Mid Term Review Packet
Algebra I CP 2013
Periods 2, 6, 8
Your midterm will take place on January ______, 2013. It will consist of 75 multiplechoice questions that will be answered on a Scantron sheet, as well as one open
ended question. You are to come prepared to the midterm with the following
materials.



2 #2 Pencils with good erasers.
A calculator.
Knowledge of all of the following topics.
The Midterm will be on Chapters 1 – 5. The following is a breakdown of topics by
Chapter and by section. Along with these topics and notes, I will provide you a list of
problems in the textbook to work on in order to be best prepared for the midterm.
This may seem like a lot, but we will break it down to bits and pieces over the next
few days to make it very manageable!
CHAPTER 1
Section 1: Displaying Data Relationships with Graphs
Mean =
𝑆𝑢𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑎𝑡𝑎 𝑖𝑡𝑒𝑚𝑠
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑡𝑎 𝑖𝑡𝑒𝑚𝑠
(Mean is also referred to as the average of the data)
Median: The middle value in an ordered set of numbers.
 Order the numbers from least to greatest.
 Cross out the first and the last number, continue this until you have reached
one number, this number is your Median.
 If you get to the point where there are two middle numbers (this happens if
there is an even number of data points) then you take the Mean (average) of
the two numbers in the middle. This average is your Median.
Mode: The number that occurs the most in a set of data.
Section 2: Modeling relationships with Variables
Variable Expression: a mathematical phrase that contains at least one variable.
Ex: s-2, where s is a variable.
Term: A number, variable, or product of numbers and variables.
Ex: The Variable Expression 4s + 8 has 2 terms (4s and 8).
Equation: where two expressions are set equal.
Ex: t = s-2
Writing Equations from a table of data (See p. 12)
Section 3: Order of Operations
***This section is EXTREEMELY IMPORTANT***
P-arenthesis
E-xponents
M-ultiplication
D-ivision
FROM LEFT TO RIGHT
A-ddition
S-ubtraction
FROM LEFT TO RIGHT
Textbook Page
Section 4: Adding and Subtracting Integers
Addition Rule: To add two numbers with the same sign, add their absolute values.
The sum has the same sign as the numbers.
Example: 3 + 5 = 8
-3 + (-5) = -8
To add two numbers with different signs, find the difference between
their absolute values. The sum has the same sign as the number with the greater
absolute value.
Example: -3 + -5 = 2
3 + (-5) = -2
Subtraction Rule: To subtract a number, add its opposite.
Example: 3 – 5 = 3 + (-5)
= -2
Section 5: Multiplying and dividing integers
Multiplication and Division Rules
The product or quotient of two positive numbers is positive.
The product or quotient of two negative numbers in positive.
The product or quotient of a positive number and a negative number is negative.
-
+
Section 6: Real Numbers and Rational Numbers
Real Numbers: any number that appears on a number line.
Rational Numbers: Any number that you can write as a fraction.
Irrational Numbers: Numbers that CANNOT be written as a fraction.
Integers: Postive and Negative Counting Numbers (…-3,-2,-1,0,1,2,3…)_
Whole Numbers: 0, 1, 2, 3, 4…
Natural Numbers: 1, 2, 3, 4…
Comparing Fractions (Rational Numbers)
 P. 32-33
Section 1-8 Organizing Data in Matrices
Read the size of a matrix as ROW X COLUMN (X is read “by”)
Rows go left and right.
Columns go up and down.
1
The Matrix 4 is 4 X 1 (Four rows by one column).
6
[−9]
Adding and subtracting Matrices.
 You can only add or subtract matrices of the SAME SIZE.
Add or subtract corresponding entries.
1−3
4−3
1 4
−2 1
3 3
Example: [
]− [
]=[
]=[
]
−4 − 4 −4 − (−1)
−4 9
−8 −3
4 −1
Multiplying a Matrix by a given value
2(3)
3 3
2[
]=[
2(4)
4 −1
2(3)
6 6
]=[
]
2(−1)
8 −2
Practice problems for chapter 1
Textbook page 51-53 breaks down each section into important problems. Try these.
Extra practice is on page. 54 and 55.
CHAPTER 2
SECTION 1: Analyzing Data Using Scatter Plots
Types of correlations: Positive, Negative, No Correlation.
 Identify a situation as having positive, negative, or no correlation.
SECTION 2: Relating Graphs to Events
Given a graph, label what is happening at each moment.
