Course Details - Mathematics and Statistics - Penn State Altoona

Math 040

Algebra, Trigonometry, and Analytic Geometry

5 credits

Blue Book Description: Concepts of algebra; equations; inequalities; functions; graphs; polynomial and rational functions; exponential and logarithmic functions; trigonometry; analytic geometry; complex numbers.

Pre-requisites: Satisfactory performance on the mathematics proficiency examination (score at least 13 on MATH 040 SOAR test, or at least 12 on MATH 140 SOAR test).

Pre-requisite for: MATH 140

Suggested Textbook:
Algebra and Trigonometry, 8th edition, by Sullivan, published by Pearson Prentice Hal, ISBN: 0-13-232903-4l.
Check with your instructor to make sure this is the textbook used for your section.

Topics:
Chapter R (Review)
R.1 Real Numbers
R.2 Algebra Essentials
R.3 Geometry Essentials
R.4 Polynomials
R.5 Factoring Polynomials
R.6 Synthetic Division
R.7 Rational Expressions
R.8 nth Roots; Rational Exponents

Chapter 1
1.1 Linear Equations
1.2 Quadratic Equations
1.3 Complex Numbers
1.4 Radical Equations/Quadratic Form
1.5 Solving Inequalities
1.6 Equations/Inequalities with Abs.Value
1.7 Problem Solving

Chapter 2
2.1 Distance and Midpoint
2.2 Graphs of Equations in two variables
2.3 Lines
2.4 Circles

Chapter 3
3.1 Functions
3.2 Graph of a Function
3.3 Properties of Functions
3.4 Piecewise-defined Functions
3.5 Graphing Techniques
3.6 Mathematical Models

Chapter 4
4.1 Linear Functions
4.3 Quadratic Functions
4.5 Inequalities involving Quadratic Functions

Chapter 5
5.1 Polynomial Functions and models
5.2 Properties of Rational Functions
5.3 Graph of Rational Functions
5.4 Real Zeros of a Polynomial Function
5.5 Complex Zeros; Fund. Thm. of Algebra

Chapter 6
6.1 Composite Functions
6.2 One-to One Functions; Inverse Functions
6.3 Exponential Functions
6.4 Logarithmic Functions
6.5 Properties of Logarithms
6.6 Logarithmic and Exponential Equations
6.7 Compound Interest
6.8 Exponential, Logistic Growth/Decay

Chapter 7
7.1 Angles and Their Measure
7.2 Right Triangle Trigonometry
7.3 Trigonometric Functions of Acute Angles
7.4 Trig. Functions of General Angles
7.5 Unit Circle Trigonometry
7.6 Graphs of Sine and Cosine
7.7 Graphs of TAN, COT, CSC, SEC
7.8 Phase Shift

Chapter 8
8.1 Inverse Sine, Cosine, and Tangent
8.2 Inverse Trig Functions, Cont.
8.3 Trigonometric Identities
8.4 Sum and Difference Formulas
8.5 Double-angle and Half-angle Formulas
8.6 Product-to-Sum; Sum-to-Product Formulas
8.7 Trigonometric Equations I
8.8 Trigonometric Equations II

Chapter 9
9.2 Law of Sines
9.3 Law of Cosines

Chapter 11
11.1, 11.2 The Parabola
11.3 The Ellipse
11.4 The Hyperbola

Chapter 12
12.1 Systems of Linear Equations
12.6 Systems of Nonlinear Equations