Algebra Midterm Study Guide 2017
*Remember - this is not everything you need to know. You will have to refer back to old packets, study
guides, and do practice questions in order to be successful on the midterm exam. :)
Calculator Keys
Negative
Fraction
Converting Fractions to Decimals/Decimals to Fractions
Absolute Value
Exponent
Graphing
Table
Graphing Picture
Test Taking Strategies
Multiple Choice Strategies
Free Response Strategies
Eliminate Choices
Guess and Check
Multiple Methods of Solution
Process of Elimination
Highlight keywords
Break the question into chunks that you understand.
Show all work!
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If the question asks you to
explain...
Is it rational?
“Yes, because it’s an integer”
Is it irrational?
“Yes, because it’s a non-terminating,
non-repeating decimal”
Is the point a solution?
“Yes, because it lies on the line”
“Yes, because it lies in the shaded region”
OR
“No, because it does not
lie on the line”
“No, because it does not
lie in the shaded
region”
What does the slope(rate of change) mean?
“Rate of _______ per ________”
What does the y-intercept mean?
“Initial amount, cost, fee…”
Is the point a solution? (system of
inequalities)
“Yes, because it lies in the double shaded
region”
OR
“No, because it does not
lie in the double
Is it a function?
“Yes, because each input has only one
output”
OR
“No, because an input has 2 different outputs”
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Unit 1 - Polynomials
Multiplying Polynomials/Distributive Property
(Box Method)
1. Identify terms that have the same base and same
exponent.
3. Keep the base and the exponent.
4. Standard form - greatest exponent first and then
follow in descending order.
1. Multiply coefficients.
2. Keep the base.
3. Add the exponents.
4. Combine like terms (see box to the left).
Example of Substitution
Example of using the “Box Method”
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Unit 2 - Equations
Example of Solving an Equation
Example of Solving a Literal Equation
Given the formula , solve for t.atd =
2
1
2
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Unit 3 - Inequalities
*When solving inequalities, we use the same steps as solving equations.*
**Remember to reverse the inequality symbol when we divide by a negative number!!**
x
< 4
x
> 4
x ≤ 4
x ≥ 4
x
is less than 4”
Open circle
x
is greater than 4”
Open circle
x
is less than or equal to 4”
Closed circle
x
is greater than or equal to 4”
Closed Circle
Interval Notation
Meaning
Compound Inequality
Graph
(-2, 3)
-2 is not included
3 is not included
{-1, 0, 1, 2}
-2 < x
< 3
(-2, 3]
-2 is not included
3 is included
{-1, 0, 1, 2, 3}
-2 < x
3
[-2, 3)
-2 is included
3 is not included
{-2, -1, 0, 1, 2}
-2 x
< 3
[-2, 3]
-2 is included
3 is included
{-2, -1, 0, 1, 2, 3}
-2 x
3
“at most”
“no more than”
“at least”
“no less than”
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Unit 4 - Graphing
Graphing Linear Equations
Standard form of a line:
y
= m
x
+ b
m
represents the slope/rate of change of the line.
b
represents the y
-intercept of the line.
x
and y
represent a point, (x
, y
), on the line.
Key Feature
Algebraic Solution
Graphic Solution
x-intercept
Cover the y
and solve for x
.
Point where the function intersects with the x
-axis.
y-intercept
Cover the x
and solve for y
.
Point where the function intersects with the y
-axis.
Solution
Substitute (x
, y
) in your equation.
If true, then it is a solution.
If false, then it is not a solution.
In order for a point to be a solution it must be on the
table and line.
Rate of Change
x x
2 1
y y
2 1
“Rise over Run”
Graphing Inequalities
Notes
Example
< is a dashed line and shade down.
> is a dashed line and shade up.
is a solid line and shade down.
is a solid line and shade up.
*Remember - you must have...
A Table
Arrows
Labels
...to earn full credit on your midterm exam!
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Unit 5 - Systems of Linear Equations & Inequalities
Linear System
Inequality System
Graph each line separately!
The point of intersection is your answer. This
is called your “Solution.”
Remember - you must have tables, arrows,
and labels for everything in order to get full
credit on your midterm!
Graph each inequality separately!
< is a dashed line and shade down.
> is a dashed line and shade up.
is a solid line and shade down.
is a solid line and shade up.
The double shaded section is your “Solution.”
Any point in this area (not on the lines) is true
for BOTH inequalities.
Remember - you must have tables, arrows, and
labels for everything to get full credit on your
midterm!
Solving Systems of Equations Algebraically
Elimination Method
Substitution Method
Step 1: Switch your coefficients and make one
negative (multiply top on bottom, and bottom on
top).
Step 2: Distribute to each term.
Step 3: Combine like terms and solve for y
.
Step 4: Substitute y
into one equation and solve
for x
.
*Make sure equations are in “y
” = format.
Step 1: Set equations equal to each other.
Step 2: Solve for x
.
Step 3: Substitute x
into one equation and solve
for y
.
Your solution should be written as a point (x
, y
)
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Your solution should be written as a point (x
, y
)
unless it is a real world situation.
unless it is a real world situation.
Unit 6 - Functions
Key Feature
Meaning
Example
Domain
“Input” of a function (x
-values).
Domain: All Real Numbers
Range: (x)f ≥ 2
Range
“Output” of a function (y
-values).
*Each input can only have 1 output.*
(see page 2 for free - response catchphrases)
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