Mathematics
Philosophy
The mathematics department of Pope John XXIII High School has designed and instituted a flexible curriculum to meet the needs of a diverse student body. Each student advances according to his/her goals and demonstrated preparation. Emphasis is placed on the five general goals of the National Council of Teachers of Mathematics so that students will value mathematics, grow confident in their ability to solve problems, and learn to communicate and reason mathematically.
Mathematics Department Faculty:
Mr. Richard Ferrise, Department Chair
Mr. Brian Corcoran
Mr. Joseph Giovannone
Ms. Donna Keller
Mrs. Margaret Maneri
Mr. Richard Murphy
Ms. Jessica Rosario
Mr. Bruce Shuert
Mrs. Diane Stankiewicz
Mrs. Belinda Toma
Rev. Benjamin Williams
NOTE: For the following 8^{th} grade courses the prime criterion for placement is performance on the Pope John Math Placement Test for 8^{th} Graders. Other criteria (when available) will include performance in 7^{th} grade, 7^{th} grade teacher recommendations, and Terra Nova scores.
Honors Algebra I (MAT802)
Algebra I/Accelerated (MAT801)
Pre-Algebra (MAT800)
MAT 800 Pre-Algebra (8^{th} Grade)
Pre-Algebra is a full-year course that provides a transition from the arithmetic of elementary school to the algebra of high school. Particular attention is given to the reinforcement of basic skills and key concepts necessary for success in high school algebra. The Pre-Algebra course grants students the additional time and opportunity to learn and master basics that are critical to success in higher-level mathematics. In addition, students will learn the building blocks of algebra through topics of algebra such as solving equations, exponents, and polynomial operations. Pre-Algebra is a course that provides students with the structure and curriculum to reinforce basic skills and develop confidence in their ability to succeed in algebra.
Credit: 5
Open to Grades: 8
Prerequisite: See note
MAT 801 Algebra 1/Accelerated (8^{th} Grade)
Algebra 1 Accelerated is a comprehensive algebra 1 course. Topics are covered at an accelerated pace and include: solving and graphing linear equations and inequalities, mathematical operations with exponents and polynomials, factoring polynomials, as well as graphing and understanding quadratic functions and equations. There is a strong emphasis on problem solving skills throughout the course with a dedicated unit on word problems. This course is the same as the 9^{th} grade Algebra I/Accelerated (MAT 101).
Credit: 5
Open to Grades: 8
Prerequisite: See note
MAT 802 Honors Algebra 1 (8^{th} Grade)
Designed for students whose placement exams demonstrate their superior ability in mathematics, the course covers the topics in Algebra I/Accelerated with a stronger emphasis on problem solving and critical thinking. The computational level is more demanding, and the course is extended to include more work with applications and algebraic modeling, more challenging coverage of factoring and radicals, and a deeper exploration of quadratic functions. This course is the same as the 9^{th} grade Honors Algebra I (MAT 102).
Credit: 5
Open to Grades: 8
Prerequisite: See note
MAT100 Algebra I
This first course in Algebra focuses on introductory algebraic topics and is designed to facilitate the transition from the concrete concepts of arithmetic to the abstract concepts of algebra. The course is designed for students who need further development of fundamental mathematical skills and algebraic concepts. Topics include signed integers; greatest common factor and least common multiple; fractions, decimals and percents; linear equations; word problems; scientific notation; geometric applications; and probability. Students earning 90 or higher in this course qualify to progress to Algebra I/Accelerated in their Sophomore year. Students earning a passing grade less than 90 will progress to Geometry.
Credit: 5
Open to Grades: 9, 10, 11
Prerequisite: For Pope John 8th graders a final grade of less than 77 in 8th grade PreAlgebra-A (MAT 800A) or final grade of less than 93 in 8th grade Pre-Algebra-B (MAT 800B). Students entering Pope John as 9th graders must take a placement test.
MAT 101 Algebra I/Accelerated
Algebra 1 Accelerated is a comprehensive algebra 1 course. Topics are covered at an accelerated pace and include: solving and graphing linear equations and inequalities, mathematical operations with exponents and polynomials, factoring polynomials, as well as graphing and understanding quadratic functions and equations. There is a strong emphasis on problem solving skills throughout the course with a dedicated unit on word problems.
Credit: 5
Open to Grades: 9, 10, 11
Final grade of 90 or better in Algebra I (MAT 100). For Pope John 8th graders, a final grade of 77 or better in 8th grade Pre-Algebra-A (MAT 800A) OR final grade of 93 or better in 8th grade Pre-Algebra-B (MAT 800B) OR final grade of less than 85 in 8th grade Algebra I Accelerated (MAT 801) OR final grade of less than 77 in 8^{th} grade Honors Algebra 1 (MAT802). Students entering Pope John as 9th graders must take a placement test.
MAT 102 Honors Algebra I
Designed for students whose placement exams demonstrate their superior ability in mathematics, the course covers the topics in Algebra I/Accelerated with a stronger emphasis on problem solving and critical thinking. The computational level is more demanding, and the course is extended to include more work with applications and algebraic modeling, more challenging coverage of factoring and radicals, and a deeper exploration of quadratic functions.
