 ## Mathematics

The Knox School Mathematics Department recognizes the need for strong mathematics skills in all students’ lives, and strives to provide a comprehensive foundation of knowledge. Every Knox student graduates with an understanding of the role that mathematics plays in his/her life, as well as the ability to use mathematics to solve everyday problems. Course offerings range from middle-school Math 6 through AP Calculus BC. Middle School students who qualify may enroll in beginning Upper School Mathematics courses.

Algebra I (8,9)
The course focuses on four conceptual categories: Number and Quantity, Algebra, Functions, and Statistics and Probability. In this course, students will learn the foundations of algebra, explore different types of functions, create and interpret graphs, study statistics and think critically to solve multi-step real-life application problems. Students are required to have a TI-84 Plus graphing calculator. It will be helpful to use as an aid to graphing and for learning the statistics portion of the class. Prerequisite: Passing grade in Pre-Algebra or similar course.

Algebra I Honors (8,9)
The course focuses on four conceptual categories: Number and Quantity, Algebra, Functions, and Statistics and Probability. In this course, students will learn the foundations of algebra, explore different types of functions, create and interpret graphs, study statistics and think critically to solve multi-step real-life application problems. Students are required to have a TI-84 Plus graphing calculator. It will be helpful to use as an aid to graphing and for learning the statistics portion of the class. Teacher has the option to both cover concepts more in depth and to move at a faster pace. Prerequisite: Earning at least a 90 for both the final grade and for the Pre-Algebra final exam.

Geometry (9, 10, 11)
The Geometry course includes an in-depth analysis of plane, solid, and coordinate geometry as they relate to both abstract mathematical concepts as well as real-world problem situations. Topics include logic and proof, parallel lines and polygons, perimeter and area analysis, volume and surface area analysis, similarity and congruence, trigonometry, and analytic geometry. Emphasis will be placed on developing critical thinking skills as they relate to logical reasoning and argument. Prerequisite: Passing grade in Algebra I.

Geometry Honors (9, 10)
The Geometry course includes an in-depth analysis of plane, solid, and coordinate geometry as they relate to both abstract mathematical concepts as well as real-world problem situations. Topics include logic and proof, parallel lines and polygons, perimeter and area analysis, volume and surface area analysis, similarity and congruence, trigonometry, and analytic geometry. Emphasis will be placed on developing critical thinking skills as they relate to logical reasoning and argument. The course is founded on this premise and requires more abstract thinking and reasoning with written and verbal justifications, as opposed to calculations. Prerequisite: Minimum grade of at least a 90 in Algebra I and Departmental Approval.

Intermediate Algebra (9, 10, 11)
This course is designed to serve as preparation for the study of Algebra II, Statistics, and other math courses. Topics include a review of the real number system, an introduction to imaginary and complex numbers, the solution of first degree, quadratic and systems of equations, polynomials, rational expressions, exponents and radicals, graphs of functions (both linear and nonlinear) and of relations, and exponential and basic logarithmic functions. This class also focuses on study skills and extra support for students by teaching some concepts using different learning modalities. Prerequisite: successful completion of Algebra I.

Algebra II (9, 10,11)
This course is designed to build on algebraic and geometric concepts. It develops advanced algebra skills such as systems of equations, advanced polynomials, imaginary and complex numbers, types of conics, exponential and logarithmic functions, arithmetic and geometric sequences and series, and includes the study of trigonometric functions. It also introduces matrices and their properties. Time permitting; students will be introduced to statistics and the normal distribution. The content of this course is important for students’ success on the SAT and ACT and also on college mathematics entrance exams. A TI-84 graphing calculator is required for this course. Prerequisite: Passing grade in Geometry.

Algebra II Honors (9, 10,11)
This course is an intensive and accelerated paced course for those students who have achieved exemplary grades in both Algebra and Geometry. The student must have excellent work habits; excellent insight into the higher level mathematics topics discussed in class, and must possess a strong desire to learn. This honors course covers all of the topics listed above in the Algebra II course description but in much greater depth and with a more demanding approach. Students are required to have a TI-84 graphing calculator. Prerequisite: Minimum grade of at least a 90 in Geometry and Departmental Approval.

Pre Calculus (10, 11, 12)
A review of selected topics in Algebra, Geometry, and Algebra II will be covered such as Trigonometry, Analytic Geometry, Inequalities, Conic Sections, Matrices, and Limits. In addition, students study techniques of graphing exponential and logarithmic functions as well as a complete analysis of Function Theory. This course is intended to provide the student with a foundation for college programs that may require a further study of college mathematics. A departmental final exam is administered at the end of the semester. Students are required to have a TI-84 graphing calculator. Prerequisite: Minimum grade of at least a 75% in Algebra II.

