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 mathematical processes to acquire and convey knowledge.
GOAL B: Systematically solve problems.
TOPIC 1. TOPICS IN ALGEBRA
Graphing using rectangular Coordinates; System of Linear Equations; and Quadratic Equations.
Student Outcomes:
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, point-slope 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 Find the sine, cosine and tangent for any acute angle in a right triangle.
3.2 Find the missing sides and angles of a right triangle.
3.3 Solve practical problems involving the right triangle.
4.1 Find the amplitude, period, frequency, and phase shift for a sine wave or a cosine wave.
3.4 Graph the sine function and the cosine function.
3.5 Solve oblique triangles using the law of sines.
3.6 Solve oblique triangles using the law of cosines.
3.7 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 emphasize problem solving and applications in each chapter.
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 Right Triangle Trigonometry 7 hours
13.1 Trigonometric Ratios
13.2 Using Trigonometric Ratios to Find Angles
13.3 Using Trigonometric Ratios to Find Sides
13.4 Solving Right Triangles
13.5 Applications Involving Trigonometric Ratios
Chapter 12 Geometry 13 hours
12.1 Angles and Polygons
12.2 Quadrilaterals
12.3* Triangles
12.4 Similar Polygons
12.5 Circles
12.6 Radian Measure
12.7 Prisms
12.8 Cylinders
12.9 Pyramids and Cones
12.10 Spheres
Chapter 8 Graphing Linear Equations 5 hours
8.1 Linear Equations with Two Variables
8.2 Graphing Linear Equations
8.3 The Slope of a Line
8.4 The Equation of a Line
Chapter 9 Systems of Linear Equations 5 hours
9.1 Solving Pairs of Linear Equations by Graphing
9.2 Solving Pairs of Linear Equations by Addition
9.3 Solving Pairs of Linear Equations by Substitution
9.4 Applications Involving Pairs of Linear Equations
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 Trigonometry with any Angle 6 hours
14.1 Sine and Cosine Graphs
14.2 Period and Phase Shift
14.3 Solving Oblique Triangles: Law of Sines
14.4 Law of Sines: The Ambiguous Case
14.5 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.