# Mathematics

### The Beauty of Mathematics

The math program is designed to help all students develop the capacity for mathematical thinking in a challenging, creative, and comprehensive way. Students progress mathematically at least as far as Calculus/Chaos Theory and often as far as AP Calculus.

Mathematics instruction is combined through the block system and year-long track classes. Main Lesson math blocks provide students with a unique and immersive mathematical experience. Students have time to explore mathematical ideas in a more creative way and within a historical context.

Students are also enrolled in year-long track courses in Algebra, Geometry, Advanced Algebra, Precalculus, and Calculus. Classes are divided by skill level; there is a traditional college prep track and an honor track. These courses are optional during senior year, though the large majority of students elect to enroll in a fourth year of study.

## Blocks

- Permutations and Combinations: 9th Grade
- Trigonometry: 10th Grade
- Projective Geometry: 11th Grade
- Calculus/Chaos Theory: 12th Grade

## Permutations and Combinations: 9th Grade

Students explore the many faces of chance: fate, destiny, randomness, risk. Introduction to the fundamentals of probability theory: definitions, the Law of Large Numbers, expected value, applications. Students work with frequency distributions and box-plots, and utilize different measures of central tendency: the mean, median, and mode.

## Trigonometry: 10th Grade

Block begins with determining when two polygons are similar. Once introduced, the sine, cosine, and tangent functions are used in calculations involving right triangles and eventually in deriving the Law of Sines and the Law of Cosines for (not necessarily right) triangles.

## Projective Geometry: 11th Grade

Block formalizes one of the central principles of perspective art: parallel lines meet at infinity. This block includes elements at infinity, the principle of duality, perspectivities and projectivities, projective generation of point and line conics, cross‐ratio and invariance, and, more specifically, study of the theorems of Desargues, Pascal, Brianchon, and Pappus.

## Calculus/Chaos Theory: 12th Grade

Block introduces the historical and mathematical development of calculus and includes elementary aspects of both differential and integral calculus.

## Track Courses

## Algebra I

Linear equations and inequalities of two variables; systems of linear equations; exponents and polynomials; factoring polynomials; rational expressions; roots and radicals; and quadratic equations and functions.

## Geometry

Plane and solid Euclidian geometry from both inductive and deductive approach. Geometrical problem solving: classical theorems on lines, angels, polygons, and circles are proved.

## Honors Geometry

Accelerated course that is more proof-based than standard geometry. Plane and solid geometry to coordinate plane and analytic geometry. Understanding of geometric proofs; study of conic sections.

## Algebra II

Concepts and techniques of advanced algebra: linear equations; graphing and functions; polynomial and rational equations; exponents, radicals; complex numbers; conic sections.

## Honors Algebra II

Concepts and techniques of advanced algebra with emphasis on problem solving and mathematical modelings. Topics includes: matrices and determinants; complex numbers; the investigation of functions (linear, quadratic, and polynomial); transformations of functions; polynomials and rational functions and their graphs; real zeros of polynomials; complex zeros and the Fundamental Theorem of Algebra; exponential and logarithmic functions; and sequences and series.

## Honors Pre-Calculus

Investigations encompass circular motions and the functions that describe it; vectors; dot products; matrices; and geometry on the surface of the Earth. Geometry and in two and three dimensions is integrated across topics and includes coordinate and transformational approaches. Counting, data analysis are included through the curriculum.

Practical and analytic trigonometry, later applied to the polar coordinate system, complex numbers, and vectors. studies of matrices, inverse functions, and sequences and series.

Prepares students for the SAT Subject Test in Mathematics - Level II.

## AP Calculus

Basics topics of differential and integral calculus, including functions, limits, and the derivative and applications of differentiation, curve sketching, the integral, and applications such as rectilinear motion and volumes. Prepares students to sit for the AP exam.

##### In college, I realized how well the high school math program had prepared me. I was able to recall the beautiful, simple, and direct explanations offered both in my track classes and the Main Lesson blocks.

#### The Exeter Method

Faculty teach honors math courses using an integrated problem-centered curriculum developed by Phillips Exeter Academy. Students receive a carefully developed series of math problems in lieu of a textbook or set of lectures, then present their well-reasoned solutions for discussion amongst the class. The seminar-style approach requires students to ask effective questions, answer inquiries, and critically assess their own work.

The mathematics department includes Dr. Cynthia Renegar, Kevin Farey, and John Jackson.