Advanced Algebra II: Activities and Homework

2009·1.1 MB·English

by  Kenny M. Felder.

Advanced Algebra II: Activities and
Homework
By:
Kenny M. Felder

Advanced Algebra II: Activities and
Homework
By:
Kenny M. Felder
Online:
< http://cnx.org/content/col10686/1.5/ >
C O N N E X I O N S
RiceUniversity,Houston,Texas
ThisselectionandarrangementofcontentasacollectioniscopyrightedbyKennyM.Felder. Itislicensedunderthe
Creative Commons Attribution 2.0 license (http://creativecommons.org/licenses/by/2.0/).
Collection structure revised: September 15, 2009
PDF generated: August 8, 2011
For copyright and attribution information for the modules contained in this collection, see p. 245.
Table of Contents
The Philosophical Introduction No One Reads ............................... ...................1
How to Use Advanced Algebra II .............................................. ...................3
1 Functions
1.1 The Function Game: Introduction ..........................................................23
1.2 The Function Game: Leader’s Sheet ........................................................23
1.3 The Function Game: Answer Sheet .........................................................24
1.4 Homework: The Function Game ............................................................25
1.5 Homework: Functions in the Real World ....................................................26
1.6 Algebraic Generalizations ...................................................................27
1.7 Homework: Algebraic Generalizations ......................................................29
1.8 Homework: Graphing ......................................................................30
1.9 Horizontal and Vertical Permutations .......................................................32
1.10 Homework: Horizontal and Vertical Permutations I ........................................33
1.11 Homework: Horizontal and Vertical Permutations II .......................................37
1.12 Sample Test: Function I ...................................................................41
1.13 Lines ......................................................................................45
1.14 Homework: Graphing Lines ...............................................................50
1.15 Composite Functions ......................................................................52
1.16 Homework: Composite Functions ..........................................................54
1.17 Inverse Functions .........................................................................55
1.18 Homework: Inverse Functions .............................................................57
1.19 TAPPS Exercise: How Do I Solve That For y? ............................................58
1.20 Sample Test: Functions II .................................................................58
2 Inequalities and Absolute Values
2.1 Inequalities .................................................................................63
2.2 Homework: Inequalities ....................................................................64
2.3 Inequality Word Problems ..................................................................65
2.4 Absolute Value Equations ..................................................................66
2.5 Homework: Absolute Value Equations ......................................................68
2.6 Absolute Value Inequalities .................................................................69
2.7 Homework: Absolute Value Inequalities .....................................................70
2.8 Graphing Inequalities and Absolute Values .................................................71
2.9 Homework: Graphing Inequalities and Absolute Values .....................................72
2.10 Sample Test: Inequalities and Absolute Values ............................................74
3 Simultaneous Equations
3.1 Distance, Rate, and Time ..................................................................75
3.2 Homework: Simultaneous Equations by Graphing ...........................................76
3.3 Simultaneous Equations ....................................................................77
3.4 Homework: Simultaneous Equations ........................................................79
3.5 The (cid:16)Generic(cid:17) Simultaneous Equations .....................................................80
3.6 Sample Test: 2 Equations and 2 Unknowns .................................................81
4 Quadratics
4.1 Multiplying Binomials ......................................................................83
4.2 Homework: Multiplying Binomials ..........................................................84
4.3 Factoring ...................................................................................86
4.4 Homework: Factoring Expressions ..........................................................87
4.5 Introduction to Quadratic Equations .......................................................88
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4.6 Homework: Introduction to Quadratic Equations ...........................................89
4.7 Completing the Square .....................................................................90
4.8 Homework: Completing the Square .........................................................91
4.9 The (cid:16)Generic(cid:17) Quadratic Equation ..........................................................92
4.10 Homework: Solving Quadratic Equations ..................................................93
4.11 Sample Test: Quadratic Equations I .......................................................94
4.12 Graphing Quadratic Functions ............................................................96
4.13 Graphing Quadratic Functions II ..........................................................97
4.14 Homework: Graphing Quadratic Functions II ..............................................99
4.15 Solving Problems by Graphing Quadratic Functions ......................................100
4.16 Homework: Solving Problems by Graphing Quadratic Functions ..........................101
