This is beta site. https://beta.mathcity.org/ 2026-06-05T14:42:18+00:00 https://beta.mathcity.org/ https://beta.mathcity.org/_media/logo.png text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/matric/9th_science/unit_02/exercise_2.6?rev=1737476041&do=diff Exercise 2.6 (Solutions) Question 1 Identify the following statements as true or false. (i) $\sqrt{-3}\cdot\sqrt{-3} = 3$ (ii) $i^{73}=-i$ (iii) $i^{10} = -1$ (iv) Complex conjugate of $(-6i + i^2) is (-1 + 6i)$ (v) Difference of complex numbers $z = a + ib$ and its conjugate is a real number. (vi) If $(a-1)-(b+3)i = 5+8i$, then a = 6 & b = -11 (vii) Product of complex number and its conjugate is always a non-negative real number.$a+ib$$(2+3i)+(7-2i)$$2(5+4i)+3(7-4i)$$-(-3+5i)-3(4+9i)$$… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/matric/9th_science/unit_02/exercise_2.1?rev=1737476041&do=diff Exercise 2.1 (Solutions) Question 1 Identify which of the following are rational and irrational numbers: (i) $\sqrt{3}$ (ii) $\frac{1}{6}$ (iii) $\pi$ (iv) $\frac{15}{2}$ (v) $7.25$ (vi)$\sqrt{29}$ Solution * Rational: $\frac{1}{6}$, $\frac{15}{2}$, $7.25$ * Irrational: $\sqrt{3}$, $\pi$, $\sqrt{29}$ Question 2 Convert the following fraction into decimal fraction.$\frac{17}{25}$$\frac{19}{4}$$\frac{57}{8}$$\frac{205}{18}$$\frac{5}{8}$$\frac{25}{38}$$\frac{2}{3}$$\pi$$\frac{1}{9}$$\fr… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/matric/9th_science/ex-6-1?rev=1737476041&do=diff Exercise 6.1 On the following page we have given the solution of Exercise 6.1 of Mathematics 9 (Science) published by Caravan Book House, Lahore. <WRAP center round info 60%> We have created this page and it will be updated to add new solutions occasionally. Please stay in touch with this page. </WRAP>$39x^7y^3z$$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\tim… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/matric/9th_science/ex-4-1?rev=1737476041&do=diff 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. <WRAP center round info 60%> We have created this page and it will be updated to add new solutions occasionally. Please stay in touch with this page. </WRAP>$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}$$Yes$$\f… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/matric/9th_science/unit_02/exercise_2.2?rev=1737476041&do=diff Exercise 2.2 (Solutions) Question 1 Identify the property used in the following, * (i) $a + b = b + a$ ... ..... * (ii) $(ab)c = a(bc)$ ... ... ... * (iii) $7 \times 1 = 7$ ... ... ... * (iv) $x > y$ or $x = y$ or $x< y$ ... ... ... * (v) $ab = ba$ ... ... ... * (vi) $a + c = b + c \Rightarrow a = b$ ... ... ... * (vii) $5 + (-5) = 0$ ... ... ... * (viii) $7 \times \frac{1}{7} = 1$$a > b \Rightarrow ac > bc? (c >0)$$a + b = b + a$$(ab)c = a(bc)$$7 \times 1 = 7$$x > y$$x = y$$… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/matric/9th_science/unit_02/exercise_2.3?rev=1737476041&do=diff Exercise 2.3 (Solutions) Question 1 Write each radical expression in exponential notation and each exponential expression in radical notation, Do not simplify. * (i) $\sqrt[3]{-64}$ *(ii) $2^{35}$ * (iii) $-7^\frac{1}{3}$ * (iv) $y^\frac{-2}{3}$$\sqrt[3]{-64} = -64^\frac{1}{3}$$2^\frac{3}{5} = \sqrt[5]{2}^{3}$$-7^\frac{1}{3} = -\sqrt[3]{7}$$y^\frac{-2}{3} = \sqrt[3]{y}^{-2}$$ 5^\frac{1}{5} = \sqrt{5}$$2^\frac{2}{3} = \sq… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/matric/9th_science/unit_02/exercise_2.5?rev=1737476041&do=diff Exercise 2.5 (Solutions) Question 1 * Evaluate (i) $i^7$ (ii) $i^{50}$ (iii) $i^{12}$ (iv) $\left(-i\right)^8$ (v) $\left(-i\right)^5$ (vi) $i^{27}$ Solution $$\begin{array}{cl} i^7 &= {i^6}\cdot i\\ &= (i^2)^3\cdot i\\ &= {-1}^3 \cdot i\\ &= -i \end{array}$$$$\begin{array}{cl} i^{50} &= (i^2 )^{25}\\ &= {-1}^{25}\\ … text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/matric/9th_science/unit_02/exercise_2.4?rev=1737476041&do=diff Exercise 2.4 (Solutions) Question 1 Use law of exponent to simplify. * (i) $\frac{(243)^{\frac{-2}{3}}(32)^{\frac{-1}{5}}}{\sqrt(196)^{-1}}$ * (ii) $\left(2x^5y^{-4}\right)\left(-8x^{-3}y^2\right)$ * (iii) $\left(\frac{x^{-2}y^{-1}z^{-4}}{x^4y^{-3}z^0}\right)^{-3}$ * (iv) $\frac{\left(81\right)^n.3^5-\left(3\right)^{4n-1}\left(243\right)}{\left(9^2n\right)\left(3^3\right)}$ Solution (i) $$\begin{array}{cl} \begin{array}{cl} \frac{(243)^{\frac{-2}{3}}(32)^{\frac{-1… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/matric/9th_science/review_exercise?rev=1737476041&do=diff Review exercise On the following page we have given the solution of Review exercise of Mathematics 9 (Science) published by Caravan Book House, Lahore. <WRAP center round info 60%> We have created this page and it will be updated to add new solutions occasionally. Please stay in touch with this page. </WRAP>$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-a… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/matric/9th_science/ex-6-3?rev=1737476041&do=diff 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. <WRAP center round info 60%> We have created this page and it will be updated to add new solutions occasionally. Please stay in touch with this page. </WRAP>$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)$$\left(… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/matric/9th_science?rev=1737476041&do=diff Mathematics 9 (Science Group) [Mathematics 9 (Science Group)] Mathematics 9 is written by Dr. Karamat H. Dar and Prof. Irfan-ul-Haq and this book is published by Carvan Book House, Lahore, Pakistan. This book consist of 302 pages and there are 17 units. Notes of Unit 1 and 3 are provided by $ka + kb + kc$$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$$(x + a) (x + b) (x + c) … text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/matric/9th_science/unit11?rev=1737476041&do=diff Unit 11: Parallelograms and Triangles On this page notes of Unit 11 of Mathematics 9 written by Dr. Karamat H. Dar and Prof. Irfan-ul-Haq are given. [Unit 08: Linear Graph and their Application] After studying this unit, the students will be able to: * prove that in a parallelogram * the opposite sides are congruent, text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/matric/9th_science/unit_05/viewer?rev=1737476041&do=diff Unit 05: Factorization: Online View On this page, online view of the notes of unit 05 are given. After studying this unit , the students will be able to: * Recall factorization of expressions of the following types. * $ka + kb + kc$ * $ac + ad + bc + bd$ * $a^2 + 2ab + b^2$ * $a^2 – b^2$ * $a^2 + 2ab + b^2 – c^2$ * Factorize the expressions of the following types.$a^4 + a^2b^2 + b^4$$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 +…