Academics
Departments
Math
Math Department
List of 1 items.
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Philosophy
The Mathematics Department of Xaverian strives to empower all students to think critically and analytically and become problem solvers capable of tackling the issues of the next generation. Through a community of discovery, exploration, and productive struggle we strive to build a connection between mathematical concepts and real-world applications. We have created an environment where students become confident and continue to grow as individuals and contribute to their community at large, whether through further education or in the real world.
Math Department Goals
List of 3 items.
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Create an Enthusiastic Environment
To create an enthusiastic environment that fosters students to collaborate, participate, and self-reflect. -
Strengthen Critical Thinking
To strengthen critical thinking skills through the use of questioning and modeling real-life situations. -
Utilize Multiple Problem-Solving Strategies
To utilize multiple problem-solving strategies to encourage differentiation in everyday instruction.
High School Courses
List of 15 items.
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Algebra I
In this course, students analyze and explain precisely the process of solving an equation. Through repeated reasoning, students develop fluency in writing, interpreting, and translating between various forms of linear equations and inequalities and make conjectures about the form that a linear equation might take in a solution to a problem. They learn the terminology specific to polynomials and understand that polynomials form a system analogous to the integers. Students develop a set of tools for understanding and interpreting variability in data and begin to make more informed decisions from data. They work with data distributions of various shapes, centers, and spreads. Students extend their study of functions to include function notation and the concepts of domain and range. They explore many examples of functions and their graphs, focusing on the contrast between linear and exponential functions. They interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. Students continue to interpret expressions, create equations, rewrite equations and functions in different but equivalent forms, and graph and interpret functions, but this time using polynomial functions, and more specifically quadratic functions, as well as square root and cube root functions. -
Algebra I Honors
In this course, students analyze and explain precisely the process of solving an equation. Through repeated reasoning, students develop fluency in writing, interpreting, and translating between various forms of linear equations and inequalities and make conjectures about the form that a linear equation might take in a solution to a problem. They learn the terminology specific to polynomials and understand that polynomials form a system analogous to the integers. Students develop a set of tools for understanding and interpreting variability in data and begin to make more informed decisions from data. They work with data distributions of various shapes, centers, and spreads. Students extend their study of functions to include function notation and the concepts of domain and range. They explore many examples of functions and their graphs, focusing on the contrast between linear and exponential functions. They interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. Students continue to interpret expressions, create equations, rewrite equations and functions in different but equivalent forms, and graph and interpret functions, but this time using polynomial functions, and more specifically quadratic functions, as well as square root and cube root functions. -
Geometry
Students will follow the NYS Regents curriculum based on Euclidean and coordinate geometry. There will be some emphasis on proofs.
Prerequisite: Successful completion of the Integrated Algebra 9 course. -
Geometry Honors
Students will follow the NYS Regents Curriculum based on Euclidean and coordinate geometry. There will be a strong emphasis placed on proofs. Students will be exposed to geometry topics seen in pre-calculus and calculus.Prerequisite:- 85% or higher on the Algebra Regents.
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Advanced Algebra/Trigonometry + Pre-Calculus Honors
Topics include algebraic fractions, inequalities, sequences, functions, limits, vectors, matrices, and trigonometric functions, statistics, integral and differential calculus. Students will recognize and graph various functions and utilize them to solve problems like compound interest and radioactive decay.Prerequisite:- 90% or higher average in the prior math course
- A minimum score of 80% on the Geometry Regents
- Approval of the Math Department and/or the instructor is required for this course.
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Algebra II / Trigonometry
This course covers the New York State Algebra II/Trig curriculum. Students will demonstrate the ability to use trigonometric relationships to solve real-world problems and will demonstrate skill in the use of the graphing calculator. In consultation with the classroom teacher, select students will be invited to take the Regents Exam in June based upon overall class performance. -
Algebra II / Trigonometry Honors
The aims of the course are to appreciate the international dimensions of mathematics and the multiplicity of its cultural and historical perspective, foster enjoyment from engaging in mathematical pursuits and to develop an appreciation of the beauty, power, and usefulness of mathematics, develop logical, critical, and creative thinking in mathematics, develop mathematical knowledge, concepts and principles, employ and refine the powers of abstraction and generalization, develop patience and persistence in problem-solving, have an enhanced awareness of, and utilize the potential of, technological developments in a variety of mathematical contexts, communicate mathematically, both clearly and confidently, in a variety of contexts.Prerequisite:- 80% on the Geometry Regents
- Approval of the Math Department and/or the instructor is required for this course.
