COURSE SYLLABUS Course Title: MATH 1250 Algebra & Trigonometry II
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1 COURSE SYLLABUS Course Title: MATH 1250 Algebra & Trigonometry II Semester Hours: 4 Instructor: Mr. Treen nl_ctreen@seovec.org Course Description: MATH 1250 furnishes students with a more rigorous background in trigonometry and algebra. Included in the topics are functions and their graphs, right triangle trigonometry, trigonometric functions of any angle, radians, vectors and their applications, Law of Sines and Law of Cosines, graphs of trigonometric functions, exponents and radicals, complex numbers, logarithmic and exponential functions, systems of equations of higher degree, logarithmic and exponential equations, equations of quadratic form, and equations with radicals. A graphing calculator is required. Rationale: The primary objective of this course is to extend the mathematical knowledge already established in MATH The topics of MATH 1240 will be expanded and include further topics in algebra and trigonometry. The broadened development will enable the student to deal with more complicated topics in application situations. Prerequisites: MATH 1240 with a grade of C or better, successful completion of MATH 1240 Credit-by-Exam, or instructor approval. Required Text and Materials: Basic Technical Mathematics with Calculus, 10th edition, Allyn J. Washington. ISBN: Pencils, erasers, highlighters, pens Loose-leaf paper, graph paper, and a binder that you will use for your notebook Graphing calculator ipad, laptop, etcetera P a g e 1 of 12
2 Goal: To provide students of ROCHS with instruction focusing on the following topics: 1.00 Significant Digits; Functions and their Graphs 2.00 Right Triangle Trigonometry 3.00 Trigonometric Functions of Any Angle 4.00 Vectors 5.00 Law of Sines and Law of Cosines 6.00 Graphs of Trigonometric Functions 7.00 Exponents and Radicals 8.00 Complex Numbers 9.00 Exponential and Logarithmic Functions Additional Types of Equations and Systems of Equations Objectives: The student will demonstrate knowledge as outlined in the following objectives by completing the assignments and scoring at least a sixty percent (60%) cumulative average for the graded work. Specifically the student will: (* These goals may require the use of a graphing calculator for all or part of their solutions.) 1.0 Significant Digits; Functions and their Graphs 1.01 Work with significant digits and round a number to a specified number of significant digits Define a function Express a specific condition as a function Evaluate a given function. 1.05* Sketch the graphs of various functions given their equations Graph functions defined by tables of data Use linear interpolation to estimate values from a graph and given in tables Use linear extrapolation to estimate values when a graph is given. 1.09* Find the zeros of a function graphically Specify the domain and range of a function Right Triangle Trigonometry 2.01 Define an angle and know the vocabulary used with angles (e.g. terminal side, initial side, rotation, co-terminal angles, standard position, quadrant angle). 2.02* Convert from degrees, minutes and seconds to decimal degrees and vice versa Write the definitions of the six trigonometric functions Explain which functions are reciprocals of each other Correctly write the specific values for trig. functions, (e.g. sin 30 o = 1/2 not sin = 1/2) Memorize and use the trig. values for 0, 30, 45, 60, and 90 (in simplified radical form - not decimal approximations) Explain which functions are co-functions of each other Use the trig. functions to solve right triangle application problems. P a g e 2 of 12
3 3.00 Trigonometric Functions of Any Angle 3.01 Determine the signs of the trigonometric functions of angles in any quadrant Determine the quadrant in which the terminal side of an angle lies subject to given conditions Determine the values of the reference angles for angles in quadrants II, III, and IV. 3.04* Analyze the calculator's results to obtain the correct reference angle. 3.05* Determine the values of the trigonometric functions of an angle in degrees or radians by using a calculator. 3.06* Convert degrees to radians and vice versa. 3.07* Determine the angle for a given trigonometric function value Solve applied problems using radians Vectors 4.01 Define a vector and a scalar Add and subtract vectors graphically Find the horizontal and vertical components of a given vector Find the magnitude and direction of the resultant of given vectors Convert vectors in rectangular form to trigonometric form and vice versa (stating magnitude and direction) Combine vectors algebraically (giving the answer in trigonometric form) Diagram and solve algebraically applied vector problems Law of Sines and Law of Cosines 5.01 Identify the different kinds of solvable oblique triangles State the Law of Sines, recognize when it can be applied, and solve problems using it State the Law of Cosines, recognize when it can be applied, and solve problems using it Graphs of Trigonometric Functions 6.01 Graph y = a sin x and y = a cos x. a. State amplitude. b. State period. c. Sketch finding values of the function for each one-fourth period, sketching a minimum of one cycle Graph y = a sin (bx + c) and y = a cos (bx + c). a. State amplitude. b. State period. c. State phase shift or displacement. d. Sketch finding values of the function for each one-fourth period, sketching a minimum of one cycle Graph y = tan x, y = cot x, y = sec x, y = csc x. P a g e 3 of 12
