# basic mathematics pdf

## basic mathematics pdf

4) $$\lim_{x \to 0} \frac{{Sinx}}{x} = 1$$, where \)x\) is measured in radians. Mathguy.us – Developed specifically for math students from Middle School to College, based on the author's extensive experience in professional mathematics in a business setting and in math tutoring. ϭ͘ Ϯ͘ ϯ͘ ϰ͘ ϱ͘ ϲ͘ ϳ͘ ϴ͘ ϵ͘ ϭϬ͘. In this khairuls ebook you will get algebra, arithmetic, geometry, trigonometry,and mental ability. If you have any question about Khairul’s basic Book download then you can comment on below section . Either it is smartphones, construction, buildings, artwork, money, sports, or engineering, etc., the application of mathematics can be seen everywhere.

" "name": "What are the Topics in Math? "@type": "Answer", Proof Ceva’s Theorem Formula, Inverse Trigonometric Functions Maths Formulas for Class 12 Chapter 2, Mid Point Theorem Proof – Converse | Mid Point Theorem Formula, What is Apollonius Theorem? }, } 6yJNA)L���h¦�,��q�R�td�T@d�M�� ��)]H��Nt� �*�6�S�l�^�%��E5���9���0)]p'L'\ [&���'�F��O�\$(����TDd��޾��9���Vt~I?�����ؼag������쇓�_�P�o���/� ���������`q]. $$Direct\; Method: x̅ = \frac{\sum_{i=1}^{n}f_i x_i}{\sum_{i=1}^{n}f_i}$$, $$Assumed\; mean\; method : x̅ = a+\frac{\sum_{i=1}^{n}f_i d_i}{\sum_{i=1}^{n}f_i}$$, $$Step \;deviation \;method : x̅ = a+\frac{\sum_{i=1}^{n}f_i u_i}{\sum_{i=1}^{n}f_i}\times h$$, $$Mode = l+\frac{f_1 – f_0}{2f_1 – f_0 – f_2} \times h$$, $$Range = Largest\; Value – Smallest\; Value$$, $$Median = l+\frac{\frac{n}{2} – cf}{f} \times h$$, $$Variance = \sigma ^{2} = \frac{\sum (x- \bar{x})^{2}}{n}$$, $$Standard\;Deviation \; \sigma = \sqrt{\frac{\sum (x-\bar{x})^{2}}{n}}$$, Area of Scalene Triangle = $$\sqrt{s(s-a)(s-b)(s-c)}$$, Perimeter of Scalene Triangle = $$a+b+c$$, Area of Isoscele Triangle = $$\frac{1}{2}bh$$, Altitude of an Isosceles Triangle = $$\sqrt{a^{2}-\frac{b^{2}}{4}}$$, Perimeter of Isosceles Triangle,P = $$2a+b$$, Area of an Right Triangle = $$\frac{\sqrt{1}}{2}bh$$, Perimeter of an Right Triangle = $$a+b+c$$, semi Perimeter of an Right Triangle = $$\frac{a+b+c}{2}$$, Area of an Equilateral Triangle = $$\frac{\sqrt{3}}{4}a^{2}$$, Perimeter of an Equilateral Triangle = $$3a$$, Semi Perimeter of an Equilateral Triangle = $$\frac{3a}{2}$$, Height of an Equilateral Triangle = $$\frac{\sqrt{3}}{2}a$$, Perimeter of a rhombus = $$4\times Side$$, Area of a Rhombus A = $$\frac{1}{2} \times d_{1} \times d_{2}$$, Area of a Parallelogram = $$b\times h$$, Perimeter of Parallelogram = $$2\left(b+h\right)$$, Area of a Trapezoid = $$\frac{1}{2} \times h \times (a + b)$$, Surface area of Cuboid = $$2(lb + bh + hl)$$, Volume of a Cuboid = $$h \times l \times w$$, Surface area of a sphere = $$4\pi r^{2}$$, Volume of a sphere = $$\frac{4}{3}\: \pi r^{3}$$, Curved Surface area of a Hemisphere = $$4\pi r^{2}$$, Total Surface area of a Hemisphere = $$3\pi r^{2}$$, Volume of a Hemisphere = $$\frac{2}{3}\: \pi r^{3}$$, Curved Surface area of a Cylinder = $$2\pi rh$$, Total Surface area of a Cylinder = $$2\pi r(r+h)$$, Total Surface Area of cone = $$\pi r \left (s+r \right )$$, Vomule of cone = $$\frac {1}{3}\pi r^{2}h$$, $$\sin \theta = \frac{Opposite}{Hypotenuse}$$, $$\sec \theta = \frac{Hypotenuse}{Adjacent}$$, $$\cos\theta = \frac{Adjacent}{Hypotenuse}$$, $$\tan \theta =\frac{Opposite}{Adjacent}$$, $$csc \theta = \frac{Hypotenuse}{Opposite}$$, $$cot \theta = \frac{Adjacent}{Opposite}$$, $$\sin\: x\cdot \cos\:y=\frac{\sin(x+y)+\sin(x-y)}{2}$$, $$\cos\: x\cdot \cos\:y=\frac{\cos(x+y)+\cos(x-y)}{2}$$, $$\sin\: x\cdot \sin\:y=\frac{\cos(x+y)-\cos(x-y)}{2}$$, $$\sin\: x+\sin\: y=2\sin\frac{x+y}{2}\cos\frac{x-y}{2}$$, $$\sin\: x-\sin\: y=2\cos\frac{x+y}{2}\sin\frac{x-y}{2}$$, $$\cos\: x+\cos\: y=2\cos\frac{x+y}{2}\cos\frac{x-y}{2}$$, $$\cos\: x-\cos\: y=-2\sin\frac{x+y}{2}\sin\frac{x-y}{2}$$<, $$\sin (x + y) = \sin(x) \cos(y) + \cos(x) \sin(y)$$, $$\cos(x + y) = \cos(x) \cos(y) – \sin(x) \sin(y)$$, $$\tan(x+y)=\frac{\tan\: x+\tan\: y}{1-\tan\: x\cdot \tan\: y}$$, $$\sin(x – y) = \sin(x) \cos(y) – \cos(x) \sin(y)$$, $$\cos(x – y) = \cos(x) \cos(y) + \sin(x) \sin(y)$$, $$\tan(x-y)=\frac{\tan\: x – \tan\: y}{1+\tan\: x\cdot tan\: y}$$, $$\tan(2x) = \frac{[2\: \tan(x)]}{[1 -\tan^{2}(x)]}$$, $$\sin\frac{x}{2}=\pm \sqrt{\frac{1-\cos\: x}{2}}$$, $$\cos\frac{x}{2}=\pm \sqrt{\frac{1+\cos\: x}{2}}$$, $$\tan(\frac{x}{2}) = \sqrt{\frac{1-\cos(x)}{1+\cos(x)}}$$, Commutative= $$A\cup B = B\cup A$$ and $$A\cap B = B\cap A$$, Associative= $$A\cup (B\cup C) = A\cup (B\cup C)$$ and $$A\cap (B\cap C) = A\cap (B\cap C)$$, Neutral element= $$A\cup \theta = A$$ and $$A\cap E = A$$, Absorbing element= $$A\cup E = E$$ and $$A\cap \theta = \theta$$, Distributive= $$A\cup (B\cap C)=(A\cup B)\cap (A\cup C)$$ and $$A\cap (B\cup C)=(A\cap B)\cup (A\cap C)$$, De Morgan’s laws= $$\bar(A\cap B) = \bar A \cup \bar B$$ and $$\bar(A\cup B) = \bar A \cap \bar B$$, Independent Events= $$P(A | B)=P(A)$$ and $$P(A\cap B)=P(A)×P(B)$$, Conditional Probability= $$P(A | B)=\frac{P(A\cap B)}{P(B)}$$, Laplace laws= $$P(A)=\frac{Number\;of\;ways\;it\;can\;happen}{Total\;Number\;of\;Outcomes}$$, Complement of an Event= $$P (\bar A)=1 – P(A)$$, Union of Events= $$P(A\cup B)=P(A)+P(B)−P(A\cap B)$$, Fraction formula = $$\sqrt{ a } = a^{ \frac{ 1 }{ 2 }}$$, Reverse formula = $$\sqrt{ n } { a } = a^{\frac{ 1 } { n }}$$, Negative power value = $$a^{ -n } = \frac{ 1 }{ a^{n} }$$, Fraction formula = $$a^{n} = \frac{1}{ a^{ -n } }$$, Product formula = $$a^{m}a^{n} = a^{ m + n }$$, Division Formula = $$\frac{ a^{ m }}{ a^{ n }} = a ^{ m-n }$$, Power of Power formula = $$(a^{ m })^{ p } = a^{ mp }$$, Power distribution Formula = $$(a^ { m }c^{ n })^{ x } = a ^ { mx } c ^{ nx }$$, The Power distribution Formula = $$\left ( \frac {a ^{ m }}{c^{ n }} \right )^{x} = \frac{a^{ mx }}{c^{ nx }}$$, Power Even Number = $$(-1)^{Even Number} = 1$$, Power Odd Number = $$(-1)^{Odd Number} = -1$$, Product of Power Formula = $$(ab)^m = a^m \times b^m$$, Addition = $$(a+bi)+(c+di)=(a+c)+(b+d)i$$, Subtraction = $$(a+bi)−(c+di)=(a−c)+(b−d)i$$, Multiplication = $$(a+bi)\times(c+di)=(ac−bd)+(ad+bc)i$$, Division = $$\frac{(a+bi)}{(c+di)} = \frac{a+bi}{c+di} \times \frac{c-di}{c-di} = \frac{ac+bd}{c^{2}+d^{2}} + \frac{bc-ad}{c^{2}+d^{2}}\times i$$, Multiplication Conjugates = $$(a+bi)(a+bi)=a^{2}+b^{2}$$, $$\lim_{x \to a} \left[ {f(x) \pm g(x)} \right] = l \pm m$$, $$\lim_{x \to a} f(x) \cdot g(x) = l \cdot m$$, $$\lim_{x \to a} \frac{{f(x)}}{{g(x)}} = \frac{l}{m}$$, where \)m \ne 0\), $$\lim_{x \to a} c{\text{ }}f(x) = c{\text{ }}l$$, $$\lim_{x \to a} \frac{1}{{f(x)}} = \frac{1}{l}$$, where \)l \ne 0\).

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