# Math Courses

**It is the concern of the Mathematics Department that our students:**

- Know and understand mathematical processes, facts, and principles;
- Understand the logical structure of mathematics and the nature of proof;
- Perform computations with understanding, accuracy, and efficiency;
- Have the ability to solve verbal problems;
- Develop attitudes and appreciation which stem from, and which lead to, greater curiosity, initiative, confidence, and interests;
- Develop proper methods of studying mathematics and communicating mathematically;
- Develop study habits essential for independent and group work;
- And develop the ability to use and apply technology in appropriate ways.

To facilitate reaching these goals, each student is required to satisfactorily complete four years of mathematics including Algebra I, Geometry, Algebra II, and PreCollege Algebra or Precalculus (or where appropriate, a more advanced sequence of courses). When courses are ability grouped, the members of the Mathematics Department will place each student in the appropriate course dependent upon their assessment of her performance in the entrance or standardized examinations, and/or prior performance in mathematics courses.

Patterns of excessive absences and participation in the exchange program will be considered in making honors placements. All placements will be made with due consideration for the needs of the student.

**Calculator Requirements:**

The TI-84 Plus graphing calculator is required.

**ALGEBRA I**

(2 semesters)

Algebra I reviews the basic terminology, notation, concepts, skills, and applications of arithmetic. Building on operations with positive and negative numbers and zero, Algebra I presents properties of polynomials and rational numbers and applies them to the solution of linear and quadratic equations and to inequalities in one and two variables. Graphing is included at appropriate points and verbal problems are integrated with each appropriate topic area.

**ALGEBRA I HONORS / GEOMETRY HONORS**

(2 semesters) (Prerequisite: Placement based on a satisfactory grade on Duchesne's Algebra I Challenge Test covering the basic skills of Algebra I and on the quantitative, mathematics and reading sections of Duchesne's entrance examination. Eighth-grade mathematics teacher recommendations are also considered.)

This course includes topics in algebraic fractions and their application, linear equations and systems, graphing, functions and inequalities with an emphasis on problem-solving with each appropriate topic area. The geometry portion of the course includes all topics which are prerequisites for subsequent mathematics courses. See Geometry course description below. Successful completion of this course freshman year and teacher recommendation will enable a student to enroll in Algebra II Honors.

**GEOMETRY**

(2 semesters) (Prerequisite: Algebra I)

Geometry stresses the logical development of analytic and synthetic thought processes, reinforcing the logical steps in thinking required for Algebra I. Proof and inquiry methods of reasoning are emphasized throughout the year. The course includes the study of the properties of both two-and three-dimensional figures including the study of area, volume, and figures as located in the coordinate plane and in space. Transformations and symmetries are studied as they relate to art. Emphasis is given to congruent, similar and right triangles and to circles. Algebraic applications are related to all topics. Computer software is used as a dynamic tool for exploring various topics.

**GEOMETRY HONORS**

(2 semesters) (Prerequisite: Algebra II Honors successfully completed in an accredited high school program or superior performance on the Algebra Challenge Test)

This honors course includes all the topics listed for Geometry with additional requirements involving more in-depth treatment of topics in both assignment work and testing.

**ALGEBRA II**

(2 semesters)(Prerequisites: Algebra 1 and Geometry and department placement)

Algebra 2 reviews basic terminology, notation, skills in operations with positive and negative numbers and zero, the solutions to polynomial equations and inequalities in one and two variables, verbal problems, and graphing of linear, quadratic and other functions. This class introduces and develops the complex number system, its properties, and operations. The class also addresses the concepts of relations and functions, logarithmic and exponential functions. Also covered in this class are conic sections, probability, and trigonometry.

**ALGEBRA II HONORS**

(2 semesters) (Prerequisite: satisfactory work in Algebra I/Geometry Honors and department placement.)

This course includes the study of linear, quadratic, polynomial, rational, exponential, and logarithmic functions, including domain, range, and intercepts. Translations of functions, solving linear, quadratic, polynomial, rational, exponential, and logarithmic equations will be explored. Right triangle trigonometry and basic analytic trigonometry are developed. Units on conic sections, sequences, series, probability, and an introduction to matrices will also be covered. Emphasis is on solving problems both algebraically and graphically, including developing application-based problem-solving skills.

