## Factors and Products Formulas

$${(a + b)^2} = {a^2} + 2ab + {b^2}$$ $${(a – b)^2} = {a^2} – 2ab + {b^2}$$ $${(a +… Click here to read more

From basic to higher mathematics

$${(a + b)^2} = {a^2} + 2ab + {b^2}$$ $${(a – b)^2} = {a^2} – 2ab + {b^2}$$ $${(a +… Click here to read more

1. If $$\frac{a}{b} = \frac{c}{d}$$ then $$ad = bc$$ 2. If $$\frac{a}{b} = \frac{c}{d}$$ then $$\frac{a}{c} = \frac{b}{d}$$ 3. If… Click here to read more

1. If $$p$$ is a positive integer and $$a \in \mathbb{R}$$, then $${a^p} = a \cdot a \cdot a \cdots… Click here to read more

1. $$y = {\log _a}x$$ if and only if $$x = {a^y}$$, $$x > 0$$ and $$y \in \mathbb{R}$$, $$a$$… Click here to read more

1. $${e^x} = 1 + x + \frac{{{x^2}}}{{2!}} + \frac{{{x^3}}}{{3!}} + \cdots $$ 2. $$\ln (1 + x) = x… Click here to read more

1. $$1 + 2 + 3 +\cdots + n = \frac{{n(n + 1)}}{2}$$ 2. $${1^2} + {2^2} + {3^2} +… Click here to read more

If $$\alpha $$ and $$\beta $$ are the roots of the Quadratic Equation $$a{x^2} + bx + c = 0$$,… Click here to read more

The $$nth$$ term $${a_n}$$ of the Arithmetic Progression (A.P) $$a,{\text{ }}a + d,{\text{ }}a + 2d, \ldots $$ is given… Click here to read more

Consider that $$a,b \in \mathbb{R}$$, then 1. $$\left| a \right| \geqslant 0$$ and $$\left| a \right| = 0 \Leftrightarrow a… Click here to read more

$$z = (a,b) = a + ib,{\text{ }}i = (0,1)$$ $$i = \sqrt { – 1} ,{\text{ }}{i^2} =- 1,{\text{}}{i^3}… Click here to read more

1) If $$\mathop {\lim }\limits_{x \to a} f(x) = l$$ and $$\mathop {\lim }\limits_{x \to a} g(x) = m$$, then… Click here to read more

If $$y = f(x)$$, then 1) $$\frac{{dy}}{{dx}} = f'(x) = \mathop {\lim }\limits_{h \to 0} \frac{{f(x + h) – f(x)}}{h}$$… Click here to read more

General Derivative Formulas: 1) $$\frac{d}{{dx}}(c) = 0$$ where $$c$$ is any constant. 2) $$\frac{d}{{dx}}{x^n} = n{x^{n – 1}}$$ is called… Click here to read more

1) \[{y_n} = \frac{{{d^n}}}{{d{x^n}}}{(ax + b)^m} = \frac{{m!}}{{(m – n)!}}{a^n}{(ax + b)^{m – n}}\] 2) \[{y_n} = \frac{{{d^n}}}{{d{x^n}}}\frac{1}{{(ax + b)}}… Click here to read more

1) \[\int {1dx = x + c} \] 2) \[\int {adx = ax + c} \] where $$a$$ is any… Click here to read more

1) \[\int {{{\sin }^n}xdx = – \frac{{\cos x{{\sin }^{n – 1}}x}}{n} + \frac{{n – 1}}{n}\int {{{\sin }^{n – 2}}xdx} }… Click here to read more

1) $$\int\limits_a^b {F'(x)dx = F(a) – F(b)} $$ is called the Fundamental Theorem of Integral Calculus. 2) \[\int\limits_a^b {f(x)dx} = –… Click here to read more

1) \[\beta (m.n) = \int\limits_0^1 {{x^{m – 1}}{{(1 – x)}^{n – 1}}dx} \] is called the Beta Integral. 2) \[\Gamma… Click here to read more

Consider that $$A$$,$$B$$ and $$C$$ are the sets, then 1. \[A \cup A = A\] 2. \[A \cap A =… Click here to read more

Consider that $$A$$,$$B$$ and $$C$$ are the sets, then 1. $$A \subseteq A \cup B$$ and $$B \subseteq A \cup… Click here to read more

MATH SYMBOLS Symbols Description Symbols Description $$ = $$ is equal to $$\vartriangle $$ triangle $$ \ne $$ is not… Click here to read more

The Greek Alphabet Symbols Description Symbols Description $${\rm A}$$ $$\alpha $$ Alpha $$\Xi $$ $$\xi $$ XI $${\rm B}$$ $$\beta… Click here to read more

$$\pi = 3.14159$$ $${\pi ^2} = 9.8696$$ $$\sqrt \pi = 1.7724$$ $$\frac{1}{\pi } = 0.3183$$ $$e = 2.7182$$ $${\log _{10}}\pi… Click here to read more