Example:
SECTION 3: Linking graphs to tables
Independent variables: a variable that does not depend on another variable
Dependent variable: a variable that relies (depends) on another variable.
THE DEPENDENT VARIABLE DEPENDS ON THE INDEPENDENT VARIABLE!
Given a table of x and y values, be able to plot these points on a graph to determine
the shape of the graph.
SECTION 4: Functions
***These next few sections are EXTREEMELY IMPORTANT***
A relation is a set of ordered pairs.
 (1,2), (0,0), (2, 9.3)
A function is a relation that assigns exactly one Y value to each X value.
 If you had a table of values or set of ordered pairs if there is a
repeated x with a different y value then that relation IS NOT A
FUNCTION!
A graph is a function if it passes the Vertical line test.
 Take a pencil and put it up against the paper with the tip pointing up.
Move across the graph. If at any point in the journey along the graph
the pencil hits MORE THAN ONE point of the graph, then it is NOT a
function.
Function Rule: an equation that describes a function. Using the input values (plug in
for x) find the output values (y).
Names of Values in a Function
Independent Variable
Input
Domain
X-Values
Dependent Variable
Output
Range
Y-Values
SECTION 5: Writing a Function Rule
Function notation: All you need to do for this is replace y with f(x).
So instead of
y=3x+2  f(x)=3x+2
the (x) part of f(x) just tells us what value to put in for x on the right hand side of the
equation!
***Writing function rules from a table.
x f(x)
1
5
2
6
3
7
Ask yourself, “What do I do to 1 to get 5, what do I do to 2 to get 6, what do I do to 3
to get 7?”
f(x)=x+4  you need to add for to all the values in the “x” column to get the value in
the f(x) column!
Find the Range of a function given the domain.
1.) Create a table
2.) Put your domain in the left column (your x values)
3.) Plug in these x values into the function for x and put your output in your f(x)
column (the right column).
Section 6: The Three Views of a Function
Given a function rule, create a table of domain and range values (try and make it
easy on yourself and pick -2, -1, 0, 1 ,2 for the domain)then from that table, plot
those points (as x,y pairs) on a graph. There are your three views of a function!
Section 7: Families of functions
Three families
Linear Function
Quadratic Function
Y=x +2
Y = x2+1
Highest power of x is 1
Highest power of x is 2
Graph: Straight Line
Graph: U shaped curve
(parabola) opens up or
down.
Absolute Value Function
Y = |x|
Absolute value symbol
Graph: V Shaped (V as in
Value!)
Be able to identify these types given an equation or graph.
CHAPTER 3
Section 1: Modeling and Solving Equations
Think of equations as a balance scale. What you do to one side you must do to the
other side of the equals sign. For example if I subtract 2 from one side, I would need
to subtract 2 from the other.
Undo Multiplication by division
Undo Division by multiplication
Undo Addition by subtraction
Undo Subtraction by addition
Section 2: Modeling and solving 2 step equations.
To solve these problems think the opposite of PEMDAS and use SADMEP to get the
desired variable by itself.
Section 3: Combining like terms to solve equations
Terms are like terms if they have exactly the same variable part to them.
 4x and 3x are like terms
 3x and 2y are NOT like terms
 x and 3 are NOT like terms
 4x + 3x = 3x
 x + 3 = x + 3 …..PLEASE! do not combine x + 3 as 3x…
Section 4: Using the Distributive Property
For all real numbers a, b and c:
a(b+c)=ab +ac
(b+c)a=ba+ca
a(b-c)=ab-ac
(b-c)a=ba-ca
Be careful if you are distributing a negative number…
Example: -2(x+3) = -2x – 6 (Note the + turned to a -)
The Commutative Property
a+b=b+a
or
ab=ba
NOTE: Subtraction is not part of the commutative property!
Section 5: Rational Numbers and Equations
The operation that holds rational numbers together is division.
If we want to get rid of rational numbers in our problem, we can multiply EVERY
SINGLE TERM by the LCD (least common denominator).
Definitely take a good look at these practice problems we need more practice with
fractions! You won’t get better at them unless you work at it!
Section 7: Percent Equations.
I=PRT
I-interest
P-principle
r-rate (%)
t-time
***IMPORTANT***
𝑖𝑠
%
=
𝑜𝑓 100
Section 8: Percent of change
***ALSO IMPORTANT*** (I’m not just saying that)
𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒
𝑝𝑒𝑟𝑐𝑒𝑛𝑡 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒 =
→ 𝐷𝑒𝑐𝑖𝑚𝑎𝑙 → 𝑃𝑒𝑟𝑐𝑒𝑛𝑡
𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑎𝑚𝑜𝑢𝑛𝑡
In order to convert a decimal to a percent move the decimal two places to the right.