4.17 Quadratic Inequalities ....................................................................102
4.18 Homework: Quadratic Inequalities .......................................................104
4.19 Sample Test: Quadratics II ...............................................................105
5 Exponents
5.1 Rules of Exponents ........................................................................107
5.2 Homework: Rules of Exponents ............................................................108
5.3 Extending the Idea of Exponents ..........................................................109
5.4 Homework: Extending the Idea of Exponents ..............................................110
5.5 Fractional Exponents ......................................................................111
5.6 Homework: Fractional Exponents ..........................................................113
5.7 Real Life Exponential Curves ..............................................................114
5.8 Homework: (cid:16)Real life(cid:17) exponential curves ..................................................116
5.9 Sample Test: Exponents ...................................................................118
6 Logarithms
6.1 Introduction to Logarithms ................................................................121
6.2 Homework: Logs ..........................................................................122
6.3 Properties of Logarithms ..................................................................124
6.4 Homework: Properties of Logarithms ......................................................125
6.5 Using the Laws of Logarithms .............................................................127
6.6 So What Are Logarithms Good For, Anyway? .............................................127
6.7 Homework: What Are Logarithms Good For, Anyway? ....................................129
6.8 Sample Test ...............................................................................130
7 Rational Expressions
7.1 Rational Expressions ......................................................................133
7.2 Homework: Rational Expressions ..........................................................134
7.3 Rational Equations ........................................................................134
7.4 Homework: Rational Expressions and Equations ...........................................135
7.5 Dividing Polynomials ......................................................................136
7.6 Sample Test: Rational Expressions ........................................................137
8 Radicals
8.1 Radicals (aka* Roots) .....................................................................139
8.2 Radicals and Exponents ...................................................................139
8.3 Some Very Important Generalizations .....................................................140
8.4 Simplifying Radicals .......................................................................141
8.5 Homework: Radicals ......................................................................141
8.6 A Bunch of Other Stu(cid:27) About Radicals ...................................................143
8.7 Homework: A Bunch of Other Stu(cid:27) About Radicals .......................................145
8.8 Radical Equations .........................................................................146
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8.9 Homework: Radical Equations .............................................................148
8.10 Sample Test: Radicals ....................................................................149
9 Imaginary Numbers
9.1 Imaginary Numbers .......................................................................153
9.2 Homework: Imaginary Numbers ...........................................................155
9.3 Complex Numbers .........................................................................157
9.4 Homework: Complex Numbers ............................................................158
9.5 Me, Myself, and the Square Root of i ......................................................159
9.6 The Many Merry Cube Roots of -1 ........................................................160
9.7 Homework: Quadratic Equations and Complex Numbers ...................................161
9.8 Sample Test: Complex Numbers ...........................................................161
10 Matrices
10.1 Introduction to Matrices .................................................................165
10.2 Homework: Introduction to Matrices .....................................................166
10.3 Multiplying Matrices I ...................................................................167
10.4 Homework: Multiplying Matrices I .......................................................169
10.5 Multiplying Matrices II ..................................................................169
10.6 Homework: Multiplying Matrices II ......................................................170
10.7 The Identity and Inverse Matrices ........................................................172
10.8 Homework: The Identity and Inverse Matrices ............................................174
10.9 The Inverse of the Generic 2x2 Matrix ...................................................175
10.10 Using Matrices for Transformation ......................................................176
10.11 Homework: Using Matrices for Transformation ..........................................178
10.12 Sample Test : Matrices I ................................................................180
10.13 Homework: Calculators .................................................................181
10.14 Homework: Determinants ...............................................................182
10.15 Solving Linear Equations ...............................................................183
10.16 Homework: Solving Linear Equations ...................................................185
10.17 Sample Test: Matrices II ................................................................186