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Pre-Calculus
This course focuses on inequalities, arithmetic and geometric sequences and series, sequences and their limits, functions and their limits, derivatives and tangent slopes, properties and graphs of polynomial, exponential, logarithmic, circular, and inverse circular function, simple max-min problems, mathematical induction, vectors in two dimensions, complex numbers in standard and trig form, polar graphs, and conic sections. Algebraic fractions, matrices, and systems of linear equations will also be covered. Students will demonstrate proficiency with limits and trigonometric concepts, as well as a familiarity with derivatives and integrals.Prerequisite:- Successful completion of Algebra II/Trig.
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St. John's University Pre-Calculus Honors
This course focuses on elementary algebra, functions & graphs, sets of linear equations, introduction to exponential & logarithmic functions, and trigonometry.Prerequisites:- Approval of the Math Department and/or the instructor
- A minimum combined Math and Verbal SAT score of 1080
- This is an approved elective course for students in any of the Honors Programs.
- This course is open to juniors or seniors for St. John’s credit
*Students successfully passing this course will be eligible to receive up to 3 college credits through St. John’s University. Students will be responsible for all additional fees charged by St. John’s as well as completing any required applications for acceptance to the College Advantage Program. -
College Prep Algebra
This course is designed for students who wish to review the basic principles of algebra and trigonometry and study additional topics. Students qualifying for Senior Pre-Calculus or Calculus should not register for this course. Essentials from algebra and geometry will be reviewed and some time will be spent in preparation for the SAT. Topics will include Trigonometry, Logarithms, arithmetic and geometric progressions, synthetic division (used in the solution of higher degree equations), determinants (used in solving simultaneous equations in three unknowns), the graphing of linear and quadratic inequalities, and some basic calculus with application to maximum and minimum problems. Students will demonstrate a mastery of algebraic techniques and trigonometric concepts.Prerequisites:- Pass Algebra II/Trig Course
- Need approval of instructor
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St. John's University - University Calculus I
This course covers critical analysis of the theories and foundations of calculus. Topics include the basic concepts and applications of limits and functions, differentiation, and integration.
Prerequisites- Approval of the Math Department and /or the instructor
- A minimum combined Math and Verbal SAT score of 1080.
- This is an approved elective course for students in any of the Honors Programs.
- This course is open to juniors or seniors for St. John’s credit.
*Students successfully passing this course will be eligible to receive up to 3 college credits through St. John’s University. Students will be responsible for all additional fees charged by St. John’s as well as completing any required applications for acceptance to the College Advantage Program. -
St. John's University Probability and Statistics Honors
This course studies basic probability laws and their application, combinatorial analysis, conditional probability and Bayes’ rule, and discrete and continuous distributions. Students learn about central limit theorem, statistical inference, sampling theory, estimation, hypothesis testing, goodness of fit, regression, correlation, and analysis of variance. This course will provide a working knowledge of probability as a foundation for the statistical concepts covered in the course. The course will provide familiarity with concepts in statistical inference for application to technical, business, and social science problems and for further study of the methods of quantitative analysis.Prerequisites:- 85% in Algebra II / Trig (H) or 80% in Geometry and a qualifying SAT Math score
- 90% in Algebra II / Trig and a qualifying SAT Math score
- Math teacher recommendation
- A minimum combined Math and Verbal SAT score of 1080
- This is an approved elective course for students in any of the Honors Programs.
- This course is open to seniors only for St. John’s credit
*Students successfully passing this course will be eligible to receive up to 3 college credits through St. John’s University. Students will be responsible for all additional fees charged by St. John’s as well as completing any required applications for acceptance to the College Advantage Program. -
AP Precalculus
In AP Precalculus, students explore everyday situations using mathematical tools and lenses. Through regular practice, students build deep mastery of modeling and functions, and they examine scenarios through multiple representations. They will learn how to observe, explore, and build mathematical meaning from dynamic systems, an important practice for thriving in an ever-changing world.- Approval of the Math Department and successful completion of #7529 is required
- A minimum PSAT/SAT math score of 600 and/or approval through AP Potential.
- This course is open to juniors and select seniors.
