MATHEMATICS

The Mathematics Department offers a wide range of courses for every level of ability.  There are three sequences from which to choose: the Dynamics College Preparatory Sequence, the Traditional College Preparatory Sequence, and the Honors College Preparatory Sequence.  It is recommended that placement into any sequence takes into consideration the ability of the student, his/her future goals, performance in previous math courses, and performance on standardized tests.  

Monroe Township provides students the opportunity to take outside summer courses for the purpose of advancement after the completion of their ninth-grade year.Courses taken for advancement purposes in an approved college program or in a state approved 120-hour program must have the prior approval of the high school principal, department coordinator and guidance counselor.  Students must also show evidence of a grade of 80 or better in the course and must receive a grade of 80 or better on the high school mathematics department final examination to advance to the next level.  Courses for advancement purposes do not receive High School credit nor do they receive credit toward the calculation of rank in class or the GPA.

Students considering a college major in mathematics, science, engineering, or other technical fields are strongly urged to successfully complete courses in computer programming and/or STEM classes within the Industrial Arts program in addition to four years of college preparatory mathematics culminating with Advanced Placement Calculus AB or BC to be adequately prepared for these fields.

All mathematics courses in grades nine and eleven will include preparation for the NJSLA or NJGPA. The level of this preparation is commensurate with the level of the class.

Courses marked with a 🌐 satisfy the 21st Century Life & Career requirement. 

Mathematics & Computer Science Electives:        

Calculus (H)*

AP Statistics*  

Computer Programming*

Web Design (H)*

AP Computer Science Principles*  

Probability & Statistics*    

AP Computer Science A*

Work Based Learning*

Application Development (H)*

*Must meet prerequisites before selecting these courses.

THE DYNAMICS COLLEGE PREPARATORY SEQUENCE

The Dynamics College Preparatory Sequence is designed for those students planning to continue their education but who need to learn at a slower pace or students who may not wish to continue their education in college. 

ALGEBRA I A/B            

CREDITS:  10 

Prerequisite:  Must have a grade below 75 in Grade 8 Mathematics.

This course is reserved for students with a grade below 75 in Grade 8 Mathematics. 

Algebra I A/B is an alternate first course of the Dynamics College Preparatory Sequence. This course meets every day and is designed for students whose mathematical abilities and learning styles lend themselves to studying through a more concrete approach. Topics included are: basic concepts of algebra, integers, equations, inequalities, absolute value, factoring, rational expressions, solving and graphing linear equations and systems of equations, real numbers and square roots, and functions and relations.

This course is specifically designed for those students who have been identified through teacher recommendation and prior academic history as needing additional instruction for a successful freshman experience.  In addition, this course will prepare students with higher order thinking skills to perform tasks with adherence to the New Jersey Student Learning Standards and NJSLA. Students will have the opportunity to strengthen skills in test-taking strategies, note-taking strategies, and study-skills as well as transitioning into the high school environment.  Differentiated instruction is used for all participants once areas of strengths and weaknesses have been identified.  A pre- and post- test will be used to determine growth. There is a summer preparation packet for this course.  Five (5) of the ten (10) credits for this course can be used to fulfill the mathematics requirement for graduation.  

DYNAMICS OF GEOMETRY

CREDITS:  5

Grade: 10-12

Prerequisite:  Successful completion of Algebra I A/B or a grade below 70 in Algebra I 

Dynamics of Geometry is the second course in the Dynamics College Preparatory Sequence.  This course is designed for students whose mathematical abilities lend themselves to studying through a more concrete approach and incorporating examples that accommodate a variety of learning styles.  This course emphasizes applications rather than the formal deductive proofs of geometry.  Topics included are: points, lines, planes, segments, angles, parallel and perpendicular lines, congruent and similar triangles, polygons, proportions, right triangles, circles, perimeter, area, and volume.  There is a summer preparation packet for this course.  

