Curriculum

# Mathematics

## DEPARTMENT PHILOSOPHY:

The philosophy of the Mathematics Department is an echo of the school’s philosophy to educate the whole person and develop the qualities of the DSHA Graduate. Our primary purpose is to educate young women in mathematics and to challenge them to do the best they can, according to their abilities. Critical thinking and communication of mathematical ideas are emphasized. The goals of the Mathematics Department are to develop and refine a student’s ability for problem solving and to equip each student with sufficient mathematical skills so that she has the freedom to pursue the college curriculum and/or career of her choice. Concepts of mathematics are related to real world situations and careers at every opportunity. The department strives to provide an atmosphere where students learn to enjoy and appreciate mathematics, and develop confidence in their mathematical skills.

## MATH DEPARTMENT COURSE OFFERINGS:

### List of 15 items.

• #### ALGEBRA I – 5251 and 5252

The main concepts of Algebra are covered in this course integrating the Common Core State Standards in Mathematics. Topics presented include operations with real numbers, solving linear equations and inequalities, solving and applying proportions, linear equations and their graphs, systems of linear equations, exponents, polynomials and factoring, finding square roots and solving quadratic equations using square roots, factoring, simplifying radical expressions, operations with radical expressions and the quadratic formula.

2 semesters
Prerequisite: Placement based on grade school recommendation and November placement test results | TI-84 + Sliver Edition or TI-84 + CE graphing calculator required
• #### ADVANCED ALGEBRA I – 5201 and 5202

This course is designed for students who have completed Algebra 1 (or a strong Pre-Algebra program) in middle school but need additional work for mastery.  Concepts are covered more in depth with an emphasis on critical thinking and application.  Linear equations, inequalities, polynomials, factoring, quadratic equations, radicals, rational expressions, and statistics are presented.  Additional emphasis will be placed on mathematical modeling, problem solving, data analysis, graphing calculator technology, and both written and oral communication.

2 semesters
Prerequisite: Placement based on grade school recommendation and November placement test results | TI-84 + Sliver Edition or TI-84 + CE graphing calculator required
• #### GEOMETRY – 5301 and 5302

This course in Euclidean Geometry develops both deductive and inductive reasoning skills.  Students use visualization and analysis, and are encouraged to make conjectures.  The close relationship of geometry to algebra and the real numbers is illustrated.  Geometry concepts covered will include elements of deductive reasoning and proofs, angle relationships, congruent triangles, similarity, right triangle trigonometry, parallel and perpendicular lines, relationships within triangles, quadrilaterals, area, solid geometry with finding surface area and volume, and circles.  Geometric relationships are used to explore and model real world applications.  Inductive reasoning skills are developed using Geometer’s Sketchpad.  In preparation for standardized testing, algebraic skills are reviewed and reinforced.

2 semesters
Prerequisite: Algebra I or Advanced Algebra I | TI-84 + Silver Edition or TI-84 + CE graphing calculator required
• #### HONORS GEOMETRY – 5361 and 5362

This course in Geometry covers concepts that include elements of deductive reasoning and proofs, angle relationships, parallel lines, congruent triangles, similar triangles, right triangle relationships, circles, solid geometry, and coordinate geometry. Deductive and inductive reasoning skills are developed throughout the coursework and by using computer software such as Geometer’s Sketchpad. This course will also include an introduction to basic trigonometry concepts. Connections between algebra and geometry are integrated into this course.

2 semesters
Prerequisite: Minimum Grade of a C in Honors Algebra II or Freshman Algebra II with teacher recommendation | TI-84 + Silver Edition or TI-84 + CE graphing calculator required

• #### FRESHMAN ALGEBRA II – 5221 and 5222

Freshman Algebra II is designed for freshmen who have completed an Algebra I course with full mastery.  After a brief review of elementary algebraic concepts, new topics are introduced.  These topics are piecewise functions, linear programming, and solving systems of linear equations in three variables. This course will also cover quadratic and higher degree polynomial functions, complex numbers, rational expressions, exponential functions, and logarithmic functions. Students will also be introduced to trigonometric ratios and functions. Completion of this course will prepare students for registration in either Geometry with Deductive Reasoning or Honors Geometry, as recommended by the instructor. Final placement is based on results of placement exam taken in May.

2 semesters
Prerequisite: Placement based on grade school recommendation and November placement test results | TI-84 + Silver Edition or TI-84 + CE graphing calculator required

• #### ALGEBRA II WITH TRIGONOMETRY – 5411 and 5412

After a brief review of elementary algebraic concepts, students in Algebra II with Trigonometry are introduced to new topics. These topics are piecewise functions, linear programming, and solving systems of linear equations in three variables. This course will also cover quadratic and higher degree polynomial functions, complex numbers, rational expressions, exponential functions, and logarithmic functions. Students will also be introduced to trigonometric ratios and functions.

2 semesters
Prerequisite: Geometry with Deductive Reasoning | TI-84 + Silver Edition or TI-84 + CE graphing calculator required
• #### HONORS ALGEBRA II – 5261 and 5262

Honors Algebra II is designed for students who have exceptional ability in mathematics and have completed the curriculum of Algebra I with mastery.  This course will cover the traditional curriculum of Algebra II including quadratic functions, complex numbers, rational expressions, higher degree polynomial equations, exponential and logarithmic functions, graphing functions.  Students will also be introduced to trigonometric ratios and functions and trigonometric graphs. Concepts will be covered at a greater depth for a clearer understanding and application to future Honors math courses.  Students will use the graphing calculator extensively as a tool for mathematical modeling and analysis.

