Download Algebra I Study Guide for End of Course Test

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Algebra I Study Guide for End of Course Test
The EOC test consists of 50 multiple choice questions. Answer ALL questions. A
formula sheet will be given, a ruler, and a graphing calculator. Please review and study
this material.
Chapter 1: The Language of Algebra
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REMEMBER: x  1 , a  a . Anything to the 0 power, is always 1.
Anything to the 1st power is always itself.
Commutative Property: communicate your order at the Sonic, therefore commutative is
to change the order of the operation.
a+b=b+a
Example: 1 + 2 = 2 + 1 (you still get the same answer)
Associative Property: You associate with your group of friends. The order does not
change, only where the sets of parenthesis go.
a + (b + c) = (a + b) + c
Example: (1 + 2) + 3 = 1 + (2 + 3) (the same answer)
Independent Variable: graphed on the horizontal axis, the thing you are changing or
manipulating. (mnemonic MIX-manipulate, in dependent, x)
Dependent Variable: graphed on the vertical axis, what is depended upon.
(mnemonic DRY- dependent, responding, y)
Relation: set of ordered pairs.
Domain: set of the first numbers of the ordered pairs, containing all values of the
independent variable. (x, y) – all x values
Range: set of second numbers of the ordered pairs, contains all values of the dependent
variable. (x, y) – all y values
Chapter 2: Real Numbers
Absolute Value: x , of a number is its distance from 0 on the number line. Since distance
is nonnegative, the absolute value of a number is ALWAYS positive.
Irrational numbers non terminating and non repeating decimals π and the √ (square
root) of a non perfect square
All other numbers are rational
Chapter 3 Notes: Solving Linear Equations
Some verbal expressions that suggest the equals sign:
Is
is equal to
is as much as
Equals
is the same as
is identical to
LESS THAN or MORE THAN - switch order
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Ratio: is a comparison of two numbers by division. The ratio of x to y can be expressed:
x
x to y
x:y
y
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Proportion: an equation stating that two ratios are equal. Example 
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X-intercept: the x-coordinate of the point at which it crosses the x-axis (where y = 0).
Y-intercept: the y-coordinate of the point at which the graph crosses the y-axis
(where y = 0).
Function: is a special type of relation in which each element of the domain is paired with
exactly one element of the range. X DOES NOT REPEAT
2 Ways to Determine if a Relation is a Function ( x cannot repeat!)
1. Mapping: shows how each member of the domain is paired with each member of the
range. A map that shows how each x value is paired with the y values.
2. Vertical Line test: determines whether a relation is a function.
If the vertical line does not intersect a graph in more than one point, the graph represents
a function.
 If the vertical line intersects the graph at two or more points, the graph does NOT
represent a function.
 Examples of graphs that are NOT functions: circles, hyperbolas, ellipses, semicircles.
 Therefore, the vertical line can only hit the graph ONCE to be a function!
Functional notation: f(x) = 2x + 1, the symbol f(x) is read “f of x,” the f is the name of
the function, it not a variable that is multiplied by x.
Chapter 5: Analyzing Linear Equations
Slope: (rate of change) of a line is the ratio of change in y-coordinate to the
corresponding change in x-coordinates. The slope measures how steep a line is. Suppose
a line passes through ( x1 , y1 ) and ( x2 , y2 ) , look at the change in the y and x coordinates:
( y  y1 )
m 2
, x1  x2
( x2  x1 )
4 types of slope:
1. Positive slope goes up from left to right, m = a positive number.
2. Negative slope goes down from left to right, m = negative number.
3. NO slope are HOrizOntal lines have, y = some number.
4. Undefined slopes are vertical lines, you cannot ski down a vertical slope, x = some
number.
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Form
Slope- intercept
Equation
y = mx + b
Point-slope
y  y1  m( x  x1 )
Standard
Ax + By = C
Description
m is the slope, and b is the
y-intercept
m is the slope and ( x1 , y1 )
is a given point.
A and B are not both zero.
Usually A is nonnegative
and A, B, and C are integers
whose greatest common
factor is 1.
slope(m) makes line steeper or flatter
b (y intercept) moves line up and down
Parallel lines: have the same slope.
