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Course Description

(As of 5/23/2021)

Students develop the foundational mathematical skills necessary for general education mathematics courses (Math 1218 and Math 1220). Content features collaborative project-based and technology-enabled group work including modeling, problem solving, critical thinking, data analysis, algebra fundamentals, and both verbal and written communication of mathematical ideas.

Topical Outline

(As of 5/23/2021)

Functions including graphical analysis
Operations on algebraic expressions including factoring
Modeling with linear functions and nonlinear functions

At least two of the following:

Modeling with systems of equations
Modeling using probability and statistics
Modeling using geometry and right triangle trigonometry
Modeling using proportional reasoning

Advice for Success

For Mr. McCabe's session

In the classroom:

Bring your textbook to class everyday.
The textbook is designed to write in and follow along during the lecture.
Take note of anything you find difficult. If there was an explanation during class that made something click be sure to highlight the explanation by writing it out and using a highlighter. If you need Mr. McCabe to explain it again so you can write it down ask again or talk to Mr. McCabe after class or during office hours.
Most sessions with have a polling activity, log into My Math Lab prior to class on your smartphone, tablet, or laptop. If you don't have any of these devices or they are not charged enough try to let me know before class.

One hour after the class session:

Complete a couple problems from the different homework assessments. This will help remember and retain the content covered in class.
Review notes and highlight things that no longer make sense or things that did make sense but now don't. These parts should be asked about at the beginning of the next session.

The night of the class session:

Attempt to complete the entire homework set.
Highlight problems that are difficult.
Highlight problems that are easy, and try to explain why they are easy.

The weekend

Hopefully, majority of all the homework sets are complete.
If all the homework sets are not complete, then complete every homework set.
Identify 2 easy problems and 2 hard problems, these questions will be used to make a practice exam later.

The Projects

As soon as the project is posted print of all the supplemental material. Read the questions, and during every class session identify when a topic is covered which will also help answer a question in the project.
Every weekend attempt to answer one, two, or many questions from the project.

Exams

With your created questions, create a test taking environment.
If you are having difficultly succeeding with the self-created practice exam schedule a meeting with Mr. McCabe.
Mr. McCabe's exams are assessed based on understanding not on getting the correct answer, practice presenting work in such a way it instructs peers on how to do a problem. Practice can be done by completing the Turn-In's.

Course Description
Course Topic Outline
Advice
Syllabus Archive

Course Description

(As of 5/23/2021)

Students develop the foundational mathematical skills necessary for general education mathematics courses (Math 1218 and Math 1220). Content features collaborative project-based and technology-enabled group work including modeling, problem solving, critical thinking, data analysis, algebra fundamentals, and both verbal and written communication of mathematical ideas.

Topical Outline

(As of 5/23/2021)

Functions including graphical analysis
Operations on algebraic expressions including factoring
Modeling with linear functions and nonlinear functions

At least two of the following:

Modeling with systems of equations
Modeling using probability and statistics
Modeling using geometry and right triangle trigonometry
Modeling using proportional reasoning

Advice for Success

For Mr. McCabe's session

In the classroom:

Bring your textbook to class everyday.
The textbook is designed to write in and follow along during the lecture.
Take note of anything you find difficult. If there was an explanation during class that made something click be sure to highlight the explanation by writing it out and using a highlighter. If you need Mr. McCabe to explain it again so you can write it down ask again or talk to Mr. McCabe after class or during office hours.
Most sessions with have a polling activity, log into My Math Lab prior to class on your smartphone, tablet, or laptop. If you don't have any of these devices or they are not charged enough try to let me know before class.

One hour after the class session:

Complete a couple problems from the different homework assessments. This will help remember and retain the content covered in class.
Review notes and highlight things that no longer make sense or things that did make sense but now don't. These parts should be asked about at the beginning of the next session.

The night of the class session:

Attempt to complete the entire homework set.
Highlight problems that are difficult.
Highlight problems that are easy, and try to explain why they are easy.

The weekend

Hopefully, majority of all the homework sets are complete.
If all the homework sets are not complete, then complete every homework set.
Identify 2 easy problems and 2 hard problems, these questions will be used to make a practice exam later.

The Projects

As soon as the project is posted print of all the supplemental material. Read the questions, and during every class session identify when a topic is covered which will also help answer a question in the project.
Every weekend attempt to answer one, two, or many questions from the project.

Exams

With your created questions, create a test taking environment.
If you are having difficultly succeeding with the self-created practice exam schedule a meeting with Mr. McCabe.
Mr. McCabe's exams are assessed based on understanding not on getting the correct answer, practice presenting work in such a way it instructs peers on how to do a problem. Practice can be done by completing the Turn-In's.

Math 1432 Homework Help¶

First Unit Material¶

Question 4 Section 2.5¶

The bearing from City A to City B is N$38^{\circ}$E. The bearing from City B to City C is S$52^{\circ}$E. An automobile driven at 65 miles per hour takes 1.4 hours to drive from City A to City B and takes 1.8 hours to drive from City B to City C. Find the distance from City A to City C.

Solution¶

q4.2.5.PNG

Remember distance equals the product of speed and time. $$d=rt$$

Therefore, the distance from City A to City B is: $$d_1=m(A,B)=(65)(1.4)=91$$ and the distance from City B to City C is: $$d_2=m(B,C)=(65)(1.8)=117$$

In the drawing above the angle for B can be found by adding the two angles: $$38+52=90$$ This means triangle(A,B,C) is a right triangle. The legs of the right triangle is $d_1$ and $d_2$. The hypotenuse, $r$, is the distance from City A to City C. Therefore, we want to solve for $r$:

$$\begin{align} (d_1)^2+(d_2)^2 & = r^2\\ r^2 & = 91^2+117^2\\ r & = \pm \sqrt{91^2+117^2}\\ & = \pm 148.2228052628879 \end{align}$$

We will use the positive distance.

