Required Text:
Washington, Allyn J., Basic Technical Mathematics with Calculus, 6th Edition, Addison Wesley Publishing Company.
Supplemental Material:
1. A scientific calculator. (Required)
2. Wilbanks, Frances Brazen and Zeigler, Anne; Student Solutions Manual for the Allyn J. Washington Series in Basic Technical Mathematics, 6th Ed., Addison Wesley Pub. (Optional)
Course Description:
A pre-calculus course designed for the student of aviation. Review of the fundamentals of algebra; linear equations and inequalities, quadratic equations; variation; polynomial, rational, exponential, logarithmic and trigonometric functions; radian measure; right triangle solutions, vectors, and the laws of sines and cosines. Prerequisite: MA006, MA106, or placement.
Goals:
This course is designed to provide students with the necessary algebra and trigonometry required for the study of advanced topics in aviation.
Performance Objectives:
Upon course completion, students will be able to:
1. Simplify and evaluate algebraic expressions involving real numbers, polynomials, rational expressions, exponents, and radicals.
2. Solve equations, transpose formulas, and solve verbal problems that require the use of linear and quadratic equations.
3. Solve linear inequalities and identify their solutions by using interval notation and graphs.
4. Use the distance, midpoint, point-slope-intercept formulas to solve problems involving line and line segments.
5. Solve verbal problems involving direct, inverse and joint variation.
6. Define function, domain and range; and identify examples of each.
7. Graph linear, quadratic, polynomial and rational functions.
8. Convert radians to degrees, degrees to radians and solve arc length problems using radians.
9. Define the six trigonometric functions and the fundamental identities, use them to find the values of various trigonometric functions if the value of
another trigonometric function is known.
10. Use the six trigonometric functions to solve right triangle problems, resolve vectors into rectangular components, and solve force and displacement problems using vectors.
11. Graph the functions y = a sin bx and y = a cos bx, and identify the amplitude and period.
12. Solve word problems by using linear systems of equations.
13. Solve oblique triangle problems using the Law of Sines and the Law of Cosines.
14. Graph exponential and logarithmic functions and solve word problems dealing with these functions.
Teaching Methods:
Class meetings will be comprised of lectures and discussions of assigned material, sample solutions to representative problems, board work, graphing calculator and computer lab demonstrations, and testing for understanding. Class participation is expected with emphasis on aviation related applications.
Class Policy:
All students are expected to bring their text, calculator, paper and pencil to each scheduled class where academic honesty is the required mode of behavior. Assignments contained herein, and as augmented at instructor's discretion, shall be completed prior to the next scheduled Monday class session and will not be accepted beyond that date without prior instructor approval. Assignments constitute minimum coverage of the required lessons and the student is encouraged to complete additional exercise problems contained within each assigned chapter to promote mastery of the objectives. Course content may vary from this syllabus to meet the needs of this particular class composition. Students are expected to attend all scheduled classes where active participation in class is an integral element and will be considered in final course grades. Should circumstances arise beyond a student's control which may force a student to miss a class session or portion thereof, all matters relating to the absence should be arranged between the student and the instructor, including making up missed work. Absences are particularly significant in this program due to the amount of material covered in each class. Thus students are encouraged to assist one another with missed classnotes and assignments.
| Area | Grade Scale | |
|---|---|---|
| Area content tests/quizzes | 50% | 90-100 A |
| Final exam | 30% | 80-89 B |
| Homework assignments | 15% | 70-79 C |
| Class participation | 5% | 60-69 D |
| Total 100% | ||
Session #1/Week #1: Monday
Topic: Course Overview and Review of Numerical Computation
Objectives:
1. The student will know the scope and concept of the course to include the classroom procedures, homework requirements, examinations and grading policy.
2. The student will be able to apply the laws of mathematics to solve addition, subtraction, multiplication, and division problems involving whole numbers, fractions, decimals and mixed numbers.
3. Demonstrate understanding of the real number system, exponents, and scientific notation.
Assignment: Read/review sections 1-1 thru 1-5 and 12-1 thru 12-2. Do assigned problems from assignment sheet handout.
Session #2/Week #1: Thursday
Topic: Review of Basic Algebra
Objectives:
1. The student will comprehend the fundamental laws of algebra, order of operations to include with zero, exponents, and the relationship between dependent and independent variables.
2. Apply operations on algebraic expressions, simple equations, formulas.
3. Apply understanding to the use of the distributive property and the difference of two squares for factoring polynomials, factor the general trinomial, and factor the sum and difference of two cubes.
Assignment: Read sections 1-7 thru 1-9 and 6-1 thru 6-4. Do problems as assigned.
Session #3/Week #2: Monday
Topic: Rational Expressions and Linear Equations
Objectives:
1. The student will comprehend and be able to simplify, add, subtract, multiply and divide rational expressions and complex fractions.
2. Be able to solve linear equations, fractional equations, and use algebraic skills to solve verbal problems.
3. Test over material covered during week #1.
Assignment: Read sections 6-5 thru 6-8 and 1-10. Do problems as assigned.