2 semesters

Prerequisite: Initial placement based on grade school  recommendation and November placement test | TI-84 + Silver Edition or TI-84 + CE graphing calculator required
Final placement based on results of  placement exam taken in May.
• #### MT 195: COLLEGE ALGEBRA – 5541 and 5542

This course provides an overview of the fundamental concepts of algebra. Topics include linear and quadratic equations and inequalities; the Cartesian plane and graphing; functions; graphs and models; polynomial and rational functions; exponential and logarithmic functions; and systems of equations and inequalities.

2 semesters
Prerequisite: Any Geometry and Algebra II class | TI-84 + Silver Edition or TI-84 + CE graphing calculator required
** Students will be eligible to receive 3 transferable college credits from Cardinal Stritch University by enrolling in the concurrent enrollment dual-credit program.
• #### PRECALCULUS WITH TRIGONOMETRY AND STATISTICS – 5501 and 5502

Precalculus with Trigonometry and Statistics extends the concepts of Algebra II, focusing on skills mentioned in the Common Core State Standards. This course encompasses a wide variety of topics, including analysis of functions (linear, polynomial, exponential, logarithmic, trigonometric, and inverse trigonometric), trigonometry, sequences and series, matrices, and combinatorics. This course also considers basic descriptive and inferential statistics. This course is intended to integrate both process and application, using technology to illustrate concepts whenever applicable.

2 semesters

Prerequisite: Algebra II with Trigonometry and Geometry with Deductive Reasoning | TI-84 + Silver Edition or TI-84 + CE graphing calculator required
• #### HONORS TRIGONOMETRY/PRECALCULUS – 5461 and 5462

Honors Trigonometry/Precalculus covers pre-calculus topics including function analysis, matrices, conic sections, exponential and logarithmic functions, sequences and series, probability, descriptive statistics, parametric equations, polar coordinate system, and trigonometry topics including circular functions, trigonometric functions and their graphs, trigonometric identities, solutions of triangles, and inverse trigonometric functions.

2 semesters
Prerequisite: Minimum Grade of a C in Honors Algebra II and Honors Geometry | TI-84 + Silver Edition or TI-84 + CE graphing calculator required
• #### DISCRETE MATHEMATICS – 5710

Discrete mathematics is a branch of mathematics that studies functions and relations which are discrete (individually separate and distinct) and not continuous. This course will introduce and study different methods of counting, sequences, symbolic logic, and graph theory. Since discrete mathematics is widely used in many fields (ex. computer science, engineering) we will look at applications to those fields. In order to run this course, at least 10 students must be enrolled. Please note that this is an elective math course and should not replace any class in the math sequence.

1 semester
Prerequisite: Pre-Calculus (completed or concurrent enrollment) | TI-84 + Silver Edition or TI-84 + CE graphing calculator required
• #### LINEAR ALGEBRA – 5720

Linear Algebra is a branch of mathematics that studies linear equations and linear functions and their representations through matrices and vector spaces. This course will introduce and study matrices, vectors and their applications. Since linear algebra is widely used in many fields (ex. computer science, engineering) we will look at applications to those fields. In order to run this course, at least 10 students must be enrolled. Please note that this is an elective math course and should not replace any class in the math sequence.

1 semester
Prerequisite: Pre-Calculus (completed or concurrent enrollment) | TI-84 + Silver Edition or TI-84 + CE graphing calculator required
• #### CALCULUS – 5531 and 5532

Calculus is designed for the fourth year math student who does not intend to take the AP Calculus test but wishes to study calculus topics. The course will emphasize limits, derivatives, integrals and Calculus-oriented applications from a variety of fields.

Prerequisite: Honors Trigonometry/Precalculus or Precalculus with Trigonometry and Statistics | TI-84 + Silver Edition or TI-84 + CE graphing calculator required
• #### AP CALCULUS (AB) – 5151 and 5152

After a brief review of the prerequisites for Calculus, students study limits, continuity, and the topics of differential and integral Calculus. The material in this course is very challenging and may require an increased amount of time to do homework. All students are expected to take the AP Calculus AB exam in May. Most colleges offer one semester credit for successful completion of the AP Calculus exam. Additional meeting times may be scheduled in April and May in preparation for the AP exam.

2 semesters, AP preparation material and exam fees
Prerequisite: Minimum grade of C in Honors Trigonometry/Precalculus and teacher recommendation | TI-84 + Silver Edition or TI-84 + CE graphing calculator required
• #### AP CALCULUS (BC) – 5141 and 5142

While similar in rigor and initial content to AP Calculus AB, this course includes additional topics from the second semester of college Calculus including concepts related to sequences and series, vectors, parametric and polar coordinates, etc.  The pace of this course is accelerated compared to AP Calculus AB and the class will be extended to 3:15 two days/week.  All students are expected to take the AP Calculus BC exam in May.  Students who successfully complete the AP Calculus BC exam may receive credit for two semesters of college Calculus.

2 semesters, AP preparation materials and exam fees
Prerequisite: Minimum Grade of a C in Honors Trigonometry/Precalculus and teacher recommendation | TI-84 + Silver Edition or TI-84 + CE graphing calculator required | extended class time until 3:15 p.m. two days each week

## Department Related Resources:

DSHA offers the following math-based courses through the new Specialized Studies Department: AP Stats, AP Computer Science, Engineering, Accounting, and College Accounting.

## Divine Savior Holy Angels High School

Sponsored by the Sisters of the Divine Savior