COURSE SYLLABUS Course Title: MATH 1350 Pre-Calculus Credit Hours: 5 Instructor: Kristen Keish E-mail: keishk@goshenlocalschools.org Course Description: Broadens the algebra background and affords students the opportunity to develop an extensive trigonometric background. Included are the topics of functions and their graphs, polynomial and rational functions, exponential and logarithmic functions, systems of equations, inequalities, conic sections, sequences and series, right triangle trigonometry, trigonometric functions of any angle, graphs of the trigonometric functions, inverse trigonometric functions, oblique triangles, vectors, and trigonometric identities, equations, and formulas. A graphing calculator is required. Prerequisites: Grade of C or better in MATH 1340, or pass the MATH 1340 Credit-by-Exam, or grade of C or better in MATH 1250, or pass the MATH 1250 Credit-by-Exam. Room: B112 Planning: 5 th Period Required Text And Materials: Precalculus, Mathematics for Calculus, 6 th ed., James Stewart Brooks/Cole, 2012. ISBN 978-0-8400-6807-1. Supplies needed: TI-83 or TI-84 graphing calculator. (we have ones in class, but highly recommended if you are able to get one for home use) Binder for this class Three Sections in your binder: Notes, Handouts, Quizzes Graph paper One spiral notebook or composition notebook (for homework) Dry Erase Markers (at least 2 markers Walmart has a 5 pack Expo markers for 2.97) Notecards Discipline: Respect your classmates, Respect your teachers, Respect yourself. Discipline issues (if there are any) will be handed on a case by case basis according to school policies. Page 1 of 11
GOALS AND OBJECTIVES Goal: To provide students of Zane State College with instruction focusing on the following topics: 1.00 Functions and Graphs 2.00 Polynomial and Rational Functions 3.00 Exponential and Logarithmic Functions 4.00 Systems of Equations and Inequalities 5.00 Conic Sections 6.00 Sequences/Series 7.00 Trigonometric Functions 8.00 Analytic Trigonometry 9.00 Additional Topics in Trigonometry 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: 1.00 Functions and Graphs 1.01 Plot points in the rectangular coordinate system. 1.02 Graph equations in the rectangular coordinate system. 1.03 Interpret information about a graphing utility s viewing rectangle or table. 1.04 Use a graph to determine intercepts. 1.05 Interpret information given by graphs. 1.06 Find the domain and range of a relation. 1.07 Determine whether a relation is a function. 1.08 Determine whether an equation represents a function. 1.09 Evaluate a function. 1.10 Graph functions by plotting points. 1.11 Use the vertical line test to identify functions. 1.12 Obtain information about a function from its graph. 1.13 Identify the domain and range of a function from its graph. 1.14 Identify intercepts from a function s graph. 1.15 Identify intervals on which a function increases, decreases, or is constant. 1.16 Use graphs to locate relative maxima or minima. 1.17 Identify even or odd functions and recognize their symmetries. 1.18 Understand and use piecewise functions. 1.19 Find and simplify a function s difference quotient. 1.20 Calculate a line s slope. 1.21 Write the point-slope form of the equation of a line. 1.22 Write and graph the slope-intercept form of the equation of a line. 1.23 Graph horizontal or vertical lines. Page 2 of 11
