# Mathematics

The mathematics program is divided into five programs to provide an excellent opportunity tailored to each student's ability level. Our programs follow the recommendations of the National Council of Teachers of Mathematics. The AP program follows the recommendations of the Committee for the Undergraduate Program in Mathematics of the Mathematical Association of America.

Mathematics courses are up-to-date with the use of computer software and instruction in the use of graphing calculators in class. These calculators may be used on the college SAT examinations.

Course Descriptions

Algebra 1 - High Honors

This course studies such topics as set theory, number properties, signed numbers, coordinate geometry, linear equations, algebra of polynomials, factoring, and rational expressions. There will be a in depth use of word problems. The use of graphing techniques will be stresses with their use in the solving of linear equations. The Distance Formula will one of the topics used to show the connection between Algebra and Geometry. The theory of quadratic equations and a basic understanding of radicals are also introduced. The theory and use of functions will be introduced. A correlation between arithmetic and algebraic principles and the vocabulary of algebra is stressed. The High Honors Algebra 1 has more challenging problems in each topic than the Honors and College Prep 1 courses.
(Freshman course)

Algebra 1 - Honors

This course studies such topics as set theory, number properties, signed numbers, coordinate geometry, linear equations, algebra of polynomials, factoring, and rational expressions. There will be a in depth use of word problems. The use of graphing techniques will be stresses with their use in the solving of linear equations. The proper applications of polynomials will be stresses. The theory of quadratic equations and a basic understanding of radicals are also introduced. A correlation between arithmetic and algebraic principles and the vocabulary of algebra is stressed.
(Freshman course)

Algebra 1 - College Prep

This course studies signed numbers, algebra of monomials, polynomials, and guidelines for solving linear and quadratic equations. Emphasis is placed on vocabulary, definitions, guidelines, and applications of fundamentals to move into the abstract concepts of algebra. Review is used to meet these ends, while set theory, rational and irrational numbers, radicals, graphing, simultaneous equations, and inequalities are previewed. Working with and thinking out word problems and preparation for post school testing is added to course structure.

Geometry - High Honors

This course deals with the properties and relationships between points, lines, planes, and solids. The logical process of a mathematical system is developed as the student learns to use defined and undefined terms to set up the basis of postulates and theorems. An understanding of the deductive method as a method of thought will be stressed in geometric proofs. Extensive use of algebra will be necessary in this course. The properties and relationships of parallel lines, polygons, and circles will be taught. An in-depth study will be made of three-dimensional figures including their surface area and volumes. Concepts of coordinate geometry will be discussed having the students see the relationship between algebra and geometry. Radicals, quadratic equations, and proportions will be used in the solving of problems. Loci, constructions and transformations will be covered in the course. The use of the Pythagorean Theorem in Mathematics is explained in detail. Simple right triangle trigonometry will also be covered. Use of calculators will be stresses in this course.
Prerequisite: Algebra 1 or passing of the Algebra Entrance Exam for freshmen who have had Algebra 1 in grade eight.

Geometry - Honors

This course presents geometry as that part of mathematics that combines figures and their properties with an algebraic approach. Students learn to use deductive reasoning in the first half of the course. During the second half, students will apply more algebra to the understanding of geometric figures. Properties and relationships of parallel lines, polygons and circles will be covered. The use of the Pythagorean Theorem in Mathematics is explained in detail. The study of three-dimensional figures, including surface areas and volumes, are included in the depth of the course. Simple right triangle trigonometry is also covered.
Prerequisite: Algebra 1

Geometry - College Prep

This course deals with the properties and relationships between points, lines, planes, and solids. The skills learned in algebra are maintained and extended. The student will learn the basic terms of Geometry and the thought process involved. The student will then proceed to a study of the principles and properties of parallel lines, polygons, and circles. The use of the Pythagorean Theorem in Geometry and other mathematical areas will be stressed. The concepts, formulas and uses of area will be covered. Geometry is part of an integrated system. The skills are used in other math courses and in everyday life.
Prerequisite: Algebra 1

Algebra 2/Trigonometry - High Honors

The topics of Algebra 1 are reviewed and more challenging problems are presented for each topic. A strong approach of functional theory, properties and applications will be presented. The additional topics of determinants, sequences, series, conic sections as well as the logarithmic and exponential functions are included. Trigonometry and circular functions and their graphs will complete the year. Computer/Calculator lab assignments will be a regular part of this course.
Prerequisite: Geometry

