Mathematics

The Marlborough High School Mathematics Department provides students with comprehensive course options to prepare them for success in post-secondary opportunities. All students are required to pass four years of math. All of our courses serve to create critical thinkers and problem solvers who can communicate using verbal and written skills; gather, analyze, and evaluate information; collaborate to achieve a common goal; apply knowledge to solve problems; and demonstrate media and technology literacy. 

The mathematics courses at Marlborough High School are aligned to the Massachusetts Mathematics Curriculum Frameworks, including the Common Core Standards for Mathematical Practice, which define the knowledge and skills that students should have to graduate from high school prepared for entry-level college courses or workforce training. The standards require students to think and reason mathematically about real-world situations; to use mathematics to analyze problems in order to understand them and make better decisions; and places an emphasis on mathematical modeling. 

Students will typically follow one of the progressions shown in the table below. Course recommendations are generally based on the course prerequisites and a student’s study and work habits. The “lanes” in the table do not represent course levels, nor are students restricted to a particular “lane” once they have started. Please note that all course offerings do not appear in the table, and parents are encouraged to discuss their child’s progress each year with his/her teacher. 

In addition to the courses listed in the table, students are encouraged to consider the following course offerings: 

• AP Calculus AB/BC

• AP Statistics

• AP Computer Science/Introduction to Programming in Java

HONORS ALGEBRA 1

COLLEGE PREP ALGEBRA 1

ALGEBRA 1 ESSENTIALS

Algebra 1 is an introduction to the major function families that will serve as the foundation for all subsequent courses. Within each function family, students will simplify, solve, write, and graph to make connections between the various representations. Students’ understanding of these functions and their relationships will be deepened as they think, reason, persevere, and model with mathematics. Topics include: equations/inequalities; functions/graphs; linear functions; systems of equations; polynomials; quadratic functions; absolute value functions; exponential functions; and statistics. All levels will use technology, such as graphing calculators, and online graphing tools throughout the course. 

PREREQUISITE: 8th grade math 

Full year course: 4 Credits

MATH SUPPORT 9 

This course is intended to assist students who were struggling with foundational skills during their previous course work. The course will offer tutorial support, basic skills review and development, pre-teaching of new concepts along with re-teaching those concepts which students still struggle with. The course is intended to increase students’ understanding and comfort level with key algebraic concepts by reviewing regularly throughout the year. Math Support 9 will be taught in partnership with an Algebra 1 course.

PREREQUISITE: 8th grade math

Semester course: 2 Credits

HONORS GEOMETRY

COLLEGE PREP GEOMETRY

GEOMETRY ESSENTIALS  

Geometry adds significant depth to the applications of the different skills students developed in Algebra 1. Students begin to transition from solving a problem given to them to instead taking given information to set up a problem on their own and then solve it. Students will learn fundamental geometric concepts regarding the building blocks of geometry, the three undefined terms of geometry and angles, along with properties of two-dimensional and three-dimensional figures. Measurement in both 2 and 3 dimensions such as area, surface area and volume are covered in depth. During their studies with right triangles, students also get their first introduction to trigonometry, an area of math they will continue to use in Algebra 2 and beyond. Students look at these different geometric properties both synthetically and analytically, sharpening their algebraic skills in conjunction with the properties and applications of geometry they learn during this course.

PREREQUISITE: Algebra I

Full year course: 4 Credits

MATH SUPPORT 10 

This course is intended to assist students who were struggling with foundational skills during their previous course work. The course will offer tutorial support, basic skills review and development, pre-teaching of new concepts along with re-teaching those concepts which students still struggle with. The course is intended to increase students’ understanding and comfort level with key algebraic and geometric concepts by reviewing regularly throughout the year. Math Support 10 will be taught in partnership with a Geometry course.

PREREQUISITE: Algebra I

Semester course: 2 Credits

HONORS ALGEBRA 2 

COLLEGE PREP ALGEBRA 2

ALGEBRA 2 ESSENTIALS  

Building on their work with linear, quadratic, and exponential functions, students extend their repertoire of functions to include logarithmic, polynomial, rational, and radical functions in Algebra II.  Students work closely with the expressions that define the functions, with algebraic manipulations of expressions, and continue to expand and hone their abilities to model situations and to solve equations, including solving polynomial equations and solving exponential equations using the properties of logarithms. All levels will use technology, such as graphing calculators, and online graphing tools throughout the course. 

