Download A simple math equation is

Basic math
A simple math equation is 5  4  9 . Another simple one is 5  4  1. Sometimes, it's important to
say that two things are not equal, and/or tell how they are not equal. You can do this with a
number of different symbols in math:
54
54
45
There are also simple math symbols for common operations like multiplication,  , and
division,  . Division is tricky, however, because it can also be written out in "long division"
form, like this:
3
6 18
This division problem has already been solved.
Sometimes a number does not divide evenly into another number. In this case, you can end up
with a fraction. For example, 4 divided by 5, also written as 4  5 , can be written out as a
fraction like this:
4
5
The same fraction can also be written 4/5. This is the way that it would be entered into a
calculator.
Multiplication also can be written in several ways. For example, 4 multiplied by 5 can be written:
45
Or, if you were entering it into a calculator:
4*5
Functions
A function is a way of relating two variables. A simple function, such as y  x , is very easy to
graph. Sometimes, math gives us more complex functions in quadratic, cubic, quartic and even
higher polynomial forms. Quadratic functions take the form:
y  ax 2  bx  c
The solution(s) to a quadratic equation, that is, where the function equals zero, can be found
using the following formula:
b  b2  4ac
x
2a
Cubic functions take the form:
y  ax3  bx 2  cx  d
Polynomials in general then, to a degree of n, may by written using the following formula:
y  an x n  an 1 x n 1  ...  a2 x 2  a1 x  a0
Higher math
Calculating derivatives and integrals of polynomials is particularly simple. For the polynomial
n
a x
i
i
i 0
the derivative with respect to x is
n
 a ix
i 1
i 1
i
and the indefinite integral is
n
ai
 i  1x
i 1
c
i 0
And now I'm tired of writing about math, so I will just be putting in some random equations. For
n
example,
(X
i 1
i
 X ) 2 is a random one I found in the MathType equations toolbar. I also found a
n
n
X i and
bunch of weird set expressions:
i 1
X i . I don't remember what these even mean.
i 1
Symbols I found in the sets include  ,  ,  ,  ,  ,  , Ð , Ñ , Ø , Ù , ô , õ , ð and â .
1
x  x 2
lim
y
n!
r ! n  r !
I am finding all kinds of standard equations in the MathType toolbars. Here's another one:
a 2  b2 .
There are also a lot of symbols on the toolbars. This list is what I found on the algebra tab: Z , k ,
F , S , A , M , ¨ ,  ,  , , , 0,1 ,  and 2 . A lot of these symbols I don't recognize,
although some, like  , I do.
dy
y
and
are both there, even though
x
dx
they're pretty much the same thing. The individual "characters", I guess you would call them, dx
and dy are also there. There are also partial expressions and characters regarding partial
derivatives. The partial expressions listed are:
Now I will go through the derivatives tab. The symbols
y
x
 2
u 2
 2
v 2
 2
uv
lim
 x 0
The symbols, other than those already listed, are: x , y , R , x  , x and x . I don't remember
what most of these mean either, except the first two.
n
X
i 1
i
n
This was the first item on the Statistics tab. The next one is
X
i 1
including:
n
XY
i 1
i i
2
i
. There are some more,
1
n
n
(X
i 1
Other choices on this tab are X 1 ,
, X n and
 X )2
i
x

symbols on the Statistics tab. The symbols are
for the expressions. There are also some
1
,  X ,  X ,  X2 , X and Y .
n
That was a pretty small tab. The next tab is Matrices, so I will go through that tab item by item
now.
 a11 a12 


 a21 a22 
 a11 a12

 a21 a22
a
 31 a32
a13 

a23 
a33 
 a11


a
 m1
a1n 


amn 
1 0


0 1
 a1

1

0
1
1
0 
1

an 
That is all of the pre-made matrix expressions. They also have a few symbols, which are
,
and .
,
,
Now it is time to go through the Trig tab. The first expression on it is cos 1  . Interestingly, they
do not include the arccos function, even though both of the following expressions are included:
sin 1 
arcsin 
Opposite


and     .
Hypotenuse
2

The Trig also includes a nice selection of common Trig symbols, all of which, I'm happy to say, I
1
   
recognize. Here they are:  ,  , , ei , 2 ,  , , , , , 90 and 60 .
2
2 3 4 6
There are also some other expressions on the Trig tab, including: ei ,
Now it is time for Mike's most requested tab, the Geometry tab. On this tab you can find the premade expressions below:
AB
AB
ABC
ABC
There are also a bunch of symbols, of course, which I will describe in case they don't come
through in MathType. The symbols are angle  , some angle with an arc through it (MathType is
calling it "measured angle) , another angle with an arc through it (MathType calls this one
"spherical angle") , the perpendicular sign  , empty triangle , filled triangle # , square ,
parallelogram and circle .
That's the end of the tabs. If there are more symbols or types of equations you would like me to
type out, please let me know.
Two and three fifths 2
3
5
Three and twelve fifty-sevenths 3
12
57
1
One half over three fourths 2
3
4
1
Two and a half over four fifths 2
4
5
2
1
One eigth over six and one fourth 8
1
6
4
3x
2
3
9
10
3
Binomial coefficient with a 3 over a 5  
5
3x all over two thirds over nine tenths
Binomial coefficient with 2 over 9
 2
 
9
 6 x3 
Binomial coefficient with 6x to the third over 9y 

9y 
+ + + + 15 or 4+ 15
4 filled square followed by 15 with no space between them
X sub 2 followed by 10 with no space between them
x210
Limit as x approaches infinity of f of x lim f ( x )
x 
Line segment XYZ XYZ
X then A bold southeast pointing arrow pointing to infinity xA
Y to the power of: (t to the power of 3)
y
A to the power of: b to the power of: c to the power of d
Integral sign with a superimposed circle
 (could not bold)
t3
ab
cd

20
Integral from 0 to 20 of 8x squared minus 3y plus 14
 8x
0
The cube root of x
The 10th root of y
The y root of z
y
3
10
x
y
z
Equations:
One plus one equals two
11  2
Two plus five is not equal to eight
25  8
Nine minus one equals eight
9 1  8
2
 3 y  14
Seven minus three is not equal to five
7 3  5
Three times five equals fifteen
3 5  15
Four times eight equals thirty-two
4  8  32
One hundred divided by ten equals ten
100 10  10
or
10
10 100
or
100
 10
10
Forty-four divided by four equals eleven
44  4  11
The square root of thirty-six equals six
36  6
Five squared equals twenty-five
52  25
Three cubed equals twenty-seven
33  27
Fractions
One half
1
2
Two thirds
2
3
Four fifths
4
5
X over y
x
y
Five x over two y equals three y over four z
5x 3 y

2 y 4z
A squared plus b squared equals c squared
a 2  b2  c2
y
 x
x  y 3

 xy tz
t
t 
x  y 
x 
x 3 w
3
5
7
7
6
21
67 84 12
3 4   x   4 
3 2   y    2 

   
 a11 a12 


 a21 a22 
 a11

 a21
a
 31
 a11


a
 m1
a12
a22
a32
a13 

a23 
a33 
a1n 


amn 
 1 6 12 


13 31 5 
 a1



0
0 


an 
 a1
an 
t