In all MATH 1111 College Algebra, MATH 1112 Trigonometry, MATH 1113 Precalculus, and MATH 2112 Probability and Statistics courses taught at CCGA, we use OpenStax College free-to-use textbooks. For MATH 1111, 1112, and 1113, we use Algebra and Trigonometry and for MATH 2112, we use Introductory Statistics. What follows are links to websites and videos for various concepts in those courses, organized by the textbook sections. Click the course names below to navigate directly to the links associated with that course.

- MATH 1111: College Algebra Links
- MATH 1112: Trigonometry Links
- MATH 1113: Precalculus Links
- MATH 2112: Probability and Statistics Links

# MATH 1111: College Algebra/

# MATH 1113: Precalculus

## Chapter 1: Prerequisites

### 1.1 Real Numbers: Algebra Essentials

- Classifying Real Numbers
- Perform Calculations Using Order of Operations
- Using the commutative, associative, distributive, associative, inverse, and identity properties
- Evaluating algebraic expressions
- Simplify algebraic expressions

### 1.2 Exponents and Scientific Notation

- Use the product rule of exponents
- Use the quotient rule of exponents
- Use the power rule of exponents
- Use the zero exponent rule of exponents
- Use the negative rule of exponents
- Find the power of a product and a quotient
- Simplify exponential expressions
- Use scientific notation

### 1.3 Radicals and Rational Expressions

- Evaluate Square roots
- Use the product rule to simplify square roots
- Use the quotient rule to simplify square roots
- Add and subtract square roots
- Rationalize denominators
- Use rational exponents

### 1.4 Polynomials

- Identify the degree and leading coefficient of polynomials
- Add and subtract polynomials
- Multiply polynomials
- Use FOIL to multiply binomials

### 1.5 Factoring Polynomials

- Factor the greatest common factor of a polynomial
- Factor a trinomial
- Factor by grouping
- Factor a perfect square trinomial
- Factor a difference of squares
- Factor a sum and difference of cubes
- Factor expressions using fractional or negative exponents

## Chapter 2: Equations and Inequalities

### 2.1 The Rectangular Coordinate Systems and Graphs

- Plot ordered pairs in a Cartesian coordinate system
- Graph equations by plotting points
- Graph equations with a graphing utility
- Find x-intercepts and y-intercepts
- Use the distance formula
- Use the midpoint formula

### 2.2 Linear Equations in One Variable

- Solve equations in one variable algebraically
- Solve a rational equation
- Find a linear equation (point and slope / two points)
- Given the equations of two lines, determine whether their graphs are parallel or perpendicular
- Write the equation of a line parallel or perpendicular to a given line

### 2.3 Models and Applications

- Set up a linear equation to solve a real-world application
- Use a formula to solve a real-world problem

### 2.4 Complex Numbers

- Add and subtract complex numbers
- Multiply and divide complex numbers
- Simplify powers of i

### 2.5 Quadratic Equations

- Solve quadratic equations by factoring
- Solve quadratic equations by the square root property
- Solve quadratic equations by completing the square
- Solve quadratic equations by using the quadratic formula
- Solve quadratic equations with complex numbers

### 2.6 Other Types of Equations

- Solve equations involving radicals (single radical, multiple radicals)
- Solve equations using factoring
- Solve radical equations
- Solve absolute value equations
- Solve other types of equations (rational)

### 2.7 Linear Inequalities and Absolute Value Inequalities

- Use interval notation
- Use properties of inequalities (addition, multiplication)
- Solve inequalities in one variable algebraically
- Solve absolute value inequalities
- Compound Inequalities (and inequalities / orinequalities)

### 11.1 Systems of Linear Equations: Two Variables

- Solve systems of equations by graphing
- Solve systems of equations by substitution
- Solve systems of equations by addition (elimination)
- Identify inconsistent systems of equations containing two variables
- Express the solution of a system of equations containing two variables

### 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables

- Solve a system of nonlinear equations using substitution
- Solve a system of nonlinear equations using elimination
- Graph a nonlinear inequality (Quadratic)
- Graph a system of nonlinear inequalities

## Chapter 3: Functions

### 3.1 Functions and Function Notation

- Determining whether a relation represents a function
- Find the value of a function
- Determine whether a function is one-to-one
- Use the vertical line test to identify functions
- Use the horizontal line test to identify one-to-one functions
- Graph the functions in the library of functions

### 3.2 Domain and Range

- Find the domain of a function identified by an equation
- Find the range of a function
- Domain and Range with a graph
- Graph piecewise-defined functions