Credit: 5
Open to Grades: 9, 10, 11
Prerequisite: For Pope John 8th graders, a final grade of 93 in 8th Grade Algebra I/Accelerated. Students entering Pope John as 9th graders must take a placement test.
MAT 200 Geometry
This course in plane geometry places more emphasis on logical reasoning and critical thinking skills. Students are taught a system of geometric definitions, theorems, and postulates using algebraic principles, constructions, and other manipulative techniques. Geometry in the coordinate plane is covered extensively and right triangle trigonometry is introduced.
Credit: 5
Open to Grades: 9, 10, 11, 12
Prerequisite: Final grade of less than 90 in Algebra I OR less than 77 in Algebra I/Accelerated
MAT 201 Geometry/Accelerated
Covering all the topics of Geometry (MAT 200), but at an accelerated pace, this course in plane geometry is a comprehensive study of the elements of analytic and solid geometry that allows deeper study of selected areas and coverage of extension topics, including formal proofs, right triangle trigonometry, and geometry in a coordinate plane. Mastery of Algebra 1 skills and facility with a scientific calculator are necessary.
Credit: 5
Quality Point Group: I
Open to Grades: 9, 10, 11, 12
Prerequisite: Final grade of 77 or better in Algebra I/ Accelerated (MAT 101) OR a final grade of less than 85 in Honors Algebra I (MAT 102) OR final grade of 85 or better in 8th grade Algebra I/Accelerated (MAT 801) OR final grade between 77 and 84 in 8th grade Honors Algebra I (MAT 802).
MAT 202 Honors Geometry
This advanced Geometry course is designed for students who have demonstrated superior ability in mathematics, and specifically, mastery of Algebra 1. The course is taught in an investigative, critical thinking style. The course covers all topics covered in Accelerated Geometry (MAT 201) but with a strong emphasis on deductive and inductive reasoning, development of formal proofs, visualization, problem solving, and the use of generalized algebraic approaches to prove theorems and solve geometric problems in a coordinate plane.
Please note that ninth grade students wishing to take Honors Geometry must complete a full year course in Algebra I with an 85 or above average and also demonstrate competency on the Honors Geometry Placement Test administered at Pope John in May of their 8th grade year.
Credit: 5
Open to Grades: 9, 10, 11, 12
Prerequisite: Final grade of 85 or better in Honors Algebra I OR 93 or better in Algebra I/ Accelerated. For students entering Pope John as 9^{th} graders, satisfactory performance on the Math Department’s Honors Geometry Placement Test.
MAT 300 Algebra II
Algebra II further develops the concepts taught in Algebra 1 and then moves on to the study of functions, linear equations and inequalities, systems of linear equations, polynomial operations, rational expressions, irrational and complex numbers, quadratic equations, exponential and logarithmic functions, and basic probability and statistics. Additionally, some time will be devoted to SAT and ACT preparation.
Credit: 5
Open to Grades: 10, 11, 12
Prerequisite: Final grade of 70 in Geometry
Requirement: TI 83+/TI 84+ graphing calculator
MAT 301 Algebra II/Accelerated
Final grade of less than 85 in Honors Algebra I and Honors Geometry OR a final grade of 70 or better in Geometry/Accelerated and 77 or better in Algebra I/Accelerated.
Credit: 5
Open to Grades: 10, 11, 12
Prerequisite: Final grade of 70 in Honors Algebra I and Honors Geometry, or a final grade of 77 in Algebra I/Accelerated and Geometry/ Accelerated.
Requirement: TI 83+/TI 84+ graphing calculator
MAT 302 Honors Algebra II
Designed to extend and further develop the concepts and theories of problem solving introduced in Algebra 1, this course covers the topics in Algebra II Accelerated with a stronger emphasis on problems solving and critical thinking. The computational level and pace is more demanding, and the course is extended to cover topics on conics, sequences and series and an introduction to trigonometry.
Credit: 5
Open to Grades: 10, 11, 12
Prerequisite: Final grade of 85 or better in Honors Geometry OR 93 or better in Algebra1/Accelerated and Geometry/Accelerated.
Requirement: TI-83+/TI-84+ graphing calculator.
NOTE: Students may elect to take both Honors Geometry and Honors Algebra II during their sophomore year.
The prerequisite for this option is a minimum of 93 in Honors Algebra I. Other doubling-up combinations involving
accelerated and honors Geometry and Algebra II are also available with Department Chair approval.
MAT 303 Pre-Calculus
This course is recommended for students who may be interested in studying mathematics in college, either as a major or in an allied science field. Pre-Calculus includes college algebra, trigonometric, exponential and logarithmic functions and their applications.
Credit: 5
Open to Grades: 11, 12
Prerequisite: Final grade of 77 – 84 in Honors Algebra II OR 85 or better in Algebra II/Accelerated
Requirement: TI 83+/TI 84+ graphing calculator
MAT 304 Honors Pre-Calculus
Honors Pre-Calculus integrates the major concepts and technology required for Calculus. The curriculum covers the areas of functions modeling change, trigonometry, combinations, transcendental functions, and a brief introduction to Calculus.
