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Mathematics

Salesianum's Mathematics curriculum teaches students to develop their critical thinking and problem solving skills. Students are guided to reason logically as well as interpret mathematics numerically, graphically, and analytically.

  • Algebra I Foundations-CP

    In Algebra I Foundations, students achieve mathematical competence in support of cross-curricular applications and future studies in math, science, and technology. They develop personal responsibility for study, understanding, homework, and general success in mathematics courses. Students learn and utilize the language of algebra and realize the unity in mathematical knowledge and the connection of algebra to past and future mathematical topics. Topics covered include the real number line, absolute value, operations with positive and negative numbers, order of operations, fractions, ratios, proportions, simplifying algebraic and numerical expressions, investigating powers, properties of exponents, simplifying and factoring polynomials, solving linear equations and inequalities, graphing linear equations, and calculating slope. If time permits, students are exposed to basic quadratic equations and techniques for solving them.

  • Algebra I-CP

    In Algebra I-CP students achieve mathematical competence in support of cross-curricular applications and future studies in math, science, and technology. They develop personal responsibility for study, understanding, homework, and general success in mathematics courses. Students learn and utilize the language of algebra and realize the unity in mathematical knowledge and the connection of algebra to past and future mathematical topics. Topics covered include the real number line, absolute value, operations with positive and negative numbers, order of operations, fractions, ratios, proportions, simplifying algebraic and numerical expressions, investigating powers, properties of exponents, simplifying and factoring polynomials, solving linear equations and inequalities, graphing linear equations, and calculating slope. Students are also exposed to basic quadratic equations and techniques for solving them.

  • Algebra I-AC

    The objective of Algebra 1-AC is to take the students proficient in arithmetic skills from their ideas of numbers to more involved algebraic concepts of variable and function.  It acquaints students with equations and formulas that are useful in science and geometry.  The course covers the following properties of real numbers, solutions of equations and inequalities, approaches to word problems, graphing, polynomials, factoring, rational expressions, irrational numbers, and quadratic equations.  The course includes the use of the graphing calculator as a tool for understanding numeric and graphical relationships.

  • Algebra I-HN

    The Algebra 1-HN course is a more rigorous approach to the topics covered in Algebra I CP and AC.  Theory and application are stressed. The course includes the advanced study of word problems and the use of the graphing calculator as a tool for understanding numeric and graphical relationships. The course is designed for highly motivated students who excel in mathematics.

  • Geometry Foundations-CP

    In Geometry Foundations-CP, students arrive at an understanding of the nature of a mathematical system in addition to learning the properties and characteristics of triangles and circles.  This course focuses on practical applications.  Algebra 1 skills are reinforced, and students are prepared for the geometric topics they encounter on the PSAT and SAT exams. The following topics are presented:  angle relationships, parallel lines, triangle congruence and similarity, properties of parallelograms, perimeter and area of polygons and circles, surface areas and volumes of selected solids.  There are some introductions to the basic trigonometric functions. If time permits, students cover a basic study of data analysis and probability.  Concepts potentially covered include probability rules and models, two-way tables, tree diagrams, categorical data, measure of center and spread, scatterplots, lines of best fit, sampling, and margin of error.

  • Geometry-CP

    In Geometry-CP students arrive at an understanding of the nature of a mathematical system in addition to learning the properties and characteristics of triangles and circles.  This course focuses on practical applications.  Algebra 1 skills are reinforced, and students are prepared for the geometric topics they will encounter on the PSAT and SAT exams. The following topics will be presented:  angle relationships, parallel lines, triangle congruence and similarity, properties of parallelograms, perimeter and area of polygons and circles, surface areas and volumes of selected solids.  There are some introductions to the basic trigonometric functions. If time permits, students cover a basic study of data analysis and probability.  Concepts potentially covered include probability rules and models, two-way tables, tree diagrams, categorical data, measure of center and spread, scatterplots, lines of best fit, sampling, and margin of error. 

  • Geometry-AC

    In Geometry-AC, students study postulates and theorems from Euclidean Geometry. Students practice visualization to connect properties of real objects with two-dimensional drawings of these objects. They begin by working with the fundamental parts of geometry: points, lines, and planes.  Students find measures of geometric figures when appropriate: length, area and surface area, volume, and angle measures. Students may complete simple geometric proofs and will discuss and identify different methods of reasoning. Students study the properties of polygons, with an emphasis on triangles and quadrilaterals. Students identify congruent triangles, work with similar figures, and the beginnings of trigonometry. They work with transformations which may be described geometrically or by coordinates.   Finally, students study and utilize the properties of circles. Upon completion of the course, the student will have a stronger logical base that can be carried into later math courses.