The weight of one cu. ft water = $$62.425{\text{ }}lb$$ The velocity of light in a vacuum $$ = 2.99776… Click here to read more

Length: 10 millimeters = 1 centimeter 10 centimeters = 1 decimeter 10 decimeters = 1 meter 10 meters = 1… Click here to read more

1. An angle whose measurement is of $${90^ \circ }$$ is called a RIGHT ANGLE. 2. An angle whose measurement is greater than… Click here to read more

1) ANGLE: The union of two non colinear rays which have a common end point is called an angle. 2)… Click here to read more

1) $$Sin\theta = \frac{{perpendicular}}{{hypotenuse}} = \frac{y}{r}$$ 2) $$Cos\theta = \frac{{base}}{{hypotenuse}} = \frac{x}{r}$$ 3) $$Tan\theta = \frac{{perpendicular}}{{base}} = \frac{y}{x} = \frac{{Sin\theta… Click here to read more

$$\alpha $$ $$Sin\alpha $$ $$Cos\alpha $$ $$Tan\alpha $$ $$Cot\alpha $$ $$Sec\alpha $$ $$Co\sec \alpha $$ $$ – \theta $$ $$… Click here to read more

\[Si{n^2}\theta + Co{s^2}\theta = 1\] \[1 + Ta{n^2}\theta = Se{c^2}\theta \] \[1 + Co{t^2}\theta = Cose{c^2}\theta \] \[Sin(\alpha + \beta… Click here to read more

\[Sina + Sinb = 2Sin\left( {\frac{{a + b}}{2}} \right)Cos\left( {\frac{{a – b}}{2}} \right)\] \[Sina – Sinb = 2Cos\left( {\frac{{a +… Click here to read more

Consider the triangle $$\Delta ABC$$, having the angles $$\alpha ,\beta ,\gamma $$ and sides $$a,b,c$$ as shown in the figure…. Click here to read more

1) If $$r$$ denotes in-radius, then \[r = \sqrt {\frac{{(s – a)(s – b)(s – c)}}{s}} = \frac{\Delta }{s}\] \[r… Click here to read more

\[Si{n^{ – 1}}a + Si{n^{ – 1}}b = Si{n^{ – 1}}(a\sqrt {1 – {b^2}} + b\sqrt {1 – {a^2}} )\]… Click here to read more

\[Sinhx = \frac{{{e^x} – {e^{ – x}}}}{2}\] \[Coshx = \frac{{{e^x} + {e^{ – x}}}}{2}\] \[Tanhx = \frac{{{e^x} – {e^{ –… Click here to read more

\[Sin{h^{ – 1}}x = {\log _e}\left| {x + \sqrt {{x^2} + 1} } \right|\] \[Cos{h^{ – 1}}x = {\log _e}\left|… Click here to read more

1) \[Sinh{\text{ }}ix = iSinx\] 2) \[Cosh{\text{ }}ix = Cosx\] 3) \[Tanh{\text{ }}ix = iTanx\] 4) \[iSinhx = Sin{\text{ }}ix\]… Click here to read more

1) \[Sinx = \frac{{{e^{ix}} – {e^{ – ix}}}}{{2i}}\] 2) \[Cosx = \frac{{{e^{ix}} + {e^{ – ix}}}}{2}\] 3) \[Tanx = \frac{{{e^{ix}}… Click here to read more

1) \[Si{n^{ – 1}}x = \frac{1}{i}Log(ix + \sqrt {1 – {x^2}} )\] 2) \[Co{s^{ – 1}}x = \frac{1}{i}Log(x + \sqrt… Click here to read more

Consider two points $$P\left( {{x_1},{y_1}} \right)$$ and $$Q\left( {{x_2},{y_2}} \right)$$, then: 01. The distance formula \[\left| {PQ} \right| = \sqrt… Click here to read more

01. The equation of a circle having the center at $$O\left( {0,0} \right)$$ and radius $$r$$ is \[{x^2} + {y^2}… Click here to read more

The formulas of tangent and normal to any curve at a given point are listed below. $${\left. {\frac{{dy}}{{dx}}} \right|_p}$$ is… Click here to read more

Here we list the equations of tangent and normal for different forms of a circle and also list the condition… Click here to read more

Here we list the equations of tangent and normal for different forms of a parabola. The euation of tangent to… Click here to read more

Here we list the equations of tangent and normal for different forms of ellipses. We also define parallel chords and… Click here to read more

Here we list the equations of tangent and normal for different forms of a hyperbola. The equation of tangent to… Click here to read more

Some important results and formulas regarding the polar equation of a conic are listed here. 1. The polar equation of a… Click here to read more

Some important results and formulas regarding the arc length of the curve are listed here. 1. The arc length for… Click here to read more

The results and formulas related to asymptotes are listed below. Asymptotes a. Obtain $${\phi _n}\left( m \right)$$ by putting $$x… Click here to read more

The commonly used results and formulas of curvature and radius of curvature are as shown below: 1. Curvature $${\rm K}$$… Click here to read more

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