2 semesters

½ credit each semester

Instructor: Rod Friedrich

Email: Rod.Friedrich@k12.sd.us

Webpage: http://rf017.k12.sd.us/algebra_ii.htm

School phone: 605-498-2700

Conference times available:

Algebra 2

Book webpage: http://www.glencoe.com/sec/math/algebra/algebra2/algebra2_05/

This course will continue with algebraic concepts. Students will study first degree equations and inequalities, polynomial and radical equations and inequalities, conic sections, exponential and logarithmic relations, and probability and statistics.

Prerequisites: Algebra I

Follow directions and all school rules and regulations found in the school handbook.

All students should bring all materials to class. These include:

Ø      Book

Ø      Completed homework

Ø      Red pen

Ø      Pencil, if your homework is done in pen, you will not get full credit

Ø      Agenda

Ø      Paper

Chapter 1 – Solving Equations and Inequalities

9-12.A.1.0 Use procedures to transform algebraic expressions.

9-12.A.1.1. Students are able to write equivalent forms of algebraic expressions using properties of the set of real numbers.

9-12.A.1.1A. Students are able to write equivalent forms of rational algebraic expressions using properties of real numbers.

9-12.A.2.0 Use a variety of algebraic concepts and methods to solve equations and inequalities.

9-12.A.2.1. Students are able to use algebraic properties to transform multi-step, single-variable, first-degree equations.

9-12.A.2.2. Students are able to use algebraic properties to transform multi-step, single-variable, first-degree inequalities and represent solutions using a number line.

9-12.A.2.2A. Students are able to determine the solution of systems of equations and systems of inequalities.

9-12.A.2.3A.  Students are able to determine solutions to absolute value statements.

9-12.A.3.0 Interpret and develop mathematical models.

9-12.M.1.3. Students are able to use formulas to find perimeter, circumference, and area to solve problems involving common geometric figures.

9-12.N.1.0 Analyze the structural characteristics of the real number system and its various subsystems.  Analyze the concept of value, magnitude, and relative magnitude of real numbers.

9-12.N.1.1. Students are able to identify multiple representations of a real number.

9-12.N.1.2. Students are able to apply the concept of place value, magnitude, and relative magnitude of real numbers.

9-12.N.1.2A. Students are able to apply properties and axioms of the real number system to various subsets, e.g., axioms of order, closure.

9-12.N.2.0 Apply number operations with real numbers and other number systems.

9-12.N.2.1. Students are able to add, subtract, multiply, and divide real numbers including integral exponents.

9-12.N.2.1A. Students are able to add, subtract, multiply, and divide real numbers including rational exponents.

Chapter 2 – Linear Relations and Functions

9-12.A.2.0 Use a variety of algebraic concepts and methods to solve equations and inequalities.

9-12.A.2.1. Students are able to use algebraic properties to transform multi-step, single-variable, first-degree equations.

9-12.A.2.3A.  Students are able to determine solutions to absolute value statements.

9-12.A.3.0 Interpret and develop mathematical models.

9-12.A.3.1. Students are able to create linear models to represent problem situations.

9-12.A.3.1A. Students are able to distinguish between linear, quadratic, inverse variation, and exponential models.

9-12.A.3.2. Students are able to distinguish between linear and nonlinear models.

Describe and use properties and behaviors of relations, functions, and inverses.

9-12.A.3.2A. Students are able to create formulas to model relationships that are algebraic, geometric, trigonometric, and exponential.

9-12.A.4.0 Describe and use properties and behaviors of relations, functions, and inverses.

9-12.A.4.1. Students are able to use graphs, tables, and equations to represent linear functions.

9-12.A.4.1A. Students are able to determine the domain, range, and intercepts of a function.

9-12.A.4.5A.  Students are able to describe characteristics of nonlinear functions and relations.

9-12.A.4.6A.  Students are able to graph solutions to linear inequalities.

9-12.S.1.0 Use statistical models to gather, analyze, and display data to draw conclusions.

9-12.S.1.1. Students are able to draw conclusions from a set of data.