Session #4/Week #2: Thursday
Topic: Quadratic Equations
Objectives:
1. The student will be able to solve quadratic equations by factoring and by the quadratic formula and to use quadratic equations to solve verbal problems.
Assignment: Read sections 7-1 thru 7-3. Do problems as assigned.
Sessions #5/Week #3: Monday
Topic: Linear Inequalities
Objectives:
1. The student will be able to solve linear inequalities and state the solution using graphs and intervals.
2. Test over week #2 material.
Assignment: Read sections 17-1 thru 17-4. Do problems as assigned.
Session #6/Week #3: Thursday
Topic: Functions
Objectives:
1. The student will be able to define a function; identify relations that are functions; use functional notation to compute functional values; graph simple functions using sets of ordered pairs; and use the distance and midpoint formulas.
2. The student will be introduced to the graphing calculator and how it can be used to display functions graphically.
Assignment: Read sections 3-1 thru 3-4 and 21-1. Do problems as assigned.
Session #7/Week #4: Monday
Topic: Linear and Quadratic Functions
Objectives:
1. The student will comprehend methods of using the point-slope and slope-intercept forms of the equation of a line to sketch the graphs of linear functions.
2. Be able to sketch the graph of a given quadratic function and to state the coordinates of the vertex and the domain and range.
3. Apply graphing methods to quadratic functions.
4. Test over week #3 material.
Assignment: Read sections 5-1,5-2 and 7-4. Do problems as assigned.
Session #8/Week #4: Thursday
Topic: Linear Systems
Objectives:
1. The student will comprehend methods of solving linear systems of equations.
Assignment: Read sections 5-3 and 5-4. Do problems as assigned.
Session #9/Week #5: Monday
Topic: Radicals and Rational Exponents
Objectives:
1. The student will be able to simplify, add, subtract, multiply and divide expressions involving radicals and define and use rational exponents to solve problems involving radicals.
2. Test over week #4 material.
Assignment: Read sections 1-6 and 11-1 thru 11-5. Do problems as assigned.
Session #10/Week #5: Thursday
Topic: Variation
Objectives:
1. The student will comprehend variations and be able to formulate a statement of variation into an equation relating different physical quantities and when given the necessary information, find K, the constant of variation and the values of unknown quantities in the variation equation.
Assignment: Read section 18-2. Do problems as assigned.
Session #11 and #12/Week #6: Monday/Thursday
Topic: Angles and the Trigonometric Functions
Objectives:
1. The student will be able to use degrees and minutes as units for measuring angles; draw given angles in standard position; find angles that are coterminal with the given angle; define the six trigonometric (trig) functions and use the definitions to compute the values of trig functions of any given angle; use a calculator to determine the values of the trig functions; know values of the trig functions for special angles (30, 45, 60, 90); find reference angles for a given angle and give the value of its trig function and that of the other related angles by using basic identities.
2. Test over week #5 material on Monday.
Assignment: Read sections 4-1 thru 4-3 and 8-1 thru 8-2. Do problems as assigned.
Session #13/Week #7: Monday
Topic: Solving Right Triangles
Objectives:
1. The student will be able to solve a right triangle given two of the six pieces of triangular information and to solve related verbal problems.
Assignment: Read sections 4-4 and 4-5. Do problems as assigned.
***NO CLASS ON HOLIDAY*** (class time to be made up by adding15 minutes to each of the first ten class sessions)
Session #14/Week 8: Monday
Topic: Radian Measure and Vectors in the Plane
Objectives:
1. The student will be able to convert from degree measure to radian measure and vice versa and solve physical problems involving radian measure.
2. Be able to define a vector in polar form; represent and add vectors geometrically; resolve vectors into rectangular components; and given the rectangular components of a vector, find its magnitude and direction.
3. Test over material cover during sessions #11 thru #13.
Assignment: Read sections 8-3 thru 8-4 and 9-1 thru 9-2. Do problems as assigned.
Session #15/Week #8: Thursday
Topic: Vector Addition and the Laws of Sines and Cosines
Objectives:
1. The student will be able to add vectors algebraically by resolving them into rectangular components and solving aviation, displacement, velocity, and force problems using vectors.
2. The student will be able to solve practical problems using the law of sines and the law of cosines.
Assignment: Read sections 9-3 thru 9-6. Do problems as assigned.
Session #16/Week #9: Monday
Topic: Graphs of the Trig Functions and Final Review
Objectives:
1. The student will be able to graph trig functions of the type: y = a sin bx,
y = a cos bx and know the period and amplitude of the various trig functions.
2. Test over material covered in week 8.
3. Practice Final Exam.
Assignment: Read sections 10-1 and 10-2. Do problems as assigned.
Session #17/Week#9: Thursday
Topic: Final Exam
Objective:
1. Assess student comprehension of materials covered in this course.
For questions contact Instructor: E-mail.
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