Algebra 2/Trigonometry - Honors

The concepts and ideas of Algebra 1 are continued and expanded upon in this course. Linear and quadratic functions are discussed at length and the graphing of such functions is introduced. More extensive material is covered on radicals and radical equations. The theory of logarithms and exponential equations is included as well as sequences and series. The course ends with the additional topics of the trigonometric and circular functions. Computer/Calculator lab assignments will be a regular part of this course.
Prerequisite: Geometry

Algebra 2 - College Prep

The concepts and skills developed in Algebra 1 are strengthened and expanded upon. Stress is placed on the precision of language and thought processes. Functions are discussed at length. Linear and quadratic functions, their graphs, quadratic equations, and radicals are covered in depth. Factoring by grouping, the remainder and factor theorems, complex fractions, complex numbers, and equations in quadratic form are some of the additional topics.
Prerequisite: Geometry

Analysis - High Honors

This course comprises of the algebra of real numbers, vectors, complex numbers, series and sequences, functions, and the concept of the limit as an introduction to calculus. Properties and graphs of conic sections will be presented. Further emphasis is placed on the understanding of the derivative and it's applications. The logarithmic and exponential functions will be discussed. A deeper look into the theory of circular functions will also be covered. This course will give a student a strong background in all the topics of mathematics needed for a comprehensive calculus program at college. A stronger emphasis will be made on the basic concepts used in Calculus.This class will cover a deeper approach into graphing and the uses of other coordinate systems. A deeper approach to Analytical Geometry will also be covered in detail.

Prerequisite: Algebra 2/Trig

Analysis - Honors

This course comprises the algebra of real numbers, vectors, complex numbers, series and sequences, functions, and the concept of the limit as an introduction to calculus. Properties and graphs of conic sections will be presented. Further emphasis is placed on the understanding of the derivative and it's applications. The logarithmic and exponential functions will be discussed. A deeper look into the theory of circular functions will also be covered. This course will give a student a strong background in all the topics of mathematics needed for a comprehensive calculus program at college.
Prerequisite: Algebra 2/Trig

AP Calculus AB - Advanced Placement

This course is the equivalent of the first semester college Calculus course as recommended by the C.U.P.M. committee of the Mathematical Association of America. A college text is used and students selecting this course must have an excellent knowledge of algebra and geometry. The extensive use of trigonometry in this class makes the knowledge of the subject a prerequisite. Topics studied include functions, the concept of a limit, limit formulas, L'Hopital's rule, the derivative, slope fields, and the applications of differential calculus. The second semester works with integral calculus and it's algebraic, geometric, and physical applications. Many techniques of solving integrals will be covered. Volumes of the solids of revolution will also be learned. Extensive work will be done of the uses of the logarithmic, exponential functions, and arc trigonometric functions in calculus. Students are required to have TI-8384 or TI-83/84 Plus calculators for use in graphing functions, running programs, and evaluating formulas. Computer/Calculator lab assignments will be a regular part of this course. Students taking this course may elect to take the Advanced Placement Exam in Calculus AB from the College Board for the possible transfer of college credit. This course has been approved by the College Board Advanced Placement Program.
Prerequisite: Analysis

Trig and Analytic Geometry - College Prep

This course expands and continues with concepts from Algebra 2. Linear, quadratic, and polynomial functions are discussed and the graphing of these functions. The theory of logarithms and exponential equations is included. Properties and graphs of conic sections will be presented. The second semester deals with trigonometric identities, the Law of Sines, and the Law of Cosines. The course reviews the topics of Algebra 2 and also gives the students a strong background for any future math classes that they may take in college.
Prerequisite: Algebra 2

Statistics/Probability - College Prep

Statistics is the science of collecting, organizing, analyzing, and interpreting data in order to make decisions. The first half of this course covers descriptive statistics including frequency distributions, the counting principle, probability, the binomial and normal distributions, correlation and regression analysis. The second half of the course works with inferential statistics covering hypothesis testing with large and small samples using z, t, F and Chi-Square distributions. Students will be using computer software to perform calculations and generate graphs.
Prerequisite: Algebra 2

Sacred Heart University 17/65 Program

Sacred Heart University will allow Notre Dame students who have finished the mathematics curriculum at Notre Dame (Advanced Placement Calculus in junior year) to continue their mathematics endeavor with courses at the Sacred Heart University campus. Students will be required to pay a registration fee and then may take the second semester of Calculus, Linear Algebra. Differential Equations or Statistics. They will receive a transcript from Sacred Heart University giving college credit for their courses. Students will not receive credit at Notre Dame for these courses. Students may present the Sacred Heart University transcript to another college for possible transfer credit. Students must check with their future college or university to see if this credit will be accepted.