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sat math
06-29-2013, 01:51 PM
SATmath4u.com is the first forum introducing the addition of LaTeX mathematical typesetting for SAT math test.
LaTeX is a professional-grade general typesetting system that centers around very pleasing mathematical presentation. Mathematical expressions are written in a markup style somewhat similar to HTML.
You may include LaTeX graphics in any post here on SATmath4u.com
To include a LaTeX graphic, simply include your LaTeX code within the tags [ /tex]. without spaces.
Or by using the rightmost button in editing bar and then use the math symbols bellow the post area as shown in the following image.


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Basic Guidelines
Lines and Text. \\ starts a new line, \ includes a space, \mbox{...} includes text

Sub- and Superscripts.
[tex]x^3[ /tex] produces [tex]x^3 while
[tex]x_{2n}[ /tex] produces x_{2n}
Here is another example:
[tex]\log_{5} 125=3[ /tex] gives \log_{5} 125=3


Fractions. Use \frac to display fractions.
Example:
[tex]\frac{\pi^2}{6}[ /tex] gives \frac{\pi^2}{6}.

Roots. Use \sqrt. For instance,
[tex]\sqrt{a^3+b^4}[ /tex] produces \sqrt{a^2+b^2}

You can also get “other” roots:

[tex]\sqrt[4]{5}[ /tex] yields \sqrt[4]{5}.

Various examples
Code:

[tex] \frac{1}{2^n} \rightarrow 0[ /tex]

produces the graphic \frac{2}{3^n} \rightarrow 0

Code:

[tex]\int_a^b f(t) dt = 1[ /tex]

produces the graphic
\int_a^b f(t) dt = 1

Code:

[tex] \sum_{n=0}^{\infty} \frac{1}{n!} = e [ /tex]

produces the graphic
\sum_{n=0}^{\infty} \frac{1}{n!} = e

Plus or minus


[tex]\pm[ /tex]

produces the graphic
\pm

multiplication or dot product


[tex]a\cdot b[ /tex]

produces the graphic
a\cdot b


Equals sign and inequalities

To get an equals sign, you simply use the ordinary = sign.

[tex]2+3=5[ /tex]

produces the graphic
2+3=5


For 'not equal to', use \not=


[tex]2^4\not=2[ /tex]
produces the graphic
2^3\not=3

For less than signs, we use <, and for greater than signs, we use >

For 'less than or equal to' signs, we use \leq, and for 'greater than or equal to' signs we use \geq


[tex]x^2 \geq 0[ /tex]
produces the graphic
x^2 \geq 0

For spaces, use "\ ".

Sigma notation

To write sums, we use the \sum command.


[tex]\sum_{i=1}^n i^2 = \frac{1}{6}n(n+1)(2n+1) [ /tex]
produces the graphic
\sum_{i=1}^n i^2 = \frac{1}{6}n(n+1)(2n+1)


Differentiation

We use \frac{}{} to write dy/dx.


[tex]\frac{d}{dx} x^4 = 4x^3[ /tex]

produces the graphic
\frac{d}{dx} x^4 = 4x^3


For f'(x), simply write it out normally within TeX tags.


[tex]f'(x)[ /tex]

produces the graphic
f'(x)


Integration

For the integral sign, use the \int command.


[tex]\int 3x^2\ dx = x^3 + C[ /tex]
produces the graphic
\int 3x^2\ dx = x^3 + C

For definite integrals, use the commands for subscripts and superscripts.


[tex]\int^1_0 x\ dx =0.5[ /tex]

produces the graphic
\int^1_0 x\ dx =0.5

Modulus sign or absolute value

Use | for the modulus sign.


[tex]\sqrt{x^2} = |x|[ /tex]

produces the graphic
\sqrt{x^2} = |x|

Factorial

Use the exclamation mark like normal.


[tex]3! = 6[ /tex]
produces the graphic
3! = 6

n choose r


[tex]^n\mathrm{C}_r[ /tex]
produces the graphic
^n\mathrm{C}_r

Greek Letters

Write \x where x is the written form of the Greek letter (i.e. alpha, beta, gamma, ... , omega).


