MATH 1465  Accelerated Precalculus Credit Hours: 5.00 Prerequisites: MATH 1050 or MATH 1050X with grade B or better; or an equivalent college course; or an acceptable score on a placement or prerequisite exam
(formerly MATH 1460)
MATH 1465 combines the content of MATH 1415 and MATH 1435 into one course. Topics include functions and their graphs, polynomial and rational functions, exponential and logarithmic functions, conic sections, trigonometric functions, inverse trigonometric functions, analytic trigonometry, polar coordinates, polar graphs, and vectors.
Billable Contact Hours: 5
Search for Sections Transfer Possibilities Michigan Transfer Network (MiTransfer)  Utilize this website to easily search how your credits transfer to colleges and universities. OUTCOMES AND OBJECTIVES Outcome 1: Upon completion of this course, students will be able to demonstrate a working knowledge of fundamental concepts of functions.
Objectives: The student will:
 Determine domain, range, intercepts, and graph a function by plotting points.
 Determine if a relation is a function.
 Demonstrate a working knowledge of function notation and terminology.
 Perform operations on functions including the difference quotient.
 Demonstrate a working knowledge of the features of the graph of a function.
 Graph functions using transformations. The functions used should include: x^2, x^3, x, 1/x, 1/x^2, square root of x, cube root of x. Use asymptotes to help graph f(x) = 1/x, g(x) = 1/x^2, and their transformations.
 Graph piecewisedefined functions.
Outcome 2: Upon completion of this course, students will be able to demonstrate a working knowledge of polynomial and rational functions.
Objectives: The student will:
 Recognize polynomial and rational functions and determine domain and range of these functions.
 Graph quadratic functions using its vertex, intercepts, and axis of symmetry.
 Graph power functions using transformations.
 Graph and analyze higher order polynomial functions (use end behavior, zeros, and sign tests).
 Find all zeros using Rational Roots Theorem and division of polynomials.
 Use quadratic and polynomial functions in various applications.
 Graph rational functions using asymptotes, zeros, and sign tests.
Outcome 3: Upon completion of this course, students will be able to demonstrate a working knowledge of exponential and logarithmic functions.
Objectives: The student will:
 Demonstrate a working knowledge of the definition of an exponential function.
 Demonstrate a working knowledge of the definition of a logarithm, including the fact that logarithmic and exponential functions are inverses.
 Use the laws of exponents and properties of logarithms to simplify or evaluate expressions.
 Graph exponential and logarithmic functions using transformations.
 Determine domain and range of exponential and logarithmic functions.
 Use the numbers 10 and e as bases for exponential and logarithmic functions, including use of ChangeofBase Formula.
 Use properties of logarithms to expand and condense logarithmic expressions.
 Solve exponential and logarithmic equations.
 Solve applications such as exponential growth/decay and other applications in physical science.
Outcome 4: Upon completion of this course, students will be able to demonstrate a working knowledge of the equations and graphs of conic sections.
Objectives: The student will:
 Find the center and radius of a circle from its equation and graph.
 Find the vertex, focus, and directrix of a parabola from its equation and graph.
 Identify key features of the ellipse and hyperbola including the center, foci, vertices, and asymptotes from their equations and graph.
 Convert equations of conic sections from general form to standard form.
 Identify a conic section from its equation.
 Find an equation of a conic section from its graph.
Outcome 5: Upon completion of this course, students will be able to demonstrate a working knowledge of angles and their measure.
Objectives: The student will:
 Draw angles in degrees and radians.
 Convert angles between radians and degrees.
 Find the arc length of a circle.
 Find the area of a sector of a circle.
 Find coterminal and reference angles.
Outcome 6: Upon completion of this course, students will be able to use and apply the trigonometry of right triangles.
Objectives: The student will:
 Use the sine, cosine, tangent, cotangent, secant, and cosecant ratios to find exact values of trigonometric functions of acute angles.
