# Mathematics

As our students pursue their study of mathematics, they align themselves with the greatest minds of all past civilizations in the never-ending quest of understanding our physical world. To some, the motivation is practical - to solve some immediate problems; while to others, the attraction is pure curiosity and fascination. To all who have the perseverance to delve beneath the surface, mathematics offers rewarding insights and surprising interdependencies.

To learn mathematics is to partake in a subject that is both an art and a science, an enterprise both discovered and invented, a unique field that, according to Bertrand Russell, “possesses not only truth but supreme beauty.” Through applications of mathematical thinking, our students gain an understanding of the value and power of mathematics, a subject that will be an essential tool in their daily lives and can unlock the complexities of the universe. We, the teachers of mathematics at La Salle, aim to develop in our students a full appreciation of mathematics as a complete language, a unified process of thought, and an underlying foundation of our world. We prepare our students to engage independently in logical problem solving and multi-dimensional critical thinking. Our students learn to collaborate as they wrestle with challenging real-world problems. Ultimately, we endeavor to build our students’ mathematical skills base through the loop of discovery, instruction, practice, and application, with feedback points occurring all along the way. We urge our students to move beyond recitation and plugging in formulas and instead towards full comprehension, really thinking in math terms.

The mathematics curriculum at La Salle is broad enough to prepare all our college-bound students with a strong foundation in mathematics and is designed to open pathways for our ambitious students to achieve their mathematical goals for high school. The members of the Mathematics Department pride themselves on their accessibility and utilize their diverse teaching experiences to make connections with students, to predict problematic topics that cause fits for most teenage students, and to support their individual needs.

## Mathematics Faculty

## Mathematics Courses Offered

- Algebra I (Freshman Required)
- Algebra I Y (Freshman)
- Integrated Algebra I and Geometry
- Algebra I Honors (Freshman)
- Algebra II (Freshman / Sophomore)
- Algebra II Honors (Freshman/Sophomore)
- Geometry Y (Recommended Sophomores)
- Geometry (Junior)
- Geometry (Summer) - (Sophomore/Junior)
- Geometry / Precalculus Honors (Sophomore / Junior)
- Algebra II Y (Junior)
- Trigonometry & Statistics (Senior Elective)
- Algebra III / Trigonometry (Senior Elective)
- Precalculus (Junior / Senior Elective)
- Precalculus Honors
- Statistics (Senior Elective)
- Advanced Placement Statistics (Junior / Senior Elective)
- Calculus Honors (Junior/Senior Elective)
- Advanced Placement Calculus AB (Junior / Senior Elective)
- Advanced Placement Calculus BC (Senior Elective)
- Calculus 3 Honors (Senior Elective)

## Algebra I (Freshman Required)

This course provides a thorough foundation in elementary algebra by developing an understanding of the central ideas of variable and function, and the ability to use the language and tools of algebraic thinking to describe mathematical relations and analyze problems of many types. In addition, focus and emphasis are placed on enabling students to integrate the concepts of functions, equations, and graphs in order to apply the concepts to a variety of mathematical and real world situations, thereby further developing their critical thinking and problem solving abilities.

1 Credit/full year

## Algebra I Y (Freshman)

Algebra 1Y is a course provided for ninth grade students who, in the opinion of the math department, need a modified course in first-year algebra. This course gives special attention to reinforcement of basic arithmetic concepts while covering the foundations in elementary algebra.

1 Credit/full year

## Integrated Algebra I and Geometry

This is an accelerated course in elementary algebra 1 and geometric concepts intended for freshmen who have a strong foundation in some Algebra 1 topics but do not qualify to take Algebra 2. The usual topics of algebra 1 are treated with an emphasis on concepts and structure rather than on how to proceed. Students will end the year with a focus on geometric concepts that are generally not covered in an elementary curriculum that would have been covered in a full-year course at La Salle. Most important is that this course introduces the student to abstract mathematical thought and also to solving problems from algebra 1 concepts. By the end of the year, the students should reach a level of insight and mathematical instinct that will enable them to proceed comfortably through Algebra 2.

## Algebra I Honors (Freshman)

This is an accelerated course in elementary algebra intended for students who have a high degree of ability and interest. The usual topics of algebra are treated with an emphasis on concepts and structure rather than on how to proceed. Most important is that this course introduces the student to abstract mathematical thought and also to solving non-routine problems. A lot of time is spent on supplementary problems taken from various contests which enhance a student’s perception and problem solving skills. By the end of the year, the students should reach a level of insight and mathematical instinct that will enable them to proceed comfortably through subsequent upper level advanced courses.

