Paramus Public Schools, New Jersey

Mathematical Analysis CP

Course Outline

Department: /

Mathematics

/ Date : / September 2005
Course: /

Mathematical Analysis CP

/ Rev Date: / September 2005
Level: / 10 , 11 , 12 Full Year
Prerequisite / High level of performance in Algebra 2

This course description incorporates the New Jersey Core Curriculum Content Standards for Mathematics - Standards and Strands 2003 appropriate for grade 12: 4.2, 4.5

I COURSE DESCRIPTION

This course builds on the mathematical foundations developed in Algebra 1 and 2, and Geometry; and exposes students to other useful mathematics – conics; exponentials and logarithms; complex numbers; and Trigonometry (including graphs, equations, identities and applications. A Mathematics Analysis CP course will well prepare students for the Calculus CP course.

II COURSE OBJECTIVES

This course exposes students to other useful mathematics – conics (focusing mirrors); exponentials and logarithms (sound levels, earthquake measurements, growth and decay, financial calculations); complex numbers (many applications); and many topics in trigonometry.

III MAJOR CONCEPTS AND TOPICS

  1. Polynomial and Rational Functions
  2. Exponential and Logarithmic Functions
  3. Trigonometry
  4. Trigonometric Graphs
  5. Solving Trigonometric Equations
  6. Trigonometric E\Identities and Proof
  7. Trigonometric Applications
  8. Analytic Geometry
  9. Systems and Matrices
  10. Statistics and Probability

IV Student Skill Objectives

1.  Polynomial and Rational Functions

1.1.  Polynomial Functions

1.2.  Real Zeros

1.3.  Graphs of Polynomial functions

1.4.  Rational Functions

1.5.  Complex Numbers

2.  Exponential and Logarithmic Functions

2.1.  Radicals and Rational Exponents

2.2.  Exponential Functions

2.3.  Applications of Exponential Functions

2.4.  Common and Natural Logarithmic Graphs and Functions

2.5.  Properties and Laws of Logarithms

2.6.  Solving Exponential and Logarithmic Equations

2.7.  Exponential, Logarithmic and Other Models

3.  Trigonometry

3.1.  Right triangle Trigonometry

3.2.  Trigonometric Applications

3.3.  Angles and Radian Measure

3.4.  Trigonometric Functions

3.5.  Basic Trigonometric Identities

4.  Trigonometric Graphs

4.1.  Graphs of Sine, Cosine and Tangent

4.2.  Graphs of Cosecant, Secant, and Cotangent

4.3.  Periodic Graphs and Amplitude

4.4.  Periodic Graphs and Phase Shifts

5.  Solving Trigonometric Equations

5.1.  Graphical solutions to Trigonometric Equations

5.2.  Inverse Trigonometric Functions

5.3.  Algebraic Solution of Trigonometric Equations

5.4.  Simple Harmonic Motion and Modeling (Optional)

6.  Trigonometric Identities and Proof

6.1.  Identities and Proof

6.2.  Addition and Subtraction Identities

6.3.  Other Identities

6.4.  Using Trigonometric Identities

7.  Trigonometric Applications

7.1.  Law of Cosines

7.2.  Law of Sines

8.  Analytic Geometry

8.1.  Ellipses

8.2.  Hyperbolas

8.3.  Parabolas

8.4.  Translations

V Evaluation Procedures

Evaluation of success will be based upon tests, quizzes, and examinations.

VI Sugested Materials

“Precalculus – A Graphing Approach” Hungerford et al, Holt Rinehart Winston, 2006

This document is for use by current faculty and current students of Paramus School District, Paramus, New Jersey. No part of this document may be used or reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic. mechanical, photocopying, recording, scanning, or otherwise, without the prior written permission of the Board of Education, Paramus School District, 145 Spring Valley Road Paramus, New Jersey, 07652.

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