Precalculus/Trigonometry is an excellent college preparatory course. Math topics include trigonometry, linear geometry, limits, functions, conic sections, unit circle, statistics, slopes, and other precalculus lessons. Homework is involved in this course, along with class lecture. Because of the extent of precalculus/trigonometry involved in this course, activities are planned to demonstrate everyday use of the math lessons. Example activities include studies and application of pendulums, wave motion, inverses, bridge building, engineering, architecture, rollercoasters, instruments, and much more.
PreCalculus/Trigonometry Syllabus
Course Objectives:
Student will develop thinking and reasoning skills.
Student will provide general knowledge of basic mathematical concepts including number systems, operations, geometry, and functions.
Student will develop problem-solving abilities.
Student will develop speed and accuracy in computation.
Student will promote an interest in and an enjoyment of mathematics.
Prerequisites
Successful completion of Algebra I & II and Geometry
Supplies
Text
College ruled paper
Graphing paper (quad ruled paper)
Pencils, NO pens (graphite & colored)
Erasers (lots of them!)
Binder with pockets & dividers
Calculator (graphing calculator)
Ruler or Straight Edge
Grading
Assignments and Homework 30%
Assessment (Exams & Quizzes) 40%
Journaling 10%
Activities and Projects 20%
100% quarter grade
Final Exams(2) 20% of semester grade
Math Class Philosophy
It is the teachers goal to allow the students to learn the material within a reasonable amount of time (based on average skill level for an 11-12th grade class). The teacher will be available within reason for tutoring or the student can seek outside tutoring. This course is intended to teach skills needed to pass math placement exams (such as junior college and California state universities) in trigonometric skills with chapters leaning toward taking calculus. Those pursuing college will find this class extremely helpful and to their advantage in future endeavors, such as engineering, construction, sports, medicine, and other science & math professions. There will be an expected amount of practice in doing problems and applying those problems to everyday life.
Standards
All assignments, assessments, lectures, and activities will be used to meet the California State and National Standards (a copy will be provided).
Assignments
These will be used to build on concepts and will include group assignments, worksheets, class discussions, application projects and activities.
Homework
Homework will be assigned and checked on a regular basis. All homework is written on the board daily. Please develop the habit of recording it in your student planner at the beginning of the class period. It will be expected that all homework is completed in pencil, neatly, in an orderly fashion, and kept in your notebook. Furthermore, it will be expected that each problem is justified with a written or mathematical explanation. (I am looking for the logical steps between the problem posted and your solution.) Credit will not be given if only the answers are shown.
Late work is not accepted. Homework is checked the day after it is assigned and will be graded based upon your effort.
Here are some helpful tips to keep your work organized and worth of a 100% homework grade
1. Include your name, date, and period in the upper right hand corner.
2. Label your assignment with section, page, and problem #’s (Ex: 3-5 page 145: # 1-20)
3. Write the original problem and show all your work!
4. Complete work in pencil.
5. Circle or box your final answer.
6. Use a Colored pencil to check each problem.
7. Circle the number of an incorrect problem then write the solution.
8. Put how many right out of how many wrong at the top of the page NEXT TO YOUR NAME.
Exams
There will be an exam for each chapter for a total of 12 exams. The student is expected to retake any exam under 70% until a passing score of 70% is met (exam and retake are not averaged) . Times will be arranged between the student and teacher outside of class time. Any student may retake an exam for a better score at the teacher’s convenience and within 1 weeks time from the day the exam results are handed back. Original scores will remain until the end of the quarter, unless a student retakes an exam.
Informal Assessment
Informal assessments are given when the teacher wants to verify competency and understanding. These will be quizzes given orally, written, or as demonstrations.
Journaling
A topic, question, activity or some other mathematical concept will be given at the beginning of class for the students to take 5-10 minutes to write about or solve. These will be evaluated for content following a grading rubric.
Final Exams
Each final is a comprehensive exam on the semester’s activities, readings, lectures, and concepts. The exams will consist of problem-solving techniques, critical analysis, prediction and application of information that will demonstrate mastery of skills and knowledge.
