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Algebra 2: 01-Expressions, Equations, and Inequalities
Algebra 2: 02-Functions, Equations, and Graphs
Algebra 2: 03-Linear Systems
Algebra 2: 04-Quadratic Functions and Equations
Algebra 2: 05-Polynomials and Polynomial Functions
Algebra 2: 06-Radical Functions and Rational Exponents
Algebra 2: 07-Exponential and Logarithmic Functions
Algebra 2: 08-Rational Functions
Algebra 2: 09-Sequences and Series
Algebra 2: 10-Quadratic Relations and Conic Sections
Algebra 2: 11-Probability
Algebra 2: 12-Matrices
Algebra 2: 13-Periodic Functions and Trigonometry
Algebra 2: 14-Trigonometric Identities and Equations
I. Expressions, Equations, and Inequalities
Patterns and Expressions
Example: What is the next number in the pattern: 3, 6, 9, 12, _ ?
Lesson: Properties of Real Numbers
Example: Which property justifies the equation ?
Lesson: Algebraic Expressions
Example: Which algebraic expression models the phrase “10 less than a number m”?
Solving Equations
Example: What is the value of in
?
Solving Inequalities
Example: Write the inequality that represents “3 less than a number is greater than 5”
Absolute Value Equations and Inequalities
Example: Evaluate
II. Functions, Equations, and Graphs
Relations and Functions
Example: What is the output of the function if
?
Direct Variation
Example: If varies directly with
, and
when
, then what is the value of
when
?
Linear Functions and Slope-Intercept Form
Example: Find the slope of the line passing through the points (2,4) and (4,-2)
More About Linear Equations
Example: Write the equation of the line with a slope of 3 that goes through the point (5,0).
Using Linear Models
Example: Can the values 2, 4, 6, 8, 10 be modeled by a linear function?
Families of Functions
Example: What is the equation of the line after it undergoes a transformation 2 units up and 3 units left?
Absolute Value Functions and Graphs
Example: Solve for :
Two Variable Inequalities
Example: Draw the graph of
III. Linear Systems
Lesson: Solving Systems of Equations Using Tables and Graphs
Example: Solve the following system of equations graphically: and
Solving Systems Algebraically
Example: Solve the following system of equations algebraically: and
Lesson: System of Inequalities
Example: Solve the following system of inequalities: and
Linear Programming
Example: What values for and
maximize the objective function
?
Systems with Three Variables
Example: Solve the following system of equations: ,
, and
Solving Systems Using Matrices
Example: Solve the following system of equations by using matrices: and
IV. Quadratic Functions and Equations
Quadratic Functions and Transformations
Example: What is the vertex of the function ?
Standard Form of a Quadratic Equation
Example: What is the vertex of the function ?
Modeling with Quadratic Functions
Example: Do the points (3,-1), (4,0), and (5,-1) lie on the function ?
Lesson: Factoring Quadratic Expressions
Example: Factor the expression
Lesson: Quadratic Equations
Example: Solve for :
Lesson: Completing the Square
Example: What are the solutions to
The Quadratic Formula
Example: Solve for using the quadratic formula:
Complex Numbers
Example: What is equivalent to ?
Lesson: Quadratic Systems
Example: Solve the following system of equations: and
V. Polynomials and Polynomial Functions
Polynomial Functions
Example: Classify the following polynomial by its degree and number of terms:
Polynomials, Linear Factors, and Zeros
Example: What is the factored form of
Solving Polynomial Equations
Example: Solve for :
Lesson: Dividing Polynomials
Example: What is the solution to ?
Rational Root Theorem
Example: What are the possible rational zeroes for ?
The Fundamental Theorem of Algebra
Example: Solve for :
The Binomial Theorem
Example: How can you expand ?
Polynomial Models in the Real World
Example: What are three points that lie on ?
Transforming Polynomial Functions
Example: What is the equation of after it is reflected in the y-axis and then translated 4 units down and 3 units left?
VI. Radical Functions and Rational Exponents
Roots and Radical Expressions
Example: What values are square roots of 25?
Lesson: Multiplying and Dividing Radical Expressions
Example: Evaluate
Binomial Radical Expressions
Example: Evaluate
Rational Expressions
Example: Evaluate
Lesson: Solving Square Root and Other Rational Expressions
Example: Solve for :
Function Operations
Example: Find if
and
Inverse Relations and Functions
Example: What is the inverse function of ?
Lesson: Graphing Radical Functions
Example: Draw the graph of
VII. Exponential and Logarithmic Functions
Exploring Exponential Models
Example: How can you describe the function ?
Properties of Exponential Models
Example: What transformation changed to
?