1.24 Recognize and use the general form of a line s equation. 1.25 Use intercepts to graph the general form of a line s equation. 1.26 Model data with linear functions and make predictions. 1.27 Find slopes and equations of parallel and perpendicular lines. 1.28 Interpret slope as rate of change. 1.29 Find a function s average rate of change. 1.30 Recognize graphs of common functions. 1.31 Use vertical shifts to graph functions. 1.32 Use horizontal shifts to graph functions. 1.33 Use reflections to graph functions. 1.34 Use vertical stretching and shrinking to graph functions. 1.35 Use horizontal stretching and shrinking to graph functions. 1.36 Graph functions involving a sequence of transformations. 1.37 Find the domain of a function. 1.38 Combine functions using the algebra of functions, specifying domains. 1.39 Form composite functions. 1.40 Determine domains for composite functions. 1.41 Write functions as compositions. 1.42 Verify inverse functions. 1.43 Find the inverse of a function. 1.44 Use the horizontal line test to determine if a function has an inverse function. 1.45 Use the graph of a one-to-one function to graph its inverse function. 1.46 Find the inverse of a function and graph both functions on the same axes. 1.47 Find the distance between two points. 1.48 Find the midpoint of a line segment. 1.49 Write the standard form of a circle s equation. 1.50 Give the center and radius of a circle whose equation is in standard form. 1.51 Convert the general form of a circle s equation to standard form. 1.52 Construct functions from verbal descriptions. 1.53 Construct functions from formulas. 2.00 Polynomial and Rational Functions 2.01 Recognize characteristics of parabolas. 2.02 Graph parabolas. 2.03 Determine a quadratic function s minimum or maximum value. 2.04 Solve problems involving a quadratic function s minimum or maximum value. 2.05 Identify polynomial functions. 2.06 Recognize characteristics of graphs of polynomial functions. 2.07 Determine end behavior. 2.08 Use factoring to find zeros of polynomial functions. 2.09 Identify zeros and their multiplicities. 2.10 Use the Intermediate Value Theorem. 2.11 Understand the relationship between degree and turning points. 2.12 Graph polynomial functions. 2.13 Use long division to divide polynomials. 2.14 Use synthetic division to divide polynomials. Page 3 of 11
2.15 Evaluate a polynomial using the Remainder Theorem. 2.16 Use the Factor Theorem to solve a polynomial equation. 2.17 Use the Rational Zero Theorem to find possible rational zeros. 2.18 Find zeros of a polynomial function. 2.19 Solve polynomial equations. 2.20 Use the Linear Factorization Theorem to find polynomials with given zeros. 2.21 Use Descartes s Rule of Signs. 2.22 Find the domains of rational functions. 2.23 Use arrow notation. 2.24 Identify vertical asymptotes. 2.25 Identify horizontal asymptotes. 2.26 Use transformations to graph rational functions. 2.27 Graph rational functions. 2.28 Identify slant asymptotes. 2.29 Solve applied problems involving rational functions. 2.30 Solve polynomial inequalities. 2.31 Solve rational inequalities. 2.32 Solve problems modeled by polynomial or rational inequalities. 2.33 Solve direct variation problems. 2.34 Solve inverse variation problems. 2.35 Solve combined variation problems. 2.36 Solve problems involving joint variation. 3.00 Exponential and Logarithmic Functions 3.01 Evaluate exponential functions. 3.02 Graph exponential functions. 3.03 Evaluate functions with base e. 3.04 Use compound interest formulas. 3.05 Change from logarithmic to exponential form. 3.06 Change from exponential to logarithmic form. 3.07 Evaluate logarithms. 3.08 Use basic logarithmic properties. 3.09 Graph logarithmic functions. 3.10 Find the domain of a logarithmic function. 3.11 Use common logarithms. 3.12 Use natural logarithms. 3.13 Use the product, quotient, and power rules of logarithms. 3.14 Expand logarithmic expressions. 3.15 Condense logarithmic expressions. 3.16 Use the change-of-base property. 3.17 Use like bases to solve exponential equations. 3.18 Use logarithms to solve exponential equations. 3.19 Use the definition of logarithm to solve logarithmic equations. 3.20 Use the one-to-one property of logarithms to solve logarithmic equations. 3.21 Solve applied problems involving exponential and logarithmic equations. 3.22 Model exponential growth and decay. Page 4 of 11
