Advanced Math
Description and Outline
Course Overview: This course is designed for the college bound mathematics student and is intended to provide trigonometry and pre-calculus skills that will prepare the student for entry into calculus or pre calculus at the college level.The student will study mathematical analysis of functions and limits and topics leading into calculus.In addition, the student will study the full scope of trigonometric functions as well as logarithmic and exponential functions.
Text: Pre Calculus with Limits, Houghton Mifflin 2001
Teacher Expectations:
1.Students will be expected to attend class on a regular basis
2.Homework must be completed and turned in on time.No late work will be accepted except in cases of excused absences.In such cases of excused absences the student will be given two days to complete work missing as a result of the absence.Time extensions will be given on a case by case basis.
3.Students must furnish their own paper, pencil.Calculators are optional but recommended.
4.Students will exhibit respect for others at all times.
5.Students will be encouraged to participate in class discussions and communicate with the teacher any difficulties with comprehension of the material covered.
Grading:
Homework: 40% per quarter
Tests/Quizzes: 60% per quarter
Each Quarter: 40% of the semester grade
Semester Test: 20% of the semester grade
Course Outline:
1.Linear Relations and Functions
a.Relations and functions
b.Composition and inverses of functions
c.Linear functions and inequalities
d.Distance and slope
e.Parallel and perpendicular lines
2.Systems of Equations and Inequalities
a.Solving systems of equations
b.Introducing matrices
c.Determinants and multiplicative inverses of matrices
d.Solving systems of equations by using matrices
e.Solving systems of inequalities
f.Linear programming
3.The Nature of Graphs
a.Symmetry
b.Families of graphs
c.Inverse functions and relations
d.Rational functions and asymptotes
e.Graphs of inequalities
f.Tangent to a curve
g.Graphs and critical points of polynomial functions
h.Continuity and end behavior
4.Polynomial and Rational Functions
a.Polynomial functions
b.Quadratic equations and inequalities
c.The remainder and factor theorems
d.The rational root theorem
e.Locating the zeros of a function
f.Rational equations and partial functions
5.The Trigonometric Functions
a.Angles and their measure
b.Central angles and arcs
c.Circular functions
d.Trigonometric functions of special angles
e.Right Triangles
f.The law of sines
g.The law of cosines
h.Area of triangles
6.Graphs and Inverses of the Trigonometric Functions
a.Graphs of the trigonometric functions
b.Amplitude, period, and phase shift
c.Graphing trigonometric functions
d.Inverse trigonometric functions
e.Principal values of the inverse trig functions
f.Graphing inverses of trigonometric functions
g.Simple harmonic motion
7.Trigonometric Identities and Equations
a.Basic trigonometric identities
b.Verifying trigonometric identities
c.Sum and difference identities
d.Double-Angle and half-angle
e.Solving trigonometric equations
8.Exponential and Logarithmic Functions, Limits, Derivatives, and Integrals
a.Rational exponents
b.Exponential functions
c.Log functions, e, natural log
d.Exponential and logarithmic equations
e.Limits
f.Derivatives and differentiation
g.Area under the curve
h.Integration
i.The fundamental theorem of calculus
Pacing:
Units 1-2: first nine weeks
Units 3-4: second nine weeks
Units 5-6: third nine weeks
Units 7-8: fourth nine weeks
pacing is dependent upon the progress of the students