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  • Intermediate Algebra

    Midterm Review Packet

    This packet is an overview of what we have covered

    during the first half of the year. This packet is a guide

    to help you study for the midterm. This is just a

    minimum of what you should be doing to prepare for

    this high-stakes test. You should be using your past

    assessments, homework, and notes to also help you

    prepare.

    Review packet:

    1. Due Dates:

    2. You must write out the ORIGINAL problem with

    the work underneath for full credit.

    3. If you have no work to support your answer, you

    will not get credit.

  • Chapter 2—Equations, Inequalities, and Problem Solving

     Equations—Section 2.1

     Solution set

     Empty set ( ) vs. All Real Numbers ( )  Clearing a fraction

     Clearing a decimal

     Problem Solving—Section 2.2

     Translating words into an equation

     5 step process

    o Don’t forget to define the variable

     Types

    o consecutive integers

    o geometric figures

    o percentage

     Literal Equations—Section 2.3

     Given a formula and be able to solve for a variable

     Treat all other variables as a ―constant‖

     Inequalities—Section 2.4

     Interval Notation

     ( or ) same as _______________________________

     [ or ] same as_______________________________

     What do you need to remember to do with the inequality

    symbol when you multiply or divide by a negative

    number?______________________________________

     Graph of the solution set

     Open circle or (

     Closed circle or [

     Shading

  •  Compound Inequalities—Section 2.5

     ―and‖  Graphs

     ―or‖--

     Absolute Value Equations—Section 2.6

     To Solve:

    1. Isolate the absolute value expression

    2. | | i. If b is negative →

    ii. If b is positive→Set up TWO equations

    3. Remember you either have TWO answers or

     Absolute Value Inequalities—Section 2.7

     To Solve:

    1. Isolate the absolute value expression

    2. If the number by itself is POSITIVE

    i. If | | , then ii. If | | then

    𝑎

    𝑎

    𝑎 𝑏

    𝑏

    𝑏

    𝑏 𝑎

  • 3. If the number by itself is NEGATIVE

    i. If | | then ii. If | | then

     Remember that you need to have TWO inequalities.

    Solve

    1) ( ) ( ) 2)

    3) ( ) ( ) 4)

    5)

    6) solve for

    7) solve for 8) | |

    9) | |

    Solve. Graph the solution set and write it in interval notation.

    10) ( ) ( ) 11) ( ) ( )

    12) ( ) ( ) 13)

    14) or 15) and

    16) | | 17) | |

    18) | | 19) ( )

  • Solve. Define your variable, set up your equation, solve your equation,

    and state your answer.

    20) Twice the difference of a number and 3 is the same as 1 add to three

    times the number. Find the number.

    21) The length of a rectangular playing field is 5 meters less than twice

    the width. If 230 meters of fencing goes around the field, find the

    dimensions of the field.

    22) Find four consecutive integers such that twice the first subtracted

    from the sum of the other three integers is 16.

    23) Determine whether there are two consecutive odd integers such

    that 5 times the first exceeds 3 times the second by 54.

    Chapter 3— Graphs and Functions

     Functions—Section 3.2

     Relation vs. function

     function notation, ( )  Domain

     Determine from a graph

     Determine from set of data

     Range

     Determine from a graph

     Determine from a set of data

     Vertical Line Test

     Evaluate a function for a given value of x

     Graphing Equations: Linear and Non-linear—Sections 3.1,

    3.4, and 3.4

     Is a point a solution to an equation

     x- and y-intercepts

     linear vs. non-linear

  •  graph non-linear using a table

     quadratic

     cubic

     absolute value

     graph linear equation

     using a table

     using and -intercepts  using slope and y-intercepts ( )

     slope

     given two points:

     given a graph:

     given a function:  VUX HOY

     Equation of a Line—Section 3.5

     Standard Form:

     Point Slope Form:

     Function Notation: ( )

     Parallel Lines

     Perpendicular Lines

     Graphing Piecewise-Defined Functions and Transformations

    --Section 3.6

     Graphing a piece-wised defined function

     domain for piecewise-defined

     open vs. closed circle at an endpoint

     graphing using a x-y chart

     Applying transformations to graph a parent function

     Vertical Shift

     Horizontal Shift

     Reflection about the x- or y-axis

  •  Graphing Linear Inequalities –Section 3.7

     Using  VUX HOY

     solid line vs. dotted line

     shading

    24) Determine if each relation is a function. State its domain and

    range.

    (a) *( ) ( ) ( ) ( ) ( )+

    (b)

    25) Let ( ) | | and ( ) evaluate the following:

    (a) ( )

    (b) ( )

  • Graph the following and state if the function is linear or non-linear.

    Use the specified method.

    Function Method

    26) x-y chart

    27) slope & y-intercept

    28) ( ) | | x-y chart

    29) any method

    30) x- and y-intercepts

    31) any method

    32) ( )

    slope & y-intercept

    33) slope & y-intercept

    34) Determine the slope of the line.

    (a) passes through ( ) and ( )

    (b) ( )

    (c)

  • 35) Determine the equation of a line given the following information

    and putting answer in the correct form.

    Given Information Form

    (a) passes through the points ( ) and ( ) Standard form

    (b) slope is undefined and passes through the point ( ) Standard form (c) perpendicular to the line and passes through the point ( ) Function notation (d) slope = and intercept is

    Slope-intercept

    form

    (e) passes through the point ( ) and parallel to

    ( )

    Standard form

    36) Graph the following piecewise-defined functions. State the domain

    and range.

    (a) ( ) {

    (b) ( ) { | |

    37) Describe the transformations with respect to its parent function.

    Graph each function.

    (a) ( ) ( )

    (b) ( ) √

  • Graph the solution set.

    38)

    39)

    40)

    For questions 41 – 43 use the graph at the below.

    41) Find all for which ( )

    42) ( )

    43) Find all for which ( )

  • Chapter 4—System of Equations

     Solve System of Linear Equations in Two Variables—Section 4.1

     Graphing Method

     Addition/Elimination Method

     Substitution Method **

    Solve **Use the Graphing Method

    44) {

    45) {

    Solve **Use the Addition/Elimination Method

    46) {

    47) {

    48) {

    49) {

  • Answers:

    1) * + 2) * + 3) 4) * +

    5) { ⁄ } 6) ⁄

    7)

    8) * + 9) 10) , )

    11) ( )

    12)

    13) ( -

    14) , )

    15)

    16) ( - , )

    17) ( )

    18) .

    /

    19) , ) 20) The number is

    21) The length is 75 m and the width is

    40 m.

    22) The integers are 10, 11, 12, & 13.

    23) No you can’t have two odd integers.

    24) (a) Not a function

    d: * + r: * +

    24) (b) Function

    d: ( ) r: (

    25) (b)

    ( ) 25) (a)

    ( )

    26—33) See graph paper 34) (a)

    34) (b)

    34) (c)

    35) (a)

    35) (b)

    35) (c) ( )

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