3.23 Use logistic growth models. 3.24 Use Newton s Law of Cooling. 3.25 Choose an appropriate model for data. 3.26 Express an exponential model in base e. 4.00 Systems of Equations 4.01 Decide whether an ordered pair is a solution of a linear system. 4.02 Solve linear systems by substitution. 4.03 Solve linear systems by addition. 4.04 Identify systems that do not have exactly one ordered-pair solution. 4.05 Solve problems using systems of linear equations. 4.06 Verify the solution of a system of linear equations in three variables. 4.07 Solve systems of linear equations in three variables. 4.08 Solve problems using systems in three variables. 4.09 Graph a linear inequality in two variables. 4.10 Graph a nonlinear inequality in two variables. 4.11 Use mathematical models involving linear inequalities. 5.00 Conic Sections and Analytic Geometry 5.01 Graph ellipses centered at the origin and not centered at the origin. 5.02 Write equations of ellipses in standard form. 5.03 Locate a hyperbola s vertices and foci. 5.04 Write equations of hyperbolas in standard form. 5.05 Graph hyperbolas centered at the origin and not centered at the origin. 5.06 Graph parabolas with vertices at the origin and not at the origin. 5.07 Write equations of parabolas in standard form. 5.08 Solve applied problems involving ellipses, hyperbolas, and parabolas. 6.00 Sequences/ Series 6.01 Find the particular terms of a sequence from the general term. 6.02 Use recursion formulas. 6.03 Use factorial notation. 6.04 Use summation notation. 6.05 Find the common difference for an arithmetic sequence. 6.06 Write terms of an arithmetic sequence. 6.07 Use the formula for the general term of an arithmetic sequence. 6.08 Use the formula for the sum of the first n terms of an arithmetic sequence. 6.09 Find the common ratio of a geometric sequence. 6.10 Write terms of a geometric sequence. 6.11 Use the formula for the general term of a geometric sequence. 6.12 Use the formula for the sum of the first n terms of a geometric sequence. 6.13 Find the value of an annuity. 6.14 Use the formula for the sum of an infinite geometric series. Page 5 of 11
7.00 Trigonometric Functions 7.01 Recognize and use the vocabulary of angles. 7.02 Use degree and radian measure. 7.03 Convert between degrees and radians. 7.04 Draw angles in standard position. 7.05 Find coterminal angles. 7.06 Find the length of a circular arc. 7.07 Use linear and angular speed to describe motion on a circular path. 7.08 Use a unit circle to define trigonometric functions of real numbers. 7.09 Recognize the domain and range of sine and cosine functions. 7.10 Find the exact values of the trigonometric functions at π/4. 7.11 Use even and odd trigonometric functions. 7.12 Recognize and use fundamental identities. 7.13 Use periodic properties. 7.14 Evaluate trigonometric functions with a calculator. 7.15 Use right triangles to evaluate trigonometric functions. 7.16 Find function values for 30 (π/6), 45 (π/4), and 60 (π/3). 7.17 Use equal cofunctions of complements. 7.18 Use right triangle trigonometry to solve applied problems. 7.19 Use definitions of trigonometric functions of any angle. 7.20 Use the signs of the trigonometric functions. 7.21 Find reference angles. 7.22 Use reference angles to evaluate trigonometric functions. 7.23 Understand the graphs of y = sin x, y = cos x, y = tan x, y = cot x, y = sec x, and y = csc x. 7.24 Graphs variations of y = sin x, y = cos x, y = tan x, y = cot x, y = sec x, and y = csc x. 7.25 Use vertical shifts of sine and cosine curves. 7.26 Model periodic behavior. 7.27 Understand and use the inverse sine, cosine, and tangent functions. 7.28 Use a calculator to evaluate inverse trigonometric functions. 7.29 Find exact values of composite functions with inverse trigonometric functions. 7.30 Solve a right triangle. 7.31 Solve problems involving bearings. 7.32 Model simple harmonic motion. 8.00 Analytic Trigonometry 8.01 Use the fundamental trigonometric identities to verify identities. 8.02 Use sum and difference formulas for sine, cosine, and tangent. 8.03 Use the double-angle formulas. 8.04 Use the power-reducing formulas. 8.05 Use the half-angle formulas. 8.06 Use the product-to-sum formulas and vice versa. 8.07 Find all solutions of a trigonometric equation. Page 6 of 11