### 3.3 Rates of Change and Behavior of Graphs

- Find the average rate of change of a function on an interval
- Use a graph to determine where a function is increasing, decreasing, or constant
- Analyzing the library of functions for increasing and decreasing intervals
- Use a graph to locate the absolute maximum and absolute minimum

### 3.4 Composition of Functions

- Combine functions using algebraic operations (addition, subtraction, multiplication, division)
- Create a function by composition of functions
- Evaluate composite functions (formula, table, graph)
- Find the domain of a composite function
- Decomposing a composite function into its component functions

### 3.5 Transformation of Functions

- Graph functions using horizontal and vertical shifts
- Graph functions using reflections about the axes
- Graph functions using stretches and compressions
- Perform a sequence of transformations

### 3.6 Absolute Value Functions

### 3.7 Inverse Functions

- Verify that two functions are inverses
- Find domain and range of inverse functions
- Find and evaluate inverse functions (linear, quadratic, radical, rational)
- Find inverse functions and their graphs

## Chapter 4: Linear Functions

### 4.1 Linear Functions

- Represent a linear function
- Determine whether a linear function is increasing, decreasing, or constant
- Interpret slope as a rate of change
- Write and interpret an equation for a linear function
- Model real-world problems with linear functions
- Graph linear functions
- Write the equation for a function from the graph of a line

### 4.2 Modeling with Linear Functions

### 4.3 Fitting Linear Models to Data

- Draw and interpret scatter diagrams
- Use a graphing utility to find the line of best fit
- Distinguish between linear and nonlinear relations
- Fit a regression line to a set of data and use the linear model to make predictions

## Chapter 5: Polynomial and Rational Functions

### 5.1 Quadratic Functions

- Recognize characteristics of parabolas
- Find domain and range of a quadratic function
- Determine a quadratic function’s maximum or minimum value

### 5.2 Power Functions and Polynomial Functions

### 5.3 Graphs of Polynomial Functions

- Use factoring to find zeros of polynomial functions
- Identify zeros and their multiplicities
- Determine end behavior for polynomial functions
- Graph polynomial functions
- Use the intermediate value theorem

### 5.4 Dividing Polynomials

### 5.5 Zeros of Polynomial Functions

- Evaluate a polynomial using the remainder theorem
- Use the factor theorem to solve a polynomial equation
- Use the rational zero theorem to find rational zeros
- Find the zeros of polynomial functions
- Use the Fundamental Theorem of Algebra
- Use the linear factorization theorem to find polynomials with given zeros
- Use Descartes’ Rule of Signs

### 5.6 Rational Functions

- Use arrow notation (local behavior)
- Find domain of rational functions
- Identify vertical asymptotes of rational functions
- Identify horizontal asymptotes of rational functions
- Identify slant (oblique) asymptotes of rational functions
- Graph rational functions
- Write rational functions

### 5.7 Inverses and Radical Functions

- Find the inverse of a polynomial function (linear, quadratic)
- Restrict the domain to find the inverse of a polynomial function

### 5.8 Modeling Using Variation

- Solve direct variation problems
- Solve inverse variation problems
- Solve problems involving joint variation

## Chapter 6: Exponential and Logarithmic Functions

### 6.1 Exponential Functions

- Identify exponential functions
- Evaluate exponential functions
- Find equations of exponential functions
- Apply compound interest formula
- Continuous growth/decay

### 6.2 Graphs of Exponential Functions

### 6.3 Logarithmic Functions

- Convert from logarithmic to exponential form
- Convert from exponential to logarithmic form
- Use common logarithms
- Use natural logarithms

### 6.4 Graphs of Logarithmic Functions

- Find the domain of a logarithmic function
- Graph logarithmic functions
- Graph transformations of logarithmic functions

### 6.5 Logarithmic Properties

- Use the product rule for logarithms
- Use the quotient rule for logarithms
- Use the power rule for logarithms
- Expand logarithmic expressions
- Condense logarithmic expressions
- Use the change of base formula for logarithms

### 6.6 Exponential and Logarithmic Equations

- Use like bases to solve exponential equations
- Solve exponential equations using logarithms
- Use the definition of logarithm to solve logarithmic equations
- Use one-to-one property of logarithms to solve logarithmic equations
- Solve applied problems using exponential and logarithmic equations

### 6.7 Exponential and Logarithmic Models

- Model exponential growth and decay
- Use logistic growth models
- Choose an appropriate model for data

### 6.8 Fitting Exponential Models to Data

- Build an exponential model from data
- Build a logarithmic model from data
- Build a logistic model from data