DYNAMICS OF ALGEBRA II

CREDITS:  5

Prerequisite:  Successful completion of Dynamics of Geometry (or taken concurrently) or a grade below 70 in Geometry

Dynamics of Algebra II is the third course in the Dynamics College Preparatory Sequence.  This course is designed for students whose mathematical abilities lend themselves to studying through a more concrete approach and incorporating examples that accommodate a variety of learning styles.  This course covers most, but not all, of the major topics offered in the regular Algebra II course.  Topics included are: rational expressions, irrational and complex numbers, quadratic equations and functions, equations and numerical methods, exponential and logarithmic functions, and matrices and determinants.  There is a summer preparation packet for this course. 

DYNAMICS OF TRIG/MATH ANALYSIS  

CREDITS:  5

Grade:  12

Prerequisite: Successful completion of Dynamics of Algebra II or a grade below 70 in Algebra II

Students must be in the 12th grade to select this course or get approval from the mathematics supervisor.

Dynamics of Trig/Math Analysis is a 12th grade course and is the fourth course in the Dynamics College Preparatory Sequence.  This course is designed for students whose mathematical abilities lend themselves to studying through a more concrete approach and incorporating examples that accommodate a variety of learning styles.  Included in this course are advanced algebraic topics that were not included in Dynamics of Algebra II.  In addition, topics from trigonometry and mathematical analysis are also included to provide a sound mathematical program to better prepare students for coursework at the post secondary level.  Topics included are: linear, quadratic and polynomial functions, exponents, logarithms, trigonometric functions and identities, solving trigonometric equations, applications involving triangles, inverse trigonometric functions, advanced graphing techniques, polar coordinates and graphing polar equations.  Due to the large number of topics that will be covered, emphasis will be placed on application of concepts rather than their theoretical basis. There is a summer preparation packet for this course.  

THE COLLEGE PREPARATORY SEQUENCE

The college preparatory sequence is the traditional program designed for students planning to pursue a college or post-secondary education.

ALGEBRA I          

CREDITS:  5

Prerequisite: Must have a grade of 75 or higher in Grade 8 Mathematics and teacher recommendation.

Algebra I is the first course in the traditional college preparatory sequence.  Some topics included are:  the basic concepts of algebra, operations with integers, solving equations and word problems, solving and graphing inequalities, absolute value, polynomials, rational algebraic expressions, systems of equations, irrational numbers, and functions.  There is a summer preparation packet for this course.  

GEOMETRY  

CREDITS:  5

Prerequisite: 

MUST have a grade of 70 or higher in Grade 8 Algebra I OR

a grade of 70 or higher in Algebra I OR 

a grade of 95 or higher in Algebra I A/B 

Geometry is the second course in the traditional college preparatory sequence.  The course is designed to stimulate and develop clear, logical, creative thinking through the study of the basic structure of geometry, geometric relationships, and formal deductive proofs.  Some topics included are: points, lines, planes, segments, angles, parallel and perpendicular lines, congruent and similar triangles, polygons, proportions, right triangles, circles, constructions, and perimeter, area, and volume.  There is a summer preparation packet for this course.  

ALGEBRA II                                                                                                  

CREDITS:  5 

Prerequisite: 

A grade of 70 or higher in Geometry OR  

A grade of 95 or higher in Dynamics of Geometry OR

A grade of 70 or higher in Algebra I (if taking Geometry concurrently with Algebra II)

Algebra II is the third course in the traditional college preparatory sequence.  The course extends the processes of algebra introduced in Algebra I and uses the geometrical concepts from Geometry to produce a more meaningful, in-depth approach to new topics in algebra.  Topics included are: rational expressions, irrational and complex numbers, quadratic equations and functions, equations and numerical methods, exponential and logarithmic functions, and matrices and determinants.  There is a summer preparation packet for this course.   

PRECALCULUS

CREDITS:  5

Prerequisite: A grade of 70 or higher in Algebra II or a grade of 95 or higher in Dynamics of Algebra II.

Precalculus is the fourth course in the traditional college preparatory sequence.  It is designed to provide a basic course in trigonometry and a sufficient background in college algebra and analytic geometry to prepare the student for the study of calculus.  Some topics included are: polynomials, inequalities, functions, exponents and logarithms, trigonometric functions, identities, trigonometric equations, solving triangles, inverse trigonometric functions, advanced graphing techniques, polar coordinates, complex numbers, sequences & series, combinatorics, and probability.  There is a summer preparation packet for this course.

