  page tools # Mathematics

## The goal of the Mathematics Department is to transmit to the student an appreciation for the beauty and structure of mathematics, the ability to visualize and abstract, reason deductively, organize data, draw conclusions, and acquire the confidence to solve problems.

Aided by the use of technology, students research, explore, and analyze real world topics which they communicate to others through writing and presentations. Three years of high school Mathematics is required to graduate; however, most students take 4 years or more of high school level Mathematics.

#### Math 6

This enriched math curriculum is designed to build thinking and problem solving skills by utilizing estimation techniques and mental math strategies. Students are encouraged to explore in depth and to master the fundamental operations with whole numbers, decimals and fractions. Topics include ratios, proportions, percents, metric conversion, graphing, statistics, and geometry. Algebraic problems are introduced throughout the year to develop abstract reasoning skills. Students will use their laptop computers to research topics on the Internet, to collect and analyze data, and to discover geometric concepts through inductive reasoning.

Available to grade 6; Full Year

#### Math 7

Students will review and extend all computational skills while working with whole numbers, fractions, decimals, and integers. There is a continuation of the study of percent, ratio, and proportion. Other topics include geometry, areas and volume, an introduction to algebra, probability, statistics, and graphing. Emphasis is placed on reasoning and non-routine problem solving. Students will use their laptop computers for Internet research, creating charts, and investigating geometric concepts.

Available to grade 7; Full Year

#### Math 7 (Accelerated)

This course integrates the seventh and eighth grade curriculum. Students review the basic operations of whole numbers, decimals and fractions, use variables, and solve equations and inequalities. Additional topics include estimation, integers, the coordinate plane, percent, geometry, probability, and statistics. Emphasis is placed on reasoning and problem solving techniques. Students will use their laptop computers for writing in math, open-ended explorations in geometry, and applications in statistics.

Available to grade 7; Full Year

This course in algebra is for eighth grade students. Topics include properties of real numbers, solving and graphing linear equations and inequalities, exponents, polynomials, quadratic functions, radicals, probability, and exploring data and statistics. Stress is placed on problem solving techniques.

Available to grade 8; Full Year

This course in algebra is for advanced eighth grade students. Topics include properties of real numbers, solving and graphing linear equations and inequalities, systems of linear equations and inequalities, exponents, polynomials, quadratic functions, and exploring data and statistics. Stress is placed on problem solving techniques. Students will use their laptop computers for in-depth mathematical investigations.

Available to grade 8; Full Year

#### Algebra 1

This course in algebra is for incoming ninth grade students. Topics include properties of real numbers, solving and graphing linear equations and inequalities, exponents, polynomials, quadratic functions, radicals, and exploring data. Stress is placed on problem solving techniques. Students will use their laptop computers for mathematical investigations.

Available to grade 9; Full Year

#### Algebra 9

This course in algebra focuses on fundamental algebra skills. Stress is placed on solving equations and inequalities, polynomials, graphing on the coordinate plane, quadratic functions, and problem solving techniques. Students will use their laptop computers to explore the relationships between algebraic and graphical solutions.

Available to grade 9; Full Year

#### Geometry 9

This course in Euclidean Geometry provides an in-depth treatment of geometry as a deductive system using formal geometric proof. Topics of study include logic, properties of polygons, circles, solid geometry, trigonometry, transformations, coordinate geometry, and probability. Laptop computers will be used to prove geometric theorems using inductive reasoning and to explore functions, polygons, and their transformations.

Available to grade 9; Full Year

#### Geometry

This course in Euclidean Geometry provides an in-depth treatment of geometry as a deductive system using formal geometric proof. Topics of study include logic, properties of polygons, circles, solid geometry, trigonometry, transformations, coordinate geometry, and probability. Laptop computers will be used to prove geometric theorems using inductive reasoning and to explore functions, polygons, and their transformations.

Available to grade 10; Full Year

#### Geometry 10

This course concentrates on concepts and application of geometry. Topics of study include an introduction to the process of geometric proof, coordinate geometry, an introduction to trigonometry, algebra, properties of polygons, and geometry of the circle. Laptop computers will be used to investigate transformations, to graph functions and to discover geometric relationships of polygons.

Available to grade 10; Full Year

#### Geometry Honors

This is the most challenging of the offerings in geometry. Emphasis is placed on the student’s ability to apply theoretical concepts and critical thinking skills to analyze and solve problems. Enriched and in-depth study is provided in the topics of logic, geometric proofs, geometry of the circle, mathematical systems, coordinate geometry, probability, transformations, and an introduction to trigonometric functions. Laptops are used throughout the curriculum to explore and discover geometric concepts. Independent projects are required.

