# MTH 220 Week 5 Final Exam

**MTH/220 College Algebra**

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**MTH 220 Week 1 Checkpoint**

**MTH 220 Week 2 Checkpoint**

**MTH 220 Week 3 Checkpoint**

**MTH 220 Week 4 Checkpoint**

**MTH 220 Week 5 Final Exam**

**MTH 220 Week 1 MyMathLab®**

Study Plan for Week 1 Checkpoint

Study Plan for Week 1 Checkpoint

**MTH 220 Week 2 MyMathLab®**

Study Plan for Week 2 Checkpoint

Study Plan for Week 2 Checkpoint

**MTH 220 Week 3 MyMathLab®**

Study Plan for Week 3 Checkpoint

Study Plan for Week 3 Checkpoint

**MTH 220 Week 4 MyMathLab®**

Study Plan for Week 4 Checkpoint

Study Plan for Week 4 Checkpoint

**MTH 220 Week 5 MyMathLab®**

Study Plan for Week 5 Final Exam

Study Plan for Week 5 Final Exam

**MTH 220 Week 5 Final Exam**

Solve for x using the

quadratic formula.

Evaluate the function at the given values of the

independent variable and simplify.

Use the graph of f to

determine each of the following.

(a) the domain of f

(b) the range of f

(c) the zero(s) of f

(d) f left parenthesis 4

right parenthesis

(e) the intervals on which

f is increasing

(f) the intervals on which

f is decreasing

(g) the values for which

f(x)less than or equals0

(h) any relative maxima or

minima

(i) the value(s) of x for

which f left parenthesis x right parenthesis equals 4

(j) Is f left parenthesis 3

right parenthesispositive or negative?

Give the slope and

y-intercept of the line whose equation is given below. Then graph the linear

function.

Use the given conditions to write an equation for

the line in point-slope

form and in slope-intercept

form.

Find the average rate of

change of the function

Use the graph of y =f (x) to

graph the function

Begin by graphing the

absolute value function, f (x)=|x|. Then use transformations of this graph

to graph the given function.

For f(x)=x+4 and g(x)=2x+1, find

the following functions.

The function f (x)=x^3+6 is

one-to-one. Find an equation for f-1(x), the inverse function.

Find the midpoint of the

line segment whose endpoints are given.

Use the graph of the

rational function to complete the following statement.

Find the vertical

asymptotes, if any, and the values of x corresponding to holes, if any, of

the graph of the rational function.

Find the horizontal

asymptote, if any, of the graph of the rational function.

The function f models the pH

level, f(x), of a mouth x minutes after eating food containing sugar. The

graph of this function is shown to the right. Complete parts (a) through

(e).

Graph the following function

by making a table of coordinates. If applicable, use a graphing utility to

confirm your hand-drawn graph.

Use transformations of the

graph of f =3^x to graph the function g(x) given below. Graph and give the

equation of the asymptote. Use the graph to determine the domain and range of

g(x).

Evaluate the following

expression without using a calculator.

Evaluate the following

expression without using a calculator.

Use properties of logarithms

to condense the logarithmic expression. Write the expression as a single

logarithm whose coefficient is 1. Evaluate logarithmic expressions if

possible.

The loudness level of a

sound can be expressed by comparing the sound's intensity to the intensity

of a sound barely audible to the human ear. The formula

Upper D equals 10 left

parenthesis log Upper I minus log Upper I 0 right parenthesis

describes the loudness level

of a sound, D, in decibels, where I is the intensity of the sound, in

watts per meter squared commaand Upper I 0 is the intensity of a sound barely

audible to the human ear. Use this information to answer parts (a) and (b)

below.

Solve the following

exponential equation by expressing each side as a power of the same base and

then equating exponents.

Complete the table shown to

the right for the population growth model for a certain country.

Solve the system by the

substitution method.

Solve the system by the

addition method.

Solve the system by the

method of your choice.

Use the graphs of the linear

functions on the right. Write the linear system whose solution set is

{(3,negative 1)}. Express

each equation in the system in slope-intercept form.

Solve the system by the

substitution method.

Graph the following

inequality.

Graph the given system of

inequalities.

Solve the system using

matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan

elimination.

Find the following matrices

where A= B=

Solve the matrix equation B-X=2A

for X.

The sequence given is

defined using a recursion formula. Write the first four terms of the

sequence.

Evaluate the factorial

expression.

Find the indicated sum.

Write the first six terms of

the arithmetic sequence with the given first term, a 1, and common

difference, d.

Write a formula for the

general term (the nth term) of the arithmetic sequence shown below. Do not

use a recursion formula. Then use the formula for An to find a20 ,the 20 th term

of the sequence.

Find 1plus2plus3plus4plus...plus30,

the sum of the first 30natural numbers.

Company A pays $24 comma 000yearly

with raises of $1 comma 400per year. Company B pays $ 28 comma 500yearly with

raises of $850 per year. Which company will pay more in year 10? How much

more?

Write the first five terms

of the geometric sequence whose first term is 32, and whose common ratio is

Find the sum of the first 14

terms of the geometric sequence shown below.

