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 50-60 test items. Answer ALL questions. A formula sheet will
be given along with scratch paper and graph paper. A graphing calculator may be used.
The calculator will have the memory cleared BEFORE and AFTER the test. Please
review and study this material.
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
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.
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
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
4 8
Proportion: an equation stating that two ratios are equal. Example =
2 4
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X-intercept: the x-coordinate of the point at which it crosses the x-axis (where x = 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.
2 Ways to Determine if a Relation is a Function
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 is not a variable that is multiplied by x.
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 )
, x1 ≠ x2
m= 2
( 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.
Form
Equation
Description
Slope- intercept
y = mx + b
m is the slope, and b is the y-intercept
Point-slope
m is the slope and ( x1 , y1 ) is a given
y − y1 = m( x − x1 )
point.
Standard
Ax + By = C
A and B are not both zero. Usually A is
nonnegative and A, B, and C are integers
whose greatest common factor is 1.
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Parallel lines: have the same slope.
Perpendicular lines: slopes are opposite reciprocals of each other. Vertical and
horizontal lines are perpendicular.
Linear Correlation: STAT, CALC, 4, ENTER, the r is the linear coefficient.
If r is close to -1 then you have a negative correlation.
If r is close to 1 you have a positive correlation.
If r is close to 0 there is NO correlation.
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 draw a dashed line.
3. If the symbols are ≤, ≥ then draw a solid line.
4. < and ≤ mean shade LEFT.
5. > and ≥ mean shade to the RIGHT.
<, < Less than: Shade LEFT
>, > Greater than: Shade RIGHT
< , > DASHED LINE
<, > SOLID LINE
FLIP THE SIGN: MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER
AND: INTERSECTION
OR: DOES NOT INTERSECT
Solving Systems of Equations
System of equations: two or more equations with the same variables.
• 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.
• Algebraically: Substitution or Elimination
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
Polynomials
a m • a n = a m+ n
(a m ) n = a mn
(ab ) m = a mb m
1
(a) − m = m , a ≠ 0 (no zeros in the denominator)
a
0
,
a
(a) = 1 ≠ 0 (any # to zero power is 1)
am
= a m−n , a ≠ 0
an
a
am
( ) m = m , b ≠ 0 (m is distributed to everything)
b
b
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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.
FOIL Method: used to multiply two binomials. (a + b) 2 = a 2 + 2ab + b2
F- multiply the First terms;
O- Outer terms,
I- Inner terms, and
L- Last terms.
F
L
(x + 3)(x – 2) Product of first terms: (x)(x) + Product of Outer terms (-2)(x) + Product of
I
inner terms (3)(x) + product of last terms (3)(-2)
O
The opposite of squaring something is to take the square root of it.
Range: (Maximum data entry) – (Minimum data entry)
Measure
Length
Metric
1 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)
Metric Conversions: K
H
D
basic
D
C
M
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