Pre Calculus Honors (10, 11, 12)
This is an intensive and accelerated course for those students who have achieved exemplary grades in the Algebra II course. The student must have excellent work habits, excellent insight into the higher level mathematics topics discussed in class, and must possess a strong desire to learn. This honors course covers selected topics of advanced algebra, analytical geometry, trigonometry, exponential and logarithmic functions, matrices, polar functions, and the theory of polynomials. In addition, this honors course covers the first three topics of Calculus: limit theory, continuity, and differentiation. A departmental final exam is administered at the end of the semester. Students are required to have a TI-84 graphing calculator. Prerequisite: Minimum grade of at least a 90% in Algebra II and Departmental Approval.

Calculus (11, 12)
Calculus is designed to prepare students for AP Calculus (AB or BC), and includes the study of a variety of functions and their graphs: linear functions, absolute value, square roots, quadratics, polynomials, rational expressions, and exponential, logarithmic, and trigonometric functions. Students will begin to learn the concepts of derivation and limits. Prerequisite: Minimum grade of at least a 75% in Pre-Calculus.

Statistics (11, 12)
Statistics develops appreciation for, and skill in, applying statistical techniques in the decision-making process. Topics include: descriptive statistics, probability, inference, methods of data collection, organization of data, and graphical techniques for exhibiting data together with measures of central tendency and variation. Specific subjects include binomial and normal distributions, hypothesis testing, and confidence intervals. Students will use multiple representations to present data including written descriptions, statistics, formulas, and graphs. Estimating with confidence, testing a claim, comparing two population parameters, inferences for regression, and chi-square procedures are also included. Prerequisite: Passing grade in Algebra II.

AP Statistics (11, 12)
The purpose of this Advanced Placement course in statistics is to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to four broad conceptual themes such as exploring data, sampling and experimentation, anticipating patterns, and statistical inference. A written final exam may be replaced with a real life application of hypothesis testing where students will work in small groups and apply knowledge learned throughout the year in order to test a hypothesis. Students are required to have a TI-84 Plus graphing calculator. A qualifying grade on the Advanced Placement Examination may earn college credit. An Advanced Placement course may require substantial summer reading and preparation work. Completion of summer assignments is essential to classroom success. Students are required to sit for the College Board AP Examination (fee required). Prerequisite: Minimum grade of at least a 90% in Algebra II, Minimum grade of at least an 85% in current English class, and Departmental Approval.

AP Calculus AB (11, 12)
This course is an offering of the College Board’s Advanced Placement Calculus AB course, and is primarily concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and applications. The courses emphasize a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The connections among these representations also are important. Students are required to have a TI-84 Plus graphing calculator. A qualifying grade on the Advanced Placement Examination may earn college credit. An Advanced Placement course may require substantial summer reading and preparation work. Completion of summer assignments is essential to classroom success. Students are required to sit for the College Board AP Examination (fee required). Prerequisite: A minimum grade of a 90% in Pre-Calculus and Departmental approval.

AP Calculus BC (11, 12)
This intensive course takes the students through the Advanced Placement Examination in Calculus BC and well beyond, in some instances into second year college Calculus. Calculus BC is an extension of Calculus AB rather than an enhancement; common topics require a similar depth of understanding. Both courses are intended to be challenging and demanding. Students are enrolled in this course by invitation only. Students are required to have a TI-84 Plus graphing calculator. In lieu of a final examination, students are required to research a further advanced selected topic and present their research to the class. A qualifying grade on the Advanced Placement Examination may earn college credit. An Advanced Placement course may require substantial summer reading and preparation work. Completion of summer assignments is essential to classroom success. Students are required to sit for the College Board AP Examination (fee required). Prerequisite: Minimum grade of at least a 90 in Pre-Calculus Honors, 90 in Calculus, OR Minimum grade of 80 in AP Calculus AB.

## Our Faculty

Debbie Mazzant

B.S., Mathematics – Pennsylvania State University

### Debbie Mazzant

Mathematics Department Chair Mathematics Teacher

Troy Doliner

M.A., Education – UMASS, Boston

### Troy Doliner

Mathematics Teacher

Angelo Mauro

M.S., Mathematics – St. Joseph’s College

### Angelo Mauro

Mathematics Teacher

Gail Roach

M.A., Mathematics – Stony Brook University
B.S., Mathematics Secondary Education – SUNY Oneonta

### Gail Roach

Mathematics Teacher