9-12.S.1.3. Represent a set of data in a variety of graphical forms and draw conclusions.

9-12.S.1.5A. Students are able to use scatterplots, best-fit lines, and correlation coefficients to model data and support conclusions.

Chapter 3 – Systems of Equations and Inequalities

9-12.A.2.0 Use a variety of algebraic concepts and methods to solve equations and inequalities.

9-12.A.2.2A. Students are able to determine the solution of systems of equations and systems of inequalities.

9-12.A.3.0 Interpret and develop mathematical models.

9-12.A.3.2A. Students are able to create formulas to model relationships that are algebraic, geometric, trigonometric, and exponential.

9-12.A.4.5A.  Students are able to describe characteristics of nonlinear functions and relations.

9-12.A.4.6A.  Students are able to graph solutions to linear inequalities.

Chapter 4 – Matrices

9-12.A.2.0 Use a variety of algebraic concepts and methods to solve equations and inequalities.

9-12.A.2.2A. Students are able to determine the solution of systems of equations and systems of inequalities.

Chapter 5 - Polynomials

9-12.A.1.0 Use procedures to transform algebraic expressions.

9-12.A.1.1. Students are able to write equivalent forms of algebraic expressions using properties of the set of real numbers.

9-12.A.1.1A. Students are able to write equivalent forms of rational algebraic expressions using properties of real numbers.

9-12.A.1.2A. Students are able to extend the use of real number properties to expressions involving complex numbers.

9-12.A.2.0 Use a variety of algebraic concepts and methods to solve equations and inequalities.

9-12.N.1.0 Analyze the structural characteristics of the real number system and its various subsystems.  Analyze the concept of value, magnitude, and relative magnitude of real numbers.

9-12.N.1.1. Students are able to identify multiple representations of a real number.

9-12.N.1.2. Students are able to apply the concept of place value, magnitude, and relative magnitude of real numbers.

9-12.N.1.2A. Students are able to apply properties and axioms of the real number system to various subsets, e.g., axioms of order, closure.

9-12.N.2.0 Apply number operations with real numbers and other number systems.

9-12.N.2.1. Students are able to add, subtract, multiply, and divide real numbers including integral exponents.

9-12.N.2.1A. Students are able to add, subtract, multiply, and divide real numbers including rational exponents.

Chapter 6 – Quadratic Functions and Inequalities

9-12.A.1.2A. Students are able to extend the use of real number properties to expressions involving complex numbers.

9-12.A.2.0 Use a variety of algebraic concepts and methods to solve equations and inequalities.

9-12.A.2.1A. Students are able to determine solutions of quadratic equations.

9-12.A.3.0 Interpret and develop mathematical models.

9-12.A.3.2. Students are able to distinguish between linear and nonlinear models.

9-12.A.3.1A. Students are able to distinguish between linear, quadratic, inverse variation, and exponential models.

9-12.A.4.0 Describe and use properties and behaviors of relations, functions, and inverses.

9-12.A.4.1A. Students are able to determine the domain, range, and intercepts of a function.

9-12.A.4.2A. Students are able to describe the behavior of a polynomial, given the leading coefficient, roots, and degree.

9-12.A.4.3A.  Students are able to apply transformations to graphs and describe the results.

9-12.A.4.5A.  Students are able to describe characteristics of nonlinear functions and relations.

9-12.A.4.6A.  Students are able to graph solutions to linear inequalities.

Chapter 7 – Polynomial Functions

9-12.A.4.0 Describe and use properties and behaviors of relations, functions, and inverses.

9-12.A.4.1A. Students are able to determine the domain, range, and intercepts of a function.

9-12.A.4.2A. Students are able to describe the behavior of a polynomial, given the leading coefficient, roots, and degree.

9-12.A.4.3A.  Students are able to apply transformations to graphs and describe the results.

9-12.A.4.5A.  Students are able to describe characteristics of nonlinear functions and relations.

9-12.A.4.6A.  Students are able to graph solutions to linear inequalities.

