Download MA106 - Mohawk Valley Community College

MOHAWK VALLEY COMMUNITY COLLEGE
UTICA, NEW YORK
COURSE OUTLINE
TECHNICAL MATHEMATICS 2
MA106
Reviewed and Found Acceptable by Robert Bernstein – 5/01
Revised by Gabriel Melendez – 12/01
Reviewed and Revised by Gabriel Melendez – 5/02
Reviewed and Found Acceptable by Gabriel Melendez – 5/03
Reviewed and Found Acceptable by Gabriel Melendez – 5/04
Reviewed and Found Acceptable by Gabriel Melendez – 5/05
Reviewed and Revised by Gabriel Melendez – 5/06
Reviewed and Revised by Terrence Ward – 5/07
Reviewed and Found Acceptable by Terrence Ward – 5/08
Reviewed and Revised by Terrence Ward – 5/09
Reviewed and Revised by D. Kolb and G. Melendez – 5/10
Reviewed and Found Acceptable by Gabriel Melendez – 5/11
Reviewed and Found Acceptable by Gabriel Melendez – 5/12
Reviewed and Found Acceptable by Gabriel Melendez – 5/13
Reviewed and Found Acceptable by Gabriel Melendez – 5/14
Reviewed and Revised by Sean Davis – 1/16
Course Outline
Title:
Technical Mathematics 2
Catalog Number:
MA106
Credit Hours:
4
Class Hours:
3
Lab. Hours:
2
Prerequisite:
MA105 Technical Mathematics 1
Catalog
Description:
This course is a continuation of MA105
Technical Mathematics 1, with further topics
from algebra as well as from geometry and
trigonometry, and an emphasis on technical
applications.
COURSE TEACHING GOALS FOR ALL TOPICS:
GOAL A: Use
knowledge.
mathematical
processes
to
acquire
and
convey
of
Linear
GOAL B: Systematically solve problems.
TOPIC 1. TOPICS IN ALGEBRA
Graphing
using
rectangular
Coordinates;
Equations; and Quadratic Equations.
Student Outcomes:
System
The student will:
1.1 Determine whether a given ordered pair is a solution of a
given equation.
1.2 Plot points on the coordinate plane.
1.3 Graph a linear equation.
1.4 Find the slope of a line given two points or the equation of
the line.
1.5 Determine whether two lines are parallel or perpendicular.
1.6 Write the equation of a line in slope-intercept form, pointslope form and/or in general form.
1.7 Solve system of linear equations graphically.
1.8 Solve pairs of linear equations by the addition method.
1.9 Solve applications involving linear equations with two
variables.
1.10 Solve pairs of linear equations by the substitution method.
1.11 Find the roots of quadratic equation by factoring.
1.12 Find the roots of quadratic equation by using the quadratic
formula.
1.13 Simplify square roots having negative radicands.
1.14 Evaluate powers of j, the imaginary unit.
1.15 Use the discriminant to predict the nature and number of
roots of a quadratic equation.
1.16 Solve quadratic equations having complex roots.
TOPIC 2. TOPICS IN GEOMETRY
Points; Lines; Angles; Polygons; Circles; Solids; Area and Volume
of Common Figures; Applications.
Student Outcomes:
The student will:
2.1
Classify angles according to measure of angle(acute, obtuse,
right).
2.2
Find the angles formed by parallel lines and a tranversal.
2.3
Calculate the area of quadrilaterals.
2.4
Classify triangles according to the lengths of sides(scalene,
isosceles, equilateral).
2.5
Apply the Pythagorean theorem.
2.6
Calculate the perimeter and area of triangles.
2.7
Solve problems involving similar polygons.
2.8
Calculate the circumference and the area of a circle.
2.9
Convert from degrees to radians and vice versa.
2.10 Calculate the arc length and the area of a sector of a
circle.
2.11 Find the lateral surface area, total surface area, and
volumes of solid figures such as prisms, cylinders, pyramids,
cones and spheres.
TOPIC 3. TOPICS IN TRIGONOMETRY
Definition of Trigonometric Functions for Acute Angles;
Values
for 0, 30, 45, 60, 90, 180, and 270 degree angles; Trigonometric
Functions of Obtuse Angles; Solutions of Right Triangles;
Solutions of Oblique Triangles; Graphs of Trigonometric Functions;
Applications
Student Outcomes:
The student will:
3.1
3.2
3.3
4.1
3.4
3.5
3.6
3.7
Find the sine, cosine and tangent for any acute angle in a
right triangle.
Find the missing sides and angles of a right triangle.
Solve practical problems involving the right triangle.
Find the amplitude, period, frequency, and phase shift for a
sine wave or a cosine wave.
Graph the sine function and the cosine function.
Solve oblique triangles using the law of sines.
Solve oblique triangles using the law of cosines.
Solve applied problems requiring oblique triangles.
Teaching Guide
Title:
Technical Mathematics 2
Catalog No.:
MA106
Credit Hours:
4
Class Hours:
3
Lab Hours:
2
Prerequisite:
MA105 Technical Mathematics 1
Catalog
Description:
This course is a continuation of MA105
Technical Mathematics 1, with further topics
from algebra as well as from geometry and
trigonometry, and an emphasis on technical
applications.
