•  
    Welcome to the Mountain Lakes High School Mathematics Department!
      
                                                   Calculus!

    Teaching Staff:

    Mr. Downes, Department Supervisor

    Ms. Alfano

    Ms. Bzdelik

    Mrs. Blood

    Mrs. Krause

    Mrs. Pasquale

    Mr. Horn

    Mr. McGrath

    Mrs. Harrington

     

    Department Mission

         The Mathematics Department at Mountain Lakes High School strives to create an environment where all students can maximize their potential, to address any fears or misconceptions they may have, and to provide them with an experience that will enable them to think critically and become better problem-solvers. Teachers seek to use examples in class that will provide a concrete and conceptual understanding of the material and to engage students by using current technology. All students benefit by having the opportunity to use what they have learned in ways that will impact their world beyond the classroom walls.

         The department offers a variety of courses that essentially fall into three levels:

    • College Prep Core
    • College Prep Enriched
    • College Prep Honors

         Each level is designed to maximize a student’s potential, satisfy personal interest, and provide a foundation to meet future goals. All courses provide an arena where students are be required to think critically, reason logically, and develop a sense about the relation and application of the mathematics to other courses, disciplines, and the real world.  The honors courses constitute the most rigorous level and require that the student have the ability to think critically, reason logically, and deal with concepts, which require more abstract reasoning than is necessary in the courses of the other two levels. The mathematics staff recommends students to that level which they believe will best serve the needs and the ability level of the student.

     
     
     
    MATHEMATICS CURRICULUM
     
    College Preparatory Algebra Enriched                                                                     
    Grade Level: 9
    5 Credits - Full Year
    This first year course in elementary algebra develops the basic concepts of algebraic skills through three key ideas: the equation and inequality, data analysis, graphs, and translation of verbal situations into algebraic symbols. Extensive use of the scientific calculator enhances the development. Geometric concepts, probability, and graph interpretation allow for the application of the algebraic skills. Formulas, function notation, graphing, the laws of exponents and radicals, operations with polynomials, factoring, and solving quadratic equations by factoring, writing equations of lines, proportions and the quadratic formula are some of the topics presented.


    College Preparatory Geometry Honors                                            
    Prerequisite: CP Algebra Enriched
    Grade Level: 9 or 10
    5 Credits - Full Year
    This is a course in geometry covering the basic concepts of plane, solid, coordinate, and some analytic geometry stressing deductive proof and reasoning. Throughout the year the properties learned in algebra are re-introduced into this course. The aims and objectives of the course are to develop and show the value of the logic of deductive reasoning and to improve and increase the understanding and application of the terminology, the symbolism, and the structure of mathematics.  The problems explored involve intense analytical thought and require strong algebraic skills.  Non-Euclidean geometries such as fractal geometry and the Lenart sphere are investigated.  Some student projects will involve the use of computer technology.

     
    College Preparatory Geometry Enriched                                        
    Prerequisite: CP Algebra Enriched
    Grade Level: 9 or 10
    5 Credits - Full Year

    This is a course in geometry covering the basic concepts of plane, solid, coordinate, and some analytic geometry stressing deductive proof and reasoning. Throughout the year the properties learned in algebra are re-introduced into this course. The aims and objectives of the course are to develop and show the value of the logic of deductive reasoning and to improve and increase the understanding and application of the terminology, the symbolism, and the structure of mathematics.



    College Preparatory Algebra II Honors                                           
    Prerequisite: CP Geometry Honors
    Grade Level 10 or 11                                      
    5 Credits - Full Year
    This course presents a rigorous and enhanced study of the algebraic concepts introduced in the Algebra I course. These concepts are extensively augmented by the usage of the graphing calculators. The functions - namely the linear, quadratic, absolute value, exponential, and logarithmic - are examined both algebraically and graphically. Because of the emphasis on the graphs of the above-mentioned functions, the graphing calculator is an integral part of this course. Additional topics include the study of the higher-order inequalities, the polynomial and rational functions, the applications of linear and quadratic equations, systems of equations and inequalities, matrix algebra, advanced techniques for graphing functions, and probability.