Chapter 8 – Conic Sections

9-12.A.2.0 Use a variety of algebraic concepts and methods to solve equations and inequalities.

9-12.A.2.2A. Students are able to determine the solution of systems of equations and systems of inequalities.

9-12.A.3.0 Interpret and develop mathematical models.

9-12.A.3.2A. Students are able to create formulas to model relationships that are algebraic, geometric, trigonometric, and exponential.

9-12.A.4.0 Describe and use properties and behaviors of relations, functions, and inverses.

9-12.A.4.2A. Students are able to describe the behavior of a polynomial, given the leading coefficient, roots, and degree.

9-12.A.4.3A.  Students are able to apply transformations to graphs and describe the results.

9-12.A.4.5A.  Students are able to describe characteristics of nonlinear functions and relations.

9-12.A.4.6A.  Students are able to graph solutions to linear inequalities.

9-12.G.2.0 Use properties of geometric figures to solve problems from a variety of perspectives.

9-12.G.2.1A. Students are able to use Cartesian coordinates to verify geometric properties.

Chapter 10 – Exponential and Logarithmic Relations

9-12.A.1.0 Use procedures to transform algebraic expressions.

9-12.A.2.0 Use a variety of algebraic concepts and methods to solve equations and inequalities.

9-12.A.3.0 Interpret and develop mathematical models.

9-12.A.3.1A. Students are able to distinguish between linear, quadratic, inverse variation, and exponential models.

9-12.A.3.2A. Students are able to create formulas to model relationships that are algebraic, geometric, trigonometric, and exponential.

9-12.A.4.0 Describe and use properties and behaviors of relations, functions, and inverses.

9-12.A.4.4A. Students are able to apply properties and definitions of trigonometric, exponential, and logarithmic expressions.

9-12.A.4.5A.  Students are able to describe characteristics of nonlinear functions and relations.

9-12.N.1.0 Analyze the structural characteristics of the real number system and its various subsystems.  Analyze the concept of value, magnitude, and relative magnitude of real numbers.

Chapter 12 – Probability and Statistics

9-12.S.1.0 Use statistical models to gather, analyze, and display data to draw conclusions.

9-12.S.1.1. Students are able to draw conclusions from a set of data.

9-12.S.1.2. Students are able to compare multiple one-variable data sets, using range, interquartile range, mean, mode, and median.

9-12.S.1.3. Represent a set of data in a variety of graphical forms and draw conclusions.

9-12.S.1.1A.  Students are able to analyze and evaluate the design of surveys and experiments.

9-12.S.1.2A. Students are able to analyze and evaluate graphical displays of data.

9-12.S.1.3A. Students are able to compare multiple one-variable data sets, using standard deviation and variance.

9-12.S.1.4A.  Students are able to describe the normal curve and use it to make predictions.

9-12.S.1.5A. Students are able to use scatterplots, best-fit lines, and correlation coefficients to model data and support conclusions.

9-12.S.2.0 Apply the concepts of probability to predict events/outcomes and solve problems.

9-12.S.2.1. Students are able to distinguish between experimental and theoretical probability.

9-12.S.2.2. Students are able to predict outcomes of simple events using given theoretical probabilities.

9-12.S.2.1A. Students are able to use probabilities to solve problems. 

9-12.S.2.2A. Students are able to determine probability of compound, complementary, independent, and mutually exclusive events.

9-12.S.2.3A. Students are able to generate data and use the data to determine empirical (experimental) probabilities.

2 semesters

½ credit each semester

Instructor: Rod Friedrich

Email: Rod.Friedrich@k12.sd.us

Webpage: http://rf017.k12.sd.us/pre_calculus.htm

School phone: 605-498-2700

Conference times available:

Advanced Mathematical Concepts

Book webpage: http://www.glencoe.com/sec/math/precalculus/amc_04/

This course will involve advanced algebraic concepts. Students will study linear relations and functions, systems of linear equations and inequalities, the nature of graphs, polynomial and rational functions, trigonometric functions and their graphs, trigonometric identities, and conic sections.

