 # Mathematics Curriculum

## Algebra I

Instructor: Jonathan Schlecht and Michael Monte
Textbook: ISBN #: 0-395-97722-3, Algebra Structure and Methods by McDougal Littell
Length/Credit: 1 year, 1 credit
Course Description: Algebra prepares students for the upper levels of mathematics by developing logical and abstract reasoning skills. Algebra is about the relationships between numbers, properties, and unknowns. We study Algebra to develop problem-solving skills and learn behaviors and thought processes that are important not only to the principles of math, but all areas of study and life.

• Unit 1: Terminology, Symbols, and Variables
• Unit 2: Real Numbers
• Unit 3: Solving Equations
• Unit 4: Polynomials
• Unit 5: Factoring "A"
• Unit 5: Factoring "B"
• Unit 6: Fractions
• Unit 7: Applications of Fractions
• Unit 8: Graphing Linear Equations
• Unit 9: Linear Systems
• Unit 10: Inequalities and Radical Expressions

## Algebra II/Trig

Instructor: Sandra Loptein and Bethany Hoehne
Textbook: Larson, et al., Algebra 2
Prerequisite: Algebra I, Geometry, Department Consent
Length/Credit: 1 year/1 credit
Course Description: This course is designed to give the student a broader understanding of the real and complex number systems. Through such an understanding, the student becomes acquainted with problem solving and develops a faculty for applying this knowledge to various types of problems. Major concepts investigated will be equations, inequalities, linear equations, functions, systems of equations, matrices, quadratic functions, polynomials, polynomial functions, powers, roots, radicals, logarithms, conic sections, trigonometric ratios, trigonometric functions, trigonometric graphs, and trigonometric equations.
Course Outcomes

• The student will appreciate God's wisdom for having created the laws found in advanced mathematics.
• The student will understand and appreciate the many unifying aspects of advanced mathematics.
• The student will learn work habits (accuracy, relative speed, estimating, checking, neatness) essential to computation.
• The student will become skilled in the art of logical thinking and problem solving.
• The student will be able to apply several strategies used for solving practical problems.
• The student will become adept in simplifying complex algebraic expressions using the proper order of operations.
• The student will master several methods for solving equations and inequalities of varying degree, including the quadratic formula and rational root theorem.
• The student will become adept in graphing functions and relations of varying degree.
• The student will use graphing technology to help simplify and solve problems involving powers and logarithms.
• The student will recognize and use mathematical symbols correctly in problem solving.

Course Outline

• Unit 1: Equations and Inequalities
• Unit 2: Linear Equations and Functions
• Unit 3: Systems of Equations and Inequalities
• Unit 4: Matrices and Determinants
• Unit 5: Quadratic Equations and Functions
• Unit 6: Polynomials
• Unit 7: Powers, Roots, and Radicals
• Unit 8: Exponential and Logarithmic Functions
• Unit 9: Rational Equations and Functions
• Unit 10: Trigonometry

## AP Calculus AB

Instructor: Bethany Hoehne
Textbook: Finney, Thomas, Demana, and Waits Calculus: Graphical, Numeric, Algebraic, Pearson Education, Inc., 2003
Prerequisite: C or better in Precalculus, Department Consent
Length/Credit: 1 year/1 credit, AP Calculus is an honors course with a weighted grade.
Course Description: Advanced Placement Calculus AB is designed to give the students experience in a college-level mathematics course in order to give them more than adequate preparation for first semester college Calculus. Students will be given the option of taking the AP exam. The Calculus AB curriculum is followed to give students the required preparation for that exam. Calculus uses and applies concepts from several branches of mathematics in new and meaningful ways. It is required to advance in the fields of engineering, physical science, economics, and advanced mathematics. It investigates problems that involve motion at a varied speed or irregular path, maximums and minimums, and areas or regions with curved boundaries. This course gives the student an intuitive understanding of the concepts of calculus and experience with its methods and applications.
Course Outcomes: Students who complete this course will

