Expectations for Math Analysis 222
Upper Dublin High School
Updated for the 2014-2015 school year
Mrs. Bech's key to review for FINAL EXAM 2015











The textbook, as well as various online supplemental materials, is available online: http://www.glencoe.com/sec/math/precalculus/amc_04/index.php/pa
click on the ‘online student edition’ link
type in this password: BFECD0861B


In the first semester those students taking 222 Math Analysis will focus on the following major areas:

Review of Linear Relations and Functions (Chapter 1)
  1. Relations and Functions (1-1)
  2. Graphing Linear Functions (1-3)
  3. Writing Linear Equations (1-4)
  4. Writing Equations of Parallel and Perpendicular Lines (1-5)
*Note: Since all of these topics are review, the entire chapter can be completed in 5 days)


one small type I think in the first slide, can you find it?





The Nature of Graphs (Chapter 3)
Symmetry and Coordinate Graphs (3-1)
HW 3-1 pg. 134 #15-25 odd, 31-35 odd




Families of Graphs (3-2)
HW 3-2 pg. 143 #13-33 odd

GREAT Sheet below with all the rules (from a diff textbook)


Piecewise Functions (1-7)
HW 1-7 #11-25 odd




Quiz on 3.1 3.2 and 1.7
Review Sheet:


Continuity and End Behavior (3-5)
  1. continuity test (worth mentioning, but not emphasizing)
  2. types of discontinuity
  3. increasing, decreasing, and constant functions
  4. end behavior
HW 3-5 pg. 166 #13-31 odd



Critical Points and Extrema (3-6) (note: NO derivatives)
HW 3-6 pg. 177 #13-31 odd






Graphs of Rational Functions (3-7)
  1. Holes
  2. Horizontal and Vertical Asymptotes
  3. Slant Asymptotes (review long division as necessary

HW 3-7 pg. 186 #15-29 odd

this powerpoint is a nice bridge between chapter 3 and chapter 4 notes

awesome awesome awesome sheet below from Dillon , thanks!!!!



Test Review Worksheet with ANSWERS(from 2013)!


Key Strokes for TI 83/84 calculators - Graphing




Polynomial Functions (Chapter 4)
Polynomial Functions (4-1)
HW 4-1 pg. 210 #15-47 odd, do not do 21 or 31


Quadratic Equations (4-2)
HW 4-2 pg. 219 #13-33 odd



Remainder and Factor Theorems (4-3)
HW 4-3 pg. 226 #15-33 odd


Rational Root Theorem (4-4)
HW 4-4 pg. 234 #11-21 odd and #25



Review and Key to 2014 please note number 8 asked for rational roots and I found a root on calculator but it wasn't rational






this is the key to 2013 review sheet

*First Marking Period Project: Create and Solve a ‘real’ polynomial function problem
Chapter 4 Review Sheet (scratch out the 4.5 problems)

Answers to Chapter 4 Review Sheet






The Trigonometric Functions (Chapter 5)
Angles and Degree Measure (5-1)
pg. 281, #’s 18-57 multiples of 3, 58, 78




Trig Ratios in Right Triangles (SOHCAHTOA) (5-2)
pg. 288, #’s 10-22 all, 30, oldie but goodie #37, 38



Trig Functions on the Unit Circle (5-3)
pg. 296, #’s 14-21 all, 23-43 odd, 60

Applying Trig Functions (5-4)
Find the missing side of triangle
Angles of elevation/depression
Inscribed polygons



pg. 302, #’s 11-19 odd, 20, 21, 25, 26, 29 and 30




Solving Right Triangles (5-5)
Find the missing angle of triangle
Application problems
pg. 309, #’s 15-33 multiples of 3, 46, 51 and 52



Law of Sines (5-6)

pg. 316, #’s 11-27 odd, 32, 33 and 38
typo in this , find it :)



Ambiguous Case (5-7)

pg. 324, #’s 11-29 odd, 38, 46

Law of Cosines (5-8)



pg. 331, #’s 11-25 odd, 30, 35

Sample Assignments:
external image pdf.png 5.1 Angles and Degree measure0001.pdf
external image pdf.png 5.2 Trig Ratios in Right Triangles0001.pdf
external image pdf.png 5.3 Trig functions on Unit Circle0001.pdf