Logarithmic Functions as Inverses
Example: What is the inverse function of ?
Properties of Logarithms
Example: Expand
Exponenital and Logarithmic Equations
Example: Solve for :
Natural Logarithms
Example: Evaluate
VIII. Rational Funtions
Lesson: Inverse Variation
Example: Suppose and
vary inversely. Write a function for when
and
The Reciprocal Family Functions
Example: What is the y-intercept of
Lesson: Rational Functions and their Graphs
Example: Draw the graph of
Rational Expressions
Example:
Lesson: Adding and Subtracting Rational Expressions
Example: Simplify
Lesson: Solving Rational Equations
Example: Solve for :
IX. Sequences and Series
Mathematical Patterns
Example: Continue the pattern with the next three values: 4, 12, 36, 108, …
Arithmetic Sequences
Example: What is the explicit formula for the sequence 12, 15, 18, 21, …?
Geometric Sequences
Example: What is the explicit formula for the sequence 2, -6, 18, -54, …?
Arithmetic Series
Example: What is the sum of the series 32, 43, 54, 65, 76?
Geometric Series
Example: What is the sum of the series -3 -6 -12 -24 …, n=6?
X. Quadratic Relations and Conic Sections
Exploring Conic Sections
Example: Which conic section is associated with the equation ?
Parabolas
Example: What is the vertex of the function ?
Circles
Example: What is the radius of the circle ?
Ellipses
Example: What are the vertices of the ellipse ?
Hyperbolas
Example: What are the vertices of the hyperbola ?
Translating Conic Sections
Example: Write the standard form equation of an ellipse with vertices at (-2,3) and (5,3), and a focus at (2,3)
XI. Probability and Statistics
Lesson: Permutation and Combinations
Example: Evaluate
Lesson: Probability
Example: Bob flipped heads 6 out of 8 times. What is the experimental probability that he flips tails on his next coin toss?
Lesson: Probability of Multiple Events
Example: What is the probability of A and B if they are independent events and the probability of A is and the probability of B is
?
Conditional Probability
Example: If the freshman students are 45% male and 55% female, and 86% of the males passed this semester while 89% of the females did, what is the probability that a student is male who failed this semester?
Probability Models
Example: The weather channel tells you that there is a 30% chance of rain on each of the next three days. What is the chance that it does not rain on all three days?
Analyzing Data
Example: What is the median of {28 26, 40, 37, 39, 29, 31, 33, 33, 33, 31, 36}?
Standard Deviations
Example: What is the standard deviation of {28 26, 40, 37, 39, 29, 31, 33, 33, 33, 31, 36}?
Lesson: Samples and Surveys
Example: If a principal wants to conduct a survey to determine which subject is the favorite in his school, so he samples the physics class to get results, is this a biased sample?
Binomial Distributions
Example: What is the fourth term in ?
Normal Distributions
Example: What percent of data is in the interval from 45 to 50 in a data set with a mean of 55 and a standard deviation of 5?
XII. Matrices
Lesson: Adding and Subtracting Matrices
Example: Simplify
Lesson: Matrix Multiplication
Example: Simplify
Determinants and Inverses
Example:
Inverse Matrices and Systems
Example: Solve the following system of equations using matrices: and
Geometric Transformations
Example: Dilate the coordinates forming a traingle given in the following matrix by a scale factor of 3.
Vectors
Example: If a vector starts at the point (2, 3) and extends to (4, 6), what is its component form?
XIII. Periodic Functions and Trigonometry
Exploring Periodic Data
Example: What is the amplitude and the period of ?
Angles and the Unit Circle
Example: If an angle extends outwards from the x-axis and touches the x-axis on the other side, what is the degree measure of the angle formed?
Radian Measures
Example: What is 50 degrees in terms of radians?
The Sine Function
Example: What is the amplitude and the period of ?
The Cosine Function
Example: What is the amplitude and the period of ?
The Tangent Function
Example: What is the amplitude and the period of ?
Translating Sine and Cosine Functions
Example: What is the amplitude and the period of ?
Reciprocal Trigonometric Functions
Example: Evaluate
XIV. Trigonometric Identities and Equations
Trigonometric Identities
Example: What is equivalent to
Solving Trigonometric Equations Using Inverses
Example: Solve for :
Right Triangles and Trigonometric Ratios
Example: In a 30-60-90 triangle, what is ?
Area and Law of Sines
Example: In ,
,
, and
. Find
The Law of Cosines
Example: In ,
,
, and
. Find
Angle Identities
Example: Evaluate
Double-Angle and Half-Angle Identities
Example: Find is
and