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AP Calculus AB
AP Calculus AB is roughly equivalent to a first-semester college calculus course devoted to topics in differential and integral calculus. The AP course covers topics in these areas, including concepts and skills of limits, derivatives, definite integrals, and the Fundamental Theorem of Calculus. The course teaches students to approach calculus concepts and problems when they are represented graphically, numerically, analytically, and verbally, and to make connections amongst these representations. Students learn how to use technology to help solve problems, experiment, interpret results, and support conclusions. -
AP Calculus BC
AP Calculus BC is roughly equivalent to both first and second-semester college calculus courses and extends the content learned in AB to different types of equations and introduces the topic of sequences and series. The AP course covers topics in differential and integral calculus, including concepts and skills of limits, derivatives, definite integrals, the Fundamental Theorem of Calculus, and series. The course teaches students to approach calculus concepts and problems when they are represented graphically, numerically, analytically, and verbally, and to make connections amongst these representations. Students learn how to use technology to help solve problems, experiment, interpret results, and support conclusions.
Middle School Courses
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Math 6
Sixth-grade mathematics introduces new topics and builds upon the skills learned in elementary school. This course focuses heavily on arithmetic including recognizing and performing computations and developing a strong number sense. Students will also learn to use formulas and analyze and interpret graphs. Sixth-grade mathematics provides a strong foundation for future classes. Mastery is crucial for success in Pre-Algebra and beyond to the high school level. Students will display their understanding of content in both written and oral forms. -
Math 7
This course is designed to enable students to become confident, competent problem solvers. Students will learn to apply mathematics in a variety of contexts, and communicate their understanding of the math content both in written and oral form. The course will help provide a solid foundation for further study in mathematics by strengthening students’ computational, procedural, and problem-solving skills. The four main areas of emphasis in Grade 7 are proportional relationships and applying those relationships to solve problems, operations with rational numbers, expressions, and linear equations, scale drawings and informal geometric constructions, and drawing inferences about populations based on samples. -
Math 8
This course is designed to enable students to become confident, competent problem solvers. Students will learn to apply mathematics in a variety of contexts and communicate their understanding of the math content both in written and oral form. The course will help provide a solid foundation for further study in mathematics by strengthening students’ computational, procedural, and problem-solving skills. Students will be encouraged to devise applications in problem-solving contexts as they explore the key concepts of algebra and geometry. -
Algebra I
This course is designed to enable students to become confident, competent problem solvers. Students will learn to apply mathematics in a variety of contexts, and communicate their understanding of the math content both in written and oral form. The course will provide students with a rigorous study of algebra. Students will be encouraged to devise applications in problem-solving contexts. Topics will include real numbers, equations, inequalities, problem-solving, graphing, systems of equations and their applications, exponents and polynomials, factoring, rational expressions, roots and radicals, quadratic equations, radical expressions, rational expressions and functions, and data analysis.
Specialized Studies Courses
List of 5 items.
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Math 9
Selected topics in algebra and geometry serve as the course content. Students will master the ability to read, analyze and solve real-world problems through a variety of methods. They will be able to demonstrate competency in various algebraic techniques. This is a NYS Regents course designed for students who will take the Regents exam in January of sophomore year. -
Math 10
The beginning of this course will focus on completing the Integrated Algebra curriculum. Students will begin their study of geometry during the second semester and will follow the NYS Regents curriculum based on Euclidean and coordinate geometry, while also understanding the fundamentals of proofs. -
Math 11
Students continue to study topics in the Geometry curriculum and continue to work with NYS Standards for Math. The concepts of Trigonometry are introduced as well as key topics from the SATs. Students move through the Math 11 curriculum as they master material appropriate to their individual Math skills. -
Algebra II
This course covers the New York State Algebra II/Trig curriculum. Students will demonstrate the ability to use trigonometric relationships to solve real-world problems and develop patience and persistence in problem-solving while demonstrating skill in the use of the graphing calculator. Students will also have an enhanced awareness of, and utilize the potential of, technological developments in a variety of mathematical contexts -
College Prep Algebra
This course is designed for students who wish to review the basic principles of algebra and trigonometry and study additional topics. Essentials from algebra and geometry will be reviewed and some time will be spent in preparation for the SAT. Topics will include trigonometry, logarithms, arithmetic and geometric progressions, synthetic division (used in the solution of higher degree equations), determinants (used in solving simultaneous equations in three unknowns), the graphing of linear and quadratic inequalities, and some basic calculus with application to maximum and minimum problems. Students will demonstrate a mastery of algebraic techniques and trigonometric concepts.
Math Department Members
List of 17 members.
Xaverian
Established in 1957, Xaverian is one of thirteen schools nationwide sponsored by the Xaverian Brothers.