 Use the Reciprocal, Quotient, and Pythagorean Identities along with Complementary Angle Theorem to find exact trigonometric values of acute angles.
 Solve right triangles and right triangle applications.
 Find the exact values of the trigonometric functions of 30°60°90°.
 Find the exact values of the trigonometric functions of 45°45°90°.
Outcome 7: Upon completion of this course, students will be able to evaluate and graph trigonometric functions.
Objectives: The student will:
 Find the exact values of the six trigonometric functions of any angle using a point on the terminal side of the angle.
 Determine the signs of the trigonometric functions of an angle in a given quadrant.
 Use the reference angle to find the exact value of a trigonometric function.
 Find the exact values of the six trigonometric functions of an angle using its corresponding point on the Unit Circle.
 Know the domain and range of the six trigonometric functions.
 Use coterminal angles, periodic properties, and even/odd properties to find exact values of the trigonometric functions.
 Graph the six trigonometric functions f in the form y=Af(BxC)+D.
 Find an equation of a trigonometric function from its graph.
 Use the Law of Sines and Law of Cosines to solve nonright triangles and applications.
 Find the area of a triangle.
Outcome 8: Upon completion of this course, students will be able to demonstrate knowledge of analytic trigonometry.
Objectives: The student will:
 Know the domain and range of the six inverse trigonometric functions.
 Find the exact values of inverse trigonometric functions.
 Find the exact values of composite trigonometric functions involving inverses.
 Solve trigonometric equations.
 Establish trigonometric identities using fundamental identities and conjugates.
 Use the sum, difference, doubleangle, and halfangle formulas to find exact values and establish identities.
Outcome 9: Upon completion of this course, students will be able to demonstrate knowledge of and use the polar coordinate system.
Objectives: The student will:
 Plot points using the polar coordinate system.
 Convert between polar coordinates and rectangular coordinates.
 Transform equations between polar and rectangular forms.
 Graph polar equations by plotting points.
Outcome 10: Upon completion of this course, students will be able to demonstrate knowledge of and use vectors.
Objectives: The student will:
 Graph vectors.
 Find a position vector.
 Add and subtract vectors geometrically and algebraically.
 Find a scalar multiple of a vector.
 Find the magnitude of a vector.
 Find a unit vector.
 Find the dot product of two vectors.
COMMON DEGREE OUTCOMES (CDO)
 Communication: The graduate can communicate effectively for the intended purpose and audience.
 Critical Thinking: The graduate can make informed decisions after analyzing information or evidence related to the issue.
 Global Literacy: The graduate can analyze human behavior or experiences through cultural, social, political, or economic perspectives.
 Information Literacy: The graduate can responsibly use information gathered from a variety of formats in order to complete a task.
 Quantitative Reasoning: The graduate can apply quantitative methods or evidence to solve problems or make judgments.
 Scientific Literacy: The graduate can produce or interpret scientific information presented in a variety of formats.