Prerequisites: Algebra II

Follow directions and all school rules and regulations found in the school handbook.

All students should bring all materials to class. These include:

Ø      Book

Ø      Completed homework

Ø      Red pen

Ø      Pencil, if your homework is done in pen, you will not get full credit

Ø      Agenda

Ø      Paper

Chapter 1 – Linear Relations and Functions

9-12.A.2.3A.  Students are able to determine solutions to absolute value statements.

9-12.A.3.0 Interpret and develop mathematical models.

9-12.A.3.1. Students are able to create linear models to represent problem situations.

9-12.A.3.1A. Students are able to distinguish between linear, quadratic, inverse variation, and exponential models.

9-12.A.3.2A. Students are able to create formulas to model relationships that are algebraic, geometric, trigonometric, and exponential.

9-12.A.4.0 Describe and use properties and behaviors of relations, functions, and inverses.

9-12.A.4.1. Students are able to use graphs, tables, and equations to represent linear functions.

9-12.A.4.1A. Students are able to determine the domain, range, and intercepts of a function.

9-12.A.4.5A.  Students are able to describe characteristics of nonlinear functions and relations.

9-12.A.4.6A.  Students are able to graph solutions to linear inequalities.

9-12.N.1.2A. Students are able to apply properties and axioms of the real number system to various subsets, e.g., axioms of order, closure.

9-12.N.2.0 Apply number operations with real numbers and other number systems.

9-12.N.2.1A. Students are able to add, subtract, multiply, and divide real numbers including rational exponents.

9-12.S.1.0 Use statistical models to gather, analyze, and display data to draw conclusions.

9-12.S.1.1. Students are able to draw conclusions from a set of data.

9-12.S.1.3. Represent a set of data in a variety of graphical forms and draw conclusions.

9-12.S.1.5A. Students are able to use scatterplots, best-fit lines, and correlation coefficients to model data and support conclusions.

Chapter 2 – Systems of Linear Equations and Inequalities

9-12.A.2.0 Use a variety of algebraic concepts and methods to solve equations and inequalities.

9-12.A.2.2A. Students are able to determine the solution of systems of equations and systems of inequalities.

9-12.A.3.0 Interpret and develop mathematical models.

9-12.A.3.2A. Students are able to create formulas to model relationships that are algebraic, geometric, trigonometric, and exponential.

9-12.A.4.6A.  Students are able to graph solutions to linear inequalities.

Chapter 3 – The Nature of Graphs

9-12.A.2.0 Use a variety of algebraic concepts and methods to solve equations and inequalities.

9-12.A.2.3A.  Students are able to determine solutions to absolute value statements.

9-12.A.3.0 Interpret and develop mathematical models.

9-12.A.3.1A. Students are able to distinguish between linear, quadratic, inverse variation, and exponential models.

9-12.A.3.2A. Students are able to create formulas to model relationships that are algebraic, geometric, trigonometric, and exponential.

9-12.A.4.0 Describe and use properties and behaviors of relations, functions, and inverses.

9-12.A.4.1A. Students are able to determine the domain, range, and intercepts of a function.

9-12.A.4.2A. Students are able to describe the behavior of a polynomial, given the leading coefficient, roots, and degree.

9-12.A.4.3A.  Students are able to apply transformations to graphs and describe the results.

9-12.A.4.5A.  Students are able to describe characteristics of nonlinear functions and relations.

9-12.A.4.6A.  Students are able to graph solutions to linear inequalities.

9-12.G.2.2. Students are able to reflect across vertical or horizontal lines, and translate two-dimensional figures.

9-12.G.2.1A. Students are able to use Cartesian coordinates to verify geometric properties.

Chapter 4 – Polynomial and Rational Functions

9-12.A.1.0 Use procedures to transform algebraic expressions.

9-12.A.1.1A. Students are able to write equivalent forms of rational algebraic expressions using properties of real numbers.

9-12.A.2.0 Use a variety of algebraic concepts and methods to solve equations and inequalities.