1 Credit/full year

## Algebra II (Freshman / Sophomore)

This course continues the arithmetic generalizations begun in Algebra 1 and explores more deeply the operations that relate numbers to one another. The students are encouraged to think of algebra as a symbolic language and to use it as a modeling tool to explore other areas of mathematics. The students gain an understanding of number systems by examining and using the operations for relating numbers. The use of graphing calculators helps students to visualize algebraic concepts.

1 Credit/full year

## Algebra II Honors (Freshman/Sophomore)

This is an accelerated advanced algebra course open to superior students. It is demanding, treating the usual topics of Algebra 2 and applying these topics to problem solving. The content covered and skills acquired in this course enable the student to advance to Geometry/Precalculus Honors.

**Prerequisite: **Minimum B+ in Algebra 1 Honors and department approval.

## Geometry Y (Recommended Sophomores)

This is a slower-paced Geometry course offered to sophomores who have completed an Algebra I or I Y Course and are recommended for a four-year math program ending with Trigonometry. Sophomores selected for this course will take Algebra2/Trigonometry Part 1 as juniors, and Algebra 2/Trigonometry Part 2 as seniors. Students learn the tenets of Euclidean Geometry and apply these concepts to the solutions of real-world problems. Emphasis is placed on the development of reasoning skills and the use of logic. Effective study of topics is facilitated by the incorporation of a “master notebook,” which strengthens organization and basic study skills.

Prerequisite: Completion of Algebra 1 or Algebra 1Y only with teacher recommendation.

1 Credit/full year

## Geometry (Junior)

“How do I know what I know?” Geometry asks and answers this question more so than any other area of mathematical study. Within the framework of Euclidean geometry, students will develop the ability to deductively and inductively reason their way through a process by working through geometric proofs. Through construction and computer software, students ultimately will learn to recognize the workings of one geometric concept within another one, thus observing the symbiotic relationships among geometric tenets.

Prerequisite: Algebra 2

1 Credit/full year

## Geometry (Summer) - (Sophomore/Junior)

This course in Geometry is offered over the summer months to allow motivated students, who enter La Salle taking an Algebra 1 course, to advance through the curriculum with the goal of taking a Calculus course before graduation. The course will cover a full year of Geometry over a six-week period, meeting five days a week for 4 ½ hours a day. Due to this intense and rigorous schedule, there will be strong prerequisites for this offering. Students will not only need to meet the prerequisites, but must also need to be incredibly motivated and extremely committed. Missing one class will be problematic and missing two classes may necessitate withdrawing from the class. Upon completion of the course, students will earn a final grade that will appear on their La Salle transcript and be calculated in their G.P.A. for the subsequent fall semester.

**Prerequisite: **Minimum of an A in Algebra 1 or B+ in Algebra 1 Honors, or A in Algebra 2 or B+ in Algebra 2 Honors; and department approval

## Geometry / Precalculus Honors (Sophomore / Junior)

This course is a highly accelerated honors curriculum involving Geometry, Trigonometry and Precalculus courses. This course must be taught at an accelerated pace to cover the enormous volume of material in a full year. Sophomores and juniors and a few exceptional freshmen are asked to do a large amount of work and study on their own time to absorb the extent and depth of the material.

Prerequisite: Minimum B+ in Algebra 2 Honors and department approval.

1 Credit/full year

## Algebra II Y (Junior)

Algebra 2 is a continuation of the basic concepts and skills of Algebra 1. The pace of this course enables students with difficulties in math to gain a better understanding of algebraic topics. Various learning approaches and active involvement during each lesson will be critical to a student’s success. In this course, students will learn the practical applications of concepts and much of their learning will include technology, primarily with the graphing calculator. Throughout the course of the year, students will work with equations, inequalities, linear systems, matrices, factoring, radicals, polynomials, relations, functions, and various other topics.

**Prerequisite: **Geometry (Y)

## Trigonometry & Statistics (Senior Elective)

This full-year mathematics course is designed for students who do not anticipate taking Calculus at the collegiate level. The course will cover trigonometric functions and their applications for one semester, and introductory, non-Calculus based statistics for the other semester. Note: Students intending to major in Mathematics, Engineering, Science, or Business are strongly encouraged to take Precalculus so that they are prepared to take Calculus in college.

**Prerequisite:** Algebra 2, Geometry, and departmental approval

## Algebra III / Trigonometry (Senior Elective)

This course is a continuation of the core curriculum designed for those students who have difficulty in mathematics. This is a slower-paced Algebra II course, beginning with the development of both linear and quadratic functions. Sets of real and complex numbers will be developed as well as systems of equations. Polynomial, exponential and logarithmic functions are studied in depth. A full course in Trigonometry follows. The six functions of angle measurements within the triangle, graphing the trig functions and the properties of right and oblique triangles will be studied.