Solutions .......................................................................................188
11 Modeling Data with Functions
11.1 Direct Variation ..........................................................................191
11.2 Homework: Inverse Variation .............................................................192
11.3 Homework: Direct and Inverse Variation .................................................194
11.4 From Data Points to Functions ...........................................................196
11.5 Homework: From Data Points to Functions ...............................................197
11.6 Homework: Calculator Regression ........................................................199
11.7 Sample Test: Modeling Data with Functions .............................................201
12 Conics
12.1 Distance .................................................................................207
12.2 Homework: Distance .....................................................................208
12.3 All the Points Equidistant from a Given Point ............................................209
12.4 Homework: Circles .......................................................................211
12.5 All the Points Equidistant from a Point and a Line .......................................212
12.6 Homework: Vertical and Horizontal Parabolas ............................................212
12.7 Parabolas: From De(cid:28)nition to Equation ..................................................214
12.8 Sample Test: Distance, Circles, and Parabolas ............................................215
12.9 Distance to this point plus distance to that point is constant .............................216
12.10 Homework: Ellipses .....................................................................217
12.11 The Ellipse: From De(cid:28)nition to Equation ...............................................219
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12.12 Distance to this point minus distance to that point is constant ..........................220
12.13 Homework: Hyperbolas .................................................................221
12.14 Sample Test: Conics 2 (Ellipses and Hyperbolas) ........................................222
13 Sequences and Series
13.1 Arithmetic and Geometric Sequences .....................................................225
13.2 Homework: Arithmetic and Geometric Sequences .........................................226
13.3 Homework: Series and Series Notation ...................................................227
13.4 Homework: Arithmetic and Geometric Series .............................................227
13.5 Homework: Proof by Induction ...........................................................228
13.6 Sample Test: Sequences and Series .......................................................229
14 Probability
14.1 How Many Groups? ......................................................................231
14.2 Homework: Tree Diagrams ...............................................................231
14.3 Introduction to Probability ...............................................................233
14.4 Homework: The Multiplication Rule .....................................................233
14.5 Homework: Trickier Probability Problems ................................................234
14.6 Homework: Permutations ................................................................237
14.7 Homework: Permutations and Combinations .............................................238
14.8 Sample Test: Probability .................................................................239
Index ...............................................................................................242
Attributions ........................................................................................245
The Philosophical Introduction No One
Reads
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(*but it’s real short so please read it anyway)
Welcome to Advanced Algebra II at Raleigh Charter High School! There are three keys to succeeding in
this math class.
1. Do the homework
2. Ask questions in class if you don’t understand anything.
3. Focus on understanding, not just doing the problem right. (Hint: you understand something
when you say (cid:16)Gosh, that makes sense! I should have thought of that myself!)
Here’s how it works. The teacher gets up and explains something, and you listen, and it makes sense, and
you get it. You work a few problems in class. Then you go home, stare at a problem that looks exactly like
the one the teacher put up on the board, and realize you have no idea how to do it. How did that happen?
It looked so simple when the teacher did it! Hmm....
So, you dig through your notes, or the book, or you call your friend, or you just try something, and
you try something else, and eventually...ta-da! You get the answer! Hooray! Now, you have learned the
concept. You didn’t learn it in class, you learned it when you (cid:28)gured out how to do it.
Or,let’srewindtimeabit. Youdigthroughyournotes,youjusttrysomething,andeventually...nothing.
You still can’t get it. That’s OK! Come in the next day and say (cid:16)I couldn’t get it.(cid:17) This time, when the
teacher explains how to do it, you will have that (cid:16)Aha!(cid:17) experience: (cid:16)So that’s why I couldn’t get it to
work!(cid:17)
Eitherway, youwin. Butifyoudon’tdothehomework, theneveniftheteacherexplainstheexactsame
thing in class the next day, it won’t help...any more than it helped the previous day.
The materials in this course-pack were originally developed for Mr. Felder’s Advanced Algebra II classes
in the 2001-2002 school year. Every single student in those classes got an A or a B on the North Carolina
End of Course test at the end of the year. You can too! Do your homework, ask questions in class, and
always keep your focus on real understanding. The rest will take care of itself.
1Thiscontentisavailableonlineat<http://cnx.org/content/m19111/1.2/>.
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