The general term of a

sequence is given. Determine whether the sequence is arithmetic, geometric,

or neither. If the sequence is arithmetic, find the common difference; if

it is geometric, find the common ratio.

A job pays a salary of $15

comma 000 the first year. During the next 11years, the salary increases by 7%

each year. What is the total lifetime salary over the 12-year period?

**MTH 220 Week 4 Checkpoint**

Write the first four terms

of the sequence whose general term is given below.

The sequence given is

defined using a recursion formula. Write the first four terms of the

sequence.

Evaluate the factorial

expression.

Find the indicated sum.A

deposit of $1000is made in an account that earns 5%

interest compounded

quarterly. The balance in the account after n quarters is given by the

following sequence. Find the balance in the account after six years.

Select the answers that best

complete the given statements.

Write the first six terms of

the arithmetic sequence with the given first term, a 1, and common

difference, d.

Use the formula for the

general term (the nth term) of an arithmetic sequence to find the indicated

term of the sequence with the given first term,a 1, and common difference,

d.

Find 1plus2plus3plus4plus...plus30,

the sum of the first 20natural numbers.

You are considering two job

offers. Company A will start you at $ 33 comma 000a year and guarantee a

raise of $ 2500per year. Company B will start you at a higher salary, $ 40

comma 000a year, but will only guarantee a raise of $ 1000per year. Find the

total salary that each company will pay over a ten-year period. Which

company pays the greater total amount?

**MTH 220 Week 3 Checkpoint**

Solve

the system of equations by the substitution method.

Solve

the system by the addition method.

Solve

the system by the method of your choice.

Four

times a first number decreased by a second number is negative 38. The first

number increased by twicethe second number is 4.Find the numbers.

Solve

the system by the substitution method.

Graph

the following inequality.

Graph

the following inequality.

Graph

the solution set of the system of inequalities.

Write

the augmented matrix for the system of equations to the right.

Write

the system of linear equations represented by the augmented matrix to the

right. Use x, y, and z for the variables.

Perform

the row operation on the given augmented matrix.

Solve

the system using matrices. Use Gaussian elimination with back-substitution

or Gauss-Jordan elimination.

a. Give

the order of the given matrix.

b. If

A equals left bracket a Subscript ij Baseline right bracket ,identify a 32and

a 23 if possible.

Find

the following matrices where A= b=

Find

the following matrices where

**MTH 220 Week 2 Checkpoint**

Use

the graph of the rational function to complete the following statement.

Find

the vertical asymptotes, if any, and the values of x corresponding to

holes, if any, of the graph of the rational function.

Find

the horizontal asymptote, if any, of the graph of the rational function.

The

function models the pH level, f(x),

of a mouth x minutes after eating food containing sugar. The graph of this

function is shown to the right. Complete parts (a) through (e).

Graph

the following function by making a table of coordinates. If applicable, use

a graphing utility to confirm your hand-drawn graph.

Use

transformations of the graph of f left parenthesis x right parenthesis equals

4 Superscript x

to

graph the function g(x) given below. Graph and give the equation of the

asymptote. Use the graph to determine the domain and range of g(x).

Evaluate

the following expression without using a calculator.

Evaluate

the expression without using a calculator.

Use

properties of logarithms to condense the logarithmic expression. Write the

expression as a single logarithm whose coefficient is 1. Evaluate logarithmic

expressions if possible.

The

loudness level of a sound can be expressed by comparing the sound's

intensity to the intensity of a sound barely audible to the human ear. The

formula describes the loudness level of a sound, D, in decibels, where I is

the intensity of the sound, in watts per meter squared,and I 0is the

intensity of a sound barely audible to the human ear. Use this information to

answer parts (a) and (b) below.

Solve

the following exponential equation by expressing each side as a power of the

same base and then equating exponents.

Complete

the table shown to the right for the population growth model for a certain

country.

**MTH 220 Week 1 Checkpoint**

Solve the following equation

using the quadratic formula.

Evaluate the function at the

given values of the independent variable and simplify.

Use the graph of f to

determine each of the following.

(a) the domain of f

(b) the range of f

(c) the zero(s) of f

(d) f left parenthesis 4

right parenthesis

(e) the intervals on which

f is increasing

(f) the intervals on which

f is decreasing

(g) the values for which

f(x)less than or equals0

(h) any relative maxima or

minima

(i) the value(s) of x for

which f left parenthesis x right parenthesis equals 4

(j) Is f left parenthesis 3

right parenthesispositive or negative?

Give the slope and

y-intercept of the line whose equation is given below. Then graph the linear

function.

Use the given conditions to write an equation for

the line in point-slope

form and in slope-intercept

form.

Find the average rate of

change of the function

Use the graph of y =f (x) to

graph the function

Begin by graphing the

absolute value function, f (x)=|x|. Then use transformations of this graph

to graph the given function.

For f(x)=x+4 and g(x)=2x+1, find

the following functions.

The function f (x)=x^3-6 is

one-to-one. Find an equation for f-1(x), the inverse function.

Find the distance between

the pair of points.

Find the midpoint of the

line segment whose endpoints are given.

