Mathematics

Philosophy
The Mathematics Department of Pope John XXIII High School offers a flexible curriculum to meet the needs of a diverse student body. Each student advances according to his/her goals and demonstrated ability. Emphasis on the five general goals of the National Council of Teachers of Mathematics encourages students to value mathematics, grow confident in their ability to solve problems, and learn to communicate and reason mathematically.
Course Offerings and Descriptions
NOTE: The prime criterion for placement in the 8th grade courses Honors Algebra I (MAT802), Algebra I/Accelerated (MAT801), and Pre-Algebra (MAT800) is performance on the Pope John Math Placement Test for 8th Graders. Other criteria (when available) will include performance in 7th grade, 7th grade teacher recommendations, and standardized test scores.
A full-year course that provides a transition from the arithmetic of elementary school to the algebra of high school, Pre-Algebra offers students additional time and opportunity to master basics that are critical to success in higher-level mathematics. In addition, students will learn the building blocks of algebra through topics such as solving equations, exponents, and polynomial operations.
 
Credit: 5
Quality Point Group: I
Open to Grades: 8
Prerequisite: See Note above
Algebra 1 Accelerated is a comprehensive algebra 1 course. Topics covered at an accelerated pace 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 and a unit dedicated to word problems. This course is identical to 9th grade Algebra I/Accelerated (MAT 101).
 
Credit: 5
Quality Point Group: I
Open to Grades: 8
Prerequisite: See Note above
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 includes a deeper and more challenging exploration of applications and algebraic modeling, factoring and radicals, and quadratic functions. This course is identical to 9th grade Honors Algebra I (MAT 102).
 
Credit: 5
Quality Point Group: II
Open to Grades: 8
Prerequisite: See Note above
Designed to ease the transition from the concrete concepts of arithmetic to the abstract concepts of algebra, this first course in Algebra focuses on fundamental mathematical skills and introductory 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 radicals. Students earning 90 or higher in this course can progress to Algebra I/Accelerated in their sophomore year; students earning a passing grade less than 90 will progress to Geometry.
 
Credit: 5
Quality Point Group: I
Open to Grades: 9, 10, 11
Prerequisite: For Pope John 8th graders, a final grade of less than 77 in 8th grade Pre-Algebra-A (MAT 800A) OR final grade of less than 90 in 8th grade Pre-Algebra-B (MAT 800B). Students entering Pope John as 9th graders must take a placement test.
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 and a unit dedicated to word problems.
 
Credit: 5
Quality Point Group: I
Open to Grades: 9, 10, 11
Prerequisite: For Pope John 8th graders, a final grade of 77 or better in 8th grade Pre-Algebra-A (MAT 800A) OR final grade of 90 or better in 8th grade Pre-Algebra-B (MAT 800B). Students who earn a final grade of less than 84 in 8th grade Algebra I Accelerated (MAT 801) OR a final grade of less than 77 in 8th grade Honors Algebra 1 (MAT802) may elect to take Accelerated Algebra I. Students entering Pope John as 9th graders must take a placement test.
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 includes more work with applications and algebraic modeling, more challenging coverage of factoring and radicals, and a deeper exploration of quadratic functions.
 
Credit: 5
Quality Point Group: II
Open to Grades: 9, 10, 11
Prerequisite: For Pope John 8th graders, a final grade of 84 or better in 8th grade Algebra I/Accelerated or less than 84 in Honors Algebra I may elect to take Honors Algebra I in 9th grade. Students entering Pope John as 9th graders must take a placement test.
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. Topics include parallel and perpendicular lines, polygons, properties of triangles and triangle congruence, coordinate plane geometry, and an introduction to right triangle trigonometry. There is a strong emphasis on the review of algebraic concepts throughout the course.
 
Credit: 5
Quality Point Group: I
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
Covering all the topics of Geometry (MAT 200) but at an accelerated pace, this course in plane geometry is a deeper and more comprehensive study of the elements of analytic and solid geometry, including formal proofs, right triangle trigonometry, transformations, and geometry in a coordinate plane. Facility with a scientific calculator is 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 84 in Honors Algebra I (MAT 102)
This advanced Geometry course is designed for students who have demonstrated superior ability in mathematics, and specifically, mastery of Algebra 1. Taught in an investigative, critical thinking style, the course covers all topics in Accelerated Geometry (MAT 201) but with a strong emphasis on deductive and inductive reasoning, development of formal proofs, visualization, problem solving, and algebraic approaches to prove theorems and solve geometric problems in a coordinate plane.
 
Credit: 5
Quality Point Group: II
Open to Grades: 9, 10, 11, 12
Prerequisite: Final grade of 84 or better in Honors Algebra I OR 93 or better in Algebra I/ Accelerated. For students entering Pope John as 9th graders, satisfactory performance on the Math Department Honors Geometry Placement.
Algebra II further develops the concepts taught in Algebra 1 and then advances 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
Quality Point Group: I
Open to Grades: 10, 11, 12
Prerequisite: Final grade of 65 or better in Geometry.
Algebra II/Accelerated begins with a review of the materials taught in Algebra 1/Accelerated and then progresses to more advanced algebraic concepts. There is a strong emphasis on functions including quadratic, polynomial, exponential, logarithmic, rational, radical and piecewise functions as well as a unit on function transformation and probability.
 