Late or Missing Assignments
The student will remain in class at lunch or after school to make up any late or missing assignments the day the assignment is due and will receive help in completing the work. If more time is needed to complete the work, the student will have to return the next day to finish with a 70% or better. This allows every child a chance to learn the material and receive a passing grade of C- or better. Math builds from year to year and it is essential the student masters each level. This is not a discipline method, but allows the student to have every opportunity to learn the material.
Make up Exams
Exams will be made up on the student’s own time, so as to not interfere with further learning. If the student does not complete the make up exam within the time allotted by the teacher, he or she will receive a zero.
***Syllabus is subject to change at the teacher’s discretion***
Precalculus Assignments First Semester
AUGUST-SEPTEMBER
Chapter 1: Trigonometry
1.1 Angle Measure & Arc Length 1-35 (odd) p.6-7
1.2 Trigonometric Ratios 1-23 (odd) p.12-13
1.3 Reference Angles 1-33 (odd) p.16-17
1.4 Right Triangle Trigonometry 1-17 (odd) p.20-21
1.5 Law of Sines 1-19 (odd) p.27
1.6 Law of Cosines 1-15 (odd) p.32-33
1.7 Applications of Trigonometry 1-27 (odd) p.38
Ch.1 Review 1-30 (all) p.42-43
SEPTEMBER
Chapter 2: Polynomials
2.1 Relations 1-27 (odd) p.49-50
2.2 Linear Functions 1-31 (odd) p.55-57
2.3 Quadratic Functions 1-27 (odd) p.64-64
2.4 Polynomial Functions 1-27 (odd) p.70-71
2.5 Factoring Higher-Degree Polynomials 1-25 (odd) p. 76-77
2.6 Zeros of Polynomial Functions 1-29 (odd) p. 84-85
2.7 Graphing Polynomial Functions 1-27 (odd) p. 97-98
Ch.2 Review 1-30 (all)
SEPTEMBER
Chapter 3: Functions
3.1 Power Functions 1-23 (odd) p. 109-110
3.2 Exponential Functions 1-21 (odd) & 23-26 (all) follow problem directions for entering into calculator
3.3 Piece Functions 1-33 (odd) p. 123-125
3.4 Periodic Functions 1-23 (odd) p. 132-133
3.5 Trigonometric Functions 1-27 (odd) p. 140-141
3.6 Reciprocal Functions 1-19 (odd) try 21, 23-31 (odd) try 33 p. 148-150
3.7 Proper Rational Functions 1-21 (odd) p. 155-156
3.8 Rational Functions 1-31 (odd) p. 164-165
Ch.3 Review 1-35 (all) p. 168-169
OCTOBER
Chapter 4: Inverse Functions
4.1 Increasing & Decreasing Functions 1-19 (odd) 21 use calculator p. 175-176
4.2 Operations with Functions 1-25 (odd) 28-32 (all) p. 181-182
4.3 Finding Inverse Functions 1-25 (odd) p. 185-186
4.4 Radical Functions 1-21 (odd) p. 191-192
4.5 Inverse Trigonometric Functions 1-29 (odd) p. 196-197
4.6 Logarithmic Functions 1-25 (all) p. 202
4.7 Laws of Logarithms 1-22 (all) p. 206-207
4.8 Applications of Logarithmic Functions 1-23 (all) skip 21 p. 213-214
Ch.4 Review 1-35 (all) p.218-219
NOVEMBER
Chapter 5: Equations
5.1 Polynomial Equations 1-19 (odd) try 21 & 22 p. 225-226
5.2 Rational Equations 1-23 (odd) try 24 & 25 p. 231-232
5.3 Radical Equations 1-21 (odd) p.235-236
5.4 Logarithmic & Exponential Equations 1-32 (all) p. 244-245
5.5 Identities 1-20 (odd) p. 249-250
5.6 Sum & Differences Identities 1-29 (odd) p.256-257