# MATH 1112: Trigonometry/MATH 1113: Precalculus

## Chapter 7: The Unit Circle: Sine and Cosine Functions

### 7.1 Angles

- Draw angles in standard position
- Introduction to radians
- Radians and Quadrants
- Converting between radians and degrees (introduction)
- Converting degrees to radians
- Add angles in DMS form
- Subtract angles in DMS form
- Find coterminal Angles using degrees (example 1 and 2)
- Find coterminal angles using radians
- Length of an arc that subtends a central angle
- Area of a sector given a central angle

### 7.2 Right Triangle Trigonometry

- SOHCAHTOA – Part 1 (Introduction), Part 2 (More examples)
- Solve for a side in a right triangle
- Basic cofunction identities
- The Trigonometric Pythagorean Identity (derivation)
- Finding the six trigonometric functions of an angle in a right triangle
- Application (Find the height of a tree)
- Application (A ladder problem)

### 7.3 Unit Circle

- Introduction to the unit circle
- Trigonometric values of 45 degree angles
- Use the trigonometric Pythagorean identity
- Find reference angles using degrees
- Find reference angles using radians
- Use reference angles to evaluate sine, cosine and tangent

### 7.4 The Other Trigonometric Functions

- Recognize and use fundamental identities
- Even-odd properties of trigonometric functions
- Use reference angles to evaluate secant and cosecant

## Chapter 8: Periodic Functions

### 8.1 Graphs of the Sine and Cosine Functions

- Graph of sine function
- Find the amplitude and period
- Find the amplitude, period (plus graphing)
- Graph basic sinusoidal functions without translations
- Graph a sinusoidal function

### 8.2 Graphs of the Other Trigonometric Functions

- Analyze the graph of y=tan(x)
- Graph a tangent function
- Analyze the graphs of y=csc(x) and y=sec(x)
- Graph a secant function
- Graph a cosecant function
- Graph a cotangent function

### 8.3 Inverse Trigonometric Functions

- Introduction to inverse trigonometric functions
- Evaluate inverse trigonometric functions
- Example of solving a right triangle given one side and an angle
- Example of solving a right triangle given two sides
- Find exact values of composite functions with inverse trig functions
- More examples of finding exact values of composite functions with inverse trig functions

## Chapter 9

### 9.1 Solving trigonometric equations with identities

### 9.2 Sum and difference identities

- Use the sum and difference formulas for cosine, sine and tangent

### 9.3 Double-angle, half-angle, and reduction formulas

### 9.4 Sum-to-product and product-to-sum identities

### 9.5 Solving trigonometric equations

- Solving trigonometric equation using identities and factoring
- Solve a trigonometric equation in sine or cosine
- Solve a trigonometric equation in tangent

## Chapter 10

### 10.1 Non-right triangles: Law of Sines

- Use Law of Sines to solve for a side or an angle
- Find the area of an oblique triangle using the sine function

### 10.2 Non-right triangles: Law of Cosines

- Use Law of Cosines to solve for a side or an angle
- Use Heron’s formula to find the area of a triangle

### 10.3 Polar Coordinates

### 10.5 Polar Form of Complex Numbers

- Plot complex numbers in the complex plane
- Find the absolute value of a complex number
- Write complex numbers in polar form
- Find product and quotient of complex numbers in polar form
- Finding powers of complex numbers in polar form
- Finding roots of complex numbers in polar form

### 10.8 Vectors

- View vectors geometrically and algebraically
- Find magnitude and direction of a vector
- Find vector addition, scalar multiplication and dot product
- Find the unit vector in the direction of a given vector

# MATH 2112: Probability and Statistics

## Chapter 1: Sampling Data (Week 1)

### 1.1 Definitions of Statistics, Probability and Key Terms

### 1.2 DATA, SAMPLING, AND VARIATION IN DATA SAMPLING

- Census and Sampling
- Samples and Surveys
- Inferring population mean from sample mean
- Reasonable samples

### 1.3 Frequency, Frequency Tables, and Levels of Measurement

### 1.4 Experimental Design and Ethics

## Chapter 2: Descriptive Statistics (Week 2)

### 2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs and Bar Graphs

- Stemplots
- Reading stem and leaf plots
- Reading bar graphs
- Creating a bar graph
- Reading bar charts: comparing two sets of data
- Reading line graphs

### 2.2 Histograms, Frequency Polygons, and Time Series Graphs

### 2.3 Measures of the Location of the Data

- Measures of Center
- Statistics intro: Mean, median, & mode
- Mean, median, & mode example
- Comparing means of distributions
- Means and medians of different distributions