• Recognize how mathematics can be used as a tool to assist one in serving God and one’s fellow man.
• Appreciate, through mathematics, the orderliness and wisdom of God’s creation.
• Be able to work with functions represented in a variety of ways: graphical, numerical, analytical or verbal. They should understand the connections among these representations.
• Understand the meaning of the derivative in terms of a rate of change and local linear approximation and should be able to use derivatives to solve a variety of problems.
• Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and should be able to use integrals to solve a variety of problems.
• Understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
• Be able to communicate mathematics and explain solutions to problems both verbally and in written sentences.
• Be able to model a written description of a physical situation with a function, a differential equation or an integral.
• Be able to use technology to help solve problems, experiment, interpret results and support conclusions.
• Be able to determine the reasonableness of solutions, including sign, size, relative accuracy and units of measurement.
• Develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.

Course Outline

• Unit 1: Functions And Graphs
• Properties of Functions
• Properties of Graphs
• Unit 2: Limits and Continuity
• Finite Limits
• Nonexistent Limits
• Continuity
• Unit 3: The Derivative
• Definition- presented graphically, numerically, and analytically
• Statements and Applications of Theorems about Derivatives
• Unit 4: Applications of the Derivative
• Geometric Applications
• Optimization problems
• Rate of change problems
• Unit 5: Integral Calculus
• Antiderivatives
• The Definite Integral
• Unit 6: Applications of the definite integral
• Area under and between curves
• Average value of a function on an interval
• Volumes of solids with known cross sections
• Volumes of solids of revolution
• Unit 7: AP Test Prep - Four to Five weeks are spent reviewing topics, taking practice exams, and learning test-taking strategy.

## AP Calculus BC

Instructor: Bethany Hoehne
Textbook: Finney, Thomas, Demana, and Waits Calculus: Graphical, Numeric, Algebraic Pearson Education, Inc., 2003
Prerequisite: B or above in Precalculus or completion of Calculus AB, Department Consent
Length/Credit: 1 year/1 credit, AP Calculus is an honors course with a weighted grade.
Course Description: Advanced Placement Calculus BC is designed to give the students experience in a college-level mathematics course in order to give them more than adequate preparation for first and second semester college Calculus. Students will be given the option of taking the AP exam. The Calculus BC curriculum is followed to give students the required preparation for that exam. Calculus uses and applies concepts from several branches of mathematics in new and meaningful ways. It is required to advance in the fields of engineering, physical science, economics, and advanced mathematics. It investigates problems that involve motion at a varied speed or irregular path, maximums and minimums, and areas or regions with curved boundaries. This course gives the student an intuitive understanding of the concepts of calculus and experience with its methods and applications.
Course Outcomes: Students who complete this course will

• Recognize how mathematics can be used as a tool to assist one in serving God and one’s fellow man.
• Appreciate, through mathematics, the orderliness and wisdom of God’s creation.
• Be able to work with functions represented in a variety of ways: graphical, numerical, analytical or verbal. They should understand the connections among these representations.
• Understand the meaning of the derivative in terms of a rate of change and local linear approximation and should be able to use derivatives to solve a variety of problems.
• Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and should be able to use integrals to solve a variety of problems.
• Understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
• Be able to communicate mathematics and explain solutions to problems both verbally and in written sentences.
• Be able to model a written description of a physical situation with a function, a differential equation or an integral.
• Be able to use technology to help solve problems, experiment, interpret results and support conclusions.
• Be able to determine the reasonableness of solutions, including sign, size, relative accuracy and units of measurement.
• Develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.

