A study of functions and their graphs, with application to
the sciences (including
linear and polynomial functions , zeroes, inverse functions exponential,
logarithmic and trigonometric functions and their inverses); counting (including
elementary probability); and arithmetic/geometric progression emphasizing
induction and critical thinking.
Prerequisites and Algebraic Notation
P.1 Real Numbers and Their Properties
P.2 Integral Exponents and Scientific Notation
P.3 Rational Exponents and Radicals
P.4 Complex Numbers
P.5 Polynomials
P.6 Factoring Polynomials
P.7 Rational Expressions
Equations, Inequalities, and Modeling
1.1 Equations in One Variable
1.2 Constructing Models to Solve Problems
1.3 Equations and Graphs in Two Variables
1.4 Linear Equations in Two Variables
1.6 Quadratic Equations
1.7 Linear and Absolute Value Inequalities
Functions and Graphs
2.1 Functions
2.2 Graphs of Relations and Functions
2.3 Families of Functions, Transformations, and Symmetry
2.4 Operations with Functions
2.5 Inverse Functions
2.6 Constructing Functions with Variation
Polynomial and Rational Functions
3.1 Quadratic Functions and Inequalities
3.2 Zeros of Polynomial Functions
3.3 Theory of Equations
3.5 Graphs of Polynomial Functions
3.6 Rational Functions and Inequalities
Exponential and Logarithmic Functions
4.1 Exponential Functions and Their Applications
4.2 Logarithmic Functions and Their Applications
4.3 Rules of Logarithms
The Trigonometric Functions
5.1 Angles and Their Measurements
5.2 The Sine and Cosine Functions
5.3 The Graphs of the Sine and Cosine Functions
5.4 The Other Trigonometric Functions and Their Graphs
5.5 The Inverse Trigonometric Functions
Trigonometric Identities and Conditional Equations
6.1 Basic Identities
6.2 Verifying Identities
Applications of Trigonometry
7.1 Law of Sines
7.2 Law of Cosines
Systems of Equations and Inequalities
8.1 Systems of Linear Equations in Two Variables
8.2 Systems of Linear Equations in Three Variables
8.5 Inequalities and systems of Inequalities in Two Variables
The Conic Sections
10.1 The Parabola
10.2 The Ellipse and the Circle
10.3 The Hyperbola
Sequences, Series, and Probability
11.1 Arithmetic Sequences
11.2 Arithmetic Series
11.3 Geometric Sequences and Series
11.4 Counting and Permutations
11.5 Combinations and the Binomial Theorem
11.6 Elementary Probability
11.7 Mathematical Induction