THE HONORS COLLEGE PREPARATORY SEQUENCE

The honors sequence is a rigorous program of study for students with exceptional mathematical ability and who wish to study mathematics in great depth.  

GEOMETRY (HONORS)

CREDITS:  5

(This course receives honors weighting for the calculation of the GPA.)

Prerequisite:  Students must have a grade of 80 or higher in Grade Eight Algebra. Ninth grade students may not waive into Geometry Honors. Accelerated students who have completed Geometry but have not met the criteria for Algebra II (Honors) should be placed in Geometry (Honors).  

Geometry (Honors) is the first course in the honors college preparatory sequence.  It is a rigorous and challenging course designed for the student with exceptional mathematical ability and leading ultimately to the study of calculus in grade 12.  Formal deductive proofs are emphasized.  Some topics included are: points, lines, planes, segments, angles, parallel and perpendicular lines, congruent and similar triangles, polygons, proportions, right triangles, circles, constructions, perimeter, area, volume, coordinate geometry, geometric loci, and inequalities.  There is a summer preparation packet for this course.  

ALGEBRA II (HONORS)            

CREDITS:  5 

(This course receives honors weighting for the calculation of the GPA.)

Prerequisite:  MUST have 

A grade of 85 or higher in Grade Eight Geometry OR

A grade of 80 or higher in Geometry Honors OR

A grade of 80 or higher in Eighth Grade Algebra I (if taking Honors Geometry concurrently with Honors Algebra II) OR

A grade of 95 or higher in Geometry OR

A grade of 95 or higher in Algebra I (if taking Honors Geometry concurrently with Honors Algebra II)

It should be noted that 9th grade students who appeal to withdraw from Algebra II (Honors) will be placed in Geometry (Honors). Ninth grade students will NOT be placed in traditional Algebra II. Ninth grade students may not waive into Algebra II Honors.

Algebra II (Honors) is the second course in the honors college preparatory sequence.  It is a rigorous and challenging course designed for the student with exceptional mathematical ability and leading ultimately to the study of calculus in grade 12.  Topics included are: rational expressions, irrational and complex numbers, quadratic equations and functions, equations and numerical methods, exponential and logarithmic functions, and matrices and determinants. There is a summer preparation packet for this course.  

PRECALCULUS (HONORS)

CREDITS:  5

(This course receives honors weighting for the calculation of the GPA.)

Prerequisite:  A grade of 80 or higher in Algebra II (Honors) or A grade of 95 or higher in Algebra II.

Precalculus (Honors) is the third course in the honors college preparatory sequence.  It is a rigorous and challenging course designed for the student with exceptional mathematical ability and leading ultimately to the study of calculus in Grade 12. Some topics included are: the trigonometric functions, identities, trigonometric equations, solving triangles, inverse trigonometric functions, advanced graphing techniques, polar coordinates and complex numbers, polynomial functions, conic sections, vectors and determinants, sequences and series, statistics, probability, and an introduction to calculus.  This course makes extensive use of the graphing calculator.  Completion of a summer preparation packet is required.  

CALCULUS (HONORS)            

CREDITS:  5

(This course receives honors weighting for the calculation of the GPA.)

Prerequisite: Successful completion of Precalculus (Honors) or a grade of 80 or higher in Precalculus.

Calculus (Honors) is the fourth course of the honors college preparatory sequence.  This course is designed for students who need additional mathematics beyond Trigonometry/Math Analysis and do not wish to take Advanced Placement Calculus.  Topics included are: relations, functions, inverses, trigonometric functions, limits, target values, differentiation, linear approximations, differentials, maxima, minima, Mean Value Theorem, Newton's Method, related rates, antiderivatives, initial value problems, definite integrals, Fundamental Theorem of Calculus, indefinite integrals, integration by substitution, numerical integration, areas between curves, and volumes of solids of revolution.  This course makes extensive use of the graphing calculator.  Completion of a summer preparation packet is required.    

ADVANCED PLACEMENT CALCULUS AB  

CREDITS:  10

(This course receives advanced placement weighting for the calculation of the GPA.)

Prerequisite:  Students MUST have a grade of 78 or higher in Precalculus (Honors). Students may not waive into AP Calculus AB.