Perpendicular lines: slopes are opposite reciprocals of each other. Vertical and
horizontal lines are perpendicular. .
Algebra I Notes Chapter 6: Solving Linear Inequalities
If each side of an inequality is DIVIDED or MULTIPLIED by a negative number then
CHANGE THE SYMBOL.
Graphing Inequalities:
1. Always solve for y. If you multiply or divide by a negative number, flip the
symbol.
2. If the symbols are <, > then use open circle.
3. If the symbols are ,  then use solid dot.
4. < and  mean shade LEFT.
5. > and  mean shade to the RIGHT.
, 
Less than: Shade LEFT
<,>
Open circle/ dotted line
, 
, 
Greater than: Shade RIGHT
SOLID DOT/ solid line
FLIP THE SIGN: MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER
Chapter 7 Notes: Solving Systems of Equations
System of equations: two or more equations with the same variables. SOLUTIONS
Graphing: solve both systems for y and type into y =, make sure you see the graph on the
screen (may need to change the window), 2nd trace, 5, enter, enter, enter.
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Product of Powers Property
Power of a Power Property
Power of a Product Property
Negative Exponent Property
Zero Exponent Property
Quotient of Powers Property
Power of a Quotient Property
Chapter 8: Polynomials
a m  a n  a m n
(a m ) n  a mn
(ab) m  a mb m
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(a )  m  m , a  0 (no zeros in the denominator)
a
0
(a)  1 , a  0 (any # to zero power is 1)
am
 a mn , a  0
n
a
a
am
( ) m  m , b  0 (m is distributed to everything)
b
b
Degree: of a monomial is the sum of the exponents of its variables. Degree of a
polynomial is the greatest degree of any term. Look at the degree of each term.
Distribute: used to multiply two binomials. (a  b) 2  a 2  2ab  b2
(x + 3)(x – 2) Product of first terms: (x)(x) + Product of Outer terms (-2)(x) + Product of
inner terms (3)(x) + product of last terms (3)(-2)
The opposite of squaring something is to take the square root of it.
Factoring- Multiply choices to find answer. first terms make first of trinomial- last
terms make last term of trinomial. Multiply inner and outer to make middle
number.
Know special rules.
Measure
Length
Metric
Kilometer (km) = 1000 meters (m)
1 meter = 100 centimeters (cm)
1 centimeter = 10 millimeters (mm)
Customary
1 mile (mi) = 1760 yards (yd)
1 mile = 5280 feet (ft)
1 yard = 3 feet
1 foot = 12 inches (in)
1 yard = 36 inches
Volume and
Capacity
1 liter (L) = 1000 milliliters (L)
1 kiloliter (kL) = 1000 liters
1 gallon (gal) = 4 quarts (qts)
1 gallon = 128 fluid ounces (fl oz)
1 quart = 2 pints (pt)
1 pint = 2 cups (c)
1 cup = 8 fluid ounces
Weight and
Mass
1 kilogram (kg) = 1000 grams (g)
1 gram = 1000 milligrams (mg)
1 ton (T) = 2000 pounds (lb)
1 pound = 16 ounces (oz)
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Metric Conversions: K
H
D
Kill Her Dead (measure) Don’t Cry Milli
D
C
M
Calculator- Reset -- blue 2nd – MEM which is add button –press 7—enter—press 2
Reset
NEED to fix table format press 2nd – TBLSET (window)—arrow down to Indpnt arrow
over to ask press enter—must enter numbers on table
Window standard
-10 to10
Quadratic- ax2 + bx +c
bigger the a is the thinner the parabola
smaller the a is the wider the parabola
negative a flips it upside down
c moves the parabola up or down
zeros or roots where
parabola crosses the x axis
Solve a quadratic
Factor
Complete the square
Quadratic Formula
RADICALS Simplify do not leave anything under the radical sign
that can be simplified.
Not simplified with a radical in denominator
Matrices - Adding/Subtacting and scalar multiplication
Arithmetic and Geometric sequences - know formulas
Exponential growth and decay