4 a. State the period. b. Identify, and indicate by dashed lines on the graph, the asymptotes. c. Sketch using asymptotes and one-fourth period values, sketching a minimum of one cycle Exponents and Radicals 7.01 Evaluate expressions with integral exponents. a. Simplify an expression using basic laws of exponents. b. Simplify an expression leaving only positive exponents Evaluate expressions with fractional exponents. a. Obtain numerical values with and without the use of a calculator (i.e. leave in simplified radical form or in decimal form). b. Simplify, expressing all answers with positive exponents. c. Change from fractional exponents to simplified radicals and vice versa Write radical expressions in their simplest form. a. Remove all perfect nth-power factors from a radicand of order n. b. Reduce the order of the radicand, if possible. c. Rationalize the denominator if a radical originally appeared in the denominator Add, subtract, multiply, and divide radical expressions leaving answers in simplest form with rationalized denominators Complex Numbers 8.01 Identify the general form of a complex number Define the imaginary unit and denote it by the symbol "j" Know the vocabulary dealing with the three forms of a complex numbers (i.e. rectangular, polar, and exponential) Perform basic operations (simplify, add, subtract, multiply, divide) with complex numbers in rectangular form Find the values for x and y when complex numbers are set equal Graph complex numbers Add and subtract complex numbers graphically Transform complex numbers to polar form. a. Know the basic relationships: x = r cos θ, y = r sin θ, r 2 = x 2 + y 2, tan θ = x / y b. Transform from rectangular form to polar form by substituting values obtained in 4.08a and vice versa. c. Recognize and write polar form in all three (3) notations Transform complex numbers to exponential form and transform from exponential to either of the other forms Determine products, quotients, powers, and roots of complex numbers in polar and exponential forms Use DeMoivre's theorem to determine roots of complex numbers. P a g e 4 of 12
5 8.12 Solve application problems involving complex numbers Exponential and Logarithmic Functions 9.01 Define a logarithm and state the relationship in both exponential form and logarithmic form Graph exponential (y= b x ) and logarithmic (y =log b x ) functions Know and use the properties of logarithms to determine products, quotients, and powers of numbers. a. Evaluate when a base is given. b. Express as a sum, difference, or a multiple of logarithms or vice versa problems such as: log log 2 x ; log Determine logarithms (base 10) both by calculator and by use of logarithmic tables. a. Find the common logarithm. b. Find the antilogarithm Identify the relationship between common (base 10) logarithms and natural (base e) logarithms. a. Convert from one base to the other with and without the use of the calculator. b. Solve for a specified variable when an equation involving natural logarithms is given. c. Find logarithms and antilogarithms using a calculator Solve exponential and logarithmic equations Additional Types of Equations and Systems of Equations Graphically solve systems of higher degree equations Algebraically solve systems of higher degree equations. a. Solve by substitution. b. Solve by addition/subtraction method Solve equations of the quadratic form Solve equations involving variables in the radical. Diversity in the Classroom: It is the responsibility of the instructor and the student to foster and maintain a harmonious, nonthreatening and non-discriminating environment in the classroom. Although students are encouraged to express their ideas freely, an instructor must be vigilant against any inflammatory and demeaning statements or arguments (in classrooms) that may promote hate toward people, beliefs, and ideals. The school is committed to follow a non-discriminatory policy and accepts diversity as part of the community environment. Therefore, all individuals regardless of their ethnicity, beliefs, age, gender, and life style, are to be respected as equal and contributing partners of our society. P a g e 5 of 12
6 Tentative Agenda: The assignments that I assign are the minimum. You may need to do more such as study review sections, or get help from another student, teacher, and/or the tutor. As you read ahead, study the examples. If you don t understand the reading or an example, ask questions during/following the lecture on the topic. Whenever you find new vocabulary words or formulas which your instructor says are important, learn them to save yourself time and grief later! The following is a tentative outline of material covered each class, subject to change by the instructor. All assignments will be posted on Blackboard or given in class. In the event that a class is canceled, it is the student s responsibility to go to Blackboard to complete the required day s assignment. The student will continue with new material as if the class had met, and the next class session will be used to begin to catch up on the material. NOTE: SINCE ALL THREE DISTRICTS HAVE DIFFERING SCHEDULES, THERE MAYBE DAYS THAT I PRESENT MATERIAL AND YOU ARE NOT IN SCHOOL. IT IS YOUR RESPONCIBILITY TO CHECK BLACKBOARD EVERYDAY (EVEN IF SCHOOL IS NOT IN SESSION) AND COMPLETE THE REQUIRED ASSIGNMENT. YOU ARE TO TRY YOUR BEST AND ASK EITHER MYSELF OR THE MONITOR FOR ASSISTANCE. IF I AM NOT TEACHING (EITHER DUE TO MY ABSENCE OR NEW LEX NOT BEING IN SESSION), ASK YOUR MONITOR FOR ASSISTANCE OR ME ANY QUESTIONS. The following are days that I do not expect you to check Blackboard. You must check Blackboard every other weekday. September 2 nd ---- Labor Day November 5 th ---- Election Day (no school New Lex) November 27 th December 2 nd ---- Thanksgiving Break December 23 rd January 3 rd ---- Winter Break Week Topic Assignment (write in assigned problems as they are given) 1 Significant Digits. Functions and Their Graphs. Read Section 1.3 Tentative Tests Read Section 3.1 Read Section 3.2 P a g e 6 of 12
