This is beta site. https://beta.mathcity.org/ 2026-06-06T14:10:26+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/ex-6-2?rev=1737476041&do=diff Exercise 6.2 On the following page we have given the solution of Exercise 6.2 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>$\frac{x^2-x-6}{x^2-9}+\frac{x^2+2x-24}{x^2-x-12}$\begin{align} \frac{x^2-x-6}{x^2-9}&+\frac{x^2+2x-24}{x^2-x-12}\\ &=\frac{x^2-3x+2x-6}{(x)^2-(3)^2}+\frac{x^2+6x-4x-24}{x^2-4x+3x-12}\\&= \frac{x(… 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/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)$$\left(… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/matric/9th_science/unit_02/exercise_2.4?rev=1737476041&do=diff Exercise 2.4 (Solutions) Question 1 Use law of exponent to simplify. * (i) $\frac{(243)^{\frac{-2}{3}}(32)^{\frac{-1}{5}}}{\sqrt(196)^{-1}}$ * (ii) $\left(2x^5y^{-4}\right)\left(-8x^{-3}y^2\right)$ * (iii) $\left(\frac{x^{-2}y^{-1}z^{-4}}{x^4y^{-3}z^0}\right)^{-3}$ * (iv) $\frac{\left(81\right)^n.3^5-\left(3\right)^{4n-1}\left(243\right)}{\left(9^2n\right)\left(3^3\right)}$ Solution (i) $$\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/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_2.1?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}$$\fr… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/matric/9th_science/unit_02/exercise_2.3?rev=1737476041&do=diff Exercise 2.3 (Solutions) Question 1 Write each radical expression in exponential notation and each exponential expression in radical notation, Do not simplify. * (i) $\sqrt[3]{-64}$ *(ii) $2^{35}$ * (iii) $-7^\frac{1}{3}$ * (iv) $y^\frac{-2}{3}$$\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}$$2^\frac{2}{3} = \sq… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/matric/9th_science/unit_02/exercise_2.2?rev=1737476041&do=diff Exercise 2.2 (Solutions) Question 1 Identify the property used in the following, * (i) $a + b = b + a$ ... ..... * (ii) $(ab)c = a(bc)$ ... ... ... * (iii) $7 \times 1 = 7$ ... ... ... * (iv) $x > y$ or $x = y$ or $x< y$ ... ... ... * (v) $ab = ba$ ... ... ... * (vi) $a + c = b + c \Rightarrow a = b$ ... ... ... * (vii) $5 + (-5) = 0$ ... ... ... * (viii) $7 \times \frac{1}{7} = 1$$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/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$$85x^2yz=3\tim… text/html 2025-01-21T16:14:00+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/matric/10th_science?rev=1737476040&do=diff Mathematics 10 (Science Group) [Matric Science 10th Book Cover] The notes/solutions, definitions, MCQs and important question for Mathematics 10 (Science Group), published by Ilmi Kitab Khana, Urdu Bazar, Lahore, Pakistan are available on this page. Whenever we found the notes we will update this page and will upload notes here. If you wish to contribute and send us the notes please contact us via our $(b^2-4ac)$$ax^2+bx+c$$\mathbb{N}$$\mathbb{W}$$\mathbb{Z}$$E$$O$$P$$\mathbb{Q}$$\cup$$\cap$$\s…