PREREQUISITE: Algebra I and Geometry

Full year course: 4 Credits

COLLEGE PREP INTERMEDIATE ALGEBRA 2A   

This course covers the curriculum standards from the first half of Algebra 2, spread out over the course of one year. Topics include: numbers and operations, equations and inequalities, linear functions, and systems of equations. There will be a focus on functions, their graphs, and problem situations that can be modeled using functions. 

PREREQUISITE: Teacher recommendation. 

Full year course: 4 Credits

COLLEGE PREP INTERMEDIATE ALGEBRA 2B 

This course covers the curriculum standards from the second half of Algebra 2, spread out over the course of one year. Topics include: quadratic functions, polynomials, exponential functions, rational expressions, and statistics/probability. There will be a focus on functions, their graphs, and problem situations that can be modeled using functions.

PREREQUISITE: College Prep Intermediate Algebra 2A

Full year course: 4 Credits

COLLEGE PREP PRE-CALCULUS   

This course combines the trigonometric, geometric, and algebraic techniques needed to prepare students for the study of calculus, and strengthens students’ conceptual understanding of problems and mathematical reasoning in solving problems.   

PREREQUISITE: Algebra 2

Full year course: 4 Credits

GRADE 12 MATH ESSENTIALS

This course will strengthen students’ algebraic and problem solving skills through real life applications. Geometry and Algebra II concepts will be expanded upon in addition to other topics that will be tailored to meet the needs of students in the class. 

PREREQUISITE: Algebra 2

Full year course: 4 Credits

COLLEGE PREP TOPICS IN MATHEMATICS

The focus of this course will be to strengthen and enhance previously learned math skills. Students will explore topics from Algebra 1, Geometry, and Algebra 2 in a deeper way and expand on their conceptual understanding in preparation for college placement exams and college-level mathematics. This course parallels Quinsigamond Community College’s MAT 099 remedial math course. Students earning a “C” or better on the MAT 099 final exam are guaranteed placement into QCC’s College Level Algebra course.

PREREQUISITE: Algebra 2

Full year course: 4 Credits

HONORS INTRO TO CALCULUS 

This course provides students with an introduction to the major topics in calculus, including how things change and how they accumulate. It provides a framework for modeling systems in which there is change, and it enables us to predict the behavior of such systems. Students will learn about integral calculus, which presents the concept of infinitesimal (tiny) change and enable them to determine instantaneous rates of change, analyze motion, perform optimization, and make predictions. Students will also be introduced to integral calculus, which can be used to determine areas and volumes as well as analyze systems that involve accumulating values over time.

PREREQUISITE: Algebra 2

Full year course: 4 Credits

ADVANCED PLACEMENT CALCULUS AB 

ADVANCED PLACEMENT CALCULUS BC  

These courses will cover the topics in differential and integral calculus as outlined in the AB/BC syllabus for the AP program. The curriculum for AP Calculus AB is equivalent to that of a first-semester college calculus course, while AP Calculus BC is equivalent to both first and second semester calculus courses. AP Calculus teaches students to approach calculus concepts and problems when they are represented graphically, numerically, analytically, and verbally, and to make connections amongst these representations. All students who take this class are expected to take the AP Calculus exam in the spring. 

PREREQUISITE: Algebra 2 or Pre-Calculus

Full year course: 4 Credits

AP CALCULUS BC & INTRO TO MULTIVARIABLE CALCULUS  

This course is intended for students who have successfully completed AP Calculus AB. This course will cover the topics in differential and integral calculus as outlined in the BC syllabus for the AP program. Students will then expand their knowledge of Calculus studying differentiation and integration of several variables, optimization, and vector fields.  

PREREQUISITE: AP Calculus AB

Full Year Course: 4 Credits

ADVANCED PLACEMENT STATISTICS  

This course will cover all topics as outlined in the syllabus for AP Statistics and is designed to cover a one-semester introductory non-calculus-based college course in statistics. Students will learn the most fundamental components of numerical data analysis, including creating experiments, choosing samples, and statistical inference. Along the way, topics in probability and regression will be covered. Students must have a handheld calculator with advanced statistics functions, such as the Texas Instruments models TI-nSpire, TI-83, or comparable models from other manufacturers. All students who take this class are expected to take the AP Statistics exam in the spring.