### 2.4 Box Plots

### 2.5 Measures of the Center of the Data

- Measures of Center
- Statistics intro: Mean, median, & mode
- Mean, median, & mode example
- Comparing means of distributions
- Means and medians of different distributions

### 2.6 Skewness and the Mean, MEdian, and Mode

### 2.7 Measures of the Spread of the Data

- Standard Deviation
- Measures of spread: range, variance, & standard deviation
- Variance of a population
- Sample variance
- Review and intuition why we divide by n-1 for the unbiased sample variance
- Simulation showing bias in sample variance
- Why we divide by n-1 in variance
- Simulation providing evidence that (n-1) gives unbiased estimate.
- Population standard deviation
- Sample standard deviation and bias
- Statistics: Standard deviation

## Chapter 3: Probability Topics (Week 4)

### 3.1 Terminology

- Introduction to Probability
- Subsets of sample spaces
- Simple probability: yellow marble
- Simple probability: non-blue marble

### 3.2 Independent and Mutually Exclusive Events

- Compound probability of independent events
- Coin flipping probability
- Die rolling probability
- Free throwing probability
- Three pointer vs free throw probability
- Probability with equally likely events
- Independent events example: test taking
- Die rolling with independent events

### 3.3 Two Basic Rules of Probability

- Addition rule for probability
- Dependent probability introduction
- Dependent probability: coins
- Dependent probability example
- Independent and dependent probability
- Analyzing event probability for independence
- Dependent probability
- Calculating conditional probability
- The Monty Hall problem

### 3.4 Contingency Tables

### 3.5 Tree and Venn Diagrams

## Chapter 4: Discrete Random Variables (Week 6)

### 4.1 Probability Distributions Function (PDF) for a discrete Random variable

- Random Variables
- Discrete and continuous random variables
- Constructing a probability distribution for random variable

### 4.2 Mean or Expected Value and Standard Deviation

- Term life insurance and death probability
- Getting data from expected value
- Expected profit from lottery ticket
- Expected value while fishing
- Comparing insurance with expected value

### 4.3 Binomial Distribution

- Binomial Distributions
- Visualizing a binomial distribution
- Binomial probability example
- Generalizing k scores in n attempts
- Free throw binomial probability distribution
- Graphing basketball binomial distribution
- Expected value of binomial distribution

### 4.4 Geometric Distribution

### 4.5 Hypergeometric Distribution

### 4.6 Poisson Distribution

## Chapter 5: Continuous Random Variables (Week 7)

### 5.1 Continuous Probability Functions

### 5.2 the Uniform Distribution

### 5.3 The Exponential Distribution

## Chapter 6: The Normal Distribution (Week 8)

### 6.1 The Standard Normal Distribution

### 6.2 Using the Normal Distribution

- Normal Calculations
- ck12.org normal distribution problems: Empirical rule
- ck12.org normal distribution problems: z-score
- ck12.org exercise: Standard normal distribution and the empirical rule
- ck12.org: More empirical rule and z-score practice

## Chapter 7: The Central Limit Theorem (Week 10)

### 7.1 the Central Limit Theorem for Sample Means (Averages)

- Sampling Distributions
- Central limit theorem
- Sampling distribution of the sample mean
- Sampling distribution of the sample mean 2

### 7.2 The Central Limit Theorem for Sums

### 7.3 Using The Central Limit Theorem

## Chapter 8: Confidence Intervals (Week 11)

### 8.1 A Single Population Mean using the normal Distribution

### 8.2 A Single Population Mean using the Student t Distribution

### 8.3 A Population Proportion

- Confidence interval example
- Mean and variance of Bernoulli distribution example
- Bernoulli distribution mean and variance formulas
- Margin of error 1
- Margin of error 2

## Chapter 9: Hypothesis Testing with One Sample (Week 12)

### 9.1 Null And Alternative Hypotheses

### 9.2 Outcomes and the Type I and Type II Errors

### 9.3 Distribution Needed for Hypothesis Testing

### 9.4 Rare Events, the Sample, Decision and Conclusion

### 9.5 Additional Information and Full Hypothesis Test Examples

## Chapter 12: Linear Regression and Correlation (Week 3)

### 12.1 Linear Equations

- See Section 2.2 in the College Algebra material above.

### 12.2 Scatter Plots

- Scatter plots
- Scatter plots: studying, shoe size, and test scores
- Scatter plot: smokers
- Constructing a scatter plot

### 12.3 The Regression Equation

- Fitting Lines to Data
- Correlation
- Correlation and causality
- Fitting a line to data
- Estimating the line of best fit exercise
- Squared error of the regression line
- Example: Correlation coefficient intuition

### 12.4 Testing the Significance of the Correlation Coefficient