Chapter 5 Review Sheet and Key




Chapter 6: Graphs of Trigonometric Functions

Angles and Radian Measure (6-1)
pg. 348, #’s 17 – 49 odd, 62, 71


Linear and Angular Velocity (6-2)
pg. 355, #’s 15-33 odd, 44, 45



Review of some chapter 5 topics and first two sections of ch 6




Graphing Sine and Cosine Functions (6-3)
pg. 364, #’s 19-43 every other odd, 59, 68


Amplitude and Period of Sine and Cosine Functions (6-4)
pg. 373, #’s 17-22 all, 23-33 odd, 37-51 odd, 55 if you have a graphing calculator, 70 (some Algebra II revisited)
Translations of Sine and Cosine (6-5)
pg. 383, #’s 21-33 odd, 53





Modeling Real World Data with Sinusoidal Functions (6-6)
pg. 391, #’s 7-12 all, 16
sinusoidal regression
sound wave, hours of sunlight, tidal motions

Graphing Other Trig Functions (6-7)

pg. 401, #’s 29-34 all except for #32
tangent, cotangent, secant, cosecant

Trigonometric Inverses and Their Graphs (6-8)

pg. 410, # ‘s 15, 22-31 all
Arcsine, Arccosine, Arctangent

*with this chapter, it is recommended that a graphing calculator not be allowed on quizzes or tests, but a scientific calculator could be used for sections 6-1, 6-2, and 6-6, at the teacher’s discretion



Midterm REVIEW


there's a typo in this answer key? What is it?




Trigonometric Identities and Equations (Chapter 7)
Basic Trig Identities (7-1)

(make sure to memorize all the identities)
pg. 428, #’s 25-53 odd, 60, 61, 68


Verifying Trig Identities (7-2)

pg. 434, #’s 13-27 odd, 47, 49, 50, 53




Sum and Difference Identities (7-3)

pg. 443, #’s 15-42 multiples of 3, 49, 50, 51, 52, 54, 56, 58, 64 #46 turned in on a separate sheet of paper (not on hw paper) to be turned in as an extra credit opportunity










Double-Angle and Half-Angle Identities (7-4)

pg. 455, #’s 15-35 odd, 41, 47, 48


Solving Trig Equations (7-5)

pg. 459, #’s 18-51 multiples of 3, 69, 72,




REVIEW for Chapter 7(1) and key





Polar Coordinates and Complex Numbers :
Chapter 9 (for 2015 we will only be doing sections 9.1-9.3)
Polar Coordinates (9-1)

pg. 558, #'s 17-43 odd, 56-59, ohhhhh do you remember how to do 62? try it and let me know :)

Graphs of Polar Equations (9-2)

pg. 565, #'s 11-16 all, 41, 44 (do 44 without a calculator)

Polar and Rectangular Coordinates (9-3)

pg. 572, #'s 15-39 odd, also number 38, 47, 51 (do not use a calculator for 51)



Review for 9.1-9.3 key

don't forget typo/mistake on number 9, r = four root 2


Simplifying Complex Numbers (9-5)

pg. 583, #'s 13-35 odd
Complex Plane and Polar Form of Complex Numbers (9-6)

pg. 590, #'s 17-41 odd, 56, 57, do you remember how to do number 58? lmk :)
Products and Quotients of Complex Numbers in Polar Form (9-7)

pg. 596, #'s 11-21 odd, 38

REVIEW problems
pg. 608, #'s 13, 15, 17, 18, 20, 24, 22, 27, 28, 36, 38, 40, 41, 45, 52, 53 and 57



HERE ARE SOME REVIEW PROBLEMS FROM STUDENTS:
(if you notice anything that needs to be corrected please let me know)







Powers and Roots of Complex Numbers (9-8)

pg. 605, #'s 15, 21, 29, 41, 46
i. DeMoivre’s Theorem
ii. Complex Roots Theorem
*should take approximately 15 to 20 school days
Third Marking Period Project: Creating a picture using Graphs of Polar Equations

Combinatorics and Probability (Chapter 13)

Practice worksheets for Ch 13:












