Algebra II Honors Academic Library (2nd semester)

As students refine and expand their algebraic skills during second semester, they will draw analogies between the operations and field properties of real numbers and those of complex numbers and algebraic expressions. Throughout the course students complete hands on activities and performance tasks which require them to write out and show calculations.

Like all math courses at NFC Academy students are provided additional math instructional videos for their use as needed for more practice and instruction. Just like Edgenuity online homeschool courses, these videos are ready when the student is 24/7 on our website. 

​alhese honor level courses from Edgenuity are not written from a biblical worldview and you may find some material that is different from that view we hold---from our web page on a biblical worldview “we look to the Bible for our beliefs and how we should operate. We believe students at this level can use wisdom in such courses, but if you are uncomfortable, please select from our Ignitia course offerings.

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THE STUDENT EXPERIENCE

MATH COURSE

ALGEBRA II HONORS online (second semester)​

Unit 9: ​Rational Functions

1. Simplifying Rational Expressions Guided Notes
   1. ​Warm-Up -Get ready for the lesson.
   2. Instruction - How can you simplify rational expressions containing multiple variables?
      1. ​Intro to rational expression simplification
      2. Simplifying rational expressions: common monomial factors
      3. Simplifying rational expressions: common binomial factors
   3. Assignment - Practice simplifying rational expressions with negative exponents.
   4. ​Quiz Answers
2. Simplifying Rational Expressions by Factoring Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can you use what you know about simplifying fractions to simplify rational expressions?
      1. ​Simplifying rational expressions: opposite common binomial factors
      2. Simplifying rational expressions: grouping
   3. Summary - Review and connect what you learned.
   4. Assignment - Practice simplifying a factored expression.
   5. Quiz Answers
3. Multiplying and Dividing Rational Expressions Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How do you multiply and divide rational expressions?
      1. Multiplying & dividing rational expressions: monomials​
      2. Multiplying rational expressions
   3. Assignment - Practice multiplying rational expressions.
   4. Quiz Answers  
4. Adding and Subtracting Rational Expressions Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can you find sums and differences of rational expressions?
      1. ​Adding & subtracting rational expressions: like denominators
      2. Intro to adding rational expressions with unlike denominators
      3. Subtracting rational expressions: unlike denominators
      4. Subtracting rational expressions
   3. Assignment - Practice adding and subtracting rational expressions with like denominators.
   4. Quiz Answers
5. Rational Equations Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can you solve an equation containing rational expressions?
      1. ​​Rational equations intro
      2. ​Equations with rational expressions
      3. Equations with rational expressions (example 2)
   3. Assignment  Practice solving rational equations.
   4. Quiz Answers - 
6. Graphing Rational Functions Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How do you graph rational functions that have vertical and horizontal asymptotes?
      1. Graphing rational functions 1
      2. Graphing rational functions 2
      3. Graphing rational functions 3
      4. Graphing rational functions 4
   3. Assignment - Identify asymptotes.
   4. Quiz Answers
7. Rational Inequalities Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - What are the steps to solving a rational inequality?
      1. ​Rational inequalities: one side is zero
      2. ​Rational inequalities: both sides are not zero
   3. Summary - Review and connect what you learned.
   4. Assignment - Find the critical points.
   5. Assignment - Solve real-world problems.
   6. Quiz Answers
8. Modeling with Rational Functions Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How are rational functions used to model and solve problems?
      
      1. ​Modeling with Rational Functions
         
      2. Rational equations word problem: combined rates
         
      3. Rational equations word problem: eliminating solutions
         
   3. Assignment - Write a rational function given a table.
   4. Quiz Answers
9. Unit Test
   1. Unit Test Review Answers
   2. ​Unit Test Answers

Unit 10: Radical Functions

1. Graphing Radical Functions Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How do you graph radical functions?
      1. ​Graphing square and cube root functions
   3. Assignment - Practice graphing radical functions.
   4. Quiz Answers
2. Rational Exponents Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - Can exponents be fractions?
      1. ​Intro to rational exponents
      2. Rewriting roots as rational exponents
   3. Assignment - Explore an equation that relates the distance from the Sun to its orbital period
   4. Assignment - Convert between radical and exponential forms.
   5. Quiz Answers
3. Multiplying Radicals Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can you multiply radical expressions?
      1. ​Multiplying Radicals and Then Simplifying
      2. Multiplying Radical Expressions With Variables and Exponents
   3. Assignment - Multiply radicals with like indices.
   4. Quiz Answers
4. Dividing Radicals Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can you write a ratio of radical expressions in simplest form?
      1. ​Intro to rationalizing the denominator
         