Course Outline

• Unit 1: Prerequisites for Calculus
• Unit 2: Limits and Continuity
• Unit 3: The Derivative
• Unit 4: Applications of the Derivative
• Unit 5: The Definite Integral
• Unit 6: Differential Equations and Mathematical Modeling
• Unit 7: Applications of Definite Integrals
• Unit 8: L’Hopital’s Rule, Improper Integrals, and Partial Fractions
• Unit 9: Infinite series
• Unit 10: Parametric, Vector, and Polar Functions
• Unit 11: AP Test Review

## Geometry

Instructor: Ben Dwinell, and Dave Hiltman
Length/Credit: 1 year, 1 credit
Textbook: ISBN 07167-1745-X

• Unit 1: Logic and Reasoning
• Unit 2: Points, Lines, And Planes
• Unit 3: Rays and Angles
• Unit 4: Congruent Triangles
• Unit 5: Inequalities
• Unit 6: Parallel Lines
• Unit 7.5: Square Roots
• Unit 9: Area
• Unit 10: Similarity
• Unit 11: The Right Triangle
• Unit 14: Regular Polygons and Circles
• Unit 15: Geometric Solids
• Unit 12: Circles

## Honors Algebra II-Trig

Instructor: Sandy Loptein
Textbook: Larson, et al., Algebra 2, McDougal Littel, 2001
Prerequisite:Algebra 1, Geometry, Department Consent
Length/Credit: 1 year/1 credit
Course Description: This course is designed to give the student a broader understanding of the real and complex number systems. Through such an understanding, the student becomes acquainted with problem solving and develops a faculty for applying this knowledge to various types of problems. Major concepts investigated will be equations, inequalities, linear equations, functions, systems of equations, matrices, quadratic functions, polynomials, polynomial functions, powers, roots, radicals, logarithms, conic sections, trigonometric ratios, trigonometric functions, trigonometric graphs, trigonometric equations, and an introduction to sequences and series. At the Honors level, specific time will be spent practicing and discussing the problem-solving process using logic puzzles, famous historical challenges, difficult problems pertaining directly to current course content, and problems relating to everyday life.
Course Outcomes: Students who complete this course will

• appreciate God's wisdom for having created the laws found in advanced mathematics.
• understand and appreciate the many unifying aspects of advanced mathematics.
• learn work habits (accuracy, relative speed, estimating, checking, neatness) essential to computation.
• become skilled in the art of logical thinking and problem solving.
• be able to apply several strategies used for solving practical problems.
• become adept in simplifying complex algebraic expressions using the proper order of operations.
• master several methods for solving equations and inequalities of varying degree, including the quadratic formula and rational root theorem.
• become adept in graphing functions and relations of varying degree.
• use graphing technology to help simplify and solve problems involving powers and logarithms.
• recognize and use mathematical symbols correctly in problem solving.

Course Outline

• Unit 1: Equations and Inequalities
• Unit 2: Linear Equations and Functions
• Unit 3: Systems of Equations and Inequalities
• Unit 4: Matrices and Determinants
• Unit 5: Quadratic Equations and Functions
• Unit 6: Polynomials
• Unit 7: Powers, Roots, and Radicals
• Unit 8: Exponential and Logarithmic Functions
• Unit 9: Rational Equations and Functions
• Unit 10: Trigonometry

## Honors Geometry

Teacher: David Renquest and Bethany Hoehne
Length:
1 year/1 credit
Textbook:
ISBN -13: 978-0-13-350041-7 or ISBN-10: 0-13-350041-1

Course Outline

• Unit 1: Tools of Geometry
• Unit 2: Reasoning and Proofs
• Unit 3: Parallel and Perpendicular Lines
• Unit 4: Congruent Triangles
• Unit 5: Relationships Within Triangles
• Unit 6: Polygons and Quadrilaterals
• Unit 7: Similarity
• Unit 8: Right Triangles and Trigonometry
• Unit 10: Area
• Unit 11: Surface Area and Volume
• Unit 12: Circles

## Honors Pre-Calculus

Instructor: Dave Hiltman
Textbook: Demana, et al., PreCalculus: Graphical, Numerical Algebraic, Pearson Education Inc., 2007
Prerequisite: C or better in Algebra II, Department Consent
Length/Credit: 1 year/1 credit, Precalculus is an honors course which carries a weighted grade
Course Description: Pre-Calculus uses and makes connections between concepts from a number of branches of mathematics. The course gives students experience in using the algebra and analytic geometry needed for the study of Calculus. Emphasis is also placed on the functions, identities, and applications of trigonometry.

