# Math Courses

### MATHEMATICS

**Core Mathematics Courses**

#### Algebra I/ Algebra I Honors

This course lays the foundation needed for the study of all later mathematics courses. Some topics studied are the following; solving equations and inequalities, working with polynomials and rational expressions, graphing of functions, the quadratic equations and radical expressions. Interspersed throughout are many and varied word problems that provide opportunities to apply the material studied. The course also works to improve student’s basic number sense and ability to work confidently with rational numbers and fractional expressions.

**Honors Eligibility Requirements: ** Students will be admitted based on their performance on a placement examination given in the spring.

#### Geometry/ Geometry Honors

This is the first mathematics course in which the student sees a mathematical system, developed from simple definitions and fundamental axioms grow into a full and useful body of knowledge. This logical development is a prime reason for the study of geometry. Topics studied include proofs of theorems about circles, triangles and quadrilaterals, as well as areas and volumes. An introduction to practical trigonometry is also included, including the laws of sines and cosines.

**Standard Eligibility Requirements:** Students taking this course have successfully completed Algebra 1

**Honors Eligibility Requirements:** Students will be admitted based on their performance on a placement examination given in the spring, current course grades, and departmental approval.

#### Algebra II / Algebra II Honors

Extending first year algebra, students explore the transformation of functions, complex numbers, the theory of polynomial equations and functions, exponential equations and functions, logarithmic equations and functions, linear and quadratic systems of three variables, matrices, conic sections, and probability.

**Standard Eligibility Requirements:** Students taking this course have successfully completed Algebra 1

**Honors Eligibility Requirements:** Students will be admitted based on their performance on a placement examination given in the spring, current course grades, and departmental approval.

#### Pre-Calculus/ Pre-Calculus Honors

Pre-Calculus introduces topics necessary for success in calculus as well as formally treating topics in discrete areas of mathematics not typically encountered in previous courses, such as sequences and series, combinatorics, the binomial theorem, and probability. Significant course time is devoted circular angles and analytic approaches to trigonometry necessary for calculus and real applications in physics and engineering. If time permits, students will define the polar coordinate system and polar representation of complex numbers, vectors, and the concept of limits.

Standard Eligibility Requirements: Students taking this course have successfully completed Algebra 2 with at least an 80.

Honors Eligibility Requirements: Students will be admitted based on their performance on a placement examination given in the spring, current course grades, and departmental approval.

#### Calculus

This course is designed to introduce the students to the fundamental principles of differential and integral calculus. Topics covered include detailed study of limits, the derivatives of polynomial, algebraic, exponential, logarithmic, and trigonometric functions with applications to curve-tracing, maxima-minima related-rate problems, and the anti-derivative. Students will also develop basic integration and its applications, including volumes of revolution.

**Eligibility Requirements:** Students score at least a B in Pre-Calculus.

### AP Mathematics Courses

#### AP Calculus AB / AP Calculus BC

AP Calculus includes two courses, AP Calculus AB and AP Calculus BC, which were developed in collaboration with college faculty. The curriculum for AP Calculus AB is equivalent to that of a first-semester college calculus course, while AP Calculus BC is equivalent to the first two semester college calculus courses.

Both courses cover topics in differential and integral calculus, including concepts and skills of limits, derivatives, definite integrals, and the Fundamental Theorem of Calculus. BC additionally includes parametric, polar, vector functions, and series. Each course teaches students to approach calculus concepts and problems when they are represented graphically, numerically, analytically, and verbally, and to make connections amongst these representations. Students learn how to use technology to help solve problems, experiment, interpret results, and support conclusions.

**Eligibility Requirements:** A student’s eligibility is based on their performance on a placement examination given in the spring, current course grades, and departmental approval.

#### AP Statistics

The AP Statistics course is equivalent to a one-semester, introductory, non-calculus-based college course in statistics. The course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. The course emphasizes understanding and analyzing statistical studies and the development of an intuitive understanding of statistics and probability. There are four themes in the AP Statistics course: exploring data, sampling and experimentation, anticipating patterns, and statistical inference. Students use technology, investigations, problem solving, and writing as they build conceptual understanding.

**Eligibility Requirements:** Students taking this course have successfully completed Algebra 2. Eligibility is based on a student’s performance on a written assignment given in the spring, current course grades, and departmental approval.

### AP Computer Science Courses

#### AP Computer Science A

AP Computer Science A is equivalent to a first-semester, college-level course in computer science. The course introduces students to computer science with fundamental topics that include problem solving, design strategies and methodologies, organization of data (data structures), approaches to processing data (algorithms), analysis of potential solutions, and the ethical and social implications of computing. The course emphasizes both object-oriented and imperative problem solving and design using Java language. These techniques represent proven approaches for developing solutions that can scale up from small, simple problems to large, complex problems. The AP Computer Science A course curriculum is compatible with many CS1 courses in colleges and universities.