Permutations and Combinations (13-1)
pg. 843, #'s 29, 37, 40-45 all, 47


Permutations with Repetitions and Circular Permutations (13-2)
pg. 849, #'s 5-31 odd

Probability and Odds (13-3)
pg. 856, #'s 13-37 odd

Probability of Compound Events (13-4)
  1. mutually exclusive vs. inclusive
  2. dependent vs. independent
pg. 864, #'s 17-37 odd

Conditional Probability (13-5)
pg. 872, #'s 15-37 odd
Solutions:

Statistics and Data Analysis (Chapter 14)
The Frequency Distribution (14-1
frequency table
histograms

Measures of Central Tendency (14-2)
mean, median, mode, max, min
stem and leaf plots

Measures of Variability (14-3)
mean deviation
standard deviation
quartiles
box and whiskers plot


Normal Distribution (14-4)
percentiles
standard normal curve



ModelingReal-World Data with Linear Functions (1-6)
HW: pg. 42, 6,7, 8, 10 and 11 (part c and d only)
Scatterplots
Writing/Graphing linear equations (remember 1-3 and 1-4)

Modeling Real-World Data w other Functions (11.7 is optional)
HW : pg. 745, #'s 14, 16a, 17 and 18



Conics (Chapter 10)
(note: eccentricity should be discussed for all 4 conic sections at some point during the chapter, Latus Rectum should be discussed for Parabolas)

Conic Sections:
Powerpoint notes for 10.2-10.5:

Circles (10-2)
pg. 628, #'s 23, 25, 27, 31, 35-39 all
Ellipses (10-3)
pg. 638, #'s 17, 19, 23, 27, 31-41 odd
Hyperbolas (10-4)
pg. 650, #'s 17-27 odd, 31-41 odd
Parabolas (10-5)
pg. 659, #'s 13-21 odd, 25-31 odd
Identify conic sections
pg. 667, #'s 13-23 odd
Systems of Second-Degree Equations and Inequalities (10-8)
pg. 683, #'s 13, 15, 19, 21, 25

here's a great website with a lot of examples and ANSWERS
http://cdn.kutasoftware.com/Worksheets/Alg2/Classifying%20Conic%20Sections.pdf


Some good review questions:
pg. 688, #'s 14, 15, 18, 24, 28 and 37
  1. Circles (10-2)
  2. Ellipses (10-3)
  3. Hyperbolas (10-4)
  4. Parabolas (10-5)
  5. Systems of Second-Degree Equations and Inequalities (10-8)

Exponential and Logarithmic Functions (Chapter 11)
This document below is nice because it gives explanations of a variety of topics
covered in exponents and logarithms:



Real Exponents (11-1)
pg. 200, #'s 21-59 odd



Exponential Functions (11-2)
pg. 708, #'s 11-21 odd



i. domain and range
ii. graphs, including transformations




Do you remember?






The Number e (11-3)
pg. 715, #'s 7, 9, 18

. Logarithmic Functions (11-4)
i. properties of logs
ii. log equations and inequalities

Common Logs (11-5)
pg. 730, #'s 35-57 odd
i. change of base
ii. solving exponential equations


Natural Logarithms (11-6)
pg. 736, #'s 19-39 odds
Applications of Exponential and Log Functions (as encountered in the chapter)
i. Compound Interest (finite number and continuously compounded)

ii. Exponential Growth and Decay (in terms of ‘e’)
iii. Newton’s Law of Cooling (optional)

  1. pH Level (optional)
*should take approximately 10 to 15 school days

END OF SECOND SEMESTER



Have a great summer!!!!!!!



