      2. Worked example: rationalizing the denominator
         
   3. Assignment - Use the quotient property of radicals.
   4. Quiz Answers
5. Radical Equations and Extraneous Roots Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How do you solve an equation when the variable is under a radical symbol?
      1. ​Solving square-root equations: one solution
         
      2. Solving square-root equations: two solutions
         
      3. Solving square-root equations: no solution
         
   3. Assignment - Solve radical equations.
   4. Quiz Answers
6. Unit Test
   1. Unit Test Review Answers
   2. ​Unit Test Answers

Unit 11: Exponential and Logarithmic Functions

1. Graphing Exponential Functions Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - What are the key features of the graph of an exponential function?
      1. ​Exponential function graph
      2. Graphs of exponential growth
   3. Assignment - Practice identifying the domain and range of an exponential function.
   4. Quiz Answers
2. Solving Exponential Equations by Rewriting the Base Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can you solve equations that have variable exponents?
      1. ​Solving exponential equations using exponent properties
      2. Solving exponential equations using exponent properties (advanced)
   3. Assignment - Practice solving exponential equations with a common base.
   4. Quiz Answers
3. Graphing Logarithmic Functions Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - What methods can you use to graph the inverses of exponential functions?
      1. ​Shape of a logarithmic parent graph
      2. ​Graphs of logarithmic functions
   3. Assignment - Identify the graph of a logarithmic function.
   4. ​Quiz Answers
4. Evaluating Logarithmic Expressions Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How do inverse relationships help you evaluate logarithmic expressions and solve equations?
      1. ​Intro to logarithms
         
      2. Evaluating logarithms (advanced)
         
   3. Assignment - Solve problems about the Richter scale.
   4. Quiz Answers
5. Solving Logarithmic Equations using Technology Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can you solve logarithmic equations both numerically and graphically?
      1. ​Solving Logarithmic Equations
         
      2. Solving Logarithmic Equations
         
   3. Assignment - Practice using the change of base formula.
   4. Quiz Answers
6. Base e Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - What other common bases are used for exponential and logarithmic functions?
      1. ​Evaluating natural logarithm with calculator
         
      2. 𝑒 as a limit
         
   3. Assignment - Practice graphing exponential functions in base e.
   4. Quiz Answers
7. Modeling with Exponential and Logarithmic Equations Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - What kinds of real-world problems can you solve using exponential and logarithmic functions?
      1. Interpreting change in exponential models​
         
      2. Constructing exponential models: half life
         
      3. Modeling with exponential and logarithmic functions
         
   3. Assignment - Explore the unusual population growth of water lilies.
   4. Instruction - What kinds of real-world problems can you solve using exponential and logarithmic functions?
   5. Summary - Review and connect what you learned.
   6. Assignment - Practice using the half-life model.
   7. Quiz Answers
8. Unit Test
   1. Unit Test Review Answers
   2. ​Unit Test Answers

Unit 12: Sequences and Series

1. Arithmetic Sequences Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How are sequences whose consecutive terms differ by a constant modeled, and what can those models tell us?
      1. ​Intro to arithmetic sequences
      2. Extending arithmetic sequences
      3. Using arithmetic sequences formulas
   3. Summary - Review and connect what you learned.
   4. Assignment - Identify an arithmetic sequence.
   5. ​Quiz Answers
2. Geometric Sequences Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can a sequence with exponential properties be defined?
      1. Intro to geometric sequences​
      2. Extending geometric sequences
      3. Using explicit formulas of geometric sequences
   3. Summary - Review and connect what you learned.
   4. Assignment - Identify geometric sequences.
   5. Quiz Answers
3. Geometric Series Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can you find the sum of the terms of a finite or infinite geometric sequence?
      1. ​Geometric series introduction
      2. Finite geometric series formula
      3. Worked examples: finite geometric series
      4. Finding The Sum of an Infinite Geometric Series
   3. Assignment - Solve a geometric series problem.
   4. Quiz Answers
4. Recursive Formulas Guided Notes
   1. Warm-Up - Get ready for the lesson.
   2. Instruction - How are recursive formulas used to describe a sequence?
      1. ​Recursive formulas for arithmetic sequences
      2. ​Converting recursive & explicit forms of arithmetic sequences
   3. Summary - Review and connect what you learned.
   4. Assignment - Convert an explicit formula to a recursive formula.
   5. Quiz Answers
5. Unit Test
   1. Unit Test Review Answers
   2. ​Unit Test Answers