Credit: 5
Open to Grades: 11, 12
Prerequisite: Final grade of 85 or better in Honors Algebra II OR 93 or better in Algebra II/Accelerated and Geometry Accelerated
Requirement: TI 83+/TI 84+ graphing calculator
MAT 401 Financial Algebra
Financial Algebra is a college-preparatory course that provides students with the practical tools to understand financial markets and transactions and related economic topics. The course employs algebra, concepts and methods of probability and statistics, and geometry to solve “real world” financial problems such as investing, credit, banking, auto insurance, mortgages, employment, income taxes, budgeting, and planning for retirement. This course is only available to students who do not qualify for statistics.
Credit: 5
Open to Grades: 12
Prerequisite: : Final grade of 70 or better in Algebra II OR less than 77 Algebra II/Accelerated
Requirement: TI 83+/TI 84+ graphing calculator
MAT 402 Statistics
This course serves as an introduction to applied statistics. Descriptive and inferential uses of statistics will be discussed in reference to business, the social and behavioral sciences, and the natural and physical sciences. Topics covered include organization of data, measures of central tendency and dispersion, probability, sampling, elementary hypothesis testing, and correlation and prediction. Microsoft Excel is used extensively.
Credit: 5
Open to Grades: 11, 12
Prerequisite: Final grade of 70 in Pre-Calculus, Honors Pre-Calculus, or Honors Algebra II, or 77 in Algebra II
or Algebra II/Accelerated
Requirement: TI-83+/TI-84+ Graphing Calculator
MAT 403 Calculus
In Calculus, the mathematical language of change, topics include limits, derivatives, and integrals. Major concepts are introduced through data, applications, mathematical modeling, and technology.
Credit: 5
Open to Grades: 12
Prerequisite: Final grade of 77 in Honors Pre-Calculus or 85 in Pre-Calculus
Requirement: TI-83+/TI-84+ Graphing Calculator
MAT 501 AP Statistics
AP Statistics is a college level course in statistics that introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to the four broad conceptual themes: exploring data; sampling and experimentation through planning and conducting a study; anticipating patterns through exploring random phenomena using probability and simulation; and statistical inference through estimating population parameters and testing hypotheses. Students who successfully complete the course and AP exam may qualify for college placement and earn credit for an introductory college statistics course.
Credit: 5
Open to Grades: 11,12
Prerequisite: Final grade of 93 or better in Pre-Calculus OR 85 or better in Honors Pre-Calculus OR 85 or better in Honors Algebra II OR 93 or better in Algebra II/Accelerated, AND final grade of 85 or better in English II or III. AP Statistics may be taken concurrently with, but not as a replacement for, Calculus, AP Calculus AB or AP Calculus BC
Requirement: TI-83+/TI-84+ Graphing Calculator
MAT 502 Advanced Placement Calculus - AB
AP Calculus AB is designed as a college level course in the calculus of functions of a single variable. The course begins with a brief review of Pre-Calculus and will move on to the study of limits and continuity of functions, the derivative and its applications, the definite integral and its applications, and some basics of differential equations.
Credit: 5
Open to Grades: 11,12
Prerequisite: Final grade of 85 in Honors Pre-Calculus or 93 in Calculus
Requirement: TI-83+/TI-84+ Graphing Calculator
MAT 503 Advanced Placement Calculus - BC
AP Calculus BC is a full year college level course in the calculus of functions of a single variable. The course covers all topics presented in Calculus AB, some in greater depth, plus additional topics primarily related to polynomial approximations and series, improper integrals, and vector, parametric and polar functions. The BC course is designed to qualify the student for college placement and credit that is one course beyond that granted for AB.
Credit: 5
Open to Grades: 11,12
Prerequisite: Final grade of 93 in Honors Pre-Calculus
Requirement: TI-83+/TI-84+ Graphing Calculator
MAT 504 Discrete Mathematics
Discrete Mathematics, when offered, is an introduction to the foundations for advanced studies in mathematics and computer science. Students will be introduced to the basics of mathematical terminology and abstract reasoning. Topics include logic, number theory, methods of mathematical proof, set theory, functions and relations, and probability.
Credit: 5
Open to Grades: 11,12
Prerequisite: Final grade of 85 or better in Honors Pre-Calculus
Requirement: TI-83+/TI-84+ Graphing Calculator
MAT 601 Multivariate Calculus
Multivariate Calculus, when offered, is an elective course for our most gifted and talented students who have a strong interest in mathematics. Many of the ideas of elementary calculus in the plane generalize naturally to space and will be extended to three dimensions whereas other concepts will be new to the student. Topics include: partial derivatives, vector valued functions, multiple integrals, vector calculus, differential equations, and relevant applications. Students will see how multivariate calculus plays a fundamental role in all of science and engineering and will gain a new appreciation foe the achievement of higher mathematics.
Credit: 5
Open to Grades: 11,12
Prerequisite: Final grade of 85 or better in AP Calculus BC and passing grade on the AP Calculus BC exam
Requirement: TI-83+/TI-84+ Graphing Calculator