  • Geometry-HN

    In Geometry-HN, students study postulates and theorems from Euclidean Geometry with an emphasis on writing Geometric proofs. This rigorous, fast-paced course will cover all of the traditional geometric concepts as seen in the CP and AC courses as well as a brisk introduction to concepts associated with Algebra 2. The geometry units include, but are not limited to the following: angles and triangles, congruency, geometric inequalities of the triangle, parallelism, perpendicularity, and transformations, quadrilaterals, similarity, trigonometry, areas and volumes, and properties and relationships found in circles. The Algebra 2 concepts include: the basic properties and operations of radicals, introduction of fractional exponents, factoring, operations with rational expressions, and determining the domain of a rational expression.

  • Algebra II-CP

    Algebra II-CP is the continuation of the College Prep Mathematics sequence.  The course consists of a brief review of essentials including axioms of real numbers, the solution of first-degree equations and inequalities, absolute value, systems of linear equations, graphing linear functions, and exponents. Primary topics include: polynomials and polynomial functions with a focus on quadratics, power functions, roots and radicals, imaginary and complex numbers, radical and rational functions, as well as exponential and logarithmic functions. 

  • Algebra II-AC

    Algebra II-AC is the logical continuation of Algebra 1-AC. This course covers linear functions, quadratic functions and their graphs, polynomial functions and equations, applications of factoring, rational algebraic expressions, power functions, function operations and compositions, inverse functions, roots and radicals, operations with radicals, complex numbers, exponential, and logarithmic functions.

  • Algebra II-HN

    Algebra II-HN is the logical continuation of Algebra 1-HN. This course covers polynomial functions, equations, and their graphs, applications of factoring, rational algebraic expressions, power functions, function operations and compositions, inverse functions, roots and radicals, operations with radicals, complex numbers, exponential, and logarithmic functions.

  • Math Analysis-HN

    Math Analysis-HN is a course offered by invitation to the most gifted mathematics students who have completed both Algebra 1 and Geometry with extraordinary results. The course is designed to cover all of the topics of both Algebra 2 HN and Precalculus HN in one year. The content is rigorous and the pacing is brisk. The concepts covered in this course include an advanced study of functions, including polynomial, power, rational, exponential, logistic, logarithmic, and trigonometric. Advanced vocabulary, notations, and nomenclature are introduced and used exclusively throughout the year. Students explore complex numbers, properties and behaviors of functions and their domains and ranges, graphical transformations, function operations and compositions, inverse functions, and modeling with functions. Students undergo an advanced study of trigonometry and the circular functions. This includes the graphs of the six trig functions, deriving and using trig identities, solving trig equations, including the derivation and extensive use of the Law of Sines and Cosines. Also included are the study of the fundamental topics of polar coordinates, the trigonometric form of complex numbers, and DeMoive’s Theorem. If time permits, students explore conic sections, vectors in the plane, counting rules, combinations and permutations, and their applications in binomial expansion. Freshmen entering this course are expected to complete AP Calculus AB, AP Calculus BC, AP Statistics, and Multivariable Calculus before graduation.

  • Precalculus-CP

    The Pre-Calculus course is intended to provide a foundation for students who intend to continue his study of mathematics at the college level.  This full year course includes a thorough study of trigonometry plus coverage of topics essential to the study of Calculus, namely: polynomial, rational, logarithmic, exponential, and inverse functions; graphical analysis, and curve sketching. Upon completion of the course, the student will be well prepared for continued college level work in Pre-Calculus or Calculus.

  • Precalculus-AC

    The Precalculus course is intended to provide a solid preparation for students who intend to continue his study of mathematics at the college level. This full year course includes a thorough study of trigonometry plus coverage of topics essential to the study of Calculus, namely: polynomial, rational, logarithmic, exponential, and  inverse functions; graphical analysis, curve sketching and, time permitting, an introduction to limits.

  • Precalculus-HN

    The Precalculus course is intended to provide a solid preparation for students who intend to continue his study of mathematics at the college level.  This full year course includes a thorough study of trigonometry plus coverage of topics essential to the study of Calculus, namely: polynomial, rational, logarithmic, exponential, and  inverse functions; graphical analysis, sequences, curve sketching, and an introduction to limits. Formal mathematical notation will be emphasized. Students will be expected to be fluent in reading the language of mathematics. 

