because it can be converted into common fraction. * **Non-termin... re numbers. * **Tabular method:** A set may be described by listing its elements within brackets
- Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib
- ===== ====Rational Number==== A number which can be expressed in the form \( \dfrac{p}{q} \), where \... ==Irrational Number==== A real number that cannot be represented as a fraction of two integers is call... her terminates nor repeats. These decimals cannot be expressed as a fraction with integer numerator an... nd a vertical y-axis. Any point in this plane can be represented by an ordered pair \( (x, y) \), wher
- Trigonometric Formulas
- d defined trigonometric functions. A PDF file can be downloaded for high quality printing and a word f... **Step II:** If $n$ is even then the answer will be in $\sin$ and if the $n$ is odd then $\sin$ will be converted to $\cos$ and vice versa (i.e. cos will be converted to sin). **Step III:** Now check in wh
- MCQs: Ch 02 Sets, Functions and Groups @fsc-part1-ptb:mcq-bank
- - Elements - None of these - A set can be describing in different no. of ways are - One... ne of these - A declarative statement which may be true or false but not both is called a - Indu... urdity - Quantifier - A statement which can be true or false depending upon the truth values of ... tion - Cartesian product - May or may not be function - None of these - For two non-empt
- MCQs: Ch 04 Quadratic Equations @fsc-part1-ptb:mcq-bank
- -4ac}}{2a}$ - A quadratic equation which cannot be solved by factorization, that will be solved by - Comparing coefficients - Completing square ... on - None of these - A polynomial in$x$ can be considered as a - Non-linear equation - P... n $w^n$ ($n$ is positive integer) - Also must be a root - May be a root - is not a root
- Ch 07: Permutation, Combination and Probability @fsc-part1-ptb:important-questions
- anwala(2015)// * How many $6-digit$ numbers can be formed from the digits $2,2,3,3,4,4$? How many of... -// BISE Gujrawala(2015)// * How many words can be formed from the letter $``PLANE"$ using all lette... // * In how many way can a hockey team of $11$ be selected out of $15$ players. ---// BISE Sargodha... argodha(2017)// * In how many ways can $4$ keys be arranged on a circular key ring? ---// BISE Sarg
- Solution and Area of Oblique Triangle
- d defined trigonometric functions. A PDF file can be downloaded for high quality printing and a word f... anel title="Area of Triangle"> Assume $\Delta$ to be area of triangle. * $\Delta=\dfrac{1}{2}bc\sin\... panel> <panel title="Circumradius"> Assume $R$ to be circumradius: <grid><col sm="6"> * $R=\dfrac{a}... > </panel> <panel title="Inradius"> Assume $r$ to be inradius * $r=\dfrac{\Delta}{s}$ </panel> <pane
- MCQs: Ch 01 Number Systems @fsc-part1-ptb:mcq-bank
- form - A rational number is a number which can be expressed in the form ------- - $\displaystyl... number - none of these - A prime number can be a factor of a square only if it occurs in the squ... - Both A and B - None of these - $i$ can be written in th form of an ordered pair as - $(... c property - None of these - $-(-a)$ should be read as - Negative of negative - Minus mi
- Ch 04: Quadratic Equations @fsc-part1-ptb:important-questions
- tion $x^2-2(m+\frac{1}{m})x+3=0$, $m \neq 0$ will be real --- //BISE Gujrawala(2017)// * Solve th... * Solve that the roots of $x^2+(mx+c)^2=a^2$ will be equal if $c^2=a^2(1+m^2)$ --- //BISE Sargodha(20... )(x-a)=0$ are real, also show that the roots will be equal only if $a=b=c$ --- //FBISE (2017)// *
- Definitions: Mathematics 11: PTB by Muzzammil Subhan
- 2=4$ * **Even Function:** A function is said to be an even function if $f(-x)=f(x)$ * **Odd Function:** A function is said to be an odd function if $f(-x)=-f(x)$ * **Circle:**
- FSc Part 1 Mathematics Notes/Solutions
- r stated otherwise. To view PDF files, there must be PDF Reader (Viewer) installed on your PC or mobile or smartphone. It can be downloaded from [[:Software]] section or a user v
- Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
- lex numbers. **Solution** Let \(z,w,\) and \(v\) be complex numbers. Then the following properties ho... Solutions** Let the two conjugate complex number be $z =x+iy$ and $\overline{z }=x-iy$, where $x,y\in
- Exercise 2.8 (Solutions) @fsc-part1-ptb:sol:ch02
- \end{array} \] **Solution** Let $x_1$ and $x_2$ be the required elements. By associativ... oup under multiplication. **Solution** Let $G$ be the all non-singular $2\times 2$ matrices over th
- Question Paper/Model Paper/Paper Pattern HSSC-I: BISE
- Punjab excluding Federal Board) These papers can be used as a model paper for other board (e.g. Multa
- MCQs Bank: FSc-I
- e MCQs are not only helpful for this book but can be considered for students of Higher Secondary Schoo