Use a graphing utility with

a viewing rectangle large enough to show end behavior to graph the polynomial

function shown below.

Use the seven step method

described in the book to graph the following rational function.

**MTH 220 Week 5 MyMathLab®**

Study Plan for Week 5 Final Exam

Study Plan for Week 5 Final Exam

Quiz Me: 8.3-8 Solve

applications.

Quiz Me: 8.3-6 Determine

whether a sequence is arithmetic, geometric, or neither.

Quiz Me: 8.3-4 Use the

formula for the sum of the first n terms of a geometric sequence.

Quiz Me: 8.3-3 Use the

formula for the general term of a geometric sequence.

Quiz Me: 8.3-2 Write terms

of a geometric sequence.

**MTH 220 Week 4 MyMathLab®**

Study Plan for Week 4 Checkpoint

Study Plan for Week 4 Checkpoint

Quiz Me: 8.2-5 Solve

applications.

Quiz Me: 8.2-4 Use the

formula for the sum of the first n terms of an arithmetic sequence.

Quiz Me: 8.2-3 Use the

formula for the general term of an arithmetic sequence.

Quiz Me: 8.2-2 Write terms

of an arithmetic sequence.

Quiz Me: 8.2-1 Concept and

Vocabulary Check

Quiz Me: 8.1-6 Solve

applications.

Quiz Me: 8.1-5 Use summation

notation.

Quiz Me: 8.1-4 Use factorial

notation.

Quiz Me: 8.1-3 Use recursion

formulas.

Quiz Me: 8.1-2 Find

particular terms of a sequence from the general term.

**MTH 220 Week 3 MyMathLab®**

Study Plan for Week 3 Checkpoint

Study Plan for Week 3 Checkpoint

Quiz Me: 6.3-5 Solve matrix

equations.

Quiz Me: 6.3-4 Perform

matrix operations.

Quiz Me: 6.3-2 Give the

order of matrices and identify elements.

Quiz Me: 6.1-5 Use matrices

and Gaussian or Gauss-Jordan elimination to solve systems.

Quiz Me: 6.1-4 Perform

matrix row operations.

Quiz Me: 6.1-3 Write linear

systems given augmented matrices.

Quiz Me: 6.1-2 Write

augmented matrices for linear systems.

Quiz Me: 5.5-4 Graph systems

of inequalities.

Quiz Me: 5.5-3 Graph

nonlinear inequalities in two variables.

Quiz Me: 5.5-2 Graph linear

inequalities in two variables.

Quiz Me: 5.4-2 Solve

nonlinear systems in two variables by substitution.

Quiz Me: 5.1-6 Solve

problems using systems of linear equations in two variables.

Quiz Me: 5.1-5 Solve linear

systems in two variables by the method of your choice.

Quiz Me: 5.1-4 Solve linear

systems in two variables by addition.

Quiz Me: 5.1-3 Solve linear

systems in two variables by substitution.

**MTH 220 Week 2 MyMathLab®**

Study Plan for Week 2 Checkpoint

Study Plan for Week 2 Checkpoint

Quiz Me: 4.5-2 Model

exponential growth and decay

Quiz Me: 4.4-2 Use like

bases to solve exponential equations.

Quiz Me: 4.3-9 Solve

applications.

Quiz Me: 4.3-6 Condense

logarithmic expressions.

Quiz Me: 4.2-5 Use basic

logarithmic properties.

Quiz Me: 4.2-4 Evaluate

logarithms

Quiz Me: 4.1-6 Graph

exponential functions using transformations.

Quiz Me: 4.1-4 Graph

exponential functions by plotting points.

Quiz Me: 3.5-10 Solve

applications.

Quiz Me: 3.5-5 Identify

horizontal asymptotes.

Quiz Me: 3.5-4 Identify

vertical asymptotes.

Quiz Me: 3.5-3 Determine

what value a function approaches as x approaches a given value.

**MTH 220 Week 1 MyMathLab®**

Study Plan for Week 1 Checkpoint

Study Plan for Week 1 Checkpoint

Quiz Me: 3.5-7 Graph

rational functions using the strategy for graphing rational functions.

Quiz Me: 3.2-3 Identify

characteristics of graphs of polynomial functions and graph the functions.

Quiz Me: 2.8-3 Find the

midpoint of a line segment.

Quiz Me: 2.8-2 Find the

distance between two points.

Quiz Me: 2.7-3 Find the

inverse of a function.

Quiz Me: 2.6-4 Form

composite functions.

Quiz Me: 2.5-4 Perform

transformations on the absolute value function.

Quiz Me: 2.5-2 Perform

transformations given the graph of a function.

Quiz Me: 2.4-3 Find a

function's average rate of change.

Quiz Me: 2.4-2 Find slopes

and equations of parallel and perpendicular lines.

Quiz Me: 2.3-4 Identify the

slope and y-intercept and graph the line.

Quiz Me: 2.2-5 Obtain

information about a function from its graph.

Quiz Me: 2.1-4 Evaluate a

function.

Quiz Me: 1.5-6 Solve

quadratic equations using the quadratic formula.

Quiz Me: 1.5-6 Solve

quadratic equations using the quadratic formula.

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