Rough Outline Of Topics
Chapter 7: Quadratic Equations
- 7.1 Extracting Roots
- Simplify Square Roots
- Rationalize Denominators
- 7.2 Completing the Square
- Solve Quadratic Equations by Completing the Square
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7.3 Quadratic Formula
- Solve Quadratic Equations by Using Quadratic Fomula
- Use the Discriminant or Graph to Determine the Number of Real Solutions
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7.4 Applications of Quadratic Equations
- Area Problems
- Pythagorean Theorem
- Projectile Motion
- Number Problems
Chapter 8: Introduction to Functions
- 8.1 Functions and Their Representations
- Domain and Range
- Function Notation
- Various Representations: Algebraic, Tabular, and Graphical
- Function Versus Not a Function
- Vertical Line Test
- 8.2 Linear Functions
- Slope: Formulas, From Graph
- Interpreting Slope
- $x$ and $y$-intercepts and their Interpretation
- Graphing Linear Functions
- Slopes of Parallel and Perpendicular Lines
- Where $f(x)$ is positive/negative
- Domain and Range
- 8.3 Absolute Value Functions
- Vertical and Horizontal Transformations
- Vertex of the graph
- Opens Up or Down?
- Minimum/Maximum $y$-value of the function
- The $x$-value at which the minimum $y$-value occurs
- The $x$-intercepts and $y$-intercept
- Where $f(x)$ is positive/negative
- Domain and Range
- Application: Probability of Sum of Two Dice
- 8.4 Quadratic Functions
- Vertical and Horizontal Transformations
- Vertex of the graph
- Opens Up or Down?
- Minimum/Maximum $y$-value of the function
- The $x$-value at which the minimum $y$-value occurs
- The $x$-intercepts and $y$-intercept
- Where $f(x)$ is positive/negative
- Domain and Range
- Application: Billy Bob Owns a Coal Mine
- 8.5 Analyzing Graphs and Functions
- Vertex of the graph
- Opens Up or Down?
- Minimum/Maximum $y$-value of the function
- The $x$-value at which the minimum $y$-value occurs
- The $x$-intercepts and $y$-intercept
- Where $f(x)$ is positive/negative
- For what values of $x$ is the function $f(x)$ increasing/decreasing?
- 8.6 Curve Fitting
- Won't be on the exam.
Chapter 9: Rational Functions and Expressions
- 9.1 Rational Functions and Rational Expressions
- Domain of Rational Functions
- Graphs of Rational Functions (Vertical Asymptotes)
- Reducing Rational Expressions
- 9.2 Multiplying and Dividing Rational Expressions
- 9.3 Adding and Subtracting Rational Expressions
- 9.4 Combining Operations and Complex Fractions
- Apply Order of Operations to Rational Expressions
- Multiply By "Fancy Ones" to Reduce Complex Fractions to Regular Fractions
- Application: Resistance in a Parallel Circuit
- 9.5 Equations Involving Rational Expressions
- Always Check for Extraneous Solutions
- Application: Resistance in a Parallel Circuit
Chapter 10: Radical Expressions
- 10.1 Radical Expressions, Square and Cube Root Functions
- Understand What an $n$th Root Is
- Evaulating/Simplifying Basic Radical Expressions
- Cube Root and Square Root Functions
- Determine Domain and Range
- Vertical Horizontal Transformations
- 10.2 Adding and Subtracting Radical Expressions
- 10.3 Multiplying and Dividing Radical Expressions
- Rationalizing Denominators with $n$th Roots
- 10.4 Solving Radical Equations
- Always Check for Extraneous Solutions
- Application: Distance Formula
- 10.5 Radicals and Rational Exponents
- Radicals are Simply Rational Exponents
- All the Same Exponent Rules Hold (Review if Necessary)
Chapter 11: Exponential and Logarithmic Functions
- 11.1 Exponential Functions and Geometric Sequences
- Definition of an Exponential Function
- Domain and Range of Exponential Functions
- How to Graph Exponential Functions
- Geometric Versus Arithmetic Series
- Solving Basic Exponential Equations
- Application: Height Sequence of a Bouncy Ball
- Application: Radioactive Decay
- 11.2 Inverse Functions
- Basic Idea of an Inverse Function
- Finding Inverses Algebraically
- Graphing Inverses
- One-to-One Functions
- Horizontal Line Test
- 11.3 Logarithmic Functions
- Logarithmic Functions are Inverses of Exponential Function
- Evaluating Basic Logarithmic Expressions
- Solving Basic Logarithmic Equations
- $N=b^M$ is equivalent to $\log_b N=M$
- 11.4 Evaluating Logarithms
- Evaluating both Common and Natural Logarithms on your TI Calculator
- 11.5 Properties of Logarithms
- A Log of a Product is a Sum of the Logs
- A Log of a Quotient is a Difference of the Logs
- Logs Bring Exponents Down to Earth
- Change of Base Formula
- Evaluating Logarithms of non-standard bases using Change of Base Formula
- 11.6 Exponential and Logarithmic Equations
- Check for Extraneous Solutions When Solving Logarithmic Equations
- Application: Depreciation
- 11.7 Applications
- Exponential
- Population Growth/Decay (Decline)
- Radio Carbon Dating
- Compound Interest
- Discrete (Banker's): $A=P(1+\frac{r}{n})^{nt}$
- Continuous: $A=Pe^{rt}$
- Logarithmic
- pH of a chemical solution
- Radio Carbon Dating
- Logarithmic Scales (Richter Scale, Decibel Scale)
- Finance
Chapter 12: Preview of Topics from College Algebra
- 12.1 Solving $2 \times 2$ Systems with Matrices.
- 12.2 Solving $3 \times 3$ Systems with Matrices.
- 12.3 Horizontal and Vertical Translations.
- 12.4 Vertical Stretching an Shrinking
- 12.5 The Algebra of Functions
Final Exam: Materials Allowed.
- Your Exam
- Pencils
- Ruler
- A TI-83/84 Style Calculator OR Basic Scientific Calculator
- A beverage and non-noisy food.
Important: Cell-phones, and other technology are NOT allowed. This includes TI-89 calculators which perform symbolic manipulation.
Practice Exams: You may use this practice exam.
OR
You may generate as many practice exams as you like using our course website.
NOTE: I will use our course website to generate the real in class exam.