9-12.A.2.1A. Students are able to determine solutions of quadratic equations.

9-12.A.3.0 Interpret and develop mathematical models.

9-12.A.3.1A. Students are able to distinguish between linear, quadratic, inverse variation, and exponential models.

9-12.A.3.2A. Students are able to create formulas to model relationships that are algebraic, geometric, trigonometric, and exponential.

9-12.A.4.0 Describe and use properties and behaviors of relations, functions, and inverses.

9-12.A.4.1A. Students are able to determine the domain, range, and intercepts of a function.

9-12.A.4.2A. Students are able to describe the behavior of a polynomial, given the leading coefficient, roots, and degree.

9-12.A.4.5A.  Students are able to describe characteristics of nonlinear functions and relations.

9-12.N.2.0 Apply number operations with real numbers and other number systems.

9-12.N.2.1. Students are able to add, subtract, multiply, and divide real numbers including integral exponents.

9-12.S.1.0 Use statistical models to gather, analyze, and display data to draw conclusions.

9-12.S.1.5A. Students are able to use scatterplots, best-fit lines, and correlation coefficients to model data and support conclusions.

Chapter 5 – The Trigonometric Functions

9-12.A.4.4A. Students are able to apply properties and definitions of trigonometric, exponential, and logarithmic expressions.

9-12.G.1.0 Use deductive and inductive reasoning to recognize and apply properties of geometric figures.

9-12.G.1.1. Students are able to apply the properties of triangles and quadrilaterals to find unknown parts.

9-12.G.1.2A. Students are able to determine the values of the sine, cosine, and tangent ratios of right triangles.

9-12.G.2.0 Use properties of geometric figures to solve problems from a variety of perspectives.

9-12.M.1.3. Students are able to use formulas to find perimeter, circumference, and area to solve problems involving common geometric figures.

Chapter 6 – Graphs of Trigonometric Functions

9-12.A.2.0 Use a variety of algebraic concepts and methods to solve equations and inequalities.

9-12.A.3.0 Interpret and develop mathematical models.

9-12.A.3.2A. Students are able to create formulas to model relationships that are algebraic, geometric, trigonometric, and exponential.

9-12.A.4.0 Describe and use properties and behaviors of relations, functions, and inverses.

9-12.A.4.3A.  Students are able to apply transformations to graphs and describe the results.

9-12.A.4.4A. Students are able to apply properties and definitions of trigonometric, exponential, and logarithmic expressions.

9-12.A.4.5A.  Students are able to describe characteristics of nonlinear functions and relations.

9-12.G.1.2A. Students are able to determine the values of the sine, cosine, and tangent ratios of right triangles.

9-12.G.1.3A. Students are able to apply properties associated with circles.

9-12.G.2.0 Use properties of geometric figures to solve problems from a variety of perspectives.

Chapter 7 – Trigonometric Identities and Equations

9-12.A.1.0 Use procedures to transform algebraic expressions.

9-12.A.2.0 Use a variety of algebraic concepts and methods to solve equations and inequalities.

9-12.A.2.1. Students are able to use algebraic properties to transform multi-step, single-variable, first-degree equations.

9-12.A.2.1A. Students are able to determine solutions of quadratic equations.

9-12.A.3.2A. Students are able to create formulas to model relationships that are algebraic, geometric, trigonometric, and exponential.

9-12.A.4.4A. Students are able to apply properties and definitions of trigonometric, exponential, and logarithmic expressions.

9-12.G.1.2A. Students are able to determine the values of the sine, cosine, and tangent ratios of right triangles.

9-12.G.2.1A. Students are able to use Cartesian coordinates to verify geometric properties.

9-12.N.2.1A. Students are able to add, subtract, multiply, and divide real numbers including rational exponents.

Chapter 10 – Conics

9-12.A.2.0 Use a variety of algebraic concepts and methods to solve equations and inequalities.

9-12.A.2.1A. Students are able to determine solutions of quadratic equations.

9-12.A.2.2A. Students are able to determine the solution of systems of equations and systems of inequalities.

