Honors Pre - Calculus

The central theme of the Honors Pre-Calculus course is functions as models of change. The emphasis is that functions can be grouped into families and that functions can be used as models for real-world behavior. Because linear, exponential, power and periodic functions are more frequently used to model physical phenomena, they are introduced before polynomial and rational functions. Once introduced, a family of functions is compared and contrasted with other families of functions. A large number of the examples and problems that students see in this Pre-Calculus course are given in the context of real-world problems. Indeed, my hope is that students will be able to create mathematical models that will help them understand the world in which they live. The inclusion of non-routine problems is intended to establish the idea that such problems are not only part of mathematics, but in some sense, are the point of mathematics.

Since students usually learn more when they are active, the exercises in a textbook are of central importance. Also, multiple representations encourage students to reflect on the meaning of the material. Therefore, this textbook is guided by the following principles ;

Course Content :

Chapter 1 Functions , Lines and Change
Chapter 2 Functions, Quadratics, and Concavity
Chapter 3 Exponential Functions
Chapter 4 Logarithmic Functions
Chapter 5 Transformations of Functions & Their Graphs
Chapter 6 Trigonometric Functions
Chapter 7 Trigonometry
Chapter 8 Compositions, Inverses, and Combinations of Functions
Chapter 9 Polynomial & Rational Functions
Chapter 10 Vectors and Matrices
Chapter 11 Sequences and Series
Chapter 12 Parametric Equations and Conic Sections

Primary Textbook :

Connally,Eric, etal ..Functions Modeling Change : A Preparation for Calculus, Hoboken : John Wiley & Sons..2004

Calculator :

A classroom set of TI-84 Plus calculators will be available for student use in the classroom. If you want to purchase a calculator for your own personal use or to use at home, I would suggest the TI-84 Plus calculator, the TI-83 Plus calculator, or the TI-89 ( classroom support by the instructor will be limited for the TI-89 calculator).

Notebooks :

Each student should keep a  2 inch , 3-ring notebook for exclusive use in this course. Based upon the design of the course, the student should organize the binder into sections for notes, worksheets, homework assignments, quizzes/tests, bonus assignments, and study guide booklets.

Assignments ;

Assignments must be done in pencil on standard loose-leaf paper. The student's name, assignment section number(s), and a list of problems should appear in the top right-hand corner of the first page of the assignment. A student who uses more than one sheet of paper to complete an assignment should be careful to arrange the papers in proper order and staple them together in the top left-hand corner. Merely writing down the final answer is almost never acceptable. After completing an assignment, final answers should be checked with the back of the textbook (when appropriate). All worksheet assignments will be checked by the teacher to see if the assignment is complete and correct. Assignments related to a given section of material will be reviewed in class on the day following the presentation of that section and must be turned-in, completely corrected, at the beginning of the class period the following day. It is not always possible to address all student questions during class. Students who are encountering difficulty should seek extra help from the teacher. Assignments will be graded on a 100-point scale (A= 93-100, B= 85-92, C= 77-84 , D =70-76 , F= 0-69). Any assignment that is not turned-in will receive a grade of zero. With rare exceptions, assignments consisting only of answers will also receive a grade of zero. Unless there are extenuating circumstances, late assignments will also receive a grade of zero.

Quizzes/Tests :

A quiz (announced or unannounced) will occur every mid-chapter. There will be a chapter test at the conclusion of every chapter.

Study Guide Booklet :

A booklet working with the types of problems encountered in that chapter will be given at the beginning of every chapter. These problems should be completed as each section is given and mastered. Each booklet will be collected on the test day for that chapter and given an appropriate grade.

Grade ( per 6 weeks ) :

Tests (50% )  , Study Guide ( 10 %) , Quizzes ( 10%) , Homework ( 20%) , Notebooks ( 10%)

Honors Pre Calculus  90 - Day Plan

          Day

       Section

        Goal

Description

             1

           1.1

          1.01

Functions & Function Notation

             2

           1.2  

           1.3                            

          1.01

          1.01

Rate of Change

Linear Functions

             3

           1.4

          2.01

Formulas for Linear Functions

             4

           1.5

          2.03

Geometric Properties of Linear Functions

             5

           1.6

          2.03

Fitting Linear Functions to Data

             6

          

 

Review (Chap. 1)

             7

 

 

Test (Chap. 1)

             8

           2.1

           2.2

1.01  , 2.08

1.01 , 2.08

Input & Output

Domain & Range

             9

           2.3

2.01 , 2.08

Piecewise-Defined Functions

             10

           2.4

           2.5

2.01 , 2.04

2.01

Inverse Functions

Concavity

             11

           2.6

1.02         

Quadratic Functions

             12

 

 

Review (Chap. 2)

             13

 

 

Test (Chap. 2)