PREREQUISITE: Algebra 2

Full year course: 4 Credits

ADVANCED PLACEMENT COMPUTER SCIENCE/INTRODUCTION TO PROGRAMMING IN JAVA 

This course covers the fundamental ideas of programming in Java, with an introduction to object-oriented methodologies. Topics include an introduction to Java syntax, class libraries, standard input and output, basic data structures, and implementation of algorithms. Students also learn methods for testing and debugging. Students taking this course should be confident using Windows, Google tools, and Web interfaces. They are expected to take the AP Computer Science A exam in the spring.

PREREQUISITE: Algebra I

Full year course: 4 Credits

ADVANCED PLACEMENT COMPUTER SCIENCE PRINCIPLES 

This course introduces students to computer programming and aspects of computer technology, including the use of abstraction and algorithms, big data, the Internet, and cybersecurity. The social, cultural, and economic impacts of computing are also considered. One aim of the course is to encourage participation in computer science among students not attracted to courses that focus on coding. Students are given the opportunity to explore how technology can help understand real-world problems and build relevant solutions. The curriculum uses materials drawn from a number of College Board endorsed curricula. All students who take this class are expected to take the AP Computer Science Principles exam, which includes projects done during the year as well as a section administered in the spring.

PREREQUISITE: Algebra I

Full year course: 4 Credits

MATHEMATICS FOR ENGLISH LEARNERS 

FUNDAMENTALS OF ALGEBRA A 

This course is designed for students with little or no English proficiency and limited or interrupted formal schooling. It provides students with the necessary foundational skills to be successful in Algebra or Integrated Math 1. Students explore the real number system and the language of Algebra. An emphasis is placed on the continued study of place value, integers, fractions, decimals, order of operations, proportional relationships, variables, expressions, equations, and basic geometry concepts. There is a focus on developing students’ language of math while learning these concepts.  

PREREQUISITE: A pretest indicating Math level, English language proficiency level 1, and limited or interrupted formal education. 

Full year course: 4 Credits

FUNDAMENTALS OF ALGEBRA B

This course provides EL students with the necessary foundational skills to be successful in Algebra or Integrated Math 1. Students explore the real number system and the language of Algebra. An emphasis is placed on the continued study of place value, integers, fractions, decimals, order of operations, proportional relationships, variables, expressions, equations, and basic geometry concepts. There is a focus on developing students’ language of math while learning these concepts.  

PREREQUISITE: A pretest indicating Math level and English language proficiency level 1 or 2. 

Full year course: 4 Credits

INTEGRATED MATH 1

This course provides a deep understanding of concepts from Algebra 1 along with application of geometric theorems and ideas. Students will study algebraic topics such as equations/inequalities, functions/graphs, linear functions, systems of equations, and statistics. Among the geometric topics studied are points, lines, and planes; triangles, polygons, and circles; angles and parallel and perpendicular lines. Students also study surface area, and volume. Additional topics may be added as needed to help students prepare for the yearly MCAS test. There is a focus on developing students’ language of math while learning these concepts.

Full Year Course: 4 Credits

INTEGRATED MATH 2

This course provides a continued deep understanding of concepts from Algebra 1 along with application of geometric theorems and ideas. It is intended for students who have successfully completed Integrated Math 1. Students will study algebraic topics such as polynomials, quadratic functions, exponential functions, absolute value functions, and probability. Among the geometric topics studied are right triangles, trigonometry, similarity, and 3D measurement. Additional topics may be added as needed to help students prepare for the yearly MCAS test. There is a focus on developing students’ language of math while learning these concepts.

Full Year Course: 4 Credits

ELECTIVES

These courses do not replace the yearly Math course requirement if taken for two consecutive semesters. 

MCAS MATH REVIEW 

This course is designed for those students who are in need of extra preparation for the yearly MCAS test. This semester offering is intended for students in grades 11-12 who have not previously passed the Mathematics MCAS in grade 10.  

Semester course: 2 Credits

INTEGRATED MATH SUPPORT

This course is intended to assist students who are struggling with foundational skills. The course will offer tutorial support, basic skills review and development, pre-teaching of new concepts along with re-teaching those concepts which students still struggle with. The course is intended to increase students’ understanding and comfort level with key algebraic concepts by reviewing regularly throughout the year. Integrated Math Support will be taught in partnership with an Integrated Math course.

PREREQUISITE: Student must be enrolled in Integrated Math 1 or 2

Semester Course: 2 Credits