[tex]\pi[ /tex]
produces the graphic
\pi


[tex]\theta[ /tex]
produces the graphic
\theta

Infinity

To insert the infinity symbol, use \infty.


[tex]\infty[ /tex]
produces the graphic
\infty

Trigonometry


[tex]\cos \theta[ /tex]

produces the graphic
\cos \theta


[tex]\sin \theta[ /tex]

produces the graphic
\sin \theta



[tex]\tan \theta[ /tex]

produces the graphic
\tan \theta


[tex]\sec \theta[ /tex]

produces the graphic
\sec \theta



[tex]\mathrm{cosec} \theta[ /tex]

produces the graphic
\mathrm{cosec} \theta



[tex]\csc \theta[ /tex]
produces the graphic
\csc \theta


[tex]\cot \theta[ /tex]
produces the graphic
\cot \theta


[tex]\sin^2 \theta + \cos^2 \theta=1[ /tex]

produces the graphic
\sin^2 \theta + \cos^2 \theta=1



To write 'degrees', you could use the \circ command.


[tex]\cos 60^{\circ} = \frac{1}{2}[ /tex]

produces the graphic
\cos 60^{\circ} = \frac{1}{2}


Logarithms



[tex]\ln x^5 = 5 \ln x[ /tex]
produces the graphic
\ln x^5 = 5 \ln x


[tex]\log_{10} x^2 = 2 \log_{10} x[ /tex]
produces the graphic
\log_{10} x^2 = 2 \log_{10} x

Matrices


[tex]\begin{pmatrix} -2 & 6 & 7 \\2 & -5 & 1 \\1 & 2 & 3 \end{pmatrix}[ /tex]
produces the graphic
\begin{pmatrix} -2 & 6 & 7 \\2 & -5 & 1 \\1 & 2 & 3 \end{pmatrix}

Determinants


[tex]\begin{vmatrix} -2 & 6 & 7 \\2 & -5 & 1 \\1 & 2 & 3 \end{vmatrix}[ /tex]
produces the graphic
\begin{vmatrix} -2 & 6 & 7 \\2 & -5 & 1 \\1 & 2 & 3 \end{vmatrix}


vectors, simply write a matrix with only one column:


[tex]\begin{pmatrix} x \\ y \\ z \end{pmatrix}[ /tex]

produces the graphic
\begin{pmatrix} x \\ y \\ z \end{pmatrix}


[tex]\vec{a}[ /tex]
produces the graphic
\vec{a}

Limits


[tex]\displaystyle\lim_{x\to 0}[ /tex]
produces the graphic
\displaystyle\lim_{x\to 0}


Sets


[tex]\cup[ /tex]
produces the graphic
\cup



[tex]\cap[ /tex]
produces the graphic
\cap



[tex]\subset[ /tex]
produces the graphic
\subset



[tex]\subseteq[ /tex]
produces the graphic
\subseteq



[tex]\nsubseteq[ /tex]
produces the graphic
\nsubseteq



[tex]\in[ /tex]
produces the graphic
\in



[tex]\not\in [ /tex]
produces the graphic
\not\in



[tex]\mathbb{P}[ /tex]
produces the graphic
\mathbb{P}



[tex]\mathbb{N}[ /tex]
produces the graphic
\mathbb{N}



[tex]\mathbb{Z}[ /tex]
produces the graphic
\mathbb{Z}



[tex]\mathbb{I}[ /tex]
produces the graphic
\mathbb{I}



[tex]\mathbb{Q}[ /tex]
produces the graphic
\mathbb{Q}



[tex]\mathbb{R}[ /tex]
produces the graphic
\mathbb{R}



[tex]\mathbb{C}[ /tex]
produces the graphic
\mathbb{C}



\forall gives
produces the graphic
\forall

Logic Symbols


[tex]\forall[ /tex]
produces the graphic
\forall



[tex]\land[ /tex]
produces the graphic
\land



[tex]\lor[ /tex]
produces the graphic
\lor



[tex]\exists[ /tex]
produces the graphic
\exists



[tex]\neg[ /tex]
produces the graphic
\neg



[tex]\sim[ /tex]
produces the graphic
\sim