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Discovering Advanced Algebra
ISBN 1-55953-607-1
Murdock, Kamischke, Kamischke
Key Curriculum Press 2004
A Note from the Publisher
The algebra you find in this book won’t look quite like the algebra you may have seen in older textbooks. The mathematics we learn and teach in school has to change continually to reflect changes in our world. Our workplaces are changing, and technology is present everywhere, fundamentally changing the work we do, There are some new topics that are now possible to explore with technology, and some standard topics that can be approached in new ways. As the National Council of Teachers of Mathematics (NCTM) Technology Principle says, “When technological tools are available, students can focus on decision making, reflection, reasoning, and problem solving.” This has been the focus of the authors and the Key Curriculum Press editorial team in the creation of Discovering Advanced Algebra: An Investigative Approach. As you progress through this book, you’ll see that graphing calculators and other technologies are used to explore patterns and to make, test, and generalize conjectures.
Pacing Guide
Algebra 2
Semester One: Chapter 0 – Chapter 5
Semester Two: Chapter 6 – Chapter 11
Algebra 2X
Semester One: Chapter 0 – Chapter 7
Semester Two: Chapter 8 – Chapter 11
Each student must have a 3-ring binder (3 inch minimum) to contain the work in portfolio form. The portfolio will be divided into the units above and will contain the section from the text book, notes, progress reports, and assignments given. It is recommended that each student will do work in pencil, have writing paper and graph paper, and carry a calculator (like at least a TI-30 scientific calculator.)
Contents:
Chapter 0Problem Solvingpg. 2
0.1Pictures, graphs, and diagrams
0.2Symbolic representation
0.3Organizing information
Chapter 0 Review
Chapter 1Patterns and recursionpg.28
1.1Recursively defined sequences
1.2Modeling growth and decay
1.3A first look at limits
1.4Graphing sequences
1.5Loans and investments
Chapter 1 Review
Chapter 2Describing datapg 77
2.1 Measures of central tendency and Box Plots
2.2 Measures of spread
2.3 Histograms and percentile ranks
Chapter 2 Review
Chapter 3Linear Models and systemspg. 114
3.1 Linear equations and arithmetic sequences
3.2 Revisiting slope
3.3 Fitting a line to data
3.4 The medial-median line
3.5 Residuals
3.6 Linear systems
3.7 Substitution and elimination
Chapter 3 Review
Chapter 4Functions, relations, and transformationspg. 172
4.1 Interpreting graphs
4.2 Function notation
4.3 Lines in motion
4.4 Translations and the quadratic family
4.5 Reflections and the square root family
4.6 Stretches and shrinks and the absolute-value family
4.7 Transformations and the circle family
4.8 Composition of functions
Chapter 4 Review
Chapter 5Exponential, power, and logarithmic functionspg. 238
5.1 Exponential functions
5.2 Properties of exponents and power functions
5.3 Rational exponents and roots
5.4 Applications of exponential and power equations
5.5 Building inverses of functions
5.6 Logarithmic functions
5.7 Properties of logarithms
5.8 applications of exponents
Chapter 5 Review
Chapter 6Matrices and linear systemspg. 300
6.1 Matrix representation
6.2 Matrix operations
6.3 Row reduction method
6.4 Solving systems with inverse matrices
6.5 Systems of linear inequalities
6.6 Linear programming
Chapter 6 Review
Chapter 7Quadratic and other polynomial functionspg. 360
7.1 Polynomial degree and finite differences
7.2 Equivalent quadratic forms
7.3 Completing the square
7.4 The quadratic formula
7.5 Complex numbers
7.6 Factoring polynomials
7.7 Higher-degree polynomial
7.8 More about finding solutions
Chapter 7 Review
Chapter 8Parametric equations and trigonometrypg. 424
8.1 Graphing parametric equations
8.2 Converting from parametric to non-parametric equations
8.3 Right triangle trigonometry
8.4 Using trigonometry to set a course
8.5 Projectile motion
8.6 The law of sines
8.7 The law of cosines
Chapter 8 Review
Chapter 9Conic sections and rational functionspg. 488
9.1 Using the distance formula
9.2 Circles and ellipses
9.3 Parabolas
9.4 Hyperbolas
9.5 The general quadratic
9.6 Introduction to rational functions
9.7 Graphs of rational functions
9.8 Operations with rational expressions
Chapter 9 Review
Chapter 10Trigonometric functionspg. 565
10.1 Defining the circular functions
10.2 Radian Measure and arc length
10.3 Graphing trigonometric functions
10.4 Inverses of trigonometric functions
10.5 Modeling with trigonometric equations
10.6 Fundamental trigonometric identities
10.7 Combining trigonometric functions
Chapter 10 Review
Chapter 11 Seriespg. 630
11.1 Arithmetic series
11.2 Infinite geometric series
11.3 Partial sums of geometric series
Chapter 11 Review
Chapter 12Probabilitypg. 656
12.1 Randomness and probability
12.2 Counting outcomes and tree diagrams
12.3 Mutually exclusive events and Venn Diagrams
12.4 Random Variables and expected value
12.5 Permutations and probability
12.6 Combinations and probability
12.7 The binomial theorem and Pascal’s Triangle
Chapter 12 Review
Chapter 13Applications of statisticspg. 724
13.1 Probability distributions
13.2 Normal distributions
13.3 z-values and confidence intervals
13.4 The central limit theorem
13.5 Bivariate data and correlation
13.6 The least squares line
13.7 Nonlinear regression
Chapter 13 Review
Selected answers796
Glossary898
Index860
Photo credits872