Proposed Course Outline - Algebra And Trigonometry

PROPOSED COURSE OUTLINE Instructor: Arlan Rodrigo e-mail: [email protected] Course Number: Course Title: Course Credit: Course Requirements: Passing Grade: Consultation Hours: Main Reference:

Math 17 COLLEGE ALGEBRA and TRIGONOMETRY 5 5 Long Exams = 2/3 of Final Grade 1 Final Exam = 1/3 of Final Grade Attendance, Participation, Quizzes, Homework (Bonus points for Exams) 60% By appointment (send me an e-mail) Modern Algebra and Trigonometry Third Edition (Vance)

Course Objectives: At the end of the course, the student is expected to know the basic concepts of College Algebra and Trigonometry. In particular, the student is expected to know the following: • • • • • • • • • • • • • • • •

Basic concepts in Set Theory Simplifying and solving algebraic expressions and algebraic equations Problem-solving using algebraic equations The Geometry of Real Numbers, The Cartesian Plane, The Circle Relations and Functions and differentiate them from each other Topics in Linear and Quadratic Functions Topics in Polynomial Functions The concept of inverse functions including its relationship with the original function Exponential and Logarithmic Functions including compound interest Matrices and Determinants including solving systems of linear equations using Cramer’s Rule The Circular Functions Inverse Circular Functions Graphs and Applications of Circular Functions The Law of Sines and the Law of Cosines and problem-solving involving Oblique Triangles Complex Numbers and Vectors Powers and roots of Complex Numbers

Exams: There will be 5 written Long Exams with a cumulative weight of 2/3 of the Final Grade. Aside from this, a Final Exam will be given at the end of the semester and this will make up 1/3 of the Final Grade. The passing grade at the end of the semester is 60%. Standard college rules will be used in determining the Final Grade to be marked in the grading sheet. Exemption from the Final Exam: If the student has obtained an average of 80% or higher for the 5 Long Exams, he/she can opt not to take the Final Exam. If he/she does so, then the Final Grade will be the average for the 5 Long Exams.

Attendance, Participation, Quizzes, Homework: Extra Bonus points or percentage points will be given to students who have a good attendance. Points Earned from quizzes and homework also have their corresponding merit in the Examinations. Please refer to the table at the end for more information. Class Policy: 1. If a student is late for more than 15 minutes for a particular class period, then he will be marked absent for that period. 2. There will be no make-up for missed quizzes and unsubmitted homework or homework submitted past the deadline. 3. If a student misses a Long Exam for a valid reason (requires documentation), then he/she must take the Final Exam and the grade for the missed Long Exam will be the grade of the Final Exam. If a student misses a second Long Exam, then it is automatically ZERO regardless of the reason. A student who misses an exam for an invalid reason will have a grade of ZERO for that exam. 4. Cheating, in any form, including copying homework will not be tolerated. COURSE OUTLINE Meeting No.

Topic

Reference/s

1

Self-Introduction by the teacher and the students, discussion of class policies, Overview of the subject / History of algebra Sets and basic notation, subsets and counting, operations on sets Algebra of Counting Numbers ( Axioms ), Integers and Factorizations Integers and Factorizations, Multiplicative Inverses and Division, Rational and Irrational Real Numbers Algebraic Expressions ( Addition, Subtraction, Multiplication, Division ) Synthetic Division, Special Products ( Factors and Factoring ), Simplification of Fractions Operations on Fractions ( Addition, Subtraction, Multiplication, Division ) Exponents ( Integral and Rational ), Introduction to Radicals Multiplication and Division of Radicals, ( short review plus QUIZ ) The Geometry of Real Numbers, the Cartesian Plane, the Distance Formula and the Slope Formula The Circle, ( review plus QUIZ )

Wikipedia / other external sources

Reading assignment

Vance ( pages 2 – 15 )

YES

Vance ( pages 17 – 24 )

YES

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Vance ( pages 24 – 33 )

Quiz

Homework

YES

Vance ( pages 36 – 44 )

YES

Vance ( pages 45 – 53 )

YES

Vance ( pages 54 – 58 )

YES

Vance ( pages 58 – 64 ) Vance ( pages 65 – 69 )

YES YES

Vance ( pages 71 – 86 ) Vance ( pages 86 – 93 )

YES YES

YES

EXAM 1 Functions and Relations, Graphical Representation of Functions and Relations Linear Functions ( plus problem solving ) Arithmetic Progressions, Introduction to the Quadratic Function The Quadratic Formula, Inequalities Relations between zeros and coefficients of the Quadratic Function, Equations in Quadratic Form Equations Involving Radicals, Variation Solution of Two Linear Equations, Solution of Three

Vance ( pages 95 – 106 ) Vance ( pages 172 – 175 ) Vance ( pages 176 – 184 )

YES

Vance ( pages 185 – 192 ) Vance ( pages 193 – 198 )

YES

Vance ( pages 199 – 203 ) Vance ( pages 204 – 215 )

YES YES YES YES

Linear Equations, Solution of One Linear and One Quadratic Equation

Meeting No.