Answer¶

Since the answer should be to the nearest mile the answer is: "The distance from City A to City C is approximately 148 miles."

In [16]:

                                                   
                                                   d14:65*1.4;
d24:65*1.8;
38+52;
float(solve((d14)^2+(d24)^2=r^2,r));

Out[16]:

\[\tag{${\it \%o}_{41}$}91.0\]

Out[16]:

\[\tag{${\it \%o}_{42}$}117.0\]

Out[16]:

\[\tag{${\it \%o}_{43}$}90\]

rat: replaced 21970.0 by 21970/1 = 21970.0

Out[16]:

\[\tag{${\it \%o}_{44}$}\left[ r=-148.2228052628879 , r=148.2228052628879 \right] \]

Question 5 Section 2.5¶

Two ships leave a port at the same time. The first ship sails on a bearing of $40^{\circ}$ at 12 knots (nautical miles per hour) and the second on a bearing of $130^{\circ}$ at 14 knots. How far apart are they after 1.5 hours?

Solution¶

q52.5.PNG

Remember distance equals the product of speed and time. $$d=rt$$ Therefore, the distance for the first boat is $$d_1=(12)(1.5)=18$$ and the distance for the second boad is $$d_2=(14)(1.5)=21$$ These are both in units of nautical miles.

Two rays can be created: ray(Port,Ship 1) and ray(Port, Ship 2). The angles between the two rays is: $$130-40=90$$

This means triangle(Port, Ship 1, Ship 2) is a right triangle. The distance for each leg is $d_1$ and $d_2$. The hypotenuse, $r$, is the distance away from each ship. Therefore, we want to solve for $r$:

$$\begin{align} (d_1)^2+(d_2)^2 & = r^2\\ r^2 & = 18^2+21^2\\ r & = \pm \sqrt{18^2+21^2}\\ & = \pm 27.65863337187866 \end{align}$$

We will use the positive distance.

Answer¶

Since the answer should be to the nearest nautical mile the answer is: "After 1.5 hours, the ships are 28 nautical miles apart."

In [17]:

                                                   
                                                   d15:12*1.5;
d25:14*1.5;
130-40;
float(solve((d15)^2+(d25)^2=r^2,r));

Out[17]:

\[\tag{${\it \%o}_{45}$}18.0\]

Out[17]:

\[\tag{${\it \%o}_{46}$}21.0\]

Out[17]:

\[\tag{${\it \%o}_{47}$}90\]

rat: replaced 765.0 by 765/1 = 765.0

Out[17]:

\[\tag{${\it \%o}_{48}$}\left[ r=-27.65863337187866 , r=27.65863337187866 \right] \]

In [ ]:

Course Description
Course Topic Outline
Advice
Syllabus Archive

Course Description

(As of 5/23/2021)

Students will be introduced to basic concepts of differential and integral calculus. This course is intended for students planning to major in business, or the behavioral, social, or biological sciences.

Topical Outline

(As of 5/23/2021)

Functions

Power and exponential functions
Polynomial functions
Rational functions and asymptotes
Natural logarithms
Graphing

Differential calculus

Limits and continuity
Derivative process
Derivative rules for products and quotients
The chain rule
Higher order derivatives
Maxima and minima of functions of one variable
Functions of more than one variable
Maxima and minima for functions of more than one variable
Maxima and minima using Lagrange multipliers
Applications from business, biology, and other areas

Integral calculus

Anti-derivatives including substitution and parts
Area and the definite integral
Fundamental theorem of calculus
Improper integrals
Numerical integration (optional)
Applications

Advice for Success

For Mr. McCabe's session

In the classroom:

Take note of anything you find difficult. If there was an explanation during class that made something click be sure to highlight the explanation by writing it out and using a highlighter. If you need me to explain it again so you can write it down ask again or talk to Mr. McCabe after class or during office hours.
Most sessions with have a polling activity, log into the prescribed session prior to class on your smartphone, tablet, or laptop. If you don't have any of these devices or they are not charged enough try to let me know before class.

One hour after the class session:

Complete a couple problems from the different homework assessments. This will help students remember and retain the content covered in class.
Review notes and highlight things that no longer make sense or things that did make sense but now don't. These parts should be asked for clarification at the beginning of the next session.

The night of the class session:

Attempt to complete the entire homework set.
Highlight problems that are difficult.
Highlight problems that are easy, and try to explain why they are easy.

The weekend

Hopefully, majority of all the homework sets are complete.
If all the homework sets are not complete, then complete every homework set.
Identify 2 easy problems and 2 hard problems, these questions will be used to make a practice exam later.

Exams

With your created questions, attempt to put yourself in a test taking environment and test yourself on the questions.
If you are having difficultly succeeding with your practice exam schedule a meeting with Mr. McCabe.
Mr. McCabe's exams are assessed based on understanding not getting the correct answer, practice presenting your work in such a way it instructs peers on how to do a problem. Practice can be done by completing the Turn-In's.

Michael McCabe

Office Hours

Course Description

Topical Outline

Advice for Success

In the classroom:

One hour after the class session:

The night of the class session:

The weekend

The Projects

Exams

Course Description

Topical Outline

Advice for Success

In the classroom:

One hour after the class session:

The night of the class session:

The weekend

The Projects

Exams

Math 1432 Homework Help¶

First Unit Material¶

Question 4 Section 2.5¶

Solution¶

Answer¶

Question 5 Section 2.5¶

Solution¶

Answer¶

Course Description

Topical Outline

Advice for Success

In the classroom:

One hour after the class session:

The night of the class session:

The weekend

Exams