Mathematics Department

Math and Computer Science Courses
MATHEMATICS
Beyond the attainment of three credits to satisfy the mathematics requirement for graduation, additional courses taken in this department satisfy the free elective requirement for graduation.
For students eligible for special education services, the selection of appropriate academic and elective classes will be determined by the IEP team.
All students need to take three years of high school mathematics in grades 912 in order to graduate. A maximum of one credit may be taken outside of the Mathematics Department (from the following: Accelerated Computer Science 1, Accelerated Computer Science 2, Advanced Placement Computer Science A, and Advanced Placement Computer Science Principles). Placement in the appropriate mathematics course is made on the basis of student success in prior mathematics courses, prognostic tests, and teacher recommendation. Although three credits of math are required for graduation, most colleges specify successful completion of a full year of Algebra 1, Algebra 2 and Geometry. Many colleges now require four years of high school math. Please note that many mathematics courses require that the student has a graphing calculator. We recommend the TI83, TI83 Plus, or TI84 Plus. (The TI85 does not have the needed statistical capabilities). Although other graphing calculators may suffice, all instruction will be done using the TI83, TI83 Plus, or TI84 Plus.
COUNCIL ROCK HIGH SCHOOL RECOMMENDED MATH PATTERNS
GRADE 9
GRADE 10
GRADE 11
GRADE 12
Concepts in Mathematics
Algebra 1
Algebra 2
Geometry
Algebra 1
Algebra 2
Geometry
Analysis
Trigonometry/Statistics
Accelerated Algebra 1
Accelerated Algebra 2
Accelerated Geometry
Accelerated Analysis
Trigonometry/Statistics
Accelerated Algebra 2
Accelerated Geometry
Accelerated Analysis
AP Calculus AB
AP Statistics
Accelerated Calculus
Accelerated Statistics
Honors Algebra 2
Honors Geometry
Honors Analysis
AP Calculus BC
AP Statistics
Placement of students will occur through their level of achievement, the results of testing, and teacher recommendation. Letters of record, including parent’s signature, are required if the student selects a course other than that recommended by the school’s professional staff.
Please also note: (1) students in the honors course sequence are expected to maintain a solid “B” average throughout these courses; and (2) all other students are expected to maintain a strong “C” average to remain in any given sequence.
CONCEPTS IN MATHEMATICS (YR)
The content and instructional practices of this course are designed to transition students to the successful completion of Algebra. Prealgebra topics will include: Number systems and operations, systems of measurement (linear, square, and cubic), ratio, proportion, percent, probability, statistics and data analysis. Algebraic topics will include the study of expressions, properties, equations, inequalities, functions and their graphs, linear system, properties of exponents, operations with polynomials and angle relationships. A graphing calculator is required for this course. The TI83, TI83 Plus and the TI84 Plus are the recommended calculators.
ALGEBRA 1 (+) (YR)
This Keystone preparation course provides students with a mathematically sound introduction to Algebra 1 and is designed for the student whose past achievement indicates a need for a more gradual pace. Course content will include the following topics: operations with real numbers and expressions, linear equations and inequalities, functions, coordinate geometry, and data analysis. A graphing calculator is required and is an integral part of the course. The TI83, TI83 Plus or the TI84 are the recommended calculators. In this course students will prepare for the Keystone Algebra 1 exam which they will take in May.
ACCELERATED ALGEBRA 1 (+) (YR)
This course is designed to give students a mathematically sound introduction to algebra. The student is given the opportunity to develop fundamental algebraic skills and concepts based on the structure of the system of real numbers such as equations, inequalities, problem solving, polynomials, factoring, graphs and functions, simultaneous equations, irrational numbers, square roots, relations, functions, and variations. Because graphing activities are integrated throughout classroom presentations and textbook activities, a graphing calculator is required for this course. The TI83, TI83 Plus, or TI84 Plus are the recommended calculators. In this course students will prepare for the Keystone Algebra 1 Exam which they will take in the spring to that school year.
ALGEBRA 2 (+) (YR)
This course extends the concepts learned in Algebra 1 and provides a sound introduction to Algebra 2. The topics covered in this course include the conceptual development and understanding of: operations and complex numbers, nonlinear expressions and equations, patterns, relations, functions, applications of functions, and data analysis. Mathematical modeling and applications will be applied with problem solving. A graphing calculator is required and is an integral part of the course. The TI83, TI83 Plus or the TI84 are the recommended calculators.