Advanced Placement Calculus AB is the fourth course of the honors college preparatory sequence.  This course will meet every day in the double-period block.  It is a rigorous and challenging course designed for the student with exceptional mathematical ability needing a strong background in mathematics for future academic work at the college level.  Topics included are: limits, target values, differentiation, linear approximations, differentials, maxima, minima, Mean Value Theorem, Newton's Method, related rates, antiderivatives, initial value problems, definite integrals, Fundamental Theorem of Calculus, indefinite integrals, integration by substitution, numerical integration, areas between curves, the natural logarithmic function, the exponential functions, inverse trigonometric functions and related integrals, integration by parts, integrals involving trigonometric functions, trigonometric substitutions, slope fields, volumes of solids of revolution, and volumes by cylindrical shells.  This course makes extensive use of the graphing calculator.  Completion of a summer preparation packet is required.  

ADVANCED PLACEMENT CALCULUS BC   

CREDITS:  5

(This course receives advanced placement weighting for the calculation of the GPA.)

Prerequisite: Successful completion of Advanced Placement Calculus AB.

Advanced Placement Calculus BC is the fifth course of the honors college preparatory sequence.  It is a rigorous and challenging course designed for the student with exceptional mathematical ability needing a strong background in mathematics for future academic work at the college level.  Topics included are: all AP Calculus AB topics in addition to the following: parametric, polar, and vector functions; analysis of planar curves given in parametric form, polar form, and vector form; numerical solution of differential equations using Euler's method; L'Hôpital's Rule; derivatives of parametric, polar, and vector functions; applications of integrals; antiderivatives by substitution of variables, parts, and simple partial fractions; improper integrals; solving logistic differential equations and using them in modeling; polynomial approximations and series; concepts of series; series of constants; geometric series, harmonic series, alternating series; terms of series; ratio test for convergence and divergence; comparing series to test for convergence or divergence; Taylor series; Maclaurin series; power series; radius and interval of convergence of power series; and Lagrange error bound for Taylor polynomials. This course makes extensive use of the graphing calculator.  Completion of a summer preparation packet is required. 

PROBABILITY & STATISTICS

CREDITS:  5

Prerequisite: Students MUST have a grade of 75 or higher in Algebra II or MUST have a grade of 90 or higher in Dynamics of Algebra II, or successful completion of Algebra II (Honors)

Probability & Statistics is an elective course for those who have successfully completed Algebra II.  It is designed for those students interested in pursuing a career in business, marketing, psychology, mathematics, or any field requiring data analysis. Topics included are: graphical techniques, analysis of data, probability, permutations, combinations, conditional probability, the Binomial Distribution, the Poisson Distribution, the normal curve, random sampling, Central Limit Theorem, hypothesis testing, linear correlation and regression, and the Chi-Square Distribution.  The graphing calculator is used extensively in this course.  

ADVANCED PLACEMENT STATISTICS

CREDITS:  5

(This course receives advanced placement weighting for the calculation of the GPA.)

Prerequisite: Students MUST have a grade of 80 or higher in Algebra II (Honors) or MUST have a grade of 90 or higher in Algebra II.

Advanced Placement Statistics is an elective course for those who have successfully completed Algebra II.  It is designed for those students interested in pursuing a career in business, marketing, psychology, mathematics, or any field requiring data analysis. This AP course in statistics will introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data.  Students are exposed to four broad conceptual themes: 

1. Exploring Data: Describing patterns and departures from patterns  

2. Sampling and Experimentation: Planning and conducting a study

3. Anticipating Patterns: Exploring random phenomena using probability and simulation

4. Statistical Inference: Estimating population parameters and testing hypotheses 

Topics included are: graphical techniques, analysis of data, probability, permutations, combinations, conditional probability, the Binomial Distribution, the Poisson Distribution, the normal curve, random sampling, Central Limit Theorem, hypothesis testing, linear correlation and regression, t-distribution, and the Chi-Square Distribution.  

The graphing calculator is used extensively in this course. Students with the appropriate mathematical background are encouraged to take both AP Statistics and AP Calculus in high school.  

