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- Exercise 6.1 @matric:9th_science
- d info 60%> We have created this page and it will be updated to add new solutions occasionally. Please... 3-2x^2)$, $54(27x^4-x)$ **Solution:**\\ (i) $\begin{align} x^2+5x+6&=x^2+3x+2x+6,\\ &=x(x+3)+2(x+3)\\ &=(x+3)(x+2) \end{align}$ $\begin{align} x^2-4x-12&=x^2-6x+2x-12,\\ &=x(x-6)+2(x... &=(x-6)(x+2) \end{align}$ H.C.F= $x+2$ (ii) $\begin{align} x^3-27 &=x^3-3^3,\\ &=(x-3)(x^2+3x+9)\e
- Exercise 2.6 (Solutions) @matric:9th_science:unit_02
- +3i^{16}-6i^{19}+4i^{25}$ **Solution**\\ (i) $$\begin{array}{cl} (2+3i)+(7-2i) &= 2+3i+7-2i\\ &= 2+7+3i-2i\\ &= 9+i \end{array}$$ (ii) $$\begin{array}{cl} 2(5+4i)-3(7+4i) &= 10+8i-21-12i... 21+8i-12i\\ &= -11-4i \end{array}$$ (iii) $$\begin{array}{cl} -(-3+5i)-(4+9i) &= 3-5i-4-9i\\... 3-4-5i-9i\\ &= -1-14i \end{array}$$ (iv) $$\begin{array}{cl} 2i^2+6i^3+3i^{16}-6i^{19}+4i^{25}
- Exercise 6.3 @matric:9th_science
- d info 60%> We have created this page and it will be updated to add new solutions occasionally. Please... (i) $4x^2-12xy +9y^2$\\ **Solution:**\\ $\begin{align}4x^2-12xy +9y^2\\&=4x^2-6xy-6xy +9y^2\\&... &= (2x-3y)(2x-3y)\\&= (2x-3y)^2 \end{align}$\\ $\begin{align} \sqrt{4x^2-12xy +9y^2}&= \pm (2x-3y) \e... frac{1}{4x^2}, (x\neq 0)$\\ **Solution:**\\ $\begin{align}x^2-1+\frac{1}{4x^2}\\&=(x)^2-1+(\frac{1
- Review exercise @matric:9th_science
- d info 60%> We have created this page and it will be updated to add new solutions occasionally. Please... (a+1)$\\ **Answer:**\\ $b$\\ (xvi) What should be added to complete the square of $x^4+64$ ? ---\\ ... $8x^4-128$ , $12x^3-96$\\ **Solution:**\\ $\begin{align}8x^4-128 &= 8(x^4-16)\\&=8[(x^2)^2-(4)^2... es 2 \times (x^2+4)(x-2)(x+2)\end{align}$\\ $\begin{align}12 x^3-96&=12(x^3-8)\\&=2 \times 2\times
- Exercise 2.5 (Solutions) @matric:9th_science:unit_02
- (vi) $i^{27}$ **Solution**\\ (i) $$\begin{array}{cl} i^7 &= {i^6}\cdot i\\ &= (i^2)^3... {-1}^3 \cdot i\\ &= -i \end{array}$$ (ii) $$\begin{array}{cl} i^{50} &= (i^2 )^{25}\\ &= {-1}^{25}\\ &= -1 \end{array}$$ (iii) $$\begin{array}{cl} i^{12} &= (i^2 )^6\\ &= {-1}^6\\ &= 1 \end{array}$$ (iv) $$\begin{array}{cl} (-i)^8 &= (-i^2 )^4\\ &= {-1
- Exercise 6.2 @matric:9th_science
- d info 60%> We have created this page and it will be updated to add new solutions occasionally. Please... rac{x^2+2x-24}{x^2-x-12}$\\ **Solution:**\\ $\begin{align} \frac{x^2-x-6}{x^2-9}&+\frac{x^2+2x-24}... \right]+\frac{4x}{x^4-1}$\\ **Solution:**\\ $\begin{align} \left[\frac{x+1}{x-1}-\frac{x-1}{x+1}-\... 4x+3}-\frac{2}{x^2-6x+5}$\\ **Solution:**\\ $\begin{align} \frac{1}{x^2-8x+15}+\frac{1}{x^2-4x+3}-
- Mathematics 9 (Science Group)
- iding these notes. The soft form of this book can be downloaded from PITB webiste from [[https://pctb.... Formulas===== In this unit, following topics has been covered: * Algebraic Expressions * Algebra... orization===== In this unit, following topics has been covered: After studying this unit , the students will be able to: * Recall factorization of expressions
