# Mathematics

## Quick Facts

## Overview

The Our Lady of Mercy Mathematics department considers the traditional mathematics curriculum most beneficial for students on their journey to college. We offer the traditional Algebra I, Geometry, Algebra II, PreCalculus/Trigonometry, and Calculus tracts. The honors classes are by teacher recommendation and include Honors Geometry and Honors Algebra II. Advanced Placement classes are available to students who have excelled in foundations classes and who have teacher recommendations.

## Philosophy

## Philosophy

The Our Lady of Mercy Mathematics department provides a college preparatory program of study, which fosters the development of problem solving skills, critical thinking skills, and logical reasoning accomplished through a careful combination of traditional Catholic educational philosophies and the instructional practices and technology of the present time. The diversity and depth of instruction given expose both the practicality and the beauty of mathematics and encourage continued independent study and exploration.

Standards

1. The mathematics curriculum should include the refinement and extension of methods of mathematical problem solving.

2. The mathematics curriculum should continue to develop the language and symbolism needed to communicate mathematical ideas.

3. The mathematics curriculum should reinforce and extend logical reasoning skills.

4. The mathematics curriculum should include investigations of the connections and interplay among various mathematical topics and their application.

5. The mathematics curriculum should include the study of mathematical structure so that students appreciate the seemingly different mathematical systems may be essentially the same.

## Goals

- Ensure that students have the prerequisite skills necessary for successful completion of future college-level mathematics courses they may wish to pursue.

2. Expose students to a rich variety of problem-solving techniques and strategies including the appropriate use of technology.

3. Teach students to effectively communicate mathematical ideas and concepts in a clear and organized fashion.

4. Help students discover their own best learning styles as applicable to mathematics and assist teachers to incorporate instructional techniques that facilitate these learning styles in their classrooms.

5. Use technology to enhance students' understanding of mathematical concepts.

6. Illustrate how mathematics can be used in everyday life and how it relates to other disciplines.

7. Develop a sense of interest and curiosity that will encourage students to become life long learners of mathematics.

## Course Offerings

- Algebra I
- Honors Algebra I
- Geometry
- Honors Geometry
- Algebra II
- Honors Algebra II
- Algebra III
- Pre-Calculus
- Honors Pre-Calculus
- Calculus
- AP Calculus AB
- AP Calculus BC
- AP Statistics
- Math Electives

## Algebra I

*Required of 9th grade students*

This course is designed for students who need reinforcement of analytical and Pre-algebra skills and introduces students to the Algebra skills necessary for future math courses. Students learn to add, subtract, multiply and divide polynomials and radical expressions. They apply these skills to solve linear equations, systems of linear equations and quadratic equations. Additional topics include graphing in the coordinate plane and solving word problems.

## Honors Algebra I

*Required of 9th grade students with Department Approval*

This advanced course provides the foundation of Algebra skills necessary for future math courses. Topics covered include algebraic concepts: emphasizes the theory and application of variables, graphing, linear equations and inequalities, radical expressions, and quadratics.

## Geometry

*Required of 9th-10th grade students with Department Approval*

Goals of the Geometry course include improvement in logical thinking skills and a deeper appreciation of mathematical structure. Algebraic problems and Geometric proofs are used in the study of congruent triangles, similar figures, parallel lines, right triangles, circles, area, volume, polygons, and the coordinate plane.

Prerequisite - Algebra I

## Honors Geometry

*Required of 9th-10th grade students with Department Approval*

Honors Geometry is a course for students who have a deeper sense of logical development. The course uses deductive proofs and Algebraic problems to study the coordinate plane, congruent triangles, similar figures, parallel lines, right triangles, circles, area, volume, and polygons. The problems and proofs are more difficult than those in MATH 27.0630713.

Prerequisite – Algebra I/Honors Algebra I

## Algebra II

Required of 10th -11th grade students with Department Approval

This course ensures the students an understanding of absolute value equations, radical equations, linear equations, quadratic equations, the coordinate plane, systems of equations including calculator driven matrices, complex numbers, functions, and many word problems of different types.

Prerequisite – Geometry/Honors Geometry

## Honors Algebra II

*Required of 10th-11th grade students with Department Approval*

This course ensures the students a deeper understanding of absolute values, radicals, linear equations, quadratic equations, functions, the coordinate plane, right triangle trigonometry, systems of equations including calculator driven matrices, complex numbers, and a variety of word problems, both linear and quadratic. The problems are more difficult than those in MATH 27.0640721.

Prerequisite – Geometry/Honors Geometry

## Algebra III

*Offered to 11th - 12th grade students with Department Approval*

This course consists of a review of selected topics from Algebra and Geometry, preparation for the SAT, and brief studies of topics that include linear programming, matrices, logarithms, functions, and right triangle trigonometry.

Prerequisite – Algebra II/Honors Algebra II

## Pre-Calculus

*Offered to 10th-12th grade students with Department Approval*

Pre-Calculus is designed to review the higher-level math skills in preparation for Calculus at OLM and in College. The topics to develop these skills include logarithmic and exponential functions, quadratic equations, matrices, and an in-depth study of Trigonometry. Some new topics include the study of higher-level polynomial functions, vectors, polar coordinates, and conic sections.

Prerequisite – Algebra II/Honors Algebra II

## Honors Pre-Calculus

*Offered to 10th-12th grade students with Department Approval*

Honors Pre-Calculus is designed to review the higher-level math skills in preparation for AP Calculus AB and AP Calculus BC at OLM and in order to receive college credit for Calculus. The topics to develop these skills include higher-level polynomial functions, logarithmic and exponential functions, quadratic equations, matrices, sequences and series, conic sections, and an in-depth study of Trigonometry including De Moivre’s Theorem, polar coordinates, and word problems involving right triangles and non-right triangles (using the law of sines and cosines). Prerequisite – Algebra II/Honors Algebra II

## Calculus

*Offered to 11th – 12th grade students with Department Approval*

Calculus is designed to bring the topics previously learned in mathematics to life. The topics include a study of functions, limits, differentials with application in maxima and minima problems, area and volume, and numerical methods of equation solving.

Prerequisite – Pre-Calculus/Honors Pre-Calculus

## AP Calculus AB

*Offered to 12th grade students with Department Approval*

AP Calculus is an advanced study of functions, limits and differentials with application in maxima and minima problems, area and volume, differential equations, and numerical methods of equation solving. The student will be prepared for the AP Calculus AB exam which is taken with the possibility of earning college credit. All students must take the Advanced Placement test in May. Prerequisite-Honors Pre-Calculus

## AP Calculus BC

*Offered to 12th grade students with Department Approval*

AP Calculus BC includes all of the elements covered in AP Calculus AB as limits, differentiation and applications, graph theory, integration and applications and slope fields. In addition to AB concepts, BC concepts covered are integration and applications, differential equations, sequences and series and parametric functions.

Prerequisite – Honors Pre-Calculus

## AP Statistics

*Offered to 10th-12th grade students with Department Approval*

AP Statistics is designed to draw connections between all aspects of statistical process, including design, analysis, and conclusions; to teach students how to communicate methods, results, and interpretations using the vocabulary of statistics; to teach students to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploring and analyzing data, assessing models, and performing simulations. All students must take the Advanced Placement test in May.

Prerequisite – Algebra II/Honors Algebra II.

## Math Electives

*Offered to selected 9th grade students in conjunction with Algebra I*

This course introduces algebraic and geometric concepts emphasizing a hands-on approach of modeling concepts of addition, subtraction, multiplication and division, evaluating expressions, solving equations and inequalities, and exploring characteristics of geometric figures. Math Strategies is taught concurrently with Algebra I.