Prerequisite: Algebra 2 (Y)

1 Credit/full year

## Precalculus (Junior / Senior Elective)

This is a traditional fourth-year mathematics course for college-bound students. The course continues with the concept of functions, working extensively with trigonometric functions and their applications, along with exponential and logarithmic functions. The concepts and applications of series and sequences, matrices and probability are fully developed.

Prerequisite: C- or higher in Algebra 2, Geometry, and department approval.

1 Credit/full year

## Precalculus Honors

This is an accelerated mathematics course designed primarily for juniors who have completed the Integrated Algebra 1 and Geometry course followed by Algebra 2. The course continues with the concept of functions, working extensively with trigonometric functions and their applications. The concepts and applications of series and sequences, matrices and probability are fully developed. Students will be introduced to the beginning concepts of Calculus such as an introduction to limits.

**Prerequisite: **completed Algebra 1 and Geometry, A in Algebra 2 and departmental approval.

## Statistics (Senior Elective)

This is a traditional fourth-year mathematics course for college-bound students who may look to go into a business, mathematical or other applicable field where statistics would be a required course. The course load will consist of introductory, non-Calculus based statistics.

Note: Students intending to major in Mathematics, Engineering, Science, or Business are strongly encouraged to take Precalculus so that they are prepared to take Calculus in college.

Prerequisite: Algebra 2, Geometry, and departmental approval

.5 Credit/semester

## Advanced Placement Statistics (Junior / Senior Elective)

The AP Statistics course is designed to provide you with a learning experience equivalent to an introductory college, non-calculus-based course in statistics and will introduce you to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. The equivalent introductory college statistics class is typically required for majors in the fields of social sciences, health sciences, and business. This course is also an effective preparation for science, engineering, and mathematics majors whose course curriculum usually dictates upper-level calculus-based statistics. Technology will be utilized in the form of computers, computer software, and graphing calculators. Students will engage in constructing their own knowledge through the incorporation of lab activities, group problem-solving, student projects, and class presentations.

Note: As with all Advanced Placement courses at La Salle, students are expected to take the A.P. exam in May.

Prerequisite: Minimum A- in Algebra 2 Honors, minimum A in Algebra 2, and department approval.

1 Credit/full year

## Calculus Honors (Junior/Senior Elective)

This course reviews analytic topics and proceeds to the study of differential calculus with applications to curve sketching, optimization, and related rates. Integrals are studied as they relate to derivatives with applications to area and volume. The calculus of exponential, logarithmic, and trigonometric functions is 26 examined. Problem solving skills are developed, especially in the life sciences, physics, economics and finance.

**Prerequisite:** B+ in Precalculus Honors and department approval. (For 2018-19, department approval.)

## Advanced Placement Calculus AB (Junior / Senior Elective)

This course is a preparation for the advanced placement Calculus AB examination. The syllabus is that prescribed by the College Board in their Calculus AB program. The ideas of limits, derivatives, and integrals are rigorously defined with appropriate applications and techniques.

Note: As with all Advanced Placement courses at La Salle, students are expected to take the A.P. exam in May.

Prerequisite: Minimum B+ in Geometry/Precalculus Honors and department approval.

1 Credit/full year

## Advanced Placement Calculus BC (Senior Elective)

This course is a more intensive examination of the basic concepts of Calculus for students who have already had Calculus AB or Introductory Calculus. The syllabus prescribed by the College Board in their BC program is covered in depth. The ideas of limits, derivatives and integrals are rigorously defined, exploring applications of each, using various teaching techniques. Besides a deeper understanding of basic Calculus through challenging applications, a wide scope of additional topics are examined, especially infinite series and differential equations.

Note: As with all Advanced Placement courses at La Salle, students are expected to take the A.P. exam in May.

Prerequisite: Advanced Placement Calculus AB and department approval.

1 Credit/full year

## Calculus 3 Honors (Senior Elective)

This course is a third year of calculus designed for students who have successfully completed Advanced Placement Calculus BC. While there is no opportunity for college credit for this course, these students will not have any gaps in their learning of various topics in calculus and will be fully prepared for the third level of calculus in college. The syllabus for this course has been developed based on the curricula of many prestigious universities, under the assumption that mathematics, engineering or science is a student’s intended major. The ideas of vectors, vector functions, vectors in calculus, partial derivatives, multiple integrals, and second-order differential equations are rigorously defined, exploring applications of each, using various teaching techniques.

**Prerequisite:** Advanced Placement Calculus BC and department approval.