- Exercise 2.1 (Solutions) @matric:9th_science:unit_02
- ational number $\frac{2}{3}$ , divide unit length between 0 and 1 into 3 equal parts. - (ii) Take 2 ... tional number $-\frac{4}{5}$ , divide unit length between 0 and -1 into 5 equal parts. - Take 4 part... (iii) - Rational number $\frac{3}{4}$ lies between 1 and 2 on the number line. - The distance between 1 and 2 is divided into 4 equal parts , from
- Exercise 2.4 (Solutions) @matric:9th_science:unit_02
- right)\left(3^3\right)}$ **Solution**\\ (i) $$\begin{array}{cl} \begin{array}{cl} \frac{(243)^{\frac{-2}{3}}(32)^{\frac{-1}{5}}}{\sqrt(196)^{-1}} &=... .\sqrt[3]{3}} \end{array}\end{array}$$ (ii) $$\begin{array}{cl} \left(2x^5y^{-4}\right)\left(-8x^{-... &= \frac{-16x^2}{y^2} \end{array}$$ (iii) $$\begin{array}{cl} \left(\frac{x^{-2}y^{-1}z^{-4}}{x^4
- Exercise 4.1 @matric:9th_science
- d info 60%> We have created this page and it will be updated to add new solutions occasionally. Please... on:**\\ (i) $\frac{120 x^2y^3z^5}{30x^3yz^2}$\\ $\begin{align}\frac{30\times 4 y^(3-1)z^(5-2)}{30x^(3-... olution:**\\ (ii) $\frac{8 a(x+1)}{2(x^2-1)}$\\ $\begin{align}\frac{2\times 4a(x+1)}{2(x+1)(x-1)}\\&= ... tion:**\\ (iii) $\frac{(x+y)^2-4xy}{(x-y)^2}$\\ $\begin{align}\frac{x^2+y^2+2xy-4xy}{x^2-2xy+y^2}\\&=
- Exercise 11.1 (Solutions) @matric:9th_science:unit11
- by Dr. Karamat H. Dar and Prof. Irfan-ul-Haq has been given. There are two questions in this exercise and solution of both the questions are given below. <grid><col sm="6"> <panel> **Q.1 One angle of... $m\angle B=m\angle D=130^\circ$ We know that\\ \begin{align} & m\angle A +\,\,m\angle B=180^\circ \\... , $m\angle DAB=?$, $m\angle C=?$, $m\angle D=?$ \begin{align} & m\angle DAM+m\angle DAB=180^\circ \\
- Exercise 2.3 (Solutions) @matric:9th_science:unit_02
- rt[3]{\frac{-8}{27}}$ **Soluton**\\ (i) $$\begin{array}{cl} \sqrt[3]{-125} &= \sqrt[3]{-5^3}\\ ... es\frac{1}{3}}\\ &= {-5} \end{array}$$ (ii) $$\begin{array}{cl} \sqrt[4]{32} &= \sqrt[4]{{2}^5}\\ &... 4]{2}\\ &= 2\sqrt[4]{2} \end{array}$$ (iii) $$\begin{array}{cl} \sqrt[5]{\frac{3}{32}} &= \left(\fr... end{array}$$ (iv) $$\begin{array}{cl} \sqrt[3]{\frac{-8}{27}} &= \sqrt[3]
- General Mathematics 9
- , Lahore. Solutions of all the chapters are given below. One can download the PDF file of the notes. P... reader installed in their system. We will try our best to add online view of the notes very soon. All
- Mathematics 10 (Science Group)
- ==== After studying this unit, the students will be able to: * measure an angle in degree, minutes ... angle in circular system) and prove the relation between radians and degree. * establish the rule $
- Unit 08: Linear Graph and their Application @matric:9th_science
- tion}} After studying this unit the students will be able to: * Identity pair of real numbers as an