9-12.A.4.0 Describe and use properties and behaviors of relations, functions, and inverses.

9-12.A.4.3A.  Students are able to apply transformations to graphs and describe the results.

9-12.A.4.5A.  Students are able to describe characteristics of nonlinear functions and relations.

9-12.A.4.6A.  Students are able to graph solutions to linear inequalities.

9-12.G.1.0 Use deductive and inductive reasoning to recognize and apply properties of geometric figures.

9-12.G.1.3A. Students are able to apply properties associated with circles.

9-12.G.2.0 Use properties of geometric figures to solve problems from a variety of perspectives.

9-12.G.2.1A. Students are able to use Cartesian coordinates to verify geometric properties.

2 semesters

½ credit each semester

Instructor: Rod Friedrich

Email: Rod.Friedrich@k12.sd.us

Webpage: http://rf017.k12.sd.us/calculus.htm

School phone: 605-498-2700

Conference times available:

Single Variable Calculus

Book webpage: http://www.mhhe.com/math/calc/smithminton/

This course will briefly review algebraic and pre-calculus concepts. Students will study limits and continuity, differentiation of algebraic, trigonometric, exponential, and logarithmic functions and their applications, integration and applications of the definite integral, and possibly parametric equations and polar coordinates

Prerequisites: Pre-Calculus

Follow directions and all school rules and regulations found in the school handbook.

All students should bring all materials to class. These include:

Ø      Book

Ø      Completed homework

Ø      Red pen

Ø      Pencil, if your homework is done in pen, you will not get full credit

Ø      Agenda

Ø      Paper

Chapter 0 – Preliminaries

0.1 The Real Numbers and the Cartesian Plane

0.2 Lines and Functions

0.3 Graphing Calculators and Computer Algebra Systems

0.4 Solving Equations

0.5 Trigonometric Functions

0.6 Exponential and Logarithmic Functions

0.7 Transformations of Functions

0.8 Preview of Calculus

Chapter 1 – Limits and Continuity

1.1 The Concept of Limit

1.2 Computation of Limits

1.3 Continuity and Its Consequences

1.4 Limits Involving Infinity

1.5 Formal Definition of the Limit

1.6 Limits and Loss-of-Significance Errors

Chapter 2 – Differentiation: Algebraic, Trigonometric, Exponential, and Logarithmic Functions

2.1 Tangent Lines and Velocity

2.2 The Derivative

2.3 Computation of Derivatives: The Power Rule

2.4 The Product and Quotient Rules

2.5 Derivatives of Trigonometric Functions

2.6 Derivatives of Exponential and Logarithmic Functions

2.7 The Chain Rule

2.8 Implicit Differentiation and Related Rates

2.9 The Mean Value Theorem

Chapter 3 – Applications of Differentiation

3.1 Linear Approximations and L’Hopital’s Rule

3.2 Newton’s Method

3.3 Maximum and Minimum Values

3.4 Increasing and Decreasing Functions

3.5 Concavity

3.6 Overview of Curve Sketching

3.7 Optimization

3.8 Rates of Change in Applications

Chapter 4 – Integration

4.1 Antiderivaties

4.2 Sums and Sigma Notation

4.3 Area

4.4 The Definite Integral

4.5 The Fundamental Theorem of Calculus

4.6 Integration by Substitution

4.7 Numerical Integration

Chapter 5 – Applications of the Definite Integral

5.1 Area between Curves

5.2 Volume

5.3 Volumes by Cylindrical Shells

5.4 Arc Length and Surface Area

5.5 Projectile Motion

5.6 Work, Moments, and Hydrostatic Force

5.7 Probability

Chapter 9 – Parametric Equations and Polar Coordinates

9.1 Plane Curves and Parametric Equations

9.2 Calculus and Parametric Equations

9.3 Arc Length and Surface Area in Parametric Equations

9.4 Polar Coordinates

9.5 Calculus and Polar Coordinates

9.6 Conic Sections

9.7 Conic Sections in Polar Coordinates