8.08 Solve equations with multiple angles. 8.09 Solve trigonometric equations quadratic in form. 8.10 Use factoring to separate different functions in trigonometric equations. 8.11 Use identities to solve trigonometric equations. 8.12 Use a calculator to solve trigonometric equations. 9.00 Additional Topics in Trigonometry 9.01 Use the Law of Sines and Law of Cosines to solve oblique triangles. 9.02 Use the Law of Sines to solve, if possible, the triangle or triangles in the ambiguous case. 9.03 Find the area of an oblique triangle using the sine function. 9.04 Solve applied problems using the Law of Sines and Law of Cosines. 9.05 Use Heron s formula to find the area of a triangle. 9.06 Use magnitude and direction to show vectors are equal. 9.07 Visualize scalar multiplication, vector addition, and vector subtraction as geometric vectors. 9.08 Represent vectors in the rectangular coordinate system. 9.09 Represent vectors in the polar coordinate system. 9.10 Perform operations with vectors in terms of i and j both graphically and algebraically. 9.11 Find the unit vector in the direction of v. 9.12 Write a vector in terms of its magnitude and direction. 9.13 Solve applied problems involving vectors. 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. Zane State College 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. Free Tutoring Services: I am available most mornings before school. Please take advantage of this. Be proactive. Page 7 of 11 TENTATIVE ASSIGNMENTS Assignments will consist of problems from the textbook or from MyMathLab assigned by the instructor. The textbook assignments appear as follows: Ex. pp. 143, 159 (Only the first page of a set is listed. Complete the entire set.). At times you may be asked to do all problems in a set or just specific problems. Check your answers with the back of the textbook. The following is a tentative page outline of material covered each week subject to change by the instructor. It will give you a reference if you miss a class or need to check an assignment.
WEEKS TOPICS ASSIGNMENTS ACTIVITY The Types of Numbers. The Properties of Real Numbers. Interval Notation. Calculus Factoring. Compound Fractions. Solving non-linear inequalities. Coordinate Geometry. Circles. Lines. What is a function? (Vertical Line Test). Graphs of Functions. Transformations of Functions. Getting Information from a Function s Graph. Combining Functions. One to One Functions and their Inverses. Quadratic Functions. Polynomial Functions and their Graphs. Dividing Polynomials. Real Zeros of Polynomials. Rational Functions. Exponential Functions. The Natural Exponential Function. Logarithmic Functions. Laws of Logarithms. Exponential and Logarithmic Equations. Angle Measure. Trigonometry of Right Triangles. Inverse Trig Functions and Right Triangles. Page 8 of 11 Read Sections 1.1, 1.3, 1.4, 1.7 Ex. p. 10: 1, 2, 5 18, 51 58 p. 33: 63, 64, 89 94, 125 128 p. 42: 59 80 p. 80: 35 72. Read Sections 1.8, 1.10 Ex. p. 92, 1 18, 33 36, 41, 57 70. p. 94, 87 108. p. 115, 1 13, 15 38, 45-56 Read 2.1, 2.2, 2.5 Ex. p. 149, 2 8, 15 41, 69 71. p. 160, 51 68. p. 160, 2 4, 33 41, 43 45. p. 187, 1 64. Read 2.3, 2.6, 2.7 Ex. p. 168, 1 22, 31 34. p. 196, 1 14, 21 54. p. 205, 1 31, 37 64. Read 3.1, 3.2, 3.3 Ex. p. 229, 1 48. p. 243, 1 39, 47 50. p. 251, 1 62. Read 3.4, 3.7, 4.1, 4.2 Ex. p. 260, 1 70. p. 289, 1 64. p. 307, 1 36, 40. p. 312, 1 14. Read Sections 4.3, 4.4 Ex. p. 322, 1 12, 19 50, 53 68, 75 78. p. 329, 1 62, 72. Read Sections 4.5, 6.1, 6.2, 6.4 Ex. p. 338, 1 54. p. 440, 3 50. p. 448, 1 42. p. 467, 2, 7 32. Daily Quizzes. Lecture. In Class Problems.