SENIOR POEM 2013


Inspirational Video
http://www.youtube.com/watch?v=7s8U1kSMm8g

Sine and Cosine Graph Transformations Applet: http://curvebank.calstatela.edu/cs390trig/cs390trig.htm

Need more Graph Paper? Click on the following link:http://incompetech.com/graphpaper/plain/

Online TEXT:


Go to this webpage: http://www.glencoe.com/sec/math/precalculus/amc_04/index.php/pa



click on the ‘online student edition’ link



type in this password: BFECD0861B

Assignments:




Enrichment Project:
external image vnd.openxmlformats-officedocument.wordprocessingml.document.png analysis polar equations project 2012.docx
Here are Chapter 9 worksheets and keys:
external image pdf.png chapter 9 worksheets.pdf
external image pdf.png keys to chapter 9 worksheets.pdf

Midterm Review Key

tan one:
external image pdf.png tan copy of review sheet key.pdf
below are the worksheets #'s 1-4:
external image pdf.png worksheets 1-4 review KEY.pdf

Chapter 13 Combinatorics and Probability

http://www.mathplayground.com/probability.html

Below are some practice worksheets:
external image pdf.png practice worksheets.pdf
Chapter 13 Notes
external image vnd.openxmlformats-officedocument.wordprocessingml.document.png 13-1 and 13-2 Notes.docx

Review for Chapter 13 test worksheets and key:


Chapter 14 Statistics


external image SCATTERPLOTS%20FOR%20MATH%20YOLO.pptx?h=52&w=320 Chapter 14 - Statistics Notes.docx

t



Chapter 14 Quiz review (also includes review for 1.3-1.6)


Projects:


Chapter 3 The Nature of Graphs
Symmetry and Coordinate Graphs (3-1)
HW 3-1 pg. 134 #15-25 odd, 31-35 odd


Families of Graphs (3-2)
HW 3-2 pg. 134 #13-33 odd

Piecewise Functions (1-7)
HW 1-7 #11-25 odd





Continuity and End Behavior (3-5)
HW 3-5 pg. 166 #13-31 odd

Critical Points and Extrema (3-6)
HW 3-6 pg. 177 #13-31 odd

Graphs of Rational Functions (3-7)
HW 3-7 pg. 186 #15-29 odd

this powerpoint is a nice bridge between chapter 3 and chapter 4 notes

awesome awesome awesome sheet below from Dillon , thanks!!!!

Test Review Worksheet with ANSWERS!


Key Strokes for TI 83/84 calculators - Graphing


Chapter 4 Polynomial Functions
Polynomial Functions (4-1)

HW 4-1 pg. 210 #15-47 odd, do not do 21 or 31
Quadratic Equations (optional) (4-2)

HW 4-2 pg. 219 #13-33 odd
Remainder and Factor Theorems (4-3)

HW 4-3 pg. 226 #15-33 odd
Rational Root Theorem (4-4)


HW 4-4 pg. 234 #11-21 odd and #25
Locating Zeros of a Polynomial Function (4-5)

HW 4-5 pg. 240 #13-31 odd
Chapter 4 Review Sheet

Answers to Chapter 4 Review Sheet


Derivative of a Polynomial Function (Supplemental Material)
Critical Points (Supplemental Material)

Conic Sections:
Powerpoint notes for 10.2-10.5:

Circles (10-2)
pg. 628, #'s 23, 25, 27, 31, 35-39 all
Ellipses (10-3)
pg. 638, #'s 17, 19, 23, 27, 31-41 odd
Hyperbolas (10-4)
pg. 650, #'s 17-27 odd, 31-41 odd
Parabolas (10-5)
pg. 659, #'s 13-21 odd, 25-31 odd
Identify conic sections
pg. 667, #'s 13-23 odd
Systems of Second-Degree Equations and Inequalities (10-8)
pg. 683, #'s 13, 15, 19, 21, 25

Some good review questions:
pg. 688, #'s 14, 15, 18, 24, 28 and 37

Chapter 11 Logarithms

This document below is nice because it gives explanations of a variety of topics
covered in exponents and logarithms:







Real Exponents (11-1)
pg. 200, #'s 21-59 odd

Exponential Functions (11-2)


pg. 708, #'s 11-21 odd
Do you remember?



The Number e (11-3)
pg. 715, #'s 7, 9, 18
Logarithmic Functions (11-4)
pg. 723, #'s 21-51 odd

Common Logs (11-5)
pg. 730, #'s 35-57 odd
Natural Logarithms (11-6)
pg. 736, #'s 19-39 odds
Applications of Exponential and Logarithmic Functions (including Compound Interest, Growth and Decay, Newton’s Law of Cooling, and pH level)

Key for the Final Exam Review: