# Mathematics

##### Beth Menzie, Department Chair

**Graduation Requirements:**

- The minimum requirements in mathematics are as follows: Students must satisfactorily complete Algebra I, Geometry, Algebra II and Precalculus or Integrated Mathematics.
- Beginning in the 9th grade, students must take at least 7 semesters of mathematics, including a full year of Precalculus or Integrated Mathematics. It is expected that these 7 semesters will be taken consecutively.

The Penn Charter Mathematics Department attempts to provide each and every student with an appropriate level of both intellectual challenge and success. As student needs evolve, the department strives to meet these needs by adding new courses and experiences.

**Current Course Offerings:**

The mathematics program in the Upper School includes courses in first-year algebra, geometry, second-year algebra, precalculus, statistics, finance and calculus. Class sections of most of these courses are grouped on the basis of ability and achievement in mathematics, as indicated by performance in previous courses and teachers’ recommendations. Every effort is made to place students new to Penn Charter at an appropriate level in the mathematics program, based on their records at previous schools, their performance on placement and standardized tests, and personal interviews.

**Advanced Placement and Advanced Courses:**

Advanced courses are indicated with an “A.” The Mathematics Department offers Advanced Placement programs in calculus and statistics for qualified students, based upon the Advanced Placement course descriptions of the College Board. Successful completion of Advanced Precalculus, with a grade of B or better and departmental approval, is the prerequisite for the AP Calculus courses.

Students enrolled in an AP courses in the first semester must remain in the course for the entire year and must take the AP exam. In all of our departmental AP courses, if a student has not managed an average of B or higher at the end of the first semester, the Mathematics Department may choose to transfer the student from the AP course to a non-AP section. If the transcript has been sent to colleges, the colleges will be notified of the change in status.

Students enrolled in the A or AA courses of mathematics are required to maintain an average of B or higher to remain in the course. If a student has not managed an average of B or higher at the end of the first semester, the Mathematics Department reserves the right to move the student to a regular section.

**Summer Mathematics Courses:**

Students have the option to enroll and earn credit in one of Penn Charter’s summer mathematics courses. Credit will not be given, however, to students who take these courses during the summer elsewhere. Students completing Algebra I in ninth grade may enroll in Penn Charter’s summer geometry course or they may take Geometry in 10th grade, Algebra II in 11th grade, and either Precalculus or Integrated Mathematics in their senior year. In this case, students must complete four full years of math in order to graduate.

**M110****ALGEBRA I****(2 UNITS) ALL YEAR**

This course is focused on the basic concepts of algebra. Particular emphasis is placed on, but not limited to, factoring, solving linear and quadratic equations, solving systems of equations and inequalities, and graphing equations. The course also explores, in an elementary fashion, functions. (9th grade)

**M120, M120A****GEOMETRY, ADVANCED GEOMETRY****(2 UNITS) ALL YEAR**

These courses, which focus on Euclidean geometry, emphasize, encourage and challenge students to discover geometric ideas through investigative activities and technology. Topics include the foundations of geometry definitions, inductive and deductive reasoning, the nature and development of a mathematical system using axioms, theorems, and proof, the close study of a wide variety of geometric figures, right triangle geometry, basic isometries, area and volume. A dynamic software package is used in this class. *Prerequisite for M120: Algebra 1; for M120A: grade of A in Algebra I and departmental approval. (9th, 10th grades)*

**M330****ALGEBRA II****(2 UNITS) ALL YEAR**

This course further explores the concepts that were introduced in Algebra I. Students examine a variety of different functions, such as linear, quadratic, polynomial, exponential and logarithmic functions. Multiple approaches to problem solving will be employed, including the use of technologies such as a graphing calculator and Desmos. *Prerequisites: successful completion of Algebra I and Geometry*. (10th, 11th grades)

**M330A****ADVANCED ALGEBRA II****(2 UNITS) ALL YEAR**

This course furthers the study of algebra by looking at classes of functions. Students will examine linear, quadratic, polynomial and exponential functions algebraically, numerically and geometrically. A graphing calculator and technologies such as Desmos, will be used to support the algebraic manipulation and allow the students to see and explore the mathematics. Advanced Algebra II moves at a rapid pace and requires students to be independent and to make conjectures on their own. *Prerequisites: **grades of A in Algebra I and Geometry and departmental approval, or a grade of B or better in Advanced Geometry. (10th grade)*

**INTEGRATED MATHEMATICS****(2 UNITS) ALL YEAR**

Integrated Mathematics reinforces and builds upon the topics studied in Algebra 1, Geometry, and Algebra II, with an emphasis on collaboration and communication, both written and verbal. Students will apply their algebraic and geometric skills, as well as technology, to support and enhance their overall understanding of high school mathematics, including selected topics from Precalculus. *Prerequisites: successful completion of Algebra I, Geometry and Algebra II, and departmental approval*. (11th, 12th grades)