Course Outcomes

Students will:

• Recognize how mathematics can be used as a tool to assist one in serving God and one’s fellow man.
• Appreciate, through mathematics, the orderliness and wisdom of God’s creation.
• Further develop logical reasoning skills and confidence in the ability to solve problems.
• Show and organize work when solving problems in order to defend answers.
• Be able to probe for and defend an answer or generalization using mathematical properties, laws, definitions, and/or reasoning.
• Choose and apply an appropriate method to solve real world problems.
• Use and apply given mathematical formulas, laws, and theorems in the proper situation.
• Use technology, when appropriate, to analyze mathematical concepts and solve problems.
• Understand the foundational concepts that are the basis for College Algebra and Calculus.

Course Outline

• Unit 1: Functions and Graphs
• Unit 2: Polynomial, Power, and Rational Functions
• Unit 3: Exponential, Logistic and Logarithmic Functions
• Unit 4: Trigonometric Functions
• Unit 5: Analytic Trigonometry
• Unit 6: Applications of Trigonometry
• Unit 7: Analytic Geometry in Two and Three Dimensions
• Unit 8: Limits
• Unit 9: Derivative Rules

## Pre-Calculus

Instructor: Ben Dwinell
Textbook: Demana, et al., PreCalculus: Graphical, Numerical Algebraic, Pearson Education Inc., 2007
Prerequisite: C or better in Algebra II, Department Consent
Length/Credit: 1 year/1 credit, Precalculus is an honors course which carries a weighted grade
Course Description: Pre-Calculus uses and makes connections between concepts from a number of branches of mathematics. The course reinforces the foundations of Algebra and Geometry through practice and application. Emphasis is also placed on the functions, identities, and applications of trigonometry.

Course Outcomes

Students will:

• Recognize how mathematics can be used as a tool to assist one in serving God and one’s fellow man.
• Appreciate, through mathematics, the orderliness and wisdom of God’s creation.
• Further develop logical reasoning skills and confidence in the ability to solve problems.
• Show and organize work when solving problems in order to defend answers.
• Be able to probe for and defend an answer or generalization using mathematical properties, laws, definitions, and/or reasoning.
• Choose and apply an appropriate method to solve real world problems.
• Use and apply given mathematical formulas, laws, and theorems in the proper situation.
• Use technology, when appropriate, to analyze mathematical concepts and solve problems.
• Understand the foundational concepts that are the basis for College Algebra and Calculus.

Course Outline

• Unit 1: Equations and Inequalities
• Unit 2: Functions and Graphs
• Unit 3: Polynomial, Power, and Rational Functions
• Unit 4: Exponential, Logistic and Logarithmic Functions
• Unit 5: Trigonometric Functions
• Unit 8: Analytic Geometry in Two and Three Dimensions
• Unit 9: Introduction to Calculus Introduction to Limits

## Statistics

Teacher: Michael Monte and Dave Renquest
Length:
1 year/1 credit
Textbook:
Elementary Statistics: A step by step approach, 6th edition ( ISBN: 0-07-304825-9)
Course Description:
In Statistics, students will work with probability, data collection, descriptive and inferential statistics, probability, and technological tools to analyze statistics. The main foci of the course will be exploring data, planning a study, producing models using probability theory, and making statistical inferences. Students will work with statistical measures of centrality and spread, methods of data collection, methods of determining probability, binomial and normal distributions, hypothesis testing, and confidence intervals. Students will use multiple representations to present data including written descriptions, numerical statistics, formulas, and graphs.

Course Outline

• Unit 1: Statistics Concepts
• Unit 2: The Nature of Probability in Statistics
• Unit 2.5: Appendix A & Mean. median and Mode
• Unit 3: Frequency Distributions and Graphs
• Unit 4: Data Description Project: Create Your Own Game
• Unit 4.5: March "Math" Madness
• Unit 5: Probability and Counting Rules Project: Statistical Data Collection and Evaluation