Pre-Calculus with Trigonometry
Recommended Prerequisite: Algebra I, Geometry, & Algebra II
Grades Offered: 9-12
Credit: 1/2-1
SDE Course Code: 3126
MNPS Course Code: MTH4413
Course Description:
Pre-Calculus with Trigonometry deals with the topics of vectors, analytic geometry, theory of equations, logic, and limits. Included in the course is an in-depth study of the straight line, the circle, the parabola, the ellipse, the hyperbola, higher degree equations, sequences and series, and the fundamental theorem of algebra. Also included is the study of the properties of the trigonometric functions, their graphs and their applications to various mathematical problems including the solution of triangles. Trigonometry has applications in surveying, navigation, and construction work.
Outline of Content:
· The student will model real-world phenomena.
° Modeling real-world phenomena using techniques of data analysis.
° Recognizing and applying mathematical models of linear, quadratic, exponential, logarithmic and trigonometric functions.
° Using scatterpolt residuals and correlation coefficients to determine whether a model is appropriate.
° Using models when appropriate to draw conclusion or make predictions.
· The student will understand functions.
° Sketching the graphs of the basic functions.
° Graphing transformations and combinations of transformations for all basic functions.
° Analyzing a function by decomposing it into simpler functions.
° Determining if a function is even, odd, or neither.
° Analyzing functions.
° Solving inequalities using an appropriate technology.
° Introducing the concept of the limit of a function.
° Applying the limit of a function to find the slope of a line tangent to a curve.
° Applying limits to develop the concept of continuity.
° Determining an equation of a rational function from a written description.
· The student will explore exponential and logarithmic functions.
° Defining and using the logarithmic function as the inverse of the exponential function.
° Sketching the graphs of exponential and logarithmic functions.
° Solving exponential and logarithmic equations modeling real-world problems.
· The student will learn applications of Trigonometry.
° Defining six circular functions.
° Sketching graphs of the six trigonometric functions involving period change, amplitude change, phase shift, and vertical shift.
° Using trigonometric functions to model periodic phenomena.
° Using graphs to develop and verify trigonometric identities.
° Finding values of inverse trigonometric functions while applying appropriate domain and range restrictions.
° Solving trigonometric equations and inequalities either algebraically or using an automatic grapher.
· The student will investigate sequences and series.
° Deriving the Law of Sines and the Law of cosines and applying them to solve problems.
° Deriving and applying the formulas for the area of a triangle and the sector of a circle.
° Understanding the relationship between measurements in radians and degrees.
° Applying radian measures in problems related to linear and angular velocity.
° Understanding and applying vectors to solve real world problems.
° Representing complex numbers in both rectangular and polar form.
° Applying the trigonometric form of complex number in calculations.
° Proving and applying DeMoivre’s Theorem to find roots and posers of complex numbers.
· The student will explore sequences and series.
° Demonstrating an understanding of sequences by representing them recursively and explicitly.
° Using sigma notation to represent a series.
° Determining whether a given series converges or diverges.
° Finding the sum of an infinite series that converges.
° Finding the sum of an infinite geometric series.
· The student discover conic sections.
° Applying equations and graphs of conic sections to model real-world phenomena.
Standards Links:
MNPS Standards:
http://www.mnps.org/PageFactory.aspx?PageID=3403
State Standards:
http://www.state.tn.us/education/ci/cistandards2001/math/cimath.htm
TEXTBOOK :
Gordon-Holliday, et al., Advanced Mathematical Concepts: Pre-Calculus with Applications, 3rd Edition, 2004, Glencoe (basal)
Online Textbook Activities:
http://www.glencoe.com/sec/math/precalculus/amc_04/
Recommended and/or Required Resources
TI 83+ Graphing Calculator/ TI-84+ Graphing Calculator
CBR2 or CBL2 with probes
A variety of manipulatives: graph paper, rulers, protractors, two-color counters, fraction bars, centimeter cubes or linking cubes, geoboards, miras, pattern blocks, algebra tiles, meter sticks, etc.