# Courses

## Mathematics

Throughout our curriculum, emphasis is placed on each student DOING mathematics. We believe it is essential students actively write and speak their mathematics in order to learn to develop sound mathematical reasoning and communication skills. Graphing calculators and computers are integrated into our teaching as they have become useful in exploring and illustrating mathematical content. TI-83 or TI-84 calculators are required for most classes.

Completion of Algebra I, Geometry, and Algebra II, usually taken in that order, satisfies the diploma requirement. However, study of the subject through this level represents a minimum and not a goal for anyone interested in continued work in the sciences, mathematics, social sciences, and many other fields. Many students are able to complete a year of calculus and/or statistics. Each year, a few students study advanced topics beyond calculus.

The mathematics department adheres to the following policies for placement of students in courses and in regards to summer or alternative courses.

1. Every new student completes a placement test. A student is placed in a course based on the score on this test, their SSAT score, the student’s prior course work and the teacher recommendation. There is an additional honors placement test for those students deemed qualified to take an honors level course in Algebra II or Precalculus.

2. Placement for returning students is based on their performance in their current courses and the recommendation of their teachers. Students recommended for Honors Algebra II or Honors Precalculus take an honors placement test.

3. While students are allowed, and at times, encouraged to do summer work in math, the St. Mark's math department will only grant credit for a summer or alternative course in Geometry. Credit will be earned, only if the student satisfactorily completes the course and passes the St. Mark’s departmental final exam. It is our belief that when studying specific mathematics topics for the first time, students should not expect that a summer course or alternative course will provide them with the necessary depth of understanding of the material. Students who have performed poorly in a course, who wish to preview a topic, or who want enrichment are encouraged to do summer or alternative courses.

For further explanation about these policies please contact the department head.

### Classes

**Algebra I - Year**

This course is an introduction to algebra. Extensive attention is given to developing algebraic and graphical problem-solving skills. The coordinate geometry of lines and parabolas, fractions, rational expressions and integral exponentials, and linear and quadratic equations through the quadratic formula are included with an eye toward developing confidence and agility in problem solving. TI-83 or TI-84 calculators are required at this level.

**Algebra I Enhanced - Year**

This course is designed for students who have already been exposed to some or all of the topics of Algebra I. Students are placed in this course in consultation with the Chair of the Math Department if there is concern that skills and confidence need further reinforcement to support higher levels of study. The Algebra I syllabus is used for this course; as time permits, topics are embellished and others added. TI-83 or TI-84 calculators are required at this level.

**Geometry - Year**

This course pursues a deepening of the students’ understanding of plane and solid geometrical figures and a building of their abilities to analyze and communicate mathematically. Much attention is given to logical structure and the writing of mathematical arguments as well as to geometrical problem solving.

**Algebra II - Year**

This course reviews, then extends, the study of algebra with greater attention toward function. Topics include linear and quadratic functions and relations, polynomial functions, rational expressions, exponents, and logarithms and elementary trigonometry. Students are expected to broaden their problem-solving skills and techniques. Increased attention is given to multiple representations with graphs and charts used to illustrate and enhance algebraic manipulation. TI-83 or TI-84 calculators are required.

**Honors Algebra II - Year**

This is an accelerated course in algebra in which topics are pursued in greater depth as well as at greater speed. Students are expected to have strong intuition and motivation for the study of mathematics. Extensive work with trigonometric functions is usually encountered, reaching beyond the topics of Algebra II. *(Prerequisites: teacher recommendation, placement test, and Departmental permission)*

**Statistics, Functions and Trigonometry - Year**

This yearlong course is for students who have completed Algebra II. It includes an introduction to the basic concepts of statistics, a review of linear, quadratic, exponential and logarithmic functions and a study of trigonometry. Modeling data using the functions and using statistics to verify the validity of the model is an emphasis. There is extensive use of the software program Fathom. Topics include: descriptive statistics, correlation, quadratic, exponential, logarithmic regression, circular trigonometry, sequences and series. This course will not be sufficient preparation for students to take a Calculus course at St. Mark’s. *(Prerequisite: completion of Algebra II. Students cannot take this if they have completed Precalculus)*

**Precalculus - Year**

Extensive discussion of polynomial, rational, exponential, logarithmic, and trigonometric functions and their properties and applications is encountered. Sequences, series, and limits are also introduced. A graphic scientific calculator is required at this level for its aid in visualization and calculation. Students gain skill in analyzing functions and drawing connections between symbolic, graphic, and numerical representations. This course is primarily designed as a final preparation for the study of calculus. *(Prerequisite: Algebra II and Departmental permission)*

**Honors Precalculus - Year**

This is an accelerated course in the elementary functions that includes an introduction to the study of calculus during the second half of the year. Students are expected to have exceptional intuition and motivation for the study of mathematics. * (Prerequisites: one full term of analytical trigonometry from Honors Algebra II, a placement test and Departmental permission)*

**Calculus - Year**

This is an introduction to calculus designed for students who want to study calculus before college, but who do not yet feel prepared for the pace or depth of an Advanced Placement course. Students who have not already done so are encouraged to consider MA42/43 as an alternative unless they expect calculus to be a required part of their future studies. *(Prerequisites: MA50 and Departmental permission)*

**Advanced Placement AB Calculus - Year**

This course prepares the students for the AB Advanced Placement Examination. Graphing calculators are used to help the students visualize critical concepts. Applications and techniques of differential and integral calculus are illuminated. Successful completion of this course is roughly equivalent to one-half year of college calculus. *(Prerequisites: MA50 and Departmental permission)*

**Advanced Placement BC Calculus - Year**

This course prepares the student for the BC Advanced Placement Examination. Successful completion of this course is roughly equivalent to a full year of college calculus. It is a more thorough and rigorous course than AB Calculus, with a more extensive syllabus, including an introduction to power series expansions, vector calculus, and the calculus of polar curves. *(Prerequisites: M5A0 and Departmental permission)*

**Topics in Advanced Mathematics - Year**

This course is redesigned annually to reflect the needs of our advanced students. *(Prerequisite: completion of AB or BC Calculus and Departmental permission)*

**Advanced Placement Statistics - Year**

This course introduces the basic concepts of statistics while preparing students for the Advanced Placement Examination in Statistics. Every student will become familiar with the use of the statistical functions found in the more useful graphing calculators. Computer statistical applications are studied using one which is commonly available and well recognized. By completing the course, a student will also be prepared to use statistics in the various pursuits which draw on this mathematical process to study and analyze data. *(Prerequisites: MA50 or an Honors grade in MA40 and Departmental permission)*

**Topics in Discrete Mathematics - Fall**

This semester-long course offers students a chance to explore a variety of topics in discrete mathematics. Graphing calculators and computers are used in the study of matrices, recursion, counting methods, sequences, series and their application to such topics as fair division and apportionment, voting methods, probability, and population growth. Particular emphasis is placed on logical argument in presenting both verbal and written solutions to problems.*(Prerequisite: completion of the math requirement and Departmental permission. May be taken concurrently with Precalculus or Calculus.)*

**History of Mathematics - Spring**

This semester-long course invites students to explore a variety of episodes from the history of mathematics. Learning about the development of mathematical concepts — and of humankind’s struggle with them — fosters a deeper understanding of the subject. The course begins by considering the relationship between the numeration systems of ancient civilizations and the development of mathematics in these cultures. Using the mathematical techniques of different times and places enables students to ask and answer questions of the type: Who is Euclid and why is his work so revered today? Who discovered zero? Who invented Calculus? What are complex numbers? The course considers both pure and applied mathematics.

**NOTE: These semester-long courses offer an alternative or an enhancement to precalculus or calculus. Students can elect to take one or both.**