WEEK TOPICS ASSIGNMENTS ACTIVITY The Law of Sines. The Law of Cosines. The Unit Circle. Trig Functions of Real Numbers (Unit Circle Trig). Trig Graphs. More Trig Graphs. Inverse Trig Functions and their Graphs. Trig Identities. Addition and Subtraction Formulas. Double Angle and Half Angle Formulas. Basic Trig Equations. More Trig Equations. Ellipses. Hyperbolas. Shifted Conics. Read 6.5, 6.6, 5.1 Ex. p. 473, 1 28. p. 480, 1 28. p. 375, 1 31, 35 52. Read 5.2, 5.3, 5.4 Ex. p. 384, 1 37, 65 72. p. 396, 1 50. p. 405, 1 54. Read 5.5, 7.1, 7.2 Ex. p. 411, 1 44. p. 498, 1 49, 91 96. p. 505, 1 31. Read 7.3, 7.4, 7.5 Ex. p. 514, 1 42, 73 78. p. 522, 1 56. p. 528, 1 34. Read 11.2, 11.3, 11.4 Ex. p. 738, 2 28, 33 41. p. 747, 2 26, 31 42. p. 755, 5 8, 13 16, 23 34. ASSESMENT: Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Systems of Linear Equations. Systems of Non-Linear Equations. Systems of Inequalities. Evaluation Policy: Assessment Grade 70% (includes tests and quizzes) Daily Grade 30% (includes homework and classwork) Page 9 of 11 Read 12.1, 12.2, 12.3 Ex. p. 792, 1 68. p. 798, 1 54. p. 805, 1 68. Read 10.2, 10.8, 10.9 Ex. p. 647, 1 36. p. 701, 1 32. p. 708, 1 46. COMPREHENSIVE FNAL EXAM Exams: There will be at least three major exams. Note that the final exam is comprehensive, i.e., it covers everything since the first day of the course! Makeup exams will only be granted in extreme situations.. Quizzes: There will be short quizzes at least two times a week, except on the first day of class, and the days of the exams.
90 % 100% A 80 % 89 % B 70 % 79% C 60 % - 69% D Below 60% F 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. PROCEDURES: Calculators: It is required to have a TI-83 or TI-84 graphing calculator. NOTE: A TI-89 calculator or any other calculators beside the TI-83 or TI-84 are NOT permitted in this course! The use of calculators will be permitted on some quizzes and exams. Please note that there will be non-calculator quizzes and non-calculator portions of exams. Borrowing calculators from fellow students during exams and quizzes is not permitted. Also, 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 re-explained. 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. Attendance Policy: Although there is no official attendance grade for this course, students are expected to be on time for class and to remain for the entire duration of class. Students who miss class are responsible for finding out from a fellow student what was covered in class and what assignments they missed. It is not the instructor s responsibility to email students what was covered in class on a day which they missed, or to re-teach the material taught in class that day. If students are late for class and the daily quiz has been given, they must re-take the quiz at another time as one of their Page 10 of 11
three makeups. Please keep in mind that there is a direct correlation between class attendance and success in the course. A student s grade tends to suffer significantly when class is missed. Make-up Policy: Make-up exams may or may not be given at the discretion of the instructor. The instructor may allow students to take makeup exams if the following procedures are followed: 1) The instructor has time to administer makeups. 2) The student notifies the instructor prior to the exam, giving a justifiable reason for the absence. 3) The instructor feels that the reason is valid (proof may be requested) 4) Emergencies will be evaluated on an individual basis. NOTE: IT IS THE STUDENT'S RESPONSIBILITY TO PERSONALLY SEE THAT THE INSTRUCTOR IS NOTIFIED PRIOR TO THE EXAM. Major exams missed by the student may be taken within the next three college class days if the student presents an explanation to the instructor in writing. It will be up to the judgment of the instructor if the explanation seems valid. Make-up exams may be given full or partial credit based on the validity of the absence. To take a written make-up, a photo ID must be shown. Students who do not take make-up exams by the deadline forfeit the opportunity. Please note that a makeup final exam must be approved by the dean of Business and Engineering Technologies (see exam section above). Also, students are only allowed three makeup quizzes (see quizzes section above). 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. Page 11 of 11