Review problems: p. 151-153, extra practice, 154-155
CHAPTER 4
Section 1: Using Proportions
Useful resources: Textbook, guided notes handout.
Things to know:
 When two fractions are set equal to each other, solve by cross-multiplying.
 If two triangles are similar their sides are in proportion (draw a picture!)
 Two fractions are in proportion if their cross product is equal.
Section 2: Equations with variables on both sides
Useful resources: Textbook, Powerpoint Slides (on website), Quiz
Things to know:
 If variables are on both sides of your equation, move all variables to one side
and everything else to the other side. Do your best to keep variables positive
(makes solving a little easier).
 There are two “special cases”
o No solution

 Ex. 7=9
o Infinite solutions/identity
 Ex. 5=5
You can always check your solution by plugging the value in for x and seeing
if both sides are equal!
Section 3: Solving Absolute Value Equations
Useful resources: Textbook, Powerpoint, Notes, Homework
Things to know:
 Absolute Value: Distances x is from 0 on a number line.
 Absolute value is ALWAYS POSITIVE!
 If you have |2x+4| = -9 There is NO SOLUTION (See above)
 The three step process to solving an absolute value equation
o Get the absolute value by itself
o Split the absolute value up into two equations (+, -)
o Simplify/Solve
Section 4: Transforming Formulas
Useful resources: Textbook, Powerpoint, Homework
Things to know:
 Solve these problems the same way you would if there were numbers instead
of a bunch of variables.
 Opposites:
o Multiplication is the opposite of Division
o Addition is the opposite of subtraction
 Do addition and subtraction FIRST then multiply and divide.
Section 5: Solving inequalities Using Addition and Subtraction
Useful resources: Textbook, Powerpoint
Things to know:
 Treat these problems the same you would an equation (only difference is you
bring down the inequality sign through your problem)
 Graphing inequalities
o Open Circle: <, >, ¹
o Closed Circle: £,³, =
 Its helpful if the variable is on the left hand side of the inequality sign before
graphing.
Section 6: Solving inequalities Using Multiplication and Division
Useful resources: Textbook, Notes, Powerpoint, Homework
Things to know:
 When you multiply or divide by a negative number, SWITCH the inequality!
Section 7: Solving Multistep Inequalities
Useful resources: Textbook, Notes, Powerpoint, Homework
Things to know:
 Solve these problems the same way you would an equation
o REMEMBER! If you multiply or divide by a NEGATIVE, switch the
signs!
 Graphing (See section 5).
 Word Problem (set up an equation)
Section 8: Compound Inequalities
Useful resources: Powerpoint, Textbook, Worksheet, Notes
Things to know:
 And: Intersection (Overlap of solutions) (Sandwich)
 Or: Union (All possible solutions)
 A<B<C is an AND statement
o B>A AND B<C
 Absolute Value Inequalities
o Get Absolute Value by itself
o Split into two inequalities
 If > split it into and OR statement
 If < split it into and AND statement
o When you split it leave the sign the same on one, flip the second (and
turn the positive into a negative.
Ex: |2x+3| - 2 < 5
GET ABSOLUTE VALUE BY ITSELF
|2x+3| < 3
Subtract 2 from both sides
2x+3 < 3 AND 2x+3 > -3
AND b/c Less than. Split into 2 Eq.
2x < 0 AND
2x > -6
- 3 (careful subtracting integers!)
x < 0 AND
x > -3
Solved 
CHAPTER 5
Section 1-3: Slope
𝑆𝑙𝑜𝑝𝑒 =
𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒 (𝑟𝑖𝑠𝑒)
ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒(𝑟𝑢𝑛)
𝑆𝑙𝑜𝑝𝑒 =
Four types of slope:
 Positive, Negative, Zero, Undefined
Slope intercept form: y=mx+b
m:slope
𝑦2 − 𝑦1
𝑥2 − 𝑥1
b:y-intercept (where the line crosses the y-axis)
MISC. INFORMATION
Probability
𝑃𝑟𝑜𝑏𝑎𝑏𝑙𝑖𝑡𝑦 𝑜𝑓 𝑎𝑛 𝐸𝑣𝑒𝑛𝑡 =
# 𝑜𝑓 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑡𝑜𝑡𝑎𝑙 # 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