Topic

Reference/s

Quiz

20

Polynomials, Synthetic Division, Fundamental Theorem of Algebra Graphing of Polynomial Functions, General Remarks on Zeros and Roots, Rational Roots Irrational and Imaginary Roots, ( plus review on polynomials )

Vance ( pages 248 – 252 )

YES

21 22 23

EXAM 2

24 25

Matrices, Basic Properties, Products of Matrices Multiplicative Inverses of Matrices, Determinants of Order Two, Solution of Systems of Equations by Matrices Determinants and Systems of Equations of Order Three Inverse Functions, Graphing certain relations The exponential function, geometric progressions Geometric Progressions with infinitely many terms, The Logarithmic Function Common Logarithms, Computation by use of Log arithms, Compound Interest and its Generalization Compound Interest and its Generalization, Applications of the Exponential Functions

26 27 28 29 30 31 32

EXAM 3

33

Brief History of Trigonometry, Definitions of the Circular Functions, Behavior of the Sine and Cosine Functions Values of the Circular Functions of Special Real Numbers, Exact Values of the Circular Functions for θ=π/5 The fundamental circular function identities, Proof of the formula for cos ( A – B ) Special Reduction Formulas, General Addition Formulas, General Reduction Formulas General Identities, Conversions of Sums and Products Function values of any number, Approximations of Function Values for small numbers Inverse Functions, Graphing of certain relations Inverse Circular Functions Operations involving inverse circular functions, graph of the curve y = a sin kx Graph of the curves y = a sin (kx + b), graphing by addition of ordinates Simple Harmonic Motion Addition of Two General sine functions, short discussion of Harmonic Analysis and Synthesis

34 35 36 37 38 39 40 41 42 43 44 45

EXAM 4

46

The Algebra of Complex Numbers, The geometry of Complex Numbers The Algebra of Ordered Pairs, The Algebra of Vectors Angles, Circular functions of angles

47 48

Vance ( pages 253 – 258 ) Vance ( pages 259 – 264 )

YES YES

Vance ( pages 217 – 228 ) Vance ( pages 229 – 237 ) Vance ( pages 237 – 244 ) Vance ( pages 266 – 271 ) Vance ( pages 307 – 311 ) Vance ( pages 312 – 318 )

YES YES YES YES YES YES

Vance ( pages 318 - 324 ) Vance ( pages 324 – 328 )

Vance ( pages 108 – 120 ) Wikipedia / other external sources Vance ( pages 120 – 125 )

YES YES

YES YES

Vance ( pages 126 – 130 ) Vance ( pages 131 – 138 )

Homework

YES YES

Vance ( pages 139 – 145 )

YES YES

Vance ( pages 145 – 152 )

YES

Vance ( pages 266 – 272 ) Vance ( pages 272 – 276 ) Vance ( pages 276 – 278 ) Vance ( pages 332 – 333 ) Vance ( pages 334 – 336 )

YES YES YES

Vance ( pages 336 – 338 ) Vance ( pages 339 – 343 )

YES

YES YES

Vance ( pages 156 – 162 )

YES

Vance ( pages 162 – 170 )

YES

Vance ( pages 346 – 354 )

YES

YES

49 Meeting No.

Geometric use of Angles

Vance ( pages 355 – 363 )

Topic

Reference/s

53 54

Powers and roots of complex numbers General discussion of triangle solutions, The Law of Sines The Law of Cosines, Applications involving Oblique Triangles More problems on Oblique Triangles Additional Topic: “Trigonometric Delights”

55

EXAM 5

56 57 58

Review For Final Exam ( Sample Exam to be given ) Review for Final Exam

50 51 52

YES Quiz

Homework

Vance ( pages 363 – 366 ) Vance ( pages 366 – 374 ) Vance ( pages 374 – 382 )

YES YES YES YES

Trigonometric Delights by Eli Maor

FINAL EXAM

BONUS POINTS !!! CRITERIA Attendance

Per 5 classes attended : + 1% in Long Exam Complete Attendance : + 1% in Final Exam

Quizzes

Per 10 points earned : + 1% in Long Exam 90% and up for total : + 3% in Final Exam

Homework

Per 15 points earned : + 1% in Long Exam 95% and up for total : + 1% in Final Exam

YES