**PRECALCULUS **

(2 semesters) (Prerequisites: satisfactory work in Algebra II and department placement.)

This course provides students with the skills and concepts necessary for the study of Calculus through its introduction of elementary concepts from Calculus, as well as its conceptual development of circular, trigonometric and inverse functions, and varied problem-solving skills for right, oblique and obtuse triangles. Pre-calculus includes detailed work with polynomial, trigonometric, exponential, and logarithmic functions plus probability and matrices. Emphasis is on technology, real-life applications and problem-solving.

**PRECALCULUS HONORS**

(2 semesters) (Prerequisites: satisfactory work in Algebra II Honors or in Algebra II and department placement. Students not taking Algebra II Honors at Duchesne must complete an independent study unit of basic and analytic trigonometry under teacher supervision.)

This course provides students with the skills and concepts necessary for the study of AP Calculus through an introductory Calculus unit, as well as its conceptual development of circular, trigonometric and inverse functions, and varied problem-solving skills for right, oblique and obtuse triangles. Precalculus Honors includes detailed work with polynomial, trigonometric, exponential, and logarithmic functions and probability and matrices. Emphasis is on technology, real-life applications and problem-solving.

**PRE-COLLEGE ALGEBRA**

(2 semesters)(Prerequisite: Algebra II and department placement.)

This course includes the study of rational expressions; solving quadratic, rational, radical and polynomial equations; relations and functions; quadratic and polynomial functions; systems of equations and inequalities; exponential and logarithmic functions; matrices; and right triangle trigonometry.

**A.P. CALCULUS AB/BC**

(2 semesters) (Prerequisite: Satisfactory completion of Pre-calculus or Pre-calculus Honors and department placement.)

This course includes the study of differentiation and integration of a variety of functions. Integration techniques, infinite series, and differential equations will also be investigated. Students will explore these concepts numerically, graphically and analytically and use them for applications in a variety of fields from economics to physics.

Upon successful completion of the course, the student can obtain credit from Creighton University and/or the Advanced Placement exam. This course carries a fee of $100* per credit hour per semester for Creighton credit and registration at the beginning of each semester. Students must comply with Creighton policies for registration or withdrawal. If the student elects to take the AP exam, there is also a fee.

**CALCULUS III HONORS**

(Semester one) (Prerequisite: Satisfactory completion of Calculus 1 and 2, and department placement.)

This course continues the studentsâ€™ study of calculus concepts. Students will explore these concepts numerically, graphically and analytically and use them for applications in a variety of fields from economics to physics.

**MATHEMATICS ELECTIVES**

### AP STATISTICS

(2 semesters) (Prerequisite: Satisfactory completion of Algebra 2 Honors and instructor permission.)

This course includes the exploration and analysis of data, scatterplots & linear regression, probability, sampling, hypothesis testing, and statistical inference. Students will explore these concepts from the textbook, but will also conduct their own study, gathering and analyzing their data. The student will use her calculator extensively, and also have some exposure to Microsoft Excel and other statistical software. Students will study statistics and its application to various fields, such as political science, medicine, and economics. This course can be used to fulfill a math requirement for students who have successfully completed A.P. Calculus I.

Upon successful completion of the course, the student will have the preparation needed to take the Advanced Placement Statistics examination. If the student elects to take the AP exam, there is an additional fee.

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**RESEARCH METHODOLOGY **

(One Semester) This course is open to seniors. Juniors may register with the recommendation of a current teacher. The first semester is offered as an independent, self-directed background into the ethics, designs, and rationale of the research. Foundational terms, principles, and concepts of research will be covered. In the second semester, students will be paired with a Creighton professor or may choose to conduct their own study under the guidance of a Duchesne teacher. Completed research will be published in a high school research journal.

Students who complete Calculus 3 will receive a half math credit for successful completion of this course.