Unit 13: Applications of Probability

1. Sets and Venn Diagrams Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - What are sets and how can they be represented?
      1. ​​Intersection of Sets, Union of Sets and Venn Diagrams
   3. Summary - Review and connect what you learned.
   4. Assignment - Practice interpreting Venn diagrams.
   5. Quiz Answers
2. Finding Outcomes Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can you use permutations or combinations to determine the number of possible outcomes of an event?
      1. ​Permutation formula
      2. ​Ways to pick officers
      3. Intro to combinations
      4. Handshaking combinations
   3. Summary - Review and connect what you learned.
   4. Assignment - Practice solving problems using factorials, permutations, and combinations.
   5. Quiz Answers
3. Theoretical and Experimental Probability Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can you calculate the probability of an event occurring?
      1. ​Theoretical and experimental probabilities
      2. Making predictions with probability​
   3. Summary - Review and connect what you learned.
   4. Assignment - Practice with experimental and theoretical probability.
   5. Quiz Answers
4. Independent and Mutually Exclusive Events Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How do you calculate the probabilities of mutually exclusive and independent events?
      1. ​Independent & dependent probability
         
      2. Probability of Mutually Exclusive Events With Venn Diagrams
         
   3. Summary - Review and connect what you learned.
   4. Assignment - Practice calculating probabilities using addition and multiplication rules.
   5. Quiz Answers
5. Conditional Probability Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can you calculate a conditional probability?
      1. ​Calculating conditional probability
         
      2. Conditional probability explained visually
         
      3. Conditional probability tree diagram example
         
   3. Summary - Review and connect what you learned.
   4. Assignment Practice calculating and applying conditional probabilities.
   5. Quiz Answers 
6. Probability and Two-Way Tables Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can two-way tables be used to find conditional probability?
      1. ​Two-way frequency tables and Venn diagrams
         
      2. Two-way relative frequency tables
         
      3. Interpreting two-way tables
         
   3. Summary - Review and connect what you learned.
   4. Assignment - Practice analyzing two-way tables to determine conditional probabilities and independent events.
   5. Quiz Answers
7. Probability with Combinations and Permutations Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can combinations and permutations help calculate the probability of compound events?
      1. ​Permutations, Combinations & Probability
         
   3. Summary - Review and connect what you learned.
   4. Assignment - Practice writing and solving problems involving probability of compound events.
   5. Quiz Answers
8. Performance Task: Applying Probability Concepts
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can probability be applied to decision making?
   3. Summary - Review and connect what you learned.
   4. Preparing for Your Performance Task - Prepare to show what you know about using probability to make decisions in a Performance Task.
   5. Performance Task - Show what you know about using probability to make decisions.
9. Unit Test
   1. Unit Test Review Answers
   2. ​Unit Test Answers

Unit 14: ​Statistics and Probability

1. Designing a Study Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can you collect data?
      1. ​Data collection and conclusions — Basic example
      2. What Are The Types Of Sampling Techniques In Statistics - Random, Stratified, Cluster, Systematic
   3. Assignment - Practice determining the sampling method.
   4. Quiz Answers
2. Representing Data Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can you describe a set of data?
      1. Representing data​
      2. Frequency tables & dot plots
   3. Assignment - Solve and write about graphs and reports.
   4. Quiz Answers
3. Standard Deviation Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can you use standard deviation to represent the spread of data?
      1. ​Measures of spread: range, variance & standard deviation
      2. ​Variance of a population
   3. Assignment - Calculate the variance.
   4. Quiz Answers
4. Properties of Probability Distributions Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - What are probability distributions and how are they used to solve problems?
      1. ​Introduction to Probability Distributions
   3. Assignment - Identify the probability distribution.
   4. Quiz Answers
5. Introduction to Normal Distributions Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can you describe normal distributions and use them to learn about data?
      1. ​Normal distribution problem: z-scores (from ck12.org)
      2. Comparing with z-scores
      3. Normal Distribution & Probability Problems
   3. Assignment - Practice Interpreting Z-Scores
   4. Quiz Answers
6. Applications with Standard Normal Distribution Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can a standard normal table be used to find any probabilities of any normally distributed data?
      1. ​Standard Normal Distribution Tables, Z Scores, Probability & Empirical Rule
   3. Assignment - Practice using the standard normal table.
   4. Quiz Answers
7. Statistical Inferences Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How confidently can you predict a parameter of a population, given data from a random sample?
      1. ​An Introduction to Statistical Inference
   3. Assignment - Practice making a statistical inference.
   4. Quiz Answers
8. Hypothesis Testing Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can you test claims about a population using a sample?
      1. Intro to Hypothesis Testing in Statistics - Hypothesis Testing Statistics Problems & Examples​
      2. ​Simple hypothesis testing | Probability and Statistics | Khan Academy
   3. Assignment - Practice identifying the null and alternative hypotheses for a statistical claim.
   4. Quiz Answers
9. Unit Test
   1. Unit Test Review Answers
   2. ​Unit Test Answers

Unit 15: ​Trigonometric Functions

1. Angles in Standard Position Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can we define and analyze angles using their characteristics?
      1. ​Angles in Standard Position
         
   3. Assignment - Identify negative angle measure.
   4. Quiz Answers
2. Radian Measure Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - What is radian measure and how is it related to degree measure?
      1. ​Radians and Degrees
         
   3. Assignment - Practice converting radians to degrees.
   4. Quiz Answers
3. The Unit Circle Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - Can trigonometric functions be extended to any angle measure?
      1. ​Unit circle
         
      2. Unit Circle Trigonometry - Sin Cos Tan - Radians & Degrees
         
   3. Assignment - Identify the coordinates of points on the unit circle.
   4. Quiz Answers
4. Evaluating the Six Trigonometric Functions Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can you use the relationships among trigonometric functions to evaluate them?
      1. ​Evaluate the six trigonometric functions given a point
         
   3. Assignment - Practice evaluating trigonometric functions given a point on the terminal ray.
   4. Quiz Answers
5. Graphing Sine and Cosine Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - Why do the graphs of the sine and cosine functions have wave shapes, and how can you change those waves?
      1. Graphing Sin and Cos​
         
   3. Assignment - Solve and write about problems involving periodic movements and wheels.
   4. Quiz Answers
6. Changes in Period and Phase Shift of Sine and Cosine Functions Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How is a transformation of the graph related to the equation of a sine or cosine function?
      1. ​Graphing Sine and Cosine Trig Functions With Transformations, Phase Shifts, Period - Domain & Range
         
      2. Transforming sinusoidal graphs: vertical stretch & horizontal reflection
         
   3. Assignment - Practice identifying transformations from a graph.
   4. Quiz Answers
7. Modeling with Periodic Functions Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can sine and cosine help you solve real-world problems involving cycles?
      1. ​Trig word problem: modeling annual temperature
         
      2. Trig word problem: length of day (phase shift)
         
   3. Assignment - Explore using a periodic function to model a rope swing.
   4. Assignment - Practice identifying situations that can be modeled by a periodic function.
   5. Quiz Answers
8. Unit Test
   1. Unit Test Review Answers
   2. ​Unit Test Answers

Unit 16: ​Mathematical Modeling

1. Absolute Value Functions Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can I analyze and apply absolute value functions?
      1. Shifting absolute value graphs​
      2. Scaling & reflecting absolute value functions: graph
   3. Summary - Review and connect what you learned.
   4. Assignment - Practice analyzing absolute value functions.
   5. Quiz Answers
2. Absolute Value Inequalities Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How do you solve an inequality that has an absolute value expression?
      1. ​Intro to absolute value inequalities
      2. Solving absolute value inequalities 1
      3. Solving absolute value inequalities 2
   3. Summary - Review and connect what you learned.
   4. Assignment - Practice choosing the compound inequality.
   5. Quiz Answers
3. Piecewise Defined Functions Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How do you define and analyze a function when it cannot be described by a single rule?
      1. ​Introduction to piecewise functions
      2. Worked example: graphing piecewise functions
   3. Assignment - Practice evaluating piecewise defined functions.
   4. Quiz Answers
4. Step Functions Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can you model a function that can only take on integer values?
      1. ​Understanding Step Functions by Shmoop
   3. Summary - Review and connect what you learned.
   4. Assignment - Evaluate step functions.
   5. Quiz Answers
5. Transformations of Functions Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How are function rules and their graphs related?
      1. ​Introduction to Transformations of Functions
   3. Assignment - Identify the equation of the transformed function.
   4. Quiz Answers
6. Modeling with Functions Guided Notes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How can you find the equation of a function that best models a data set?
      1. ​Modeling with Functions Part 1
      2. ​Modeling with Functions Part 2
   3. Assignment - Practice identifying the type of function that best models a data set.
   4. Quiz Answers
7. Performance Task: Production Schemes
   1. ​Warm-Up - Get ready for the lesson.
   2. Instruction - How do piecewise functions help you model and analyze production schemes?
   3. Performance Task - Production Schemes
8. Unit Test
   1. ​Unit Test Review Answers
   2. Unit Test Answers

Unit 17: ​Cumulative Exam
Cumulative Exam Review Answers
Cumulative Exam Answers