Advanced Functions & Modeling (AFM)
Advanced Functions & Modeling is a course that was developed to bridge the courses of Algebra 2 and Honors Pre-Calculus. The purpose of this course is to construct a solid foundation in the content area that will be needed for success in this course and in the Honors Pre-Calculus course. The content of this course integrates functions, statistics, and trigonometry and apply the algebra and geometry that students have studied in previous years. Sequences, counting problems and other topics from discrete mathematics are also found, and this course contains many topics of a traditional pre-calculus course. The AFM course is a classic example of how a single mathematics course can involve all of the major areas of mathematics.
As the content described in the preceding paragraph indicates, there is a wider scope in this AFM course. The topics are not isolated as separate units of study of enrichment. They are employed to motivate, justify, extend, and otherwise enhance important concepts of functions, statistics, and trigonometry. A real-world orientation guides the teaching method and allows the student to work out problems to connect to real life applications. The use of up-to-date technology is integrated throughout the course. The course organization is designed to maximize the acquisition of both skills and concepts. Ideas introduced in a lesson are reinforced through review questions in succeeding lessons. This constant review allows students several nights to learn and master important concepts and skills.
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Chapter 1 |
Sets & Set Notation |
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Chapter 2 |
Statistics and Data Analysis |
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Chapter 3 |
Probability (1) |
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Chapter 4 |
Probability (2) |
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Chapter 5 |
Trigonometric Functions |
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Chapter 6 |
Unit Circle Trigonometry |
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Chapter 7 |
Trigonometric Graphing & Identities |
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Chapter 8 |
Sequences & Series |
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Chapter 9 |
Exponential Functions & Logarithmic Functions |
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Chapter 10 |
Extras ; Vectors, Matrices, Transformations, Curves of Best Fit, etc. |
90 - Day Plan
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Day |
Section |
Description |
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1 |
1.1 |
Introduction : Summation Notation |
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2 |
1.2 1.3 |
Factorials Sets |
|
3 |
1.4 1.5 |
Number
Systems Functions; Composition of Functions; Inverse Functions Distance, Midpoint, Slope, Standard Linear Equations |
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4 |
1.6 |
Quiz ; Review Sheet Chapter 1 |
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5 |
|
Review ( Chapter 1) |
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6 |
|
Test (Chapter 1) |
|
7 |
2.1 |
Data Types; Bar Graphs, Histograms, Freq. Tables, Circle Graphs |
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8 |
2.2 |
Measures of Central Tendencies |
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9 |
2.3 |
Boxplots & 5-Number Summaries |
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10 |
2.4 |
Measures of Variability |
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11 |
2.5 |
The Normal Distribution |
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12 |
|
Review #1 ; Review # 2 ; Quiz (2.1-2.5) |
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13 |
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Review ( Chapter 2) |
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14 |
|
Test( Chapter 2) |
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15 |
3.1 |
Permutations |
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16 |
3.2 |
Permutations |
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17 |
3.3 |
Combinations ; Quiz ( 3.1-3.3) |
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18 |
|
Review (Chapter 3) |
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19 |
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Test (Chapter 3) |
|
20 |
4.0 |
Introduction to Probability |
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21 |
4.1 |
Probability |
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22 |
4.2 |
Independent and Dependent Events |
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23 |
4.3 |
Exclusive and Inclusive Events ; Quiz (ch. 4) |
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24 |
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Review (Chapter 4) |
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25 |
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Test (Chapter 4) |
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26 |
|
Review for Exam ; Intro. to Review Booklet |
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27 |
|
Review for Exam (Chapters 1-4) |
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28 |
|
EXAM (Chapters 1-4) |
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29 |
5.0 |
Introduction to Trigonometry |
|
30 |
5.1 |
The Pythagorean Theorem |
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31 |
5.2 |
Special Right Triangles |
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32 |
5.3 |
Right Triangle Trigonometry |
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33 |
5.4 |
Finding Angles of Right Triangles |
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34 |
5.5 |
Angles of Elevation & Depression |
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35 |
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Review (5.0-5.5) ; Quiz ( 5.0-5.5) |
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36 |
5.6 |
The Law of Sines |
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37 |
5.7 |
The Law of Cosines |
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38 |
5.8 |
Areas of Triangles ( Trig. Approach) |
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39 |
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Quiz (5.5-5.8) ; Review (Chapter 5) |
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40 |
|
Review (Chapter 5) |
|
41 |
|
Test (Chapter 5) |
|
42 |
6.1 |
Introduction to the Unit Circle |
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43 |
6.2 |
Radians on the Unit Circle ; UC Quiz #1 |
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44 |
6.3 |
Arc Length & Area of a Sector ; UC Quiz #2 |
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45 |
6.4 |
Converting Degrees to Radians & Radians to Degrees ; UC Quiz #3 |
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46 |
6.5 |
Summarizing Six Trigonometric Functions ; UC Quiz #4 |
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47 |
|
Mini-Review (6.1-6.5) ; Quiz (6.1-6.5) |
|
48 |
6.6 |
Special Angles |
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49 |
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Review (Chapter 6) |
|
50 |
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Test (Chapter6) |
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51 |
7.1 |
Trigonometric Graphs |
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52 |
7.2 |
Amplitude, Period, Phase Shifts |
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53 |
7.3 |
Graphing Practice |
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54 |
7.4 |
Basic Trigonometric Identities |
|
55 |
7.5 |
Verifying Trigonometric Identities |
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56 |
|
Review (Chapter 7) |
|
57 |
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Test (Chapter 7) |
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58 |
|
Exam Review (Ch. 5-7) |
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59 |
|
EXAM (Chapters 5-7) |
|
60 |
8.1 |
Arithmetic Sequences |
|
61 |
8.2 |
Geometric Sequences |
|
62 |
8.3 |
Infinite Sequences |
|
63 |
8.4 |
Sum of Infinite Series |
|
64 |
8.5 |
Sigma Notation & the nth Term |
|
65 |
8.6 |
Binomial Theorem ; Pascal's Triangle |
|
66 |
|
Mini-Review ; Quiz (8.1-8.6) |
|
67 |
|
Review (Chapter 8) |
|
68 |
|
Test (Chapter 8) |
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69 |
9.1 |
Rational Exponents |
|
70 |
9.2 |
Exponential Functions |
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71 |
9.3 |
Logarithmic Functions |
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72 |
9.4 |
Common Logarithms ; Quiz (9.1-9.3) |
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73 |
9.5 |
Exponential Equations |
|
74 |
9.6 |
Growth & Decay Formulas |
|
75 |
|
Review (chapter 9) |
|
76 |
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Test (Chapter 9) |
|
77 |
|
Work on Review Booklet |
|
78 |
|
EMPT Review |
|
79 |
|
EMPT Test |
|
80 |
Extra #1 |
Vectors |
|
81 |
Extra #2 |
Matrices |
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82 |
Extra #3 |
Transformations of Basic Graphs |
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83 |
|
Transformations of Basic Graphs ( continued) |
|
84 |
Extra #4 |
Graphical Interpretation of Polynomials (roots, bounds, etc) |
|
85 |
Extra #5 |
Graphical Interpretation of Rational Functions (roots, VA, HA, etc) |
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86 |
|
Graphical Interpretation of Rational Functions (continued) |
|
87 |
|
Quiz( extra topics 1-5) |
|
88 |
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|
89 |
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Final Exam |
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90 |
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