             14

           3.1

2.01 , 2.03

Introduction to the Family of Exponential Functions

             15

           3.2

2.01 , 2.03

Comparing Exponential & Linear Functions

             16

           3.3

2.01 , 2.03

Graphs of Exponential Functions

             17

           3.4

2.01 , 2.03

Continuous Growth & the Number e

             18

 

 

Review (Chap. 3)

             19

 

 

Test (Chap. 3)

             20

           4.1

2.01 , 2.03

Logarithms & Their Properties

             21

           4.2

2.01,2.03

Logarithms & Exponential Models

             22

           4.3

2.01, 2.03

The Logarithmic Function

             23

          

 

Intro. Review Booklet

Partial Fractions (linear)

             24

 

 

Review (Chap. 4)

             25

 

 

Test (Chap. 4)

             26

 

 

Review for 1st 6-weeks EXAM

             27

 

 

EXAM (Ch. 1-4)

             28

           5.1

2.01 , 2.03

Vertical & Horizontal Shifts

             29

           5.2

2.01 , 2.03

Reflections & Symmetry

Partial Fractions (quad)

             30

           5.3

2.01 , 2.03

Vertical Stretches & Compressions

             31

           5.4

2.01 , 2.03

Horizontal Stretches & Compressions

             32

           5.5

2.01 , 2.03

The Family of Quadratic Functions

             33

 

 

Review (Chap. 5)

             34

 

 

Test (Chap. 5)

             35

 

 

Unit Circle

             36

           6.1

2.02

Introduction to Periodic Functions ;

UC Quiz # 1

             37

           6.2

2.02

The Sine & Cosine Functions :

UC Quiz # 2

             38

           6.3

2.02

Radians :

UC Quiz # 3

             39

           6.4

2.02

Graphs of the Sine & Cosine ;

UC Quiz # 4

             40

           6.5

2.02

Sinusoidal Functions ;

UC Quiz # 5

             41

           6.6

2.02

Other Trigonometric Functions

             42

           6.7

2.02

Inverse Trigonometric Functions

             43

 

 

Review (Chap. 6)

             44

 

 

Test (Chap. 6)

             45

           7.1

2.02

General Triangles :

Laws of Sine/Cosine

             46

           7.2

2.02

Trigonometric Identities

             47

           7.3

2.02

Sum & Difference Formulas for Sine & Cosine

             48

           7.4

2.02

Trigonometric Models

             49

           7.5

2.05

Polar Coordinates

             50

           7.6

2.02 , 2.05

Complex Numbers & Polar Coordinates

             51

 

 

Review (Chap. 7)

             52

 

 

Test (Chap. 7)

             53

           8.1

2.04

Composition of Functions

             54

           8.2

2.04

Inverse Functions

             55

           8.3

2.04

Combinations of Functions

             56

 

 

Review (Chap. 8)

             57

 

 

Test (Chap. 8)

             58

 

 

Review for 2nd 6-weeks EXAM

             59

 

 

EXAM (Ch. 5-8)

             60

           9.1

2.01

Power Functions

             61

           9.2

2.01

Polynomial Functions

             62

           9.3

2.01

The Short-Run Behavior of Polynomials

             63

           9.4

2.01

Rational Functions

             64

           9.5

2.01

The Short-Run Behavior of Rational Functions

             65

           9.6

2.01 , 2.03

Comparing Power, Exponential & Log Functions

             66

           9.7

2.01 , 2.03

Fitting Exponentials & Polynomials to Data

             67

 

 

Review (Chap. 9)

             68

 

 

Test (Chap. 9)

             69

           10.1

1.03

Vectors

             70

           10.2

1.03

The Components of a Vector

             71

           10.3

1.03

Application of Vectors

             72

           10.4

1.03

The Dot Product

             73

           10.5

1.03

Matrices

             74

 

 

Review (Chap. 10)

             75

 

 

Test (Chap. 10)

             76

           11.1

2.07

Sequences

             77

           11.2

2.07

Defining Functions Using Sums : A.S.

             78

           11.3

           11.4

2.07

2.07

Finite Geometric Series

Infinite Geometric Series

             79

          

 

Review (Chap. 11)

             80

 

 

Test (Chap. 11)

             81

           12.1

2.06

Parametric Equations

             82

           12.2

2.06, 1.02

Implicitly Defined Curves and Circles

             83

           12.3

           12.4

2.06 , 1.02

2.06 , 1.02

Ellipses

Hyperbolas

             84

           12.5

2.06

Hyperbolic Functions

Review (Chap. 12)

             85

 

 

Test (Chap. 12)

             86

 

 

Review (EXAM)

Calculus  Worksheet

             87

 

 

Review (EXAM)

Calculus Worksheet

             88

 

 

EXAM

             89

 

 

EXAM

             90

 

 

EXAM