ACCELERATED ALGEBRA 2 (+) (YR)
This course reviews and extends the concepts of Accelerated Algebra 1 by going into more depth in studying equations, inequalities, problem solving, factoring, irrational numbers, linear equations, and simultaneous equations. New topics include the study of polynomial, quadratic, radical, rational, exponential, greatest integer, and logarithmic functions. Also covered in the course are matrices, linear regression lines, and scatter plotting graphs. A graphing calculator is required for this course. The TI83, TI83 Plus, or TI84 Plus are the recommended calculators. Recommended prerequisite is a grade of at least “C” in Accelerated Algebra 1.
HONORS ALGEBRA 2 (+) (YR)
This course covers the same material as Accelerated Algebra 2 but in greater depth. The course also covers additional topics; therefore, the pace is more rapid than that of Accelerated Algebra 2. Honors Algebra 2 reviews and extends the concepts of Honors Algebra 1 by going into more depth in studying equations, inequalities, problem solving, factoring, irrational numbers, linear equations and simultaneous equations.
New topics include the study of complex numbers, functions and their inverses, matrices, linear programming, polynomial, quadratic, exponential and logarithmic functions. Students will be required to research and present a minimum of three topical projects that relate to specific concepts that are presented during the course of the year.
Students should be highly motivated, able to think and process math concepts quickly and in alternate fashion. Students should be recommended by their teacher and must have earned a solid “B” in Honors Algebra 1 in the middle school. Because graphing activities are integrated throughout classroom presentations and textbook activities, a graphing calculator is required for this course. The TI83, TI83 Plus, or TI84 Plus are the recommended calculators.
GEOMETRY (+) (YR)
This fullyear course is a study of the major ideas of geometry and the basic properties of geometric figures, without an emphasis on formal proof. Topics include angles, angle measurement, triangles, congruent triangles, quadrilaterals and other polygons, circles, parallel lines, solid figures, perimeter, area, volume, and geometric probability. An ability to perform basic algebra skills is necessary. Students who were successful in Algebra 1 will be encouraged to continue their study of mathematics with Geometry.
This course is not appropriate for students preparing for a scientifically oriented college curriculum and does not satisfy prerequisites for Accelerated Analysis. A graphing calculator is required for this course. The recommended calculators are the TI83, TI83 Plus, or TI84 Plus.
ACCELERATED GEOMETRY (+) (YR)
This course is a rigorous study of the concepts of geometry requiring analytical thinking in addition to factual knowledge of the material. Students develop their deductive reasoning skills throughout the course through informal justifications and arguments as well as formal proofs. All of the topics of Geometry are covered but in greater depth. Other topics such as symbolic logic, loci, and coordinate transformation are also included. Many algebraic concepts and skills from Accelerated Algebra 2 are integrated throughout the course. This course is recommended for those who have successfully completed Accelerated Algebra 2 with a grade of “C” or better and who plan to study Accelerated Analysis. A graphing calculator is required in the course. The TI83, TI83 Plus, or TI84 Plus are the recommended calculators.
HONORS GEOMETRY (+) (YR)
In addition to the topics covered in Accelerated Geometry, this course includes the following topics: NonEuclidean geometry, rules of logic, extensive analytical problem solving, the axiomatic development of Euclidean geometry, and historical contributions in the development of geometry. Although many topics are similar between the two courses, Honors Geometry students are expected to study these same topics in greater depth and at a more rapid pace, with a significant emphasis on analytical reasoning skills, a formal mathematical vocabulary, techniques in perspective drawing, and formal geometric construction.
Students are also required to independently research and deliver a presentation on an assigned mathematical topic. Students will read and write a critical analysis of the book Flatland. Students should have earned at least a strong “B” in Honors Algebra 2 with teacher recommendation. The TI83, TI83 Plus, and TI84 Plus are the recommended graphing calculators for this course.
TRIGONOMETRY (+) (S)
This course has been designed for collegebound students who have completed Accelerated Algebra 2 and Accelerated Geometry with a grade of at least “C,” or Algebra 2, Part B and Geometry with a grade of at least “B.” Course content includes the study of trigonometric functions both as circular functions and as ratios in similar right triangles. Throughout the course reallife problem situations will be used to connect trigonometry to many other fields and occupations. Algebra skills will be strengthened as needed. Technology will be an integral part of instruction.
A graphing calculator is required for this course. The TI83, TI83 Plus or TI84 Plus are the recommended calculators. Students who require a more rigorous precalculus preparation should take Accelerated Analysis, which includes all of the trigonometry presented in this course.