     

    College Preparatory Algebra II Enriched                                     
    Prerequisite: CP Geometry Enriched
    Grade Level: 10-12
    5 Credits - Full Year
    The second course in algebra enhances the topics begun in the Algebra I course.  The operations with polynomials include advanced factoring skills, working with negative and rational exponents, complex numbers, absolute value, the quadratic formula, graphing lines and parabolas and deriving their equations.  Systems of linear equations, inequalities and applications of linear programming are included.  In depth discussions of the linear, quadratic, polynomial, exponential and logarithmic functions are visited.  Probability, data analysis and statistics are also covered.  Operations and applications using matrices may be investigated with the graphing calculator used extensively as a tool.  Synthetic division, arithmetic and geometric sequences round out the course.

     

    College Preparatory Algebra II Core       
    Prerequisite: CP Geometry Core or CP Geometry Enriched
    Grade Level: 11
    5 Credits - Full Year

    This is the third course of a sequence of a mathematics program. This course provides a general review of the fundamental algebra skills and concepts, and introduces functions and relations. Linear equations and inequalities, quadratic systems of equations, and polynomial and rational expressions are studied in detail. Topics in trigonometry, probability, and statistics are explored. Applications with an algebraic perspective are emphasized. This course would provide qualified students with a third year of college preparatory mathematics.

                                                                                                               
    Discrete Mathematics with Financial Literacy
    Prerequisites: CP Algebra II Enriched, CP Algebra II Core, CP 
    Geometry Enriched
    Grade Level: 12
    5 Credits - Full Year
    The course begins with a review of topics from Trigonometry, followed by a survey of Statistics and Discrete Mathematics, and culminates with a thorough study of Financial Literacy and Economics. All topics lend themselves to a student’s development of problem solving, communication, reasoning, and modeling skills. By modeling real world events, students will view mathematics as a useful tool in human decision-making. Successful completion of the course fulfills the graduation requirements of financial literacy.

     
    Pre-Calculus (Honors)                                                                      
    Prerequisite: CP Algebra II Honors
    Grade Level: 11 or 12
    5 Credits - Full Year
    This Pre-Calculus Honors course is somewhat similar in content to the Pre-Calculus course, although more emphasis is given to the development of mathematical concepts and is considerably more abstract and rigorous in approach.  In addition, more work is undertaken on the study of vector algebra and the vector equations, parametric equations, and rectangular equations of lines and planes.  Topics in advanced algebra are studied including the binomial theorem, mathematical induction, parametric equations, and polar coordinates. Some emphasis is placed on the study of limits in order to provide sufficient background for the next course in calculus.

     
    Pre-Calculus                                              
    Prerequisite: CP Algebra II Enriched, CP Algebra II Honors
    Grade Level: 10-12
    5 Credits - Full Year
    This course is essentially the study of elementary functions and their graphs.  The graphing calculator is used extensively. Much time is given to the study of analytic geometry, advanced algebra, and trigonometry. A student who successfully completes this course is prepared to study calculus.

     
    Pre-College Math                                                                             
    Prerequisite: CP Algebra II Enriched
    Grade Level: 11-12
    5 Credits - Full Year
    This course is essentially the study of elementary functions and their graphs.  The graphing calculator is used extensively. Much time is given to the study of analytic geometry, advanced algebra, and trigonometry. This course is recommended for students who have demonstrated difficulty in College Preparatory Algebra II Enriched.  The pace of this course will be determined by the abilities of the class. A student who successfully completes this course is recommended to take Discrete Mathematics. Students who have already taken and passed Pre-calculus cannot enroll in this course as the concepts have already been covered.


    Calculus                                                                    
    Prerequisite: Pre-calculus or Honors Pre-calculus
    Grade Level: 12
    5 Credits - Full Year
    The Calculus course presented at the high school level is intended to serve those students who have successfully competed Pre-Calculus or Pre-Calculus Honors. The purpose of this course is to serve as the first study of differential and integral calculus. Much attention is given to the central ideas of the calculus such as limit the slope of the tangent line, the rate of change, and the area under a curve. At the same time, students will deepen their knowledge and understanding of a function and its utility in representing and answering questions about real-world phenomena. The course differs with AP Calculus significantly in both the depths of similar topics, as well as in the range of the topics considered.
    In summary, Calculus will enable and provide students with the opportunity to explore the central topics and methods of calculus while developing an awareness of, and appreciation for, the historical origins and the cultural contributions of the calculus.

     
    Advanced Placement Statistics                           
    Prerequisite: Pre-Calculus or CP Algebra II Honors
    Co-requisite: Honors Pre-Calculus
    Grade Level:  11 or 12
    6 Credits – Full Year
    The AP Statistics program is built around four essential topics:  exploring data, planning a study, probability as it relates to distributions of data, and inferential reasoning.  Exploratory analysis of data will make use of graphical and numerical techniques in order to study patterns and departures from patterns.  The collection of data will be done according to a well-developed plan in an effort to obtain valid inferences.  Probability is the tool used for anticipating what the distribution of data should look like under a given model.  Finally, statistical inference will guide the selection of appropriate models.  Students who successfully complete this course are expected to take the AP Statistics exam.


    Advanced Placement Calculus - AB Level                                     
    Prerequisite:  Honors Pre-Calculus
    Grade Level: 12
    6 Credits - Full Year
    Advanced Placement Calculus is a college-level course offered to those who successfully complete Honors Pre-calculus and are recommended for further study. The course concerns itself with the material of the calculus of the single variable, as outlined for an AB level curriculum in the College Board’s Course Description. Students who successfully complete this course are expected to take the AP Calculus AB exam. Based on the results of this exam, colleges offer advanced placement and/or credit.

     
    Advanced Placement Calculus - BC Level                                     
    Prerequisite:  Honors Pre-Calculus
    Grade Level:  12
    6 Credits - Full Year
    Advanced Placement Calculus BC is a college-level course offered to those who successfully complete Honors Pre-calculus and are recommended for further study. The topic outline includes all of the AB topics as well as additional topics required for the AP Exam. The course concerns itself with a rigorous treatment of the calculus of a single variable, as outlined for a BC level curriculum in the College Board’s Course Description. Examples of additional topics include Taylor series, parametric, polar, and vector functions, and the various applications of integrals. Students who successfully complete this course are expected to take the AP Calculus BC exam. Based on the results of this exam, colleges offer advanced placement and/or credit.  Permission of instructor required for admittance into this course.  Students may not waive into this course.

     
    Honors Multivariable Calculus                                                                                      
    Prerequisite:  Calculus
    Grade Level: 12
    5 Credits - Full Year
    Multivariable calculus is a course designed to study the topics from regular calculus extended into three or more dimensions. The class will prove very beneficial for those students interested in advancing their studies in physics, engineering, or applied mathematics at the university level.
    The course begins with Euclidean geometry in three dimensions.  Topics to be studied include points, lines, and planes, as well as dot and cross product. Functions of two variables will be plotted and analyzed.  Contour plots and level curves in various dimensions will be analyzed as well.  Part of the course will cover differentiation in multiple dimensions, including the analysis of partial derivatives and tangent planes.  Topics such as the chain rule will be extended into n-dimensions. The remainder of the course will also be devoted to the analysis of multiple integrals and how to physically interpret them.  The relation to volume will be studied.  Physical interpretations of these concepts – like center of mass – will be thoroughly developed. A strong relation to physics concepts will be fostered.


