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) ( )

35) (d)

35) (e)

36—40) See graph paper

41) (approx. values)

42) ( ) 43) there are no values of

.

1 2

6 1

44) 45) ( ) 46) ( ) 47) infinitely many soln

48) ( ) 49) .

/