**M570****PRECALCULUS****(2 UNITS) ALL YEAR**

Precalculus prepares students for the study of calculus by building on the topics studied in Algebra II. Students will apply their algebraic skills, as well as technology, to support and enhance their overall understanding of functions and statistics. The course will include trigonometric, exponential, logarithmic and polynomial functions.* Prerequisites: successful completion of Algebra I, Geometry and Algebra II.* *(11th, 12th grades)*

**M570A****ADVANCED PRECALCULUS****(2 UNITS) ALL YEAR**

This course continues to build on the concepts studied in Advanced Algebra II. Students will explore a variety of functions, including trigonometric, polynomial, exponential and logarithmic functions. The course requires students to think independently and to make conjectures on their own, preparing them to begin the study of AP Calculus AB in the spring.* Prerequisites: grades of B or better in Advanced Algebra II and Advanced Geometry, or grades of A in Algebra II and Geometry, and departmental approval. (11th grade)*

**ADVANCED PRECALCULUS****(2 UNITS) ALL YEAR**

This rapidly moving and intense course prepares students for AP Calculus BC. The properties and transformations of functions, including linear, quadratic, polynomial, rational, exponential and logarithmic functions are examined algebraically, numerically and geometrically. Mathematical models are created to solve real-life applications. The pace of this course is particularly fast because students begin the AP Calculus curriculum, including learning to differentiate using numerical methods, the limit definition and the differentiation rules. *Prerequisites: grade of A in the advanced sections of Algebra II and Geometry, and departmental approval*. (11th grade)

**M660****AP STATISTICS****(2 UNITS) ALL YEAR**

AP Statistics introduces students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to exploring data, sampling and experimentation, exploring random phenomena using probability and simulation, and statistical inference. This course provides students with the opportunity to earn Advanced Placement credit in college. The The TI-84 graphing calculator is used in this class. *Prerequisites: Algebra 2 and departmental approval. (11th and 12th grade)*

**AP CALCULUS (AB)****(2 UNITS) ALL YEAR**

This is a full-year calculus course designed to provide students with the opportunity to earn Advanced Placement credit in college. The course provides a study of differential and integral calculus.* Prerequisites: grade of B or higher in Advanced Precalculus and departmental approval*. (12th grade)

**M790AA****AP CALCULUS (BC)****(2 UNITS) ALL YEAR**

This course is similar to AP Calculus (AB) but covers additional material such as sequences and series and also provides students with the opportunity to earn Advanced Placement credit in college. The TI-Nspire CAS is used in this class. *Prerequisites: grade of B or higher in Advanced Precalculus AA and departmental approval*. (12th grade)

**M661, M664****INTRODUCTION TO STATISTICS, PART 1****(1 UNIT) SEMESTER 1 & SEMESTER 2**

This course, intended for juniors and seniors, will focus on the study of real data and gives students a significant introduction to several core topics of statistics. These include displaying and describing distributions, measures of center, measures of spread, comparing distributions of both categorical and quantitative variables, graphical displays of data, normal distributions and the correlation coefficient. Emphasis is placed on the development of effective verbal and written explanations, and technology will be utilized. If a student has not maintained an average of B or higher at the end of semester 1, that student will need departmental approval in order to continue in Introduction to Statistics, Part II. *Prerequisites: Algebra II*. (11th, 12th grades)

**M662****INTRODUCTION TO STATISTICS, PART II****(1 UNIT) SEMESTER 2**

This course is a continuation of the Introduction to Statistics, Part 1 course. Students will continue with the study of real data and should complete a curriculum roughly equivalent to an undergraduate introductory course. Topics include randomness in data, inference from data (principles and comparisons), inferences with categorical data, and relationships in data. *Prerequisites: Introduction to Statistics, Part 1 with a grade of B or better, and/or department approval.* (11th, 12th grades)

**M791, M792****CALCULUS****(1 UNIT EACH) SEMESTER 1, SEMESTER 2**

These calculus courses are sequential classes. M791 (Semester 1) introduces students to the concepts of calculus and includes the study of limits and derivatives. M792 (Semester 2) continues with the study of derivatives and adds the study of integrals. If taken all year, these courses cover a full-year course in differential and integral calculus. Students may not enroll in M792, without having taken M791. If a student has not maintained an average of B or higher at the end of semester 1 in M791, Calculus Part I, that student will need departmental approval in order to continue in M792 Calculus, Part II. *Prerequisites: Precalculus and departmental approval. (12th grade)*

**M795, M796**

**MATHEMATICS OF FINANCE**

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**1 UNIT) SEMESTER 1 & SEMESTER 2**

In this senior elective course, the students acquire the knowledge and skills required to make sound financial decisions and to manage their own personal finances. The lessons engage students in critical thinking, problem solving, and decision-making. Topics covered include budgeting, saving and investing, mortgages, credit and interest, insurance, and taxes. *Prerequisites: Algebra II*. (12th grade)