Credit: 5
Quality Point Group: I
Open to Grades: 10, 11, 12
Prerequisite: Final grade of less than 84 in Honors Algebra I and Honors Geometry OR a final grade of 65 or better in Geometry/Accelerated and 77 or better in Algebra I/Accelerated.
Requirement: TI 84+ graphing calculator
Designed to extend and further develop the concepts and theories introduced in Algebra 1, Algebra II Accelerated places a stronger emphasis on problem solving and critical thinking. The computational level and pace is more demanding, and the course is extended to cover conics, sequences and series, and an introduction to trigonometry.
 
Credit: 5
Quality Point Group: II
Open to Grades: 10, 11, 12
Prerequisite: Final grade of 84 or better in Honors Geometry OR 93 or better in Algebra 1 Accelerated and Geometry Accelerated.
Requirement: 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 85 in Honors Algebra I. Other doubling-up combinations involving accelerated and honors Geometry and Algebra II are also available with Department Chair approval.
This course in Precalculus will cover functions and their graphs, including linear, quadratic, polynomial, rational, exponential and logarithmic. It will also include an exploration of trigonometric functions and their graphs. This course is designed for students who need an introduction to precalculus topics before college.
 
Credit: 5
Quality Point Group: I
Open to Grades: 11, 12
Prerequisite: 70 – 79 in Algebra II/Accelerated or 90+ in Algebra II and Math Department Chair approval
Requirement: TI 84+ graphing calculator
This course will cover functions, concepts of trigonometry and their application. It will also include algebraic, trigonometric, exponential and logarithmic functions. This course will emphasize through technology a comprehensive coverage of the topics of trigonometry including polar coordinates and their use in problem solving.
 
Credit: 5
Quality Point Group: I
Open to Grades: 11, 12
Prerequisite: Final grade of less than 84 in Honors Algebra II OR 80 or better in Algebra II/Accelerated.
Requirement: TI 84+ graphing calculator
Honors Precalculus integrates the major concepts and technology required for Calculus. The curriculum covers functions, modeling change, exponential and logarithmic functions, trigonometry, combinations, and a brief introduction to Calculus.
 
Credit: 5
Quality Point Group: II
Open to Grades: 11, 12
Prerequisite: Final grade of 84 or better in Honors Algebra II OR 93 or better in Algebra II/Accelerated and Geometry Accelerated.
Requirement: TI 84+ graphing calculator
Students will learn to manage personal finances and make intelligent, daily consumer decisions. Topics include: budget preparation, saving and investing, insurance protection, income tax preparation, credit, and consumer/internet fraud protection laws.
 
Credit: 5
Quality Point Group: I
Open to Grades: 12
Prerequisite: None
This course serves as an introduction to applied statistics. Descriptive and inferential uses of statistics in reference to business, the social and behavioral sciences, and the natural and physical sciences will be discussed. 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
Quality Point Group: I
Open to Grades: 11, 12
Prerequisite: Final grade of 70 or better in Precalculus, Accelerated Precalculus, Honors Pre-Calculus, or Honors Algebra II, OR 73 or better in Algebra II or Algebra II/Accelerated
Requirement: TI-84+ Graphing Calculator
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
Quality Point Group: II
Open to Grades: 11, 12
Prerequisite: Final grade of 77 or better in Honors Pre-Calculus OR 84 or better in Accelerated Pre-Calculus.
Requirement: TI-84+ Graphing Calculator
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
Quality Point Group: III
Open to Grades: 11,12
Prerequisite: Final grade of 93 or better in Accelerated Pre-Calculus OR 84 or better in Honors Pre-Calculus OR 84 or better in Honors Algebra II OR 93 or better in Algebra II/Accelerated, AND final grade of 84 or better in English II or III. AP Statistics may be taken concurrently with, but not as a replacement for, Honors Calculus, AP Calculus AB or AP Calculus BC.
Requirement: TI-84+ Graphing Calculator
AP Calculus is designed as a college level course. The course begins with a brief review of Pre-Calculus and progresses 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
Quality Point Group: III
Open to Grades: 11,12
Prerequisite: Final grade of 84 or better in Honors Precalculus, OR final grade of 93 or better in Accelerated Precalculus, OR 93 or better in Honors Calculus.
Requirement: TI-84+ Graphing Calculator
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 topics primarily related to polynomial approximations and series, improper integrals, 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
Quality Point Group: III
Open to Grades: 11,12
Prerequisite: Final grade of 93 or better in Honors Pre-Calculus.
Requirement: TI-84+ Graphing Calculator
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
Quality Point Group: III
Open to Grades: 11, 12
Prerequisites: Final Grade of 84 or better in Honors Precalculus
Multivariable Calculus 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 by extending 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 recognize the fundamental multivariable calculus plays in all of science and engineering and will gain a new appreciation for the achievement of higher mathematics.
 
Credit: 5
Quality Point Group: III
Open to Grades: 12
Prerequisite: Final grade of 84 or better in AP Calculus BC and passing grade on the AP Calculus BC exam
Requirement: TI-84+ Graphing Calculator