Math+Analysis

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: [] 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) //*Note: Since all of these topics are review, the entire chapter can be completed in 5 days)//
 * 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)

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

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:

Chapter 5 Review Sheet and Key

__ **Chapter 6: Graphs of Trigonometric Functions** __

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

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

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

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

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



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

pg. 401, #’s 29-34 all except for #32 tangent, cotangent, secant, cosecant
 * Graphing Other Trig Functions ** (6-7)


 * 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

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

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)



pg. 605, #'s 15, 21, 29, 41, 46 //Third Marking Period Project: Creating a picture using Graphs of Polar Equations//
 * Powers and Roots of Complex Numbers (9-8) **
 * i. DeMoivre’s Theorem **
 * ii. Complex Roots Theorem **
 * //*should take approximately 15 to 20 school days//**

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) pg. 864, #'s 17-37 odd
 * 1) mutually exclusive vs. inclusive
 * 2) dependent vs. independent

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**__// []

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) i. change of base ii. solving exponential equations
 * pg. 730, #'s 35-57 odd **

Natural Logarithms (11-6) 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) //*should take approximately 10 to 15 school days//
 * pg. 736, #'s 19-39 odds **
 * 1) pH Level (optional)

**__ END OF SECOND SEMESTER __**

Have a great summer!!!!!!!

= = = = =SENIOR POEM 2013= Inspirational Video []

Sine and Cosine Graph Transformations Applet: []

Need more Graph Paper? Click on the following link:[]

Online TEXT:

Go to this webpage: []

click on the ‘online student edition’ link

type in this password: BFECD0861B

Assignments:

Enrichment Project: Here are Chapter 9 worksheets and keys:

‍ Midterm Review Key
tan one: below are the worksheets #'s 1-4:

**Chapter 13 Combinatorics and Probability**

[]

Below are some practice worksheets:
 * Chapter 13 Notes **

Review for Chapter 13 test worksheets and key:

**Chapter 14 Statistics**



t




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

=Projects:= ** Chapter 3 The Nature of Graphs ** HW 3-1 pg. 134 #15-25 odd, 31-35 odd HW 3-2 pg. 134 #13-33 odd HW 1-7 #11-25 odd
 * Symmetry and Coordinate Graphs (3-1)**
 * Families of Graphs (3-2)**
 * Piecewise Functions (1-7)**



HW 3-5 pg. 166 #13-31 odd HW 3-6 pg. 177 #13-31 odd 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!
 * Continuity and End Behavior (3-5)**
 * Critical Points and Extrema (3-6)**
 * Graphs of Rational Functions (3-7)**

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 HW 4-2 pg. 219 #13-33 odd HW 4-3 pg. 226 #15-33 odd HW 4-4 pg. 234 #11-21 odd and #25 HW 4-5 pg. 240 #13-31 odd Chapter 4 Review Sheet Answers to Chapter 4 Review Sheet
 * Quadratic Equations (optional) (4-2)**
 * Remainder and Factor Theorems (4-3)**
 * Rational Root Theorem (4-4)**
 * Locating Zeros of a Polynomial Function (4-5)**

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 :



Key for the Final Exam Review:
 * 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)**