### ABOUT MATHEMATICS

The Mathematics Department provides a challenging and varied curriculum that is strongly rooted in the fundamentals of algebra. A full array of college preparatory and honors courses from algebra through two levels of Advanced Placement calculus and statistics is available. The fostering of critical and analytical thinking is a basic element of all classes. Emphasis is placed upon bridging the academic study of mathematics to “real world” applications. A drop-in mathematics tutorial center, staffed by faculty, is available to students throughout the day. Additionally, after completing Precalculus, students have the opportunity to take AP Computer Science A as an elective.

Placement: For current Mitty students, subsequent class placement is determined by the students' grades in their current course. Requests for concurrent enrollment, summer advancement or honors placement must be made through the Placement Request Form on MyMitty by February 28 of the current school year. For incoming freshmen, class placement is determined by the challenge exams in April. After the challenge exams, requests for advancement beyond Algebra II/Trig can be made to the department chairperson.

### Algebra I - Grade 9 - Yearlong course

This first year course in Algebra covers operations with variables. Linear and quadratic equations and inequalities are solved, graphed and used to solve word problems. Problem solving skills are emphasized.

UC/CSU approved course

NCAA Core Course

### Algebra I Accelerated - Grade 9 - Yearlong course

The course will cover content of a first year algebra class at an accelerated pace. This will allow for extended work and exploration of other topics found in algebra. Content will include all concepts stated in the course goals. Emphasis will be placed on application and development of problem solving skills.

UC/CSU approved course

NCAA Core Course

Prerequisite: Qualifying score on the Algebra I placement exam in April.

### Geometry - Grade 9 -10 - Yearlong course

This course is an investigation of the properties and relationships of points, lines and planes, and of two and three dimensional figures and their applications in area, volume, and proportion. It includes an introduction to analytic geometry, a study of the structure of logic and deductive, inductive and intuitive reasoning, and the development of proof and construction.

UC/CSU approved course

NCAA Core Course

Pre-Requisite: Algebra I or Algebra I Accelerated. Incoming freshmen: qualifying score on the Algebra I placement exam in April.

### Geometry Honors - Grades 9-10 - Yearlong course

The course is an honors course in plane Euclidean geometry. Constructions and proofs will be stressed. In addition, beginning algebra will be reviewed to prepare for the PSAT examination.

UC/CSU approved course

NCAA Core Course

Prerequisite: Algebra I Accelerated with B+ both semesters. Algebra I with an A of 96% or above both semesters. Incoming freshmen: qualifying score on the Algebra I placement exam in April.

### Algebra II - Grades 9 -11 - Yearlong course

This course will review and extend those concepts introduced in Algebra I. New topics will include complex numbers, polynomial functions, analytic geometry, exponential and logarithmic functions, sequences and series, and development of problem solving skills.

UC/CSU approved course

NCAA Core Course

### Algebra II Honors - Grades 9 -11 - Yearlong course

Algebra II Honors is a course designed to introduce advanced topics of Algebra II in addition to the basic topics. The basic topics include quadratics, complex numbers, polynomial functions, exponential and logarithmic functions, and the development of problem solving skills. The advanced topics include; functional analysis of higher degree polynomials; analysis interpretation, and graphing of rational functions, including asymptotic behavior; analysis of conic sections and equations; arithmetic and geometric sequences and series; binomial expansions; statistics and probability.

UC/CSU approved course

NCAA Core Course

Prerequisite: Geometry Honors with B both semesters. Geometry with A of 96% or above both semesters. Incoming freshmen: qualifying score on the Geometry challenge exam in April.

### Algebra II/Trigonometry Honors - Grades 9 -11 - Yearlong course

Algebra II/Trigonometry Honors is an honors course and the second course in the Algebra sequence. This course involves reading and analyzing material and problems. Much of the theoretical work is supported by "real world" examples. In this class an emphasis is placed on developing mathematical models which allow a solution to be found to an involved problem. The course also deals with functions (linear, quadratic, higher degree functions, inverse functions), systems of equations, series and sequences, and trigonometry. All topics are supported by applications of the theories involved.

