College Mathematics Preparation • Math 0995

At Utah State University, Math 0995 covers college mathematics prep. This page is a summary of many topics covered in preparation for college mathematics.

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Order of Operations | P•E•M•D•A•S

Symbol	Operation
( ) , [ ] , { }	Parentheses, Brackets, Braces
$x^a$, $ \sqrt{x}$	Exponents, Radicals
$\times, \div $	Multiplication, Division
+ , -	Addition, Subtraction

$A set of algebraic equations.$

English to Metric Conversions

Length

Imperial	Metric
1 inch	2.54 centimeters
0.39 inch	1 centimeter
1 foot	30.48 centimeters
3.28 feet	1 meter
1 yard	0.91 meters
1.09 yards	1 meter
1 mile	1.61 kilometers
0.62 miles	1 kilometer

Weight

Imperial	Metric
1 ounce	28.35 grams
0.035 ounces	1 gram
1 pound	0.45 kilograms
2.21 pounds	1 kilogram
1 ton	0.91 metric tons
1.1 tons	1000 kilograms

Geometric Figures

Circle

$ P = 2\pi r $
$ A = \pi r^2$

Square

$ P = 4s$
$ A = s^2$

Triangle

$ P = a + b + c$
$ \displaystyle A = \frac{1}{2}bh$

Eclipse

$ A = \pi a b$

Rectangle

$P=2l+2w$
$ A = bh $

Trapezoid

$P = a + b + c + d$
$ \displaystyle A = \frac{(a+b)}{2}h$

Sphere

$\displaystyle V= \frac{4}{3}\pi r^3$

Cube

$\displaystyle V= s^3$

Cone

$ \displaystyle V= \frac{\pi r^2 h}{3} $

Cylinder

$\displaystyle V= \pi r^2 h$

Rectangular Prism

$\displaystyle V= l \cdot w\cdot h$

Triangular Prism

$\displaystyle V= \frac{l \cdot w\cdot h}{3}$

Manipulating and Simplifying Expressions

Try these methods to manipulate or simplify your expression.

Consider your goal. Do you want your expression to look like a certain form, or be as simple as possible?
Add or substract to combine terms.
Try multiplying or distributing across parentheses $a(x+b) \rightarrow ax+ab $ or factoring common factors $ (5x+15) \rightarrow 5(x+3) $
Apply exponents or square roots.
Remember not to change your expressions value, just manipulate and simplify.

Solving Equations and Inequalities

Tips to Remember:

Anything you do to one side of an equation or inequality, you must do to the other side ( multiplication, division, addition, subtraction, etc.)
When working with Inequalties, if you multiply or divide both sides by a negative number you must flip the inequaltiy.

Graphing

For equations and inequatlites containing both an x and a y you can use the slope intercept form to graph the equation or expression.
Slope Intercept Form: $ y = mx+b $ ($m$: slope, $b$: y-intercept)

Number Line (where c is some constant number)

If $x=c$ use a solid dot at c
If $x>c$ mark a hole/hollow dot on c and shade to the right
If $x$ < $c$ mark a hole/hollow dot on c and shade to the left
If $x\geq c$ mark a solid dot on c and shade to the right
If $x \leq c$ mark a solid dot on c and shade to the left

Coordinate Plane

If $y=x$ use a straight line on a coordinate plane.
If $y$ < $x$ mark a dashed line on the coordinate plane and shade to the right.
If $y>x$ mark a dashed line on the coordinate plane and shade to the left.
If $y\leq x$ mark a solid line on the coordinate plane and shade to the right.
If $y\geq x$ mark a solid line on the coordinate plane and shade to the left.

Try graphing Inequalties and Equations on Desmos to become more comfortable with them.