STATISTICS (S) (+)
This introductory statistics course has been designed for collegebound students who have completed Accelerated Algebra 2 and Accelerated Geometry with a grade of at least “C” or Algebra 2, Part B and Geometry with a grade of at least “B.” Students will learn methods for displaying distributions with graphs and numbers as well as the normal distribution. They will examine relationships using scatter plots and least squares regression and correlation. They will work with designing samples and experiments in combination with some basic principles of probability.
Throughout the course reallife problem situations will be used to connect statistics to many other fields and occupations. Algebra skills will be strengthened as needed. Technology will be an integral part of instruction. A graphing calculator is required for this course. The TI83, TI83 Plus, or TI84 Plus are the recommended calculators.
ACCELERATED STATISTICS (+) (YR)
This statistics course has been designed for collegebound students who have completed Accelerated Algebra 2 and Accelerated Geometry with a grade of at least “C” or Algebra 2, Part B and Geometry with a grade of at least “B”. There will be an emphasis on organizing data, averages and variation, elementary probability, the binomial and normal distributions and inferential statistics. Throughout the course reallife problem situations will be used to connect statistics to many other fields and occupations. Algebra skills will be strengthened as needed. Technology will be an integral part of instruction. A graphing calculator is required for this course. The TI83, TI83 Plus and TI84 Plus are the recommended calculators.
ADVANCED PLACEMENT STATISTICS (+) (YR)
The purpose of this course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes. They are exploring data: observing patterns and departures from patterns; planning a study: deciding what and how to measure; anticipating patterns: producing models using probability theory and simulation, and statistical inference: confirming models.
Students who successfully complete the course and take the Advanced Placement Statistics examination may receive credit, advanced placement or both for a one semester introductory college statistics course. The TI83, TI83 Plus, or TI84 Plus graphing calculator is required for this course. The prerequisite for this course is Accelerated Algebra 2.
ANALYSIS (+) (YR)
This course has been designed for collegebound students who have completed Algebra 2 and Geometry. Topics covered include an extension of algebra skills including using functions as models for a number of applied settings; sequences and series; probability and statistics; matrices; trigonometry; linear, quadratic, exponential and logarithmic functions. A graphing calculator is required for this course. The TI83, TI83 Plus, or TI84 Plus are the recommended calculators.
ACCELERATED ANALYSIS (+) (YR)
This course is designed to provide a strong foundation in precalculus concepts, techniques, and applications to prepare students for more advanced work in mathematics. The primary topics studied are graphical analysis; functions including polynomial, rational, exponential, and logarithmic; complex numbers; polar coordinates and complex numbers in polar form; discrete mathematics; data analysis; and trigonometry. Problems will relate abstract concepts to real world situations. Students electing this course should have completed Accelerated Algebra 2 and Accelerated Geometry with grades of “B” or better in both courses. A graphing calculator is required for this course. The TI83, TI83 Plus, or TI84 Plus are the recommended calculators.
Students electing this course will be required to complete a review packet over the summer to be submitted at the beginning of the school year. A grade for this assignment will be part of the student’s first marking period grade.
HONORS ANALYSIS (+) (YR)
This course covers the same material as Accelerated Analysis, although in greater depth and at a faster pace. It also includes limits, parametric equations, and some topics from statistics. Students must have the recommendation of their previous teacher. Juniors intending to take AP Calculus BC Level as seniors should elect this course and must maintain a “B” average throughout this course to do so. A graphing calculator is required for this course. The TI83, TI83 Plus, or TI84 Plus are the recommended calculators.
Students electing this course will be required to complete a review packet over the summer to be submitted at the beginning of the school year. A grade for this assignment will be part of the student’s first marking period grade.
ACCELERATED CALCULUS (+) (YR)
This course is intended to provide an introduction to college mathematics. The topics covered will include functions, graphs, limits, rate of change, formal differentiation, applications of the derivative, integration, applications of integration, and transcendental functions. A graphing calculator is required for this course. The TI83, TI83 Plus, or TI84 Plus are the recommended calculators. Students are expected to have a strong background in Accelerated Algebra 2, Accelerated Geometry, and Accelerated Analysis. This course does not prepare students to take the Advanced Placement Exam in May.
ADVANCED PLACEMENT CALCULUS AB (+) (YR)
This course is provided as an introduction to college mathematics. The topics covered are those typically found in the first semester and some of the second semester of a college level course, including functions, graphs, limits, rate of change, formal differentiation, applications of the derivative, integration, applications of integration, and transcendental functions. A graphing calculator is required for this course. The TI83, TI83 Plus, or TI84 Plus are the recommended calculators.
