The goal of the mathematics department at Pope John Paul II High School is to empower the students by providing the skills and confidence necessary to do mathematics. Students will be actively involved in the development of concepts by doing “hands on” activities as well as by using technology such as graphing calculators and computers with suitable software that will build a power of visualization. This visualization will be fostered by exploring problems from the numeric, algebraic, and graphical perspectives. “When am I ever going to use this?” is a common question that is asked by students at some point in their study of mathematics. Exposure to real-world applications in a wide variety of disciplines will enable students to learn the value of mathematics and allow them to develop the self-confidence necessary to undertake challenging problems. Mathematics’ classrooms will be laboratories with interactive instructional approaches that focus on problem solving where students will grow excited by their successes. With an applications-oriented and investigative curriculum that is designed to enhance the understanding of mathematics, students will be able to say “I know when I am going to use this in my world”.
The mathematics curriculum requires the completion of four credits for graduation. This curriculum is designed to meet the needs of students with diverse ability levels. All students will have the opportunity to undertake an advanced placement course. Any student that wishes to enter Pope John Paul II High School and take a course higher that Algebra I must take a placement test.
Suggested Course Sequences: Mathematics Page – Please go to end of curriculum guide.
Algebra is a way of thinking about and representing many situations. Changes in technology dictate the algebraic concepts and skills that should be taught as well as the way they should be applied. This course introduces to students these new ideas and new ways of learning. It is important the students view algebra as a tool for problem solving, reasoning, communication, and making connections. The main topics of algebra I are equation solving, graphing linear functions, exponents, factoring, and data analysis. Mathematical models will be emphasized in contextual settings that provide students the opportunity to make connections between algebra and other disciplines.
ALGEBRA 1 ADV
The scope and sequence of algebra topics occur at faster pace in this course. Rapid generalization and the ability to use abstraction are expected. The language and methods of algebra are the tools, while multi stop problems are the context. This course is preparing the base of knowledge required to understand and master calculus topics.
Multiple types of assessment will be utilized in this course. Projects that involve communication both in verbal and in written form are used in this course. Emphasis will also be placed on understanding topics extending far beyond the requirement of a normal algebra class. Problem solving skills necessary to be successful at mathematics’ competitions will be emphasized in this course.
Charts, diagrams, and graphs will be used extensively to enhance the level of understanding as well as to provide alternative approaches to problem solving. The TI83+/TI 84 along with computers with suitable software will be used.
The emphasis in the Algebra II curriculum is on the study of functions: linear, quadratic, polynomial, exponential, rational, and logarithmic. These functions are studied symbolically, graphically, and numerically. Through use of mathematical modeling, data analysis, matrices, and algorithmic thinking, students will see algebra as a problem solving tool The TI-83+ /TI 84 graphing calculator as well as a computer with suitable software will be used throughout the course.
ALGEBRA 2 ADV / PRECALCULUS
Students in this course must have solid mathematical fundamentals, a genuine enjoyment of mathematics, and willingness to pursue it enthusiastically. Limited time will be spent reviewing Algebra I concepts, so a strong proficiency of these fundamentals, including linear functions, is required. This course requires the successful completion of a summer homework assignment to confirm mastery of basic Algebra I skills.
This course enhances traditional algebra with in-depth investigations of functions and algebraic applications. Students will be expected to do more independent study than is required in the college prep Algebra II. Any student completing this course successfully should be prepared to begin an in depth study of calculus beginning with a semester of trigonometry in the precalculus course. The use of a TI-83+ /TI 84 graphing calculator along with a computer with suitable software will be utilized extensively in this course. Emphasis will be placed on the construction of logical and valid proofs throughout the course. This course covers all the algebraic concepts that are normally covered in a precalculus course.
A comprehensive coverage of formal geometric concepts will be emphasized. Topics in this course include the study of points, lines, and planes, similarity and congruence of polygons, right triangle relationships including trigonometry, area and volume concepts, circle concepts, constructions, locus of points, and transformations. Students will see the connections between these formal geometric ideas and the geometry of the real world. The development and discovery of ideas, the formulation and investigation of conjectures, and problem-solving that requires multi-step thinking and logical reasoning will be emphasized much more than rigorous proof and will be accomplished using hands on manipulatives, TI-83 /TI 84 graphing calculator, and Geometer Sketchpad (version 4.0)
Prerequisite: High School Algebra I ADV or appropriate score on the Freshman Algebra Placement Test
The philosophy of accelerated geometry is much the same as that for college placement geometry. Emphasis will also be placed on understanding topics extending far beyond the requirement of the college placement class and students will be expected to do more independent study. This course focuses on both the content and form of geometry, with emphasis on the techniques of formal proof and the application of geometric concepts to solve complicated problems. Problem solving skills necessary to be successful at mathematics’ competitions will be investigated daily.
