# Mathematics

**Graduation Requirement:** Three Credits

The Mathematics Department at Mounds Park Academy strives to help each student discover, appreciate, and enjoy mathematics through active learning at all levels. We believe in giving every student a chance to succeed in the most challenging yet appropriate math classes. By focusing on in-depth content and problem-solving at all levels—combined with creating a climate that celebrates learning—we have a school of successful students who commit to math throughout their high school careers while being prepared for college and lives beyond the classroom.

Typical Mounds Park Academy Sequence of Math Classes

Grade | Regular | Advanced | Honors |

9 | Geometry | Adv. Alg2/Trig | Hon. Alg.2/3 |

10 | Algebra 2/Trig | Adv. Alg3/Adv. Trig | Hon. Pre-Calculus |

11 | F.P.T. | Hon. Pre-Calculus | AP Calculus AB * |

12 | Hon. Pre-Calculus and/or Statistics/Discrete |
AP Calculus AB * and/or AP Statistics * |
AP Calculus BC * and/or AP Statistics * |

* All students enrolled in the AP Statistics or AP Calculus courses are strongly encouraged to take the College Board’s AP exam.

Courses Offered

Course offerings are contingent on MPA policies regarding student enrollment numbers for each class.**Grades:** 9-11

**Prerequisites:** Successful completion of Advanced Geometry

**Credit:** 1.0

This is the year to become fluent in mathematics. Correct vocabulary, writing clear solutions, using the graphing calculator to its full potential, and viewing problems both algebraically and graphically are emphasized. Students improve their mathematical proficiency by investigating properties and transformations of various functions, including linear, quadratic, absolute value, exponential, rational, and trigonometric functions, with an introduction to logarithms. Mathematical modeling of real-world situations is done as much as possible, and writing thorough, well-thought-out solutions is required.

**Grade:** 10

**Prerequisites:** Successful completion of Advanced Algebra 2/Trigonometry

**Credit:** 1.0

This is a class where students can begin to appreciate the beauty of mathematics. Students have already mastered the basic algebraic concepts - in this class they are encouraged to use these skills to make connections between topics and to analyze functions from a variety of perspectives. The focus is on using mathematics to model exponential, logarithmic and periodic functions including complex trigonometric equations. In addition, this course includes an intense study of rational functions from a graphical and algebraic analysis of critical values as they pertain to asymptotes and symmetry. This course is an advanced level course and prepares students to take Honors Pre-Calculus.

**Grade: **9

**Prerequisites:** None

**Credit:** 1.0

This course is designed for students who struggled with Algebra 1 in 8th grade. The topics are the same, but they are tailored to meet each student’s individual needs. After completing this class, students will be prepared to continue with the regular math course sequence.

**Grade:** 10

**Prerequisites:** Successful completion of Geometry

**Credit:** 1.0

The central focus of this course is mathematical functions. Students become fluent in the use of graphing calculators and learn how to investigate a function both graphically and algebraically. Writing clear solutions and using correct mathematical vocabulary are emphasized. Students learn the skills required to investigate properties and transformations of various functions, including linear, quadratic, absolute value, with an introduction to exponential, rational, and trigonometric functions. Mathematical modeling of real-world situations is done as much as possible.

**Grades:** 11-12

**Prerequisites:** Successful completion of Honors Pre-Calculus

**Credit:** 1.0

In this course, students learn how to use calculus to describe movement, area, volume and density. Students are expected to use technology to help them solve problems, to be able to communicate mathematics clearly and to model physical situations using functions, derivatives and integrals. To qualify for AP Calculus, a student must display superior algebra skills and well-developed geometric thinking, as well as excellent recall of previously learned math not directly covered in this course. Students must be able to understand the mathematical processes beyond rote memorization of the material. An AP Calculus student is pro-active with regard to homework, displays maturity in small group situations and takes ownership of the entire learning process. Preparation for the AP Calculus AB Exam will involve enrichment beyond the work involving the daily lessons.

**Grade:** 12

**Prerequisites:** Successful completion of AP Calculus AB

**Credit:** 1.0

This course is a continuation of calculus topics from Advanced Placement Calculus. Students will use advanced methods of integration to solve problems based on science and engineering. Students are expected to use technology to help them solve problems, to be able to communicate mathematics clearly and to model physical situations with functions and integrals. To qualify for Advanced Placement Calculus, a student must display superior algebra skills and well-developed geometric thinking, as well as excellent recall of previously learned math not directly covered in this course. Students must be able to understand the mathematical processes beyond rote memorization of the material. An Advanced Placement Calculus student is pro-active with regard to homework, displays maturity in small group situations and takes ownership of the entire learning process. Preparation for the AP Calculus BC Exam will involve enrichment beyond the work involving the daily lessons.

