# Upper School Mathematics

Freshmen will typically be placed in Algebra I, Honors Algebra I, Geometry, or Honors Geometry. The diagram to the right illustrates typical paths followed by Holy Child students, although exceptions are made and based on individual needs. You can find full course descriptions below for more information on each class.

**Full Year | 1 Mathematics Credit **

*Prerequisite: placement test and/or department recommendation.*

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This course forms an introduction to Algebra, enabling students to receive a strong grounding in the fundamentals of high school mathematics. The program covers topics including arithmetic operations on integers and on rational numbers, the properties of the real number system, linear equations and inequalities, absolute value equations and inequalities, graphing in the coordinate plane, coordinate geometry, and mathematical functions. The course broadens logic skills, strengthens mathematics computation, and enhances concept formation and mastery. An emphasis is placed on verbal and written communication of math concepts.

**Full Year | 1 Mathematics Credit **

*Prerequisite: placement test and/or department recommendation.*

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This course reviews those topics of Algebra commonly covered in Pre-Algebra and middle school Algebra 1 courses, and extends into other fundamental areas of algebra that are required as a basis for further study. The program begins with a review of content areas from Concepts of Algebra 1. New subject matter includes operations on polynomials, factoring, quadratic equations, exponents and exponential functions, radicals and connections to geometry, rational equations and functions, probability, counting theory, and statistics.

**Full Year | 1 Mathematics Credit **

*Prerequisite: placement test and/or department recommendation.*

This course is designed to provide students with a greater depth of understanding of algebraic concepts, and proceeds at an accelerated pace. The aim is to help students develop their critical thinking and problem-solving ability. Modeling and problem-solving are at the heart of the curriculum. Mathematical modeling consists of formulating a problem in mathematical terms, using mathematical strategies to reach a solution and interpreting the solution in the context of the original problem. Students are encouraged to represent problems algebraically, graphically, and in tabular form, thus promoting the creation of connections between different mathematical concepts. Topics covered in this course include arithmetic operations on integers and on rational numbers, the properties of the real number system, linear equations and inequalities, systems of linear equations, absolute value equations and inequalities, graphing in the coordinate plane, mathematical functions, operations on polynomials, factoring, quadratic equations, exponents and exponential functions, radicals and connections to geometry, probability, counting theory, and statistics.

**Full Year | 1 Mathematics Credit **

*Prerequisite: Algebra I and department recommendation.*

This is a course on Euclidian Geometry. Topics include theorems and proofs on congruency and similarity of polygons, parallelism, circles, areas and volumes, coordinate geometry and trigonometry. Various software programs, including Geogebra, are integrated throughout the course to create dynamic constructions.

**Full Year | 1 Mathematics Credit**

*Prerequisite: Algebra I and department recommendation.*

With a renewed emphasis on the aesthetic elements of design in many products, many new applications of Geometry have arisen in the last decade. This is a rigorous real-life based study of Euclidian and Coordinate Geometry, integrating the skills learned in Honors Algebra 1. Topics include logical reasoning through deductive and inductive proofs, parallelism, similarity, congruence, circle theorems, area, volume, transformations in both two and three dimensions, constructions and trigonometry. Geogebra and other internet resources are integrated throughout the course to create dynamic constructions and extend learning. A greater knowledge of the proofs of classical theorems is the primary (but not the only) differentiation between this course and Geometry.

**Full Year | 1 Mathematics Credit**

*Prerequisite: Geometry. *

This course builds upon the content of Algebra I and Geometry. Topics include the study of linear, quadratic, rational, polynomial, logarithmic and exponential functions and their graphs. Properties of the complex numbers, circular trigonometry and an introduction to sequences and series are also studied in this course.

**Full Year | 1 Mathematics Credit**

*Prerequisite: B average in previous mathematics courses and department approval.*

As an extension of Honors Algebra I and Honors Geometry, this course includes an in-depth study of polynomial theory, including both real and complex solutions, and rational, logarithmic, exponential and trigonometric functions and their graphs, as well as an introduction to sequences and series. The study of systems of equations and inequalities with two or three variables, matrices and determinants is included.

**Full Year | 1 Mathematics Credit **

*Prerequisite: Algebra II/Trigonometry.*

Course topics include linear, polynomial, exponential, logarithmic and trigonometric functions. A study of sequences and series, introductory probability and statistics is included in this course. Students in Pre-Calculus are asked to complete a project each year based around one topic in math, and to build their own resources portfolio to assist them in further study.

**Full Year | 1 Mathematics Credit**

*Prerequisite: B average in Honors Algebra II/Trigonometry and department approval. ** *

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This course is designed to provide the student with the necessary skills and concepts to study calculus the following year. Course topics include polynomial, linear, exponential, logarithmic, and trigonometric functions. Sequences and series, introductory probability and statistics, and an introduction to Calculus are included in this course. In order to advance to AP Calculus, students completing this course must successfully complete additional summer work, earn a high grade in Precalculus and have departmental approval.

**Full Year | 1 Mathematics Credit **

*Prerequisite: Precalculus (Regular or Honors) ** *

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This course is an introduction to the applications of calculus in business and in the social sciences. The course presents the main ideas of Calculus in a simple manner accompanied with several concrete applications in order to improve students’ understanding. It covers topics such as continuity, limits, differentiation, and integration. Proficiency in algebraic manipulations and solid understanding of Precalculus concepts are essential.

**Full Year | 1 Mathematics Credit **

*Prerequisite: Department approval. ** *

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This course is designed to prepare the student for the AB Advanced Placement Calculus exam, which is taken in May. Topics contained in the College Board’s Advanced Placement syllabus are studied in this course. These topics include differential and integral calculus and their applications. All students are required to take the AP Exam at the end of this course.

**Full Year | 1 Mathematics Credit **

*Prerequisite: Department approval.*

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This course explores limits, derivatives, and integrals as well as the Fundamental Theorem of Calculus, and also adds the big idea of series. The concept of limits is foundational and the understanding of this fundamental tool leads to the development of more advanced tools and concepts that prepare students to grasp the Fundamental Theorem of Calculus, a central idea of AP Calculus.

**Full Year | 1 Mathematics Credit**

*Prerequisite: current study (either Algebra II/Trigonometry or Precalculus) at the Honors level, and department approval.*

This course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Topics contained in the College Board’s Advanced Placement syllabus are studied in this course. These topics include exploratory data analysis and descriptive statistics, probability for anticipating patterns in the distribution of data, designing experiments, and confirming models through statistical inferences. In addition, the course makes extensive use of real-world data. This course is designed to prepare students for the AP Statistics exam, in May, which all students are required to take.