**Eligibility Requirements:** Students taking this course have successfully completed Algebra 2. Eligibility is based on a student’s performance on a written assignment given in the spring, current course grades, and departmental approval.

#### AP Computer Science Principles

AP Computer Science Principles offers a multidisciplinary approach to teaching the underlying principles of computation. The course will introduce students to the creative aspects of programming, abstractions, algorithms, large data sets, the Internet, cyber security concerns, and computing impacts. AP Computer Science Principles also gives students the opportunity to use current technologies to create computational artifacts for both self-expression and problem solving. Together, these aspects of the course make up a rigorous and rich curriculum that aims to broaden participation in computer science.

**Eligibility Requirements:** Students taking this course have successfully completed Algebra 1. Eligibility is based on a student’s performance on a written assignment given in the spring, current course grades, and departmental approval.

*** A vs. Principles: What is the difference?

The AP Computer Science A course and exam focus on computing skills related to programming in JAVA. The new AP Computer Science Principles course complements AP Computer Science A and focuses on the fundamentals of computing, including problem solving, large-scale data, the Internet, and cyber-security.

As of 2019, a passing score on the AP Computer Science A exam typically gives students credit for a first semester computer programming course, while a passing score on the AP Computer Science Principles exam typically gives students credit for a one semester elective.

### Other Math Elective Courses

#### Computer Science

This half-year (half-credit science elective) course will introduce you to the field of computer science and the fundamentals of computer programming. Computer Science is specifically designed for students with no prior programming experience. Students will be introduced to the processing and JavaScript languages, along with logic, computer hardware and software, multimedia, computer security, web economics, and game design.

**Eligibility Requirements:** Students taking this course have successfully completed Algebra 2.

#### Statistics

This course is an introductory, non-calculus based statistics course that emphasizes understanding and analyzing statistical studies. Participants develop skills in sampling procedures, analyzing data, designing and analyzing surveys and experiments, as well as hypothesis testing. The course emphasizes the development of an intuitive understanding of statistics and probability. Students gain a sense of the importance/relevance of statistics in the real world and are able to evaluate the use and misuse of statistics.

**Eligibility Requirements**: Students taking this course have successfully completed Algebra 2.

### IB Mathematics Courses

***Eligibility Requirements: Generally, IB Mathematics courses are reserved for students admitted to the IB program; however, non-IB students may enroll in a course with special permission of the instructor and IB program director.

#### IB Mathematical Studies Standard Level

This is a one-year course that caters to students with varied backgrounds and abilities. It is designed to build confidence and encourage an appreciation of mathematics in students who do not anticipate a need for mathematics in their future studies. Students embarking on this course need to be equipped with fundamental skills and a rudimentary knowledge of basic processes.

#### IB Mathematics Standard Level

This is a one-year course that is focused on the study of elementary functions, basics of calculus, vector geometry, matrices, probability and statistics, and other advanced topics along with an appreciation of the international dimensions of mathematics and the multiplicity of its cultural and historical perspectives. Mathematics SL is a demanding course due to the broad range of mathematical topics. Students will receive more in-depth preparation for internal assessments and the IB Mathematics SL exam (given in May). IB Math SL includes material similar to that in Pre-Calculus through Calculus.

#### IB Mathematics Higher Level

This is a two-year course that is focused on the study of elementary functions, basics of calculus, vector geometry, matrices, probability and statistics, and other advanced topics along with an appreciation of the international dimensions of mathematics and the multiplicity of its cultural and historical perspectives. Mathematics HL is a demanding course due to the broad range of mathematical topics. Students will receive more in-depth preparation for internal assessments and the IB Mathematics HL exam (given in May of the senior year). IB Math HL includes material similar to that in Pre-Calculus Honors through AP Calculus BC and AP Statistics.

#### General Comments on Placement in Honors and AP Courses

The Honors and Advanced Placement courses have a much higher degree of rigor. These courses are designed for students who can learn at an accelerated pace and wish to go beyond the normal scope and sequence of our standard advanced courses. Students can expect more challenging and in-depth homework and assignments. Students will have to devote a larger percentage of their time to studying the material. Students taking Advanced Placement courses are required to take the examination in May.

A student’s eligibility is based on their performance on a placement examination given in the spring, current course grades, and departmental approval. Contact John Zak (jzak@philasd.org) with questions or concerns.