    Intro to Computer Programming                                                
    Pre-requisite:  CP Geometry Enriched
    Co-requisite:  CP Geometry Honors
    2 1/2 Credits – 1/2 year
    Intro to CP is a foundational computer science course. No previous experience with computer science is required. Students with more experience will have opportunities to extend projects and to expand their knowledge.
    Intro to CP emphasizes programming more than MLHS's AP CS Principles course. The focus is on getting students comfortable with foundational concepts while introducing students to the power of computer science. Students will spend a significant portion of class time programming collaboratively and individually. The course is presented using a combination of Java and Processing (a language based on Java).

    Intro to CP topics include:

         Representations of spaces and colors (ex: RGB color)
         Programming tools (ex: the Processing IDE)
         Variables, data types and mathematical operations
         Boolean expressions and conditional statements

    Students who take this course can progress to Computer Programming 2 the same year.
    This course may fulfill the Practical Arts requirement. Students should speak with their Guidance Counselor.
     

    Computer Programming 2                                                                       
    Prerequisite: Intro Comp. Prog.
    Grade Level:  9-12
    2 1/2 Credits – 1/2 year
    Computer Programming II introduces students to Object-oriented programming concepts, teaches them the fundamentals of the Java language and syntax, introduces them to the major class libraries in Java, and prepares them to begin development of applications in Java. Students familiar with object-oriented concepts can learn how to develop Java applications.  This course may fulfill the Practical Arts requirement.  Students should speak with their Guidance Counselor.

     
    Advanced Placement Computer Science A           
    Prerequisites:  B- or above in Intro to Computer
    Programming and Computer Programming 2
    Grade Level:  10-12
    Full Year – 5 Credits
    AP Computer Science is an advanced course in computer programming and problem solving. Students will study standard computer algorithms, data structures, computer systems, and file types using the Java programming language. This fast-paced course follows the curriculum set up by the College Board for the AP Computer Science course. The topic outline for this course is as follows:
     
    1.         Program Design
    2.         Program Implementation
    3.         Program Analysis
    4.         Standard Data Structures
    5.         Standard Algorithms
    6.         Computer Systems

    Although students will be using the Java programming language, programming skills are the focus of this course. All students enrolled in this course are expected to take one of the two levels of the AP Computer Science tests in the spring. Intro to Computers and Computer Programming 2 are prerequisites for Advanced Placement Computer Science. Students who successfully complete this course are expected to take the AP Computer Science exam. 

     
    Honors Advanced Data Structures                                                                      
    Prerequisites: APCS A  
    Grade Level:  11,12
    Full Year – 5 Credits
    Honors Advanced Data Structures is the continuation of AP Computer Science A. This course covers advanced data structures such as two dimensional arrays, Linked Lists, Sets, Maps, Stacks, Queues, Binary Trees, and hashing. Algorithms to traverse, insert, delete, search and sort using each of these data structures will be analyzed for average efficiency. Students will also work with case studies to gain experience with large programs comprised of several classes.  AP Computer Science A is a prerequisite for Honors Advanced Data Structures.

     
    Advanced Placement Computer Science Principles                                         
    Prerequisite:  CP Geometry Enriched
    Corequisite:  CP Geometry Honors
    Grade Level:  10-12
    Full Year – 5 Credits
    AP Computer Science Principles (CSP) introduces students to the central ideas of computer science.  No previous experience with computer science is required.  AP CSP emphasizes programming less than MLHS’s Intro Computer Programming course.  AP CSP focuses on 7 big ideas:  Creativity, Abstraction, Data & Information, Algorithms, Programming The Internet and Global Impact.
     
    AP CSP topics include:

    What happens when you enter a URL in a web browser?
    How does your phone store your text messages, pictures and videos?
    How does computing impact your privacy?
    How can you create apps?

    Students taking AP CSP are expected to participate in the AP CSP Performance Tasks (during the course) and the AP CSP Exam.

    AP CSP can be taken in any order relative to MLHS’s other computer science courses.  Students who take AP CSP as a first course can progress to Into to Computer Programming, or with approval, directly into AP Computer Science A.