5.7 Double-Angle & Half-Angle Identities 1-23 (odd) p. 260-261
5.8 Trigonometric Equations 1-29 (odd) 25 is a bit long p. 265-266
Ch.5 Review 1-32 (all) p. 270-271
DECEMBER
Chapter 6: Conic Sections & Polar Graphs
6.1 Conic Sections 1-26 (all) try 27 & 28 p. 280-281
6.2 Ellipses 1-16 (odd),calculator for 17 & 18, 19-27 (odd) p.289-290
6.3 Parabolas 1-29 (odd) do 22 on calculator p. 297-298
6.4 Hyperbolas 1-25 (odd) p. 305-306
6.5 Variation 1-21 (all) calculator for #11 & try 22 p. 309-310
6.6 Polar Coordinates 1-22 (odd) 23-32 (all) p. 319-320
6.7 Polar Coordinates & Graphs 1-24 (all) try 25 on calculator p. 325
6.8 Graphing Polar Equations 1-25 (all) p. 330-331
Ch.6 Review 1-40 (all) p. 336-337
PRECALCULUS: HOMEWORK Second Semester
JANUARY
Chapter 7 Complex Number
7.1 Standard Form page 344-345 (1-35) odd
7.2 Graphs of Complex Numbers page 350-351 (1-25) odd
7.3 Polar Form page 361-363 (1-25) odd
7.4 Powers and Roots of Complex Numbers page 367-368 (1-23) odd
7.5 Complex Numbers as Vectors page 372 (1-19) odd
7.6 Dot Products page 377-378 (1-25) odd
7.7 Applications of Vectors page 383-384 (1-10) all
Chapter 7 Review page 388-389 (all)
FEBRUARY
Chapter 8 Matrix Algebra
8.1 Solving Systems Algebraically page 397-398 (1-17) odd
8.2 Matrices page 405-407 (1-21) odd
8.3 Solving Systems by Gaussian Elimination page 417 (1-17) odd
8.4 Determinants page 424-425 (1-21) odd
8.5 Properties of Determinants page 429-430 (1-15) odd
8.6 Solving Systems by Cramer’s Rule page 434-434 (1-19) odd
8.7 Inverses of Matrices page 439-441 (1-25) odd
Chapter 8 Review page 444-445 (all)
FEBRUARY/MARCH
Chapter 9 Statistics
9.1 Samples and Central Tendency page 451-452 (1-23) odd
9.2 Variability page 456-457 (1-23) odd
9.3 Transformations of Data page 460-461 (1-23) odd
9.4 Theorems About Variability page 464-465 (1-19) odd
9.5 The Bell Curve page 472 (1-27) odd
9.6 Linear Correlation page 477-478 (1-25) odd
9.7 Tests of Hypotheses (optional) page 485-486 (1-21) odd
Chapter 9 Review page 490-491 (all)
MARCH
Chapter 10 Sequences
10.1 Recursive Formulas page 497-498 (1-23) odd
10.2 Explicit Formulas page 502 (1-27) odd
10.3 Arithmetic and Geometric Sequences page 508-509 (1-27) odd
10.4 Mathematical Induction page 516 (1-15) all
10.5 Sums and Their Properties page 521-522 (1-23) odd
10.6 Special Sums page 528-529 (1-19) odd
Chapter 10 Review page 536-537 (all)
APRIL
Chapter 11 Limits and Calculus
11.1 Limits of Sequences page 545 (1-25) odd
11.2 Series page 552 (1-19) odd
11.3 Limits and Graphs page 557-559 (1-27) odd
11.4 Continuous Functions page 562-565 (1-29) odd
11.5 Infinite Limits and Asymptotes page 569-570 (1-23) odd
11.6 Limit Theorems page 578 (1-19) odd
Chapter 11 Review page 584-585 (all)
MAY
Chapter 12 Differential Calculus
12.1 Definition of Derivatives page 591 (1-21) odd
12.2 Derivatives and Graphs page 595-596 (1-25) odd
12.3 Properties of Derivatives page 602-603 (1-23) odd
12.4 Chain Rule page 607-608 (1-25) odd
12.5 Quotient Rule page 611-612 (1-21) odd
12.6 Motion Applications page 619-620 (1-25) odd
Chapter 12 Review page 626-627 (all)
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