UC/CSU approved course

NCAA Core Course

Prerequisite: Geometry Honors with A both semesters.

### Pre-Calculus - Grades 10 -12 - Yearlong course

Pre-calculus is a course designed to prepare students for calculus. The course will begin with an extensive study of trigonometry. Students will be introduced to trigonometric identities, graphing, and solving equations. The course will continue with a study of vectors, polar coordinates, and analytic trigonometry. In addition, the following topics will be covered: functions; analytic geometry; arithmetic and geometric sequences and series; polynomial equations; and a review of calculus. The review of calculus will introduce students to the limit, derivative, and integral of a function.

UC/CSU approved course

NCAA Core Course

Prerequisite: Algebra II with B both semesters. Algebra II Honors with **B- **both semesters.

### Pre-calculus Honors - Grades 10 -12 - Yearlong course

Pre-calculus Honors is a course designed to prepare students for calculus. The course will begin with analysis of functions and their graphs. The different types of functions include; polynomial; rational; exponential; logarithmic. The course will then continue the study of functions by introducing trigonometry, and analytic trigonometry. In addition, the following topics will be covered; polar coordinates; vectors; analytic geometry; systems of equations and inequalities; arithmetic and geometric sequences and series; counting and probability. Students will be introduced to the limit, derivative, and integral of a function.

UC/CSU approved course

NCAA Core Course

Prerequisite: Algebra II Honors with B+ both semesters. Algebra II with A of 96% or above both semesters.

### Calculus - Grades 10 -12 - Yearlong course

This course is a two-semester course that covers the elements of beginning college calculus. Topics to be studied include limits, differentiation and integration of polynomial, trigonometric, logarithmic, exponential and other functions, and their applications to area, volume, arc length and optimization problems. This course does not follow the curriculum needed to take the Advanced Placement Exam in Calculus.

UC/CSU approved course

NCAA Core Course

Prerequisite: Pre-Calculus with B both semesters. Algebra II/Trig Honors with B both semesters.

### AP Calculus AB - Grades 9 -12 - Yearlong course

AP Calculus AB is a two-semester course covering the topics prescribed by the College Board/Advanced Placement Program for advanced placement in Calculus AB. This course is designed for students who have completed the regular four-year college preparatory mathematics sequence through Pre-Calculus or Algebra II/Trig Honors.

Students enrolled in this course are required to take the AP examination in May. There is a College Board fee assessed for this examination that will be added to the students' tuition. No final exam is administered in this course in the spring semester.

UC/CSU approved course

NCAA Core Course

Prerequisite: Algebra II/Trig Honors with an A- both semesters; Pre-Calculus with an A of 96% or above both semesters; Pre-calculus Honors with an B+ both semesters; Calculus with a B or higher both semesters.

### AP Calculus BC - Grades 10 -12 - Yearlong course

This course will cover the topics prescribed by the College Entrance Examination Board for advanced placement in Calculus. This course is designed for students who have completed the AP Calculus AB curriculum. Methods of integration, applications of the integral, convergence/divergence of series and sequences, Taylor and Maclaurin series, derivatives of functions in polar and parametric form, vector calculus and elementary differential equations are studied.

Students enrolled in this course are required to take the AP examination in May. There is a College Board fee assessed for this examination that will be added to the students' tuition. No final exam is administered in this course in the spring semester.

UC/CSU approved course

NCAA Core Course

Prerequisite: AP Calculus AB with B both semesters; Calculus with an A both semesters and department chair approval.

### Linear Algebra and Multivariable Calculus – Grades 11 – 12 – Yearlong Course

Linear Algebra and Multivariable Calculus is a year-long elective course designed to give students a third year advanced course in mathematics, covering linear algebra, multivariable calculus, ordinary differential equations, and graph theory. This is a college level mathematics course, covering differential and integral calculus of multiple variables, including the geometry of space, vector functions, partial derivatives, multiple integrals, vector calculus and first- and second- order differential equations. A survey of advanced topics and projects in advanced topics will be explored. The course is intended to give students experience in the topics listed above through a strong foundation in proof- based mathematical reasoning. Students will use computers to solve complex systems and to visualize graphs in more than two dimensions.