Students are expected to have a strong background (minimum grade of “B”) in Accelerated Algebra 2, Accelerated Geometry, and Accelerated Analysis. This course consists of a full academic year of work in calculus and topics covered in courses at the college level. It is expected that students taking this course will seek college credit or placement by taking the Advanced Placement examination in May.
Students electing this course will be required to complete a review packet over the summer to be submitted at the beginning of the school year. A grade for this assignment will be part of the student’s first marking period grade.
ADVANCED PLACEMENT CALCULUS BC (+) (YR)
This course is provided as an introduction to college mathematics. The topics covered are those typically found in the first two and onehalf semesters of college level courses, including functions, graphs, limits, rate of change, formal differentiation, applications of the derivative, integration, applications of integration, transcendental functions, differential equations, polar equations, vectors and parametric equations, and sequences and series.
In order to be successful in this course, students must have a strong background in Honors Algebra 2, Honors Geometry and Honors Analysis. This course will cover the content in the BC level of the Advanced Placement examination which students are strongly encouraged to take in May. Graphing calculators will be used extensively in the course and are required on the Advanced Placement examination. The TI83, TI83 Plus, or TI84 Plus are the recommended calculators.
Students electing this course will be required to complete a review packet over summer to be submitted at the beginning of the school year. A grade for this assignment will be part of the student’s first marking period grade.
COMPUTER COURSES
Computer programming courses may satisfy up to one of the three mathematics credits required for graduation.
ACCELERATED COMPUTER SCIENCE 1 (S) (AD) GRADES 912
This course is open to all high school students who are at least taking Accelerated Algebra I and are interested in the study of computer programming. This entrylevel course is taught using the C# (pronounced “see sharp”) language, within the Microsoft Visual Studio. NET environment and will focus on the development of fundamental programming skills. The topics in this course of study include a review of the .NET Integrated Development Environment, basic structure and syntax of the C# language, an introduction to objectoriented design using classes and objects, decision making statements, iteration structures (loops), arrays, and string manipulation. The history of computers and programming will also briefly be discussed. Upon completion of Computer Science 1 with at least a “C”, students are encouraged to move on to Computer Science 2.
ACCELERATED COMPUTER SCIENCE 2 (S) (AD) GRADES 912
This course is open to all high school students who are at least taking Accelerated Algebra 2 and have successfully completed Computer Science 2. Students will learn the fundamental skills that are required to design and develop objectoriented applications for the Web and Microsoft Windows. This course is taught using the C# language and will serve as an extension to the concepts introduced in Computer Science 1. Additional topics in the course of study include file handling and database manipulation, methods, enumerations and structures, and an introduction to windows forms and painting. The course will be highly project based and geared towards realworld applications using a variety of handson lab exercises, case studies, and team learning tasks. It is highly recommended that students take Computer Science 2 before taking Advanced Placement Computer Science.
ADVANCED PLACEMENT COMPUTER SCIENCE A (YR) GRADES 1112
This advanced course is provided as an introduction to collegelevel computer programming, using the Java language. It is open to students who have at least successfully completed Accelerated Algebra 2 and have a solid foundation in objectoriented computer programming concepts (i.e. C#, C++, Visual Basic, and Java). A fundamental skill to the study of computer science is to develop computer programs to solve problems. A large part of this course is built around the development of computer programs or parts of programs to solve a given problem using objectoriented designs. The topics in the course of study include the use of standard Java classes, objects, data types, methods, decision making statements, string handling, the application of data storage and data processing, and other algorithms. Students will also learn to create and manipulate applications, applets, and GUI components. The course will be highly project based and geared towards realworld applications using a variety of handson lab exercises, case studies, and team learning tasks. It is expected that students will seek college credit by taking the Advanced Placement Computer Science Examination (Level A) in May.
ADVANCED PLACEMENT COMPUTER SCIENCE PRINCIPLES (YR) GRADES 1012
AP Computer Science Principles offers a multidisciplinary approach to teaching the underlying principles of computation. It is open to students who have completed Algebra 2 with a strong foundation in function notation and problem solving. The course will introduce students to the creative aspects of programming, abstractions, algorithms, large data sets, the Internet, cybersecurity concerns, and computing impacts. AP Computer Science Principles also gives students the opportunity to use current technologies to create innovative computational artifacts for both selfexpression and problem solving. Students will develop these artifacts using the same creative processes artists, writers, computer scientists, and engineers use to bring ideas to life. It is expected that students will seek college credit by taking the Advanced Placement Computer Science Principles Examination in May.