Students enrolling in Precalculus should have a very solid background in algebraic skills, a working knowledge of linear, quadratic, and polynomial functions, and a willingness to work hard. Successful completion of summer homework is mandatory to confirm that mastery of the necessary algebraic concepts is evident. Throughout the course, a TI-83 /TI 84 graphing calculator along with appropriate computer software will be used to offer alternative solution methods and to enhance the visualization of mathematical concepts. The first half of the course will deal with trigonometry and the second half will be devoted to the study of limits and derivatives in the calculus book. Precalculus is a rigorous course that fully prepares the student for college level calculus.
This course is designed to give students an opportunity to review and master the algebra concepts previously studied in Algebra I and Algebra II. Students will increase their understanding of functions and mathematical relationships. Special emphasis will be placed on graphing: linear, polynomial, quadratic, and rational functions. This class is also offered as a dual enrollment class with Volunteer State Community College. Students will receive high school credit as well as up to two college credits: one in College Algebra and the other in Precalculus.
Calculus AB and Calculus BC are primarily concerned with developing the students’ understanding of the concepts of calculus and providing experiences with its methods and applications. These courses emphasize a multirepresentational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The connections between these representations are vital to the successful understanding of calculus. Calculus BC is an extension of Calculus AB rather than an enhancement. Common topics require similar depth of understanding and both courses are intended to be challenging and demanding. Through the use of unifying themes of derivative, integral, limits, and approximation, and applications and modeling, both course become a cohesive whole rather than a collection of unrelated topics.
AP CALCULUS AB
Prerequisite: Successful completion of a summer home work assignment.
AP Calculus AB is designed to follow the AP Calculus AB curriculum established by the College Board. This curriculum can be found and is available online at http:/apcentral.collegeboard.com. Students are expected to posses the determination and initiative to take on a college level course as well as the corresponding workload. Students are required to take Calculus AP exam. Students will have completed one third of the topics found in this curriculum in the precalculus class.
AP CALCULUS BC
Prerequisite: Successful completion of a summer home work assignment.
AP Calculus BC – AP Calculus BC is designed to follow the AP Calculus BC curriculum established by the College Board. This curriculum can be found and is available online at http:/apcentral.collegeboard.com. This course examines both differential and integral calculus, focusing on a wide variety of functions. Students are expected to posses the determination and initiative to take on a college level course as well as the corresponding workload. Students are required to take Calculus AP exam. Students will have completed one fourth of the topics found in this curriculum in the precalculus class.
Prerequisite: Algebra II
Introduction to elementary methods and techniques. Topics include sampling, frequency distributions, elementary probability, binomial distributions, and uniform distributions. Tests of hypothesis and significance of data and simple correlation will be emphasized.
PROBABILITY AND STATISTICS AP
Prerequisite: Enrollment in and/ or completion of Algebra II ADV or teacher recommendation.
The Statistics AP course is designed to introduce students to major concepts and tools for collecting, analyzing, and drawing conclusions from data. This course follows the AP Statistics curriculum established by the College Board while also including material that will guide students in conducting and communicating their own statistical analyses. Students will be required to communicate their analysis through formal writing. Technology will be an integral part of the course, as students will be expected to use statistical software, spreadsheets, presentation software, and the TI-83 calculator to perform their analyses, present their findings and investigate topics visually. Students are required to take the AP Statistics exam.
DIFFERENTIAL EQUATIONS (AP level weighting)
Differential Equations is open to students who have successfully completed BC calculus. This class is also offered as a dual enrollment class with Volunteer State Community College. Students will receive one Advanced high school credit in addition to two college credits: one in Calculus and Analytic Geometry III and the other in Differential Equations if this option is selected.
This course covers the following information: Three dimensional vectors, quadratic surfaces, vector valued functions and space curves; arc length; unit tangent vector; acceleration; partial derivatives and their applications; linearization ; differentials; extreme values; Lagrange multipliers; multiple integration ; cylindrical and spherical coordinates; vector fields; line integrals; Green’s Theorem; Stokes’ Theorem. Linear First order differential equations, applications of linear equations, homogeneous linear differential equations, complementary and particular solutions, applications including undamped and damped vibrations, nonhomogeneous linear differentiations; equations including variation of parameter. LaPlace transform methods, linear systems, and series solutions.
Academic Extracurricular Activities in the Math Area
MATH CLUB: MU ALPHA THETA
The math club at Pope John Paul II High School will be an organization that is dedicated to promoting scholarship and enjoyment in mathematics. The club will also be active in mathematics’ competitions as well as being a service club for Pope John Paul II High School. Members of the club will offer tutoring services for students needing assistance and challenges.