Text:
Elementary
Technical
Mathematics,
11th
edition, Ewen and Nelson, Brooks/Cole Cengage
Learning
Note:
The calculator may be used on graded work in
this course once the student has demonstrated
to
the
instructor's
satisfaction,
an
understanding of the concepts that can be
duplicated by a calculator.
The instructor
may require that the student have access to a
scientific calculator in this course.
Calculators may be used for tests and the final. Test problems
should be designed to insure that the student has learned the
fundamental concepts and does not depend on the calculator for
thinking as well as
computing.
The student should show all
equations and required backup work for a problem.
Attention should be given to the correct use of significant digits
and appropriate rounding of approximate numbers (measured
quantities.)
Lab work should include hands-on applications and provide
additional drill material on the given topics, as well as
individual help to students. It should be a time of supervised,
guided student work.
(Samples on file in bottom drawer of file
cabinet located in PH379.
There are also some books you may
borrow and sign out.)
Note:
The instructor should
applications in each chapter.
emphasize
problem
solving
and
Note:
The order of the topics was chosen with the Technical
Trades Departments.
Instructor may prefer to do 12.1 and 12.3
(Pythagorean Theorem) before chapter 13.
Chapter 13
13.1
13.2
13.3
13.4
13.5
12.1
12.2
12.3*
12.4
12.5
12.6
12.7
12.8
12.9
12.10
Geometry
13 hours
Angles and Polygons
Quadrilaterals
Triangles
Similar Polygons
Circles
Radian Measure
Prisms
Cylinders
Pyramids and Cones
Spheres
Chapter 8
Graphing Linear Equations
5 hours
Linear Equations with Two Variables
Graphing Linear Equations
The Slope of a Line
The Equation of a Line
Chapter 9
9.1
9.2
9.3
9.4
7 hours
Trigonometric Ratios
Using Trigonometric Ratios to Find Angles
Using Trigonometric Ratios to Find Sides
Solving Right Triangles
Applications Involving Trigonometric Ratios
Chapter 12
8.1
8.2
8.3
8.4
Right Triangle Trigonometry
Systems of Linear Equations
Solving Pairs of Linear Equations by Graphing
Solving Pairs of Linear Equations by Addition
Solving Pairs of Linear Equations by Substitution
Applications Involving Pairs of Linear Equations
5 hours
Chapter 11
Quadratic Equations
5 hours
11.1** Solving Quadratic Equations by Factoring
11.2
The Quadratic Formula
11.3
Applications Involving Quadratic Equations
11.3***Graphs of Quadratic Equations - Optional
11.4
Imaginary Numbers
** Note: You may need to review factoring before this section.
After completing this section you may want to use graphing
calculators to investigate quadratic functions which have two real
roots, one real root, or no real roots.
*** Note:
The use of graphing calculators to sketch, analyze
solutions, and visualize maximum or minimum values is suggested.
Chapter 14
14.1
14.2
14.3
14.4
14.5
Trigonometry with any Angle
6 hours
Sine and Cosine Graphs
Period and Phase Shift
Solving Oblique Triangles: Law of Sines
Law of Sines: The Ambiguous Case
Solving Oblique Triangles: Law of Cosines
Lecture Hours
41
The teaching guide allows 4 additional hours for the in-class
assessment of student learning.
A two hour comprehensive final
examination will also be given.
Thoughts to share for MA106
In the bottom drawer of the file cabinet in PH379 is an
expandable folder with material that may be copied for MA106.
There are also books that may be checked out. Please feel free to
share any of your comments, ideas, or labs with others teaching
the course now or in the future. Most folders contain both a lab
and extra problems which are in the same folder separated by a
colored piece of paper.
Please leave at least one copy in the
folder, thank you.
Lab on Angles: Before doing the lab, students should be able to
1) draw and measure angles, 2) work with parallel lines and
transversals, and 3) use the Pythagorean Theorem.
Circle Lab:
See first page of lab for equipment needed, etc.
Surface Area/Volume Lab:
(Redoing to measure objects - the 3
dimensional models as well as objects in their field of work located in AB 208)
Plotting Points: (For now plots a cartoon character but would like
to redo one that plots a technical diagram.)
y = mx and y = mx + b: These might be used as the introduction to
these sections as class discussion with students. By using
graphics calculators, they explore and discover the effects of
m and b, etc.
Application of lines: Students will write equations of lines from
information gathered from using protractors to measure acute,
obtuse and reflex angles.
Solving Pairs of Linear Equations: This lab uses the CBL units and
the graphics calculators. If you need help or have questions,
contact Gabriel Melendez or Nelissa Rutishauser.
y = a sin x and y = a cos x: These might be used as the
introduction to Chapter 14 as class discussion with students.
(You might go over page 1 of the lab together with the graphics
calculator overhead screen and then the student can complete the
other pages).
By using graphics calculators, they explore and
discover the effects of a.
Graphing Trigonometric Functions by plotting points: This might
be used to introduce 14.1, calculating and plotting points, and
then followed by frequency and period examples from the text.
y = a sin bx and y = a cos bx: Colored pencils are helpful (and
may be found in AB208 cabinet or file drawers).
Law of Sines:
This lab takes two hours and covers all of the
cases of the law of sines through construction.
Hence,
protractors are needed again.
Law of Cosines:
This may take one hour.