INTRODUCTION TO COMPUTER SCIENCE 🌐 

CREDITS:  5

Prerequisite:  Students MUST have a grade of 75 or higher in Algebra I/Grade 8 Algebra I or MUST have a grade of 80 or higher in Algebra I A/B

Introduction to Computer Science is designed to introduce the fundamental concepts of computer science and programming. Students will learn about and explore topics and programming constructs such as hardware, software, networking, number systems, algorithms, sequence, selection, and iteration. The course emphasizes problem-solving, program analysis, and testing. Students will work individually and collaboratively with hands-on use of technology being emphasized.

ADVANCED PLACEMENT COMPUTER SCIENCE PRINCIPLES 🌐

CREDITS:  5

Grade:  10-11 (9th grade STEM program)

(This course receives advanced placement weighting for the calculation of the GPA.)

Prerequisite: Students MUST have a grade of 85 or higher in Algebra I/Grade 8 Algebra I. This course is a prerequisite for students taking AP Computer Science A.

The AP Computer Science Principles course is designed to be equivalent to a first-semester introductory college computing course. Students develop computational thinking skills vital for success in all disciplines, such as using computational tools to analyze and study data and working with large data sets to analyze, visualize, and draw conclusions from trends. The course is unique in its focus on fostering student creativity. Students are encouraged to apply creative processes when developing computational artifacts and to think creatively while using computer software and other technology to explore questions that interest them. They will also develop effective communication and collaboration skills, work individually and collaboratively to solve problems, and discuss and write about the importance of these problems and the impacts to their community, society, and the world.

ADVANCED PLACEMENT COMPUTER SCIENCE A            

CREDITS:  5

Grade:  10-12

(This course receives advanced placement weighting for the calculation of the GPA.)

Prerequisite: Students MUST have a grade of 85 or higher in AP Computer Programming Principles or MUST have a grade of 90 or higher in Computer Programming.

Advanced Placement Computer Science A is the second course in the computer programming sequence of courses and includes an in-depth study of the JAVA computer programming language.  This course emphasizes the design and testing of computer programs and focuses on the analysis of complex problems from a wide variety of areas.  Topics included are: 

• Object oriented program design (program design, class design)

• Program implementation (implementation techniques, programming constructs, and Java library classes (included in the A-level AP Java Subset)

• Program analysis (testing, debugging, understanding and modifying existing code, extending existing code using inheritance, understanding error handling, reasoning about programs, analysis of algorithms, numerical representations and limits)

• Standard data structures (simple data types, classes, one-dimensional arrays)

• Standard algorithms (operations on A-level data, searching, sorting)

• Computing in context (major hardware components, system software, types of systems, responsible use of computer systems)

Students planning to major in a technical field at the college level are strongly urged to complete this course. 

ADVANCED WEB DESIGN USING PHP AND Web MySQL (HONORS)

Offered the 25-26 SY. NOT Offered during the 24-25 SY.

CREDITS:  5

(This course receives honors weighting for the calculation of the GPA.)

Prerequisite:Successful completion of Advanced Placement Computer Science A

Advanced Web Design Using PHP and Web MySQL (Honors) is the third or fourth course in the sequence of computer programming courses.  This course relies heavily on prior knowledge to explore advanced website design using HTML, CSS, PHP, MySQL and more. The course concludes with students designing a professional, interactive website.  Topics included are:

1. Designing a web page with the HTML basics.

2. Controlling the style and layout of multiple web pages using CSS.

3. Designing dynamic and interactive web pages using PHP in coordination with the MySQL database.

4. Adding functionality to web pages using Javascript. 

Students planning to major in a technical field at the college level are strongly urged to complete this course.  

APPLICATION DEVELOPMENT (HONORS) 

Offered the 25-26 SY. NOT Offered during the 24-25 SY.

CREDITS:  5

(This course receives honors weighting for the calculation of the GPA.)

Prerequisite:  Advanced Placement Computer Science A.

Placement Recommendation:  Successful completion of Advanced Placement Computer Science A.

Using a variety of development software, Application Development is an advanced course designed for students interested in exploring and designing mobile applications for iOS, Android and/or other mobile operating systems. The course relies heavily on prior knowledge (Java) to work at an accelerated and independent pace to develop applications for mobile devices. Independent, hands-on development and research are strongly emphasized.