CDO marked YES apply to this course: Critical Thinking: YES Quantitative Reasoning: YES COURSE CONTENT OUTLINE
 Functions
 Evaluate a function
 Sum, difference, product, quotient, and composition of two functions
 Difference quotient
 The graph of a function
 Vertical Line Test
 Domain, range, and intercepts
 Symmetry
 Even and odd
 Increasing, decreasing, and constant
 Local and absolute extrema
 Evaluate and graph piecewisedefined functions
 Graph functions using transformations
 Vertical and horizontal shifting
 Reflection
 Stretching and compressing
 Polynomial and Rational Functions
 Quadratic functions
 Graph using vertex, axis of symmetry, and intercepts
 Maximum and minimum value
 Quadratic models and optimization
 Graph power functions using transformations
 Zeros of a polynomial function
 Remainder, factor, and rational root theorems
 Division of polynomials including synthetic division
 Fundamental Theorem of Algebra
 Complex zeros and conjugate pairs
 Graph higherdegree polynomial functions
 End behavior (Leading Term Test)
 Zeros and their multiplicity
 Sign tests
 Graph rational functions
 Domain
 Vertical and horizontal asymptotes (optional: slant asymptotes)
 Graph y = 1/x and y = 1/x^2 using transformations, intercepts, and asymptotes
 Graph other rational functions using intercepts, symmetry, asymptotes, and sign tests
 Exponential and Logarithmic Functions
 Onetoone and inverse functions
 Evaluate exponential functions including base 10 and e
 Evaluate logarithmic expressions including base 10 and e
 Graph exponential and logarithmic functions using domain, intercepts, asymptotes, and transformations
 Properties of logarithms including product property, quotient property, power property, and changeofbase formula
 Solve exponential and logarithmic equations
 Financial and exponential growth and decay models
 Conic Sections
 Graph from standard form of the equation with center/vertex at (h,k)
 Circle  use center and radius
 Parabola  use vertex, focus, and directrix
 Ellipse  use center, vertices, and foci
 Hyperbola  use center, vertices, foci, and asymptotes
 Find an equation from the graph
 Write the standard form of the equation from the general form by completing the square
 Trigonometric Functions
 Angles and their measure
 Draw angles in degrees and radians
 Convert from degrees to radians
 Convert from radians to degrees
 Find length of an arc of a circle
 Find area of a sector of a circle
 Coterminal and reference angles
 The Unit Circle
 Find the exact values of the six trigonometric functions using a point on the unit circle
 Find the exact values of the six trigonometric functions of quadrantal angles
 Properties of the trigonometric functions
 Find the domain and range of the six trigonometric functions
 Find the period of the six trigonometric functions
 Find the signs of the six trigonometric functions in a given quadrant
 Use transformations to graph y = Asin(BxC)+D, y = Acos(BxC)+D, y = Atan(BxC)+D, y = Acsc(BxC)+D, y = Asec(BxC)+D, and y= Acot(BxC)+D
 Analytic Trigonometry
 Inverse trigonometric functions
 Find the domain and range of the 6 inverse trigonometric functions
 Find the exact value of all 6 inverse trigonometric functions
 Composite functions involving inverses
 Write a trigonometric expression as an algebraic expression in u
 Establish trigonometric identities
 Use fundamental identities
 Use a common denominator, factoring, conjugate, or any other algebraic technique
 Sum and difference formulas
 Find exact values
 Establish identities
 Find exact values involving inverse trigonometric functions
 Double and halfangle formulas
 Find exact values
 Establish identities
 Solving trigonometric equations
 Solve equations involving a single trigonometric function
 Solve equations involving multiple trigonometric functions
 Solve trigonometric equations in quadratic form
 Solve trigonometric equations using identities
 Applications of Trigonometric Functions
 Right triangle trigonometric applications
 Find the value of trigonometric functions of acute angles
 Use the Complementary Angle Theorem
 Solve right triangles
 Solve applied problems including angles of elevation and depression
 Law of Sines
 Solve SAA or ASA Triangles
 Solve SSA Triangles
 Solve Applied Problems
 Law of Cosines
 Solve SAS Triangles
 Solve SSS Triangles
 Solve Applied Problems
 Area of a triangle
 Find the Area of SAS Triangles
 Find the Area of SSS Triangles using Heron’s Formula
 Polar Coordinates
 Polar coordinates
 Plot points using polar coordinates
 Convert from polar coordinates to rectangular coordinates
 Convert from rectangular coordinates to polar coordinates
 Graph polar equations by plotting points
 Vectors
 Graph Vectors
 Find a Position Vector
 Add and Subtract Vectors
 Find a Scalar Product of a Vector
 Find the Magnitude of a Vector
 Find a Unit Vector in the direction of the given vector
 Find the dot product of two vectors
Primary Faculty Miller, Faith Secondary Faculty Friday, David Associate Dean McMillen, Lisa Dean Pritchett, Marie
Primary Syllabus  Macomb Community College, 14500 E 12 Mile Road, Warren, MI 48088
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