Discovering Advanced Algebra
An Investigative Approach

Contents of the Student Text

Chapter 0, Problem Solving with Algebra

Reviews important concepts from Algebra 1 such as slope, solving linear systems, using the distributive property, simplifying expressions, and using exponents. Covers problem solving by using graphs and diagrams, representing problems algebraically, and organizing information.

Chapter 1, Sequences

Uses recursive formulas to model growth and decay, and represents arithmetic and geometric sequences in tables, formulas, and graphs.

Chapter 2, Describing Data

Presents methods of analyzing and describing one-variable data sets. Topics include measures of central tendency, standard deviation, and percentiles.

Chapter 3, Linear Models and Systems

Explores lines first as mathematical objects that can model two-variable data, and then as graphical representations of linear equations. The recursive formulas for arithmetic growth from Chapter 1 are developed into explicit linear formulas. Students find lines of fit for data, learn the median-median line of fit, and evaluate quality of fit using residuals. Students solve systems graphically and using substitution and elimination.

Chapter 4, Functions, Relations, and Transformations

Distinguishes between relations and functions and introduces function notation. Explores translations, reflections, and horizontal and vertical dilations, and investigates different families of functions and graphs, including quadratic, square root, absolute value, and circles and ellipses.

Chapter 5, Exponential, Power, and Logarithmic Functions

Introduces exponential functions to model growth and decay, and explores real-world applications. Students learn about inverses and the logarithmic function, and study properties of exponents and logarithms.

Chapter 6, Matrices and Linear Systems

Explores the value of matrices to organize data and solve systems and covers operations on matrices and inverse matrices. Real-world applications of linear systems and inequalities and linear programming are explored.

Chapter 7, Quadratic and Other Polynomial Functions

Explores applications of quadratic models, various forms of quadratic functions, and solving quadratic functions. Methods of solving polynomial functions are covered, and complex numbers arise as nonreal solutions to polynomial functions.

Chapter 8, Conic Sections and Rational Functions

Extends earlier coverage of circles, ellipses, and parabolas to the context of conic sections. Students also study hyperbolas and explore the general quadratic equation and its relationship to the conic sections. Students investigate characteristics of the graphs of rational functions and perform operations on rational expressions.

Chapter 9, Series

Covers summation notation, partial sums, and infinite series.

Chapter 10, Probability

Explores experimental and theoretical probabilities, tree diagrams, Venn diagrams, expected value, permutations and combinations, Pascal's triangle, and binomial expansion.

Chapter 11, Applications of Statistics

Introduces experimental design and explores different types of studies. Explores relative frequency histograms, probability distributions, normal distributions, z-values and confidence intervals, correlation, and linear regression.

Chapter 12, Trigonometry

Presents trigonometric ratios as way to model and solve problems, and extends trigonometry to nonright triangles using the Law of Sines and the Law of Cosines. Introduces vectors and parametric equations as ways to model and solve problems about motion.

Chapter 13, Trigonometric Functions

Presents sinusoidal models in real-world applications. Properties of trigonometric graphs are explored, and trigonometric identities are introduced.