  • Calculus with Trigonometry-AC

    In Calculus with Trigonometry-AC, students are introduced to the topics of Calculus in a typical first semester college Calculus course (Calculus I).  This includes a review of functions and an introduction to limits, differentiation, and applications of differentiation. Time permitting, the course covers basic integration and its applications. Part of this course is a rigorous presentation of trigonometry; this includes trigonometric definitions, applications, identities, solving triangles, and inverse trigonometric functions. This course gives students who take Calculus in college a solid foundation for such study.

  • Calculus with Trigonometry-HN

    In Calculus with Trigonometry-HN, students are introduced to the topics of Calculus typical in a first semester freshman college Calculus course (Calculus I) and some of the topics of the typical second semester course (Calculus B). In addition to the study of limits, advanced differentiation and its applications, and integration completed in the Accelerated course, this course also explores derivatives of logarithmic and exponential functions. Part of this course is a rigorous presentation of trigonometry; this includes trigonometric definitions, applications, identities, solving triangles, and inverse trigonometric functions. This course is not intended as preparation for the AP Calculus AB examination, but it is given to students who take Calculus in college as a good foundation for such study.
    Prerequisite: Successful completion of Math Analysis or Precalculus.

  • AP Calculus AB

    AP Calculus AB meets the needs of college students taking the first and second semester of college calculus. This course prepares students to take the Advanced Placement Calculus Examination of the College Board given in May of each year.  The first semester of the course covers Differential Calculus analytically, numerically, and geometrically.  These topics include the tangent line problem, limits, intermediate forms, derivatives of algebraic and transcendental functions, optimization problems and their applications, rectilinear motion, related rates, and curve sketching.  The second semester of the course covers Integral Calculus.  These topics include the area problem, Riemann sums, integration, differential equations, and slope fields.  Applications of integration such as volume of solids, distance traveled, and area between two curves are also covered.  Definitions and theorems are carefully stated.  Simple proofs are given in full.  Students are required to sit for the AP Calculus AB (or BC) Examination in May.  Prerequisite:  Department approval.

  • AP Calculus BC

    Advanced Placement Calculus BC is intended for students who have completed AP Calculus AB. It is considered an extension of the AB course and includes some fundamental review of differentiation and integration. The content will be explored in graphical, numeric, algebraic, and verbal representations.  Topics include, but are not limited to, a further study of limits, derivatives, definite and indefinite integrals. Students also analyze planar curves given in parametric form, vector form, and polar form. Also included is the study of polynomial approximations using Taylor and Maclaurin Series and error analysis. Concepts are investigated and explored intensively, with a focus on applications. As time permits, other mathematical topics may be investigated, including discrete mathematics, conic sections, and mathematical modeling. All students taking AP Calculus BC sit for the AP Calculus BC exam offered in May. Prerequisite:  Department approval.

  • AP Statistics

    The purpose of the Advanced Placement course in Statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data.  Students are exposed to four broad conceptual themes: 1. Exploring Data: Observing patterns and departures from patterns,  2. Planning a Study: Deciding what and how to measure, 3. Anticipating Patterns: Producing models using probability and simulation,   4. Statistical Inference: Confirming models.  AP Statistics is an excellent option for a strong mathematics student who has completed Algebra II.  Students may take the AP Statistics course in conjunction with Precalculus-AC, Trigonometry/Calculus-AC or -HN, AP Calculus (AB or BC), or AP Computer Science.  Students are required to sit for the AP Statistics Examination in May. Juniors may only take this course as an electives; seniors may take this core to satisfy the core math requirement.
    Prerequisite:  Department approval.

  • Multivariable Calculus: Advanced Topics in Discrete Mathematics, Linear Algebra, and Calculus

    Students will explore principles of Discrete Mathematics, including, but not limited to, advanced counting and probability theory, the binomial theorem, combinatorics, and elements of graph theory. The course also includes the study of Linear Algebra, including systems of linear equations and linear transformations using matrices and vector spaces. From there, students will move to traditional Multivariable Calculus content: Polar and Parametric Representations of Curves, Vectors and Vector Valued Functions, Partial and Directional Derivatives in a multivariable setting, and Multiple Integrations. 
    Prerequisites: Completion of AP Calculus AB AP Calculus BC. This course may be taken concurrently with AP Statistics.
     

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Wilmington, DE 19802

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Salesianum School educates and develops the whole person based on the teaching of Saint Francis de Sales, whose spirituality can be summarized in “Live Jesus.” As an independent Catholic secondary school founded by the Oblates of St. Francis de Sales in 1903, Salesianum challenges young men through dynamic college preparatory and extracurricular programs to live as Salesian Gentlemen devoted to faith, community, and service.