**Grade:** 12

**Prerequisites:** Completion of Honors Precalculus or Functions/Probability/Trigonometry and consent of instructor.

**Credit:** 1.0

Our world is increasingly running on data. AP Statistics will help students to interpret and navigate that data. This course is a college level statistics course. AP Statistics focuses on the introduction to data analysis. By exploring current data, students learn graphing methods, calculate measures of central tendencies, and analyze statistical hypotheses by hypothesis testing. To evaluate trends students will construct scatter plots and determine regression lines and correlation coefficients. This course emphasizes reading, communication, and writing abilities over computation skills. Each student will be involved in many statistical projects.

**Grade:** 12

**Prerequisites:** Successful completion of Algebra 2.

**Credit:** .5

Problems that depend upon mathematics for their solution arise in many fields, and discrete math tackles some of those fields. Interested in different fair ways to run an election? Ever wonder how airlines run their schedules, or how a city plans subway routes? This course is designed to introduce students to various applied math topics including election theory, weighted voting, graph theory, apportionment, networks, scheduling, and fair division. All units will be taught from the perspective of discovering new ideas and applying them to current issues.

**Grade:** 11

**Prerequisites:** Successful completion of Algebra 2

**Credit:** 1.0

The study of Algebra teaches students to think logically and sequentially. This course is the capstone of a student’s study of Algebra. Students will build their problem-solving skills as they connect prior knowledge to new ideas and contexts. The course covers probability, trigonometry and further study of functions. Some of the topics covered in this course are logarithms, matrices, trigonometric functions, polynomial functions, conic sections, arithmetic and geometric series and analytical trigonometry. Additionally, students will explore topics related to probability and statistics including combinations and permutations, expected value, conditional probabilities and The Fundamental Principle of Counting.

**Grades: **9-10

**Prerequisites:** Successful completion of Algebra 1.

**Credit:** 1.0

How are good arguments developed? How do you flow from a hypothesis to a conclusion? What is the relationship between points and distance? This course uses deductive reasoning to uncover the beauty of geometric shapes and how they are related to standard Euclidean Geometry. Concepts are presented with and without proof and include points, lines, rays, angles, and triangles; congruent and similar triangles; perpendicular and parallel lines; quadrilaterals; right triangles, including right triangle trigonometry; area and volume; circles; regular polygons; geometric solids; transformations; and tessellations. Maintaining and building algebra skills is emphasized throughout the course.

**Grade:** 9

**Prerequisites:** Successful completion of Advanced Geometry & teacher permission

**Credit:** 1.0

This is a very fast-paced class that will combine the topics from Advanced Algebra 2/Trigonometry and Advanced Algebra 3/Advanced Trigonometry into a one-year class in order to prepare students for Honors Pre-Calculus.

**Grades:** 10-12

**Prerequisites:** Successful completion of Honors Algebra 2/3 or Advanced Algebra 3/Advanced Trigonometry

**Credit:** 1.0

This course emphasizes experimentation and mathematical problem solving. There will be a focus on logic, including trigonometric proof using identities. Students are required to understand how to find area under a curve and use summation notation to express this area. Students will also develop the notion of limit and apply this to rational functions, infinite geometric series and rates of change. This course includes vectors, parametric equations, Newton’s method for finding roots of polynomials, complex numbers, Decartes’ Rule of Signs and polar coordinates.

**Grade: **12

**Prerequisites****:** Successful completion of Algebra 2

**Credit:** .5

The main purpose of this course is an introduction to mathematical modeling through graphical, numerical, symbolic, and verbal techniques. We will focus on data from and explore social justice issues such as the Wealth Gap, Achievement Gap, Climate Change and others. We will use elementary functions (polynomial, exponential, logarithmic, etc.) to build models and address questions with the goal of developing scientific reasoning and problem-solving skills. Students will also use technology in a range of ways to effectively communicate their hypotheses and conclusions.

**Grade:** 12

**Prerequisites:** Successful completion of Algebra 2

**Credit:** .5

The study of statistics brings us fact-to-face with the contemporary world. Statistics is used in business, social sciences, technology, and the natural sciences. Students explore problems that may be part of their everyday life and learn to apply the tools and vocabulary of data collection and statistics. This course is designed to introduce students to both descriptive and inferential statistics. They will learn measures of central tendencies and spread, confidence intervals, and hypothesis testing. Students will also learn how to use the many statistical functions on the graphing calculator and how to analyze the results.