The course will begin the year with a study of linear algebra and vectors. Class discussion will then build on these ideas to develop student understanding of multivariable calculus and applications. During the second semester, students in the course will continue to study multivariable calculus and its applications. Finally, the course will include a study of advanced topics in mathematics including a study of first order and second order linear ordinary differential equations and an introduction to graph theory.

UC/CSU approval pending

NCAA approval pending

Prerequisite**: **Successful completion of AP Calculus BC with grade of A- or better and instructor recommendation.

### Introduction to Computer Programming - Grades 10-12 - Yearlong Course

This introductory course is designed to make students proficient in writing, reading, and applying computer code. It is designed for beginners with no previous experience in coding. The course is extremely hands-on, with a significant portion of each class period dedicated to writing and improving a student’s computer code. Through creative, personalized projects, students will learn to incorporate user input, basic graphics, randomized numbers, command loops, and other techniques into their programs. Students will discuss their code with literacy and clarity, and also interpret and improve upon the function of programs they are given. Students will also conduct independent research into wider topics in the field of Computer Science, including its history, current applications, and career opportunities. Students completing this class will be well prepared to continue with the AP Computer Science class.

UC/CSU approved course

NCAA Core Course

Prerequisite: Completion of Algebra I with B or better. This course may be taken concurrently with another mathematics course.

### AP Computer Science A - Grades 11-12 - Yearlong Course

The purpose of the class is to introduce students to object-oriented programming using JAVA. Students will study concepts such as classes, objects, inheritance, polymorphism, and code reusability. Hands-on programming is always emphasized, and students will complete at least one functional program component each class such that they have immediate feedback for their work. Students will be asked to employ critical thinking in searching for multiple solutions or for the most efficient solution. Students will be given the tools and time to explore numerous challenging problems from not only programming, but math, economics, and game theory. In addition, students will have the opportunity to propose, outline, and develop an independent, long- term project that will be presented to their peers. This course teaches students to use the standard Java library from the AP Java subset in the AP Computer Science A Course Description.

Students enrolled in this course are required to take the AP examination in May. There is a College Board fee assessed for this examination that will be added to the students' tuition. No final exam is administered in this course in the spring semester.

UC/CSU approved course

NCAA Core Course

Prerequisite: Completion of Precalculus or Algebra II Honors with an A-. This course may be taken concurrently with another mathematics course.

### Introduction to College Statistics – Grades 11-12 – Yearlong course

This is a yearlong course covering typical content in a standard introductory college statistic course. Topics covered are descriptive statistics both graphically and numerically, statistical simulation, methods of collecting data, discrete and continuous random variables, statistical inference and estimation. The course introduces the students in many applications, including but not limited to business, economic, medicine, sciences and those pertaining to issues of contemporary interests. The use of technology (primarily graphing calculator) will be required in certain applications. This course is ideal for those students who wish to major in none science fields in college.

UC/CSU approved course

NCAA Core Course

Prerequisite: Successful completion of Algebra II or Algebra II Honors.

### AP Statistics - Grades 11-12 - Yearlong course

This is a year-long course covering the topics prescribed by the College Board/Advanced Placement Program. The course focuses on graphical and numerical methods of describing and analyzing data sets, probability, discrete and continuous random variables, linear regression and correlation, hypothesis testing and confidence intervals.

Students enrolled in this course are required to take the AP examination in May. There is a College Board fee assessed for this examination that will be added to the students' tuition. No final exam is administered in this course in the spring semester.

UC/CSU approved course

NCAA Core Course

Prerequisite: Pre-Calculus or Calculus with a grade of A. Pre-Calculus Honors, AP Calculus AB with a minimum grade of B, Introduction to College Statistics with a grade of A both semesters.

### DEPARTMENT CONTACT

**Department Chair of Mathematics**

Matt DePalma