# Mathematics

## Mathematics Faculty

### Mr. Nicholas Denari

- 4 Years at Cheverus
- BA, Boston College
- MEd, University of Notre Dame

### Mrs. Reggie Hackleman

- 2 Years at Cheverus
- BA, SUNY, Geneseo
- MEd, Boston University

### Mr. Daniel LaVallee

- 26 Years at Cheverus
- Cheverus High School, 1984
- BA, College of the Holy Cross
- MST, University of New Hampshire

## Our Mission

The Cheverus Mathematics Department believes math should be studied for its beauty as well as its utility. The mysteries of science are written in the language of mathematics and the department hopes to open their students’ eyes to the power of math, as well as develop a catalog of skills for daily living. Technology will be used where appropriate and the department requires the purchase of a TI-83/84 graphing calculator for its upper-level courses.

### Typical Mathematics Course Progressions

Algebra IA → Geometry A → Algebra IIA → Statistics

Algebra I → Geometry → Algebra II → Statistics, AP Statistics, or Pre-Calculus

Algebra I Honors → Geometry Honors → Algebra II Honors → AP Calculus AB, AP Statistics, or Pre-Calculus

Geometry Honors → Algebra II Honors → AP Calculus AB* → AP Calculus BC*

*Taking AP Statistics concurrently with AP Calculus AB or AP Calculus BC is strongly encouraged.

## Course Descriptions

Algebra I is the foundation course for all secondary mathematics. For most students, it is their first exposure to an axiomatic approach to learning mathematics. Symbolic manipulation will be important, but problem solving will be the main focus of our study. Topics covered in this course include linear equations, inequalities, polynomials, and quadratic equations.

**Term: Full Year (1 Credit)**

Designed for the student taking first-year algebra who wants to challenge him/herself, this course covers all the essentials of elementary algebra included in the regular program as well as challenges the student to grasp advanced concepts. The subject matter enhances the problem-solving capabilities of the student. Students selected for this course must be highly motivated and have a history of outstanding grades in mathematics.

**Term: Full Year (1 Credit)**

This algebra course is designed for the student who needs extra time to understand mathematical concepts, such as polynomials and linear/quadratic equations. The course is informal, inductive, and the pace slowed so that fewer topics are covered, but they are mastered in preparation for Geometry.

**Term: Full Year (1 Credit)**

This course is designed to provide the student with a review of skills from first-year algebra and then to study trigonometric, logarithmic, and exponential functions as well as other topics as time allows. The emphasis is on equation solving and its application to the solution of word problems.

**Term: Full Year (1 Credit)**

This course is designed for highly motivated math students who have excelled in Algebra I Honors and Geometry Honors. Algebra II and trigonometry topics are studied in great detail and depth. Conic sections and matrices, typically covered in Pre-Calculus classes, are examined. The next course in the sequence is AP Calculus AB.

Prerequisite: Geometry H and Algebra I H

**Term: Full Year (1 Credit)**

This course is designed to provide the student with a review of skills from first-year algebra and then to study rational, radical, and trigonometric functions, but with extra time allotted to ensure concepts are mastered. The course finishes with counting methods and probability in preparation for the next course in the sequence, which is Statistics.

**Term: Full Year (1 Credit)**

This is a college-level course for students who have completed Algebra II Honors. Some time is spent strengthening the student’s pre-calculus background, but the focus of the course is differential and integral calculus. Students will grapple with the idea of instantaneous change and the area under a curve, and the numerous applications of these concepts.

Prerequisites: Algebra II Honors

**Term: Full Year ( 1 Credit)**

This course is both a more rigorous examination and an extension of the topics studied in AP Calculus AB. The calculus of parametric and polar functions are introduced and series as approximations for functions are studied in detail.

Prerequisite: Calculus AB

**Term: Full Year (1 Credit)**

The focus of the course is on the four critical ideas of elementary statistics: planning a survey, probability, describing data, and making inferences about a population from a survey. This course is equivalent to a one semester college statistics class. Dual enrollment credit with St. Joseph’s College is available.

Prerequisites: Algebra II

**Term: Full Year (1 Credit)**

This course extends the topics learned in AP Calculus BC into multiple dimensions. The same concepts of limits, differentiation, and integration are studied, but are no longer restricted to the Cartesian plane. Partial derivatives, multiple integrals, and line integrals are among the new ideas introduced. This course is honors level.

**Term: Full Year (1 Credit)**

This course covers the essentials of plane geometry from a formal point of view. Topics covered in this course include parallelism, congruent triangles, parallelograms, similarity, right triangles, circles, areas, volumes, and coordinate geometry. An introduction to some concepts in elementary logic is included.

**Term: Full Year ( 1 Credit)**

This course covers the essential topics of geometry from an inductive point of view. Algebra skills are continuously reinforced while topics such as parallelism, congruent triangles, similarity, right triangles, area, and volume are examined.

**Term: Full Year (1 Credit)**

Geometry Honors presents a complete course in plane geometry for the well-prepared mathematics student. The course is theoretical and an introduction to formal, deductive proof begins very early. Algebraic skills will be constantly reviewed and strengthened through application to solving geometric problems. Supplemental material will be used to enrich the text. Freshmen selected for this course must be highly motivated, have a history of outstanding grades in mathematics, and score well on the Cheverus math assessment.

Prerequisite: Algebra I Honors

**Term: Full Year (1 Credit)**

The topics in this course include matrix operations, determinants, vector spaces, inner product spaces, eigenvalues, and linear transformations. This course is honors level.

Prerequisites: Department approval

**Term: Full Year (1 Credit)**

This course develops a foundation so students will be well-prepared for a college calculus course, such as in an economics or business program. Trigonometric, logarithmic, and exponential functions will be studied in detail. Limits will be introduced in the second semester.

Prerequisite: Algebra II

**Term: Full Year (1 Credit)**

This course introduces students to the fundamentals of statistical thought. Methods to describe data, both visually and numerically, are examined as well as topics from linear regression, survey and experimental design, probability, and basic hypothesis testing. Topics in financial literacy, such as interest, loans, budgeting, and credit cards, will be considered in the second semester.

**Term: Full Year (1 Credit)**