7 Read Section Functions and Their Graphs (continued). Right Triangle Trigonometry. Read Section 3.5 Read Section 3.6 Read Section Right Triangle Trigonometry. Read Section 4.2 Read Section 4.3 Read Section 4.4 Read Section Trigonometric Functions of Any Angle. Read Section 8.1 Test 1 Read Section 8.1 Read Section 8.2 Read Section 8.3 P a g e 7 of 12
8 Read Section Vectors. Read Section 9.1 Read Section 9.2 Read Section 9.3 Read Section Law of Sines. Law of Cosines. Read Section 9.5 Read Section Graphs of Trigonometric Functions. Read Section 10.1 Read Section 10.2 Read Section Graphs of Trigonometric Functions (continued). Read Section 10.4 Test 2 after section 10.4 P a g e 8 of 12
9 Exponents and Radicals. Read Section 11.1 Read Section Exponents and Radicals. Read Section 11.3 Read Section 11.4 Read Section Complex Numbers. Read Section 12.1 Read Section 12.2 Read Section Complex Numbers (continued). Read Section 12.4 Test 3 Read Section 12.5 Read Section 12.6 P a g e 9 of 12
10 12 Exponential Functions. Logarithmic Functions. Read Section 13.1 Read Section 13.2 Read Section 13.3 Read Section Logarithmic Functions (continued). Exponential and Logarithmic Equations. Read Section 13.5 Read Section Systems of Equations of Higher Degree. Equations of Quadratic Form. Read Section 14.1 Read Section 14.2 Read Section Equations with Radicals. Review and/or Catch-Up Read Sections: 14.4 Test 4 16 Review and/or Catch-Up COMPREHENSIVE FINAL EXAM P a g e 10 of 12
11 Assessment: Grades will be calculated on a total point basis. Students will be graded on tests, quizzes, and possibly homework throughout the semester. Homework will consist of all assigned exercises. Each student is expected to do the problems with substantiating work shown, check the answers, correct his/her work, and ask questions about any problems to which the solutions are unclear. These problems may or may not be collected. If collected, the assignments must be completed by the designated deadline to receive credit. There will be detailed solutions manuals for all homework problems so that you may check your answers. Just copying the correct work from the solution guide will not help you perform on assessments. Completing homework is critical to understanding the content. Quizzes will be over any material covered since the previous quiz. There will be one to four quizzes a week, depending on the content and how the three schools schedules coincide. Quizzes may be timed, so if students have a documented learning disability which requires extra time be given, they must see the instructor/monitor the first week of class. No review sheets are provided for quizzes. To study for quizzes, students should do the homework and any worksheets passed out in class. There will tentatively be 4 tests over larger sections of material. There will also be a comprehensive final exam, i.e., it covers everything since the first day of class. NOTE: If students fail to take the final exam, their final grade for the course will be an F, no matter their final course average. Grade Scale: A 90% - 100% B 80% - 89% C 70% - 79% D 60% - 69% F 0% - 59% Make-up Policy: Quizzes and tests may be made-up in the case of excused absences outside of the class period. It is the student s responsibility to schedule a make-up quiz or test with the instructor/monitor. The assessment must be taken within a week unless school policy permits otherwise. Calculators: It is required to have any version of a TI-83 or TI-84 graphing calculator. Restrictions: 1. You may not borrow another's calculator while the class is taking a test or a quiz. P a g e 11 of 12
12 2. If specific values are given for your use, do not use a calculator key which will give another or a more detailed value. (e.g. π as 3.14 instead of a 10-place decimal). 3. Answers alone will not be accepted. You must show the formula or equation, the steps involved, the intermediate answers, and the final answers. Examples will be given in class. 4. Calculators with more advanced features such as the TI-89 and any of the TI-90s will not be permitted for use in this course. 5. The student is responsible to understand his/her own calculator. Refer to the manual. Electronic Devices: Electronic devices including cell phones, computers, tape recorders, ipods, etc. must be turned off and out of sight. They are not to be used in the classroom for any reason, without the permission of the instructor. Deliberate violation of this policy could result in removal from the course. Instructor's Responsibilities: The role of the instructor will be to explain new material and review previous material when questions are raised by students after attempting to do the material as an outside assignment. Student's Responsibilities: The student's responsibilities are a major consideration in this course. After material has been discussed, it is the student's responsibility to complete the outside assignment(s) prior to the next class meeting so that material that remains unclear may be reexplained. In addition, the student is expected to read through the new material that is scheduled to be presented so that the material will be generally familiar and so that preliminary questions may be asked. Blackboard: Every student is to have a Blackboard account. You need to access Blackboard for assignments and possible quizzes. If you are absent or we do not have class on a day that class was scheduled, you MUST check Blackboard for any messages and complete any assignments posted. Attendance Policy: Attendance will be taken daily. The student is expected to be in class on time. If a student is absent, he/she is responsible to notify the instructor and to complete the material missed. Academic Dishonesty: Academic dishonesty will not be tolerated. A student, whether a helper or recipient, will receive a ZERO on any assignment for academic dishonesty. P a g e 12 of 12
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