Science

ing at a rigorous level as well. The material includes a brief review of linear equations and solutions of systems of equations, followed by solutions of linear equations using matrices and determinants, rational functions and equations, exponential and logarithmic functions, conic sections, and complex numbers. The study of trigonometry includes the study of right triangle trigonometry, solving triangles, and introduction to sine and cosine as circular functions, including working with identities as well as solving equations. The content of this course is particularly important for standardized exams.

Algebra II & Trigonometry

with Precalculus Honors (Grade 10) This course is an accelerated study of Algebra II, Trigonometry, and Precalculus that extends past other courses into the faculty planning weeks and emphasizes both the breadth of Algebra II & Trigonometry and the depth of Precalculus. The course begins with a general study of algebraic skills, functions, and graphs. Students will explore quadratic, polynomial, rational, exponential, logarithmic, logistic, and trigonometric functions, focusing on properties, equations, inequalities, graphs, and applications of each type of function. Students will then study probability, statistics, conics, and matrices. The course culminates with a study of continuity and limits, the first key topics of calculus.

Precalculus (Grade 11) This class is a grade 11 mathematics option that begins with the in-depth study of key precalculus concepts of function and trigonometry. Statistics and discrete mathematics topics are included to prepare students for grade 12 electives. The graphing calculator is used extensively throughout the course. Students develop mathematical models for real-world applications from a wide range of fields, including business and science. The end of the second semester is devoted to the study of the beginning of basic differential and integral calculus. By year's end, students will have been introduced to all topics covered on the SAT II subject test. This course will be taught using the iPad and an e-text. The iPad will be used to deliver content and provide a more customized approach to learning. By the end of the year, students will have been introduced to all topics covered on the Math II Subject Test.

Honors Precalculus (Grades 10 and 11) This course begins with a rigorous precalculus program focusing on the properties of trigonometric, logarithmic, exponential and polynomial functions; appropriate integration of graphing calculator technology and algebra is emphasized. The end of the second semester is devoted to the study of the beginning of basic differential and integral calculus using the syllabus of the Advanced Calculus course. This course will be taught using the iPad and an e-text. The iPad will be used to deliver content and provide a more customized approach to learning.

Calculus (Grade 12) This course continues the study of basic differential and integral calculus started in the Precalculus course. It begins with a rigorous study of limits in calculus. Students will then study the main branches of college Calculus; derivatives and integrals. Students will use derivatives in applications that include business applications, optimization, and related rates, as well as applications of integration to find the area under a curve. Students will apply differentiation and integration to polynomials, radical and rational functions, exponential and logarithmic functions, as well as trigonometric functions. A strong background in precalculus is a requirement.

Advanced Calculus AB (Grades 11 and 12) This course is a continuation of the Precalculus class in grade 11 and continues the study of basic differential and integral calculus using the syllabus of the Advanced Placement AB level course. Advanced Calculus AB will focus on the four major concepts of college Calculus: functions, limits, derivatives, and integrals. Students will not only learn the skills and concepts associated with the four major concepts of calculus, but they will apply them to real world phenomena. Their processing, decision-making, and other problem-solving skills will develop throughout the course. Students will become comfortable with multiple representations of functions (numeric, graphic, algebraic, verbal) and solve problems using each representation. Students will also use technology to deepen their understanding of how various representations of problems are related to each other. The graphing calculator is essential to this course and the student’s ability to create and share mathematical representations of problems and solutions.

Advanced Calculus BC (Grades 11 and 12) This course is a continuation of the Honors Precalculus class in grade 11 and continues the study of basic differential and integral calculus using the syllabus of the Advanced Placement BC level course. Advanced Calculus BC will focus on the four major concepts of college Calculus: limits, derivatives, integrals and the Fundamental Theorem of Calculus, and Series. Students will not only learn the skills and concepts associated with the four major concepts of calculus, but they will apply them to real

world phenomena. Their processing, decision making, and other problem-solving skills will develop throughout the course. Students will become comfortable with multiple representations of functions (numeric, graphic, algebraic, verbal) and solve problems using each representation. Students will also use technology to deepen their understanding of how various representations of problems are related to each other. The graphing calculator is essential to this course and the student’s ability to create and share mathematical representations of problems and solutions.

Advanced Statistics (Grade 12) This course follows the syllabus set by the Advanced Placement program of the College Board, but is designed to be accessible to a wider range of students than calculus. Students are introduced to major concepts and tools for collecting, organizing, analyzing and drawing conclusions from data. Topics include univariate and bivariate data distributions, measures of center, measures of spread, developing models and correlation and residual plots, among others. Both graphing calculators and computers are used extensively, and students do substantial independent project work.

Multivariable Calculus (Grade 12) Students will build upon the concepts introduced in Advanced Calculus BC and extend their knowledge of functions to include more than two dimensions. Focus will be placed on parametric equations and vector functions. Vectors will be graphed in three dimensions, to allow students to analyze quadratic surfaces and cylindrical and spherical coordinates. Students will use a wide variety of techniques to maximize and minimize functions. Arc length, speed, rectilinear motion, and other topics introduced in Advanced Calculus BC are extended to the third dimension. Limits, continuity, derivatives, and integrals are analyzed with multivariate functions. The course includes numerous applications to physics.

Linear Algebra: Topics in Discrete Mathematics

(Grade 12) Students will build upon their prior knowledge of linear equations to discuss the linear dependence/independence of vectors and to analyze vector spaces and subspaces. Students will use matrices to solve systems of linear equations using inverses, matrix multiplication, and Gaussian elimination. Determinants of matrices will be used to explore the properties of matrices, such as eigenvalues, eigenvectors, and eigenspaces. This course will involve computations, proofs, and applications in its study of solving linear equations.

THEOLOGY

The academic study of theology is at the heart of the curriculum for all Sacred Heart students during each year of their Upper School education. The curriculum is rooted in the Hebrew and Christian scriptures and explores Catholic sacraments, ethics and philosophy, as well as the quest for life’s meaning in other world religions. The church’s teaching regarding social and moral issues is emphasized as a call to faith that expresses itself in charity and service. Students are encouraged to reflect on what they learn in light of their faith experience. In light of the framework of the Catholic Church, a Christo-centric approach is used in all courses.

Scripture (Grade 9) During the course of this year, students explore the Bible and the revelation of Jesus Christ in Scripture. They learn how to read the Bible and become familiar with the major sections of the Bible and the books included in each section. They learn about divine and natural revelation and how the Scriptures are authored by God through inspiration. Students become familiar with the role of tradition and the importance of interpretation. They pay particular attention to Jesus Christ Incarnate as the ultimate Revelation to us from God. In analyzing who Jesus is, the living Word of God, the Second Person of the Trinity, the students will also learn who he calls them to be.

World Religions (Grade 10) The course examines the nature of religious experience and expression in the symbols, rituals and stories of the world’s religions. In addition to studying many of the world’s major religious beliefs and practices, students will also spend time visiting religious sites and watching videos or reading stories from members of various traditions. By reading and exploring the religious experiences of others, students will gain a better understanding of the world’s religious diversity and will build greater appreciation for how religious traditions are variously lived by their adherents. The study of world religions will also serve to develop in students an empathetic appreciation for diverse peoples and the practices and beliefs they hold dear. Ideally, this empathy and understanding will lead to a deepening of the students’ own religious self-understanding and awareness. This course will also pay special attention to the Catholic Church’s Vatican II emphasis on dialogue and cooperation with non-Christian traditions, and we will revisit aspects of Christian theology and Christology as the touchstone and axis point for the study of comparative religions.