Available to grade 9; Full Year

#### Algebra 2

This tenth grade mathematics course reinforces the fundamental concepts of algebra, and continues with an in-depth study of advanced algebra topics including polynomial, exponential, rational and logarithmic functions, complex numbers and statistics. Laptop computers and calculators are used for modeling and non-routine problem solving activities.

Available to grade 10; Full Year

#### Algebra 2H

This challenging tenth grade mathematics course reinforces the fundamentals of algebra, and continues with an in-depth study of advanced algebra topics including polynomial, exponential, rational and logarithmic functions, complex numbers, and statistics. Laptop computers and calculators are used for modeling and non-routine problem solving activities. Internet research projects are integrated throughout the course to enhance the curriculum.

Available to grade 10; Full Year

#### Algebra 2/Trigonometry

Topics covered in this course include the study of polynomial and rational functions, complex numbers, exponential and logarithmic equations. Students investigate trigonometric ratios and their applications, graph functions, verify identities and solve trigonometric equations. The graphing calculator is used to graph algebraic and trigonometric functions, and for non-routine problem solving.

Available to grade 11; Full Year

#### Algebra 2/Trigonometry 11

Algebraic concepts and problem solving are strengthened and expanded during the first semester. Topics include rational expressions, exponents and radicals, relations and functions, the real and imaginary number systems. In the second semester trigonometric functions, their graphs and applications, trig equation solving and trig identities are explored. In June there is a comprehensive examination on the second semester’s material.

Available to grade 11; Full Year

#### Precalculus/Trigonometry

This course includes the study of advanced algebra, matrices, polynomial, rational, exponential, and logarithimic functions and their graphs and applications. Topics in trigonometry are explored, including periodic functions and their graphs, solutions of oblique triangles, identities, equations, and modeling. The TI-Nspire graphing calculator is used throughout the course.

Available to grade 11; Full Year

#### Precalculus/Trigonometry Honors

In the Honors course, students investigate topics in greater depth with more emphasis on higher level problem solving. This course is open to students who have been accelerated in mathematics. Students study advanced algebra, matrices, polynomial, rational, exponential, and logarithmic functions and their applications. Topics in trigonometry are explored, including periodic functions and their graphs, solutions of oblique triangles with real life applications, trigonometric identities and equations. The TI-Nspire graphing calculator is used throughout the course.

Available to grade 11; Full Year

#### Precalculus

This course presents advanced algebraic and geometric techniques of mathematical analysis. Topics include linear, quadratic, polynomial, and rational functions and their transformations. Matrices, sequences and series, limits, and derivatives are explored. The graphing calculator is used to solve application problems.

Available to grade 12; Full Year

#### Math 12

This is a college preparatory precalculus course. Topics include linear, quadratic, polynomial and rational functions, their graphs and transformations, matrices, logarithms, sequence and series, statistics and probability. The TI-NSpire graphing calculator and real world applications are used throughout the course.

Available to grade 12; Full Year

#### Calculus Honors

This is a full year course in the fundamental techniques of calculus. Topics include limits and their properties, differentiation, integration, differential equations, and trigonometric functions. Applications are drawn from business, economics, physics, environmental studies, and the social and biological sciences. The graphing calculator is used as a tool for problem solving, exploration, and discovery.

Available to grade 12; Full Year

This is a college level course in calculus. The successful completion of the course is equivalent to one semester of college calculus. Topics include limits, differentiation, integration, logarithmic and exponential functions, area between two curves, volume of solids of revolution, and slope fields. Students are required to take the AP Examination at the completion of the course.

Available to grade 12; Full Year

In addition to being enrolled in the Calculus AB course, qualified students will have the option of studying the additional BC topics independently. The successful completion of this course is equivalent to two semesters of college calculus. Topics include those taught in AB, parametric, polar, and vector functions, and the derivative and integral applications of them, integration by parts and simple partial fractions, solving logistic differential equations and using them in modeling, polynomial approximations and series.

Available to grade 12; Full Year

#### Calculus & Statistics

The first semester presents an overview of the fundamental techniques of calculus. Students are introduced to limits and their properties, differentiation, and integration. Applications are drawn from business and economics, environmental studies, and the social and biological sciences. The graphing calculator is used as a tool for problem solving, exploration, and discovery.

The second semester introduces students to the concepts, techniques, and applications of statistics. Topics include organization and interpretation of data, measures of central tendency and dispersion, hypothesis testing, and analysis of variance. Realistic applications from sports, physical science, health, medicine, and weather demonstrate the relevance of statistics to the real world. The TI-Nspire graphing calculator is used extensively for all aspects of the course. Microsoft Excel is used for graphing data.

Available to grade 12; Full Year

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THE URSULINE SCHOOL   |   1354 NORTH AVENUE   |   NEW ROCHELLE, NY 10804-2192 © 2013
A Catholic, college preparatory school for girls, grades 6 through 12 