Course Selection

Mathematics

The Mathematics Department at Springside Chestnut Hill Academy provides rigorous and challenging courses for all levels of students during each year of study in the Upper School. All students are required to take four years of mathematics and some elect to take one or more additional elective math courses. The typical four years of mathematics begin with Advanced Algebra 1 or Geometry and extend through Pre-Calculus, Calculus, or Statistics. Courses in 9th and 10th grade are sectioned into Honors and College Prep while in 11th grade the classes are sectioned into Pre-AP, Honors, and College Prep, allowing for each student to be challenged at an appropriate level. AP Statistics and AP Calculus are taught to the specific AP curriculum and will prepare students for the AP examination given in May of each year. The College Prep and Honors courses will provide students with a solid, fundamental understanding and preparation for college-level mathematics.
 
Logical and critical thinking and the interdependence of ideas are stressed as much as the accumulation of factual information. The mathematics curriculum strives to respond to the prior experience, current knowledge, aspirations, and learning style of each student, through the teaching of the fundamental skills and concepts.
 
Evaluation of students’ progress is based on their performance in the classroom: their homework, quizzes, tests, projects, presentations, and papers.
 
  • Advanced Algebra 1

    Grade 10; full-year course; 1 credit
    This course will provide a thorough review of Algebra 1 and introduce important topics from Algebra 2. The review includes properties of real numbers, graphing and solving linear equations, graphing and solving linear inequalities, and solving systems of linear equations. Students are then introduced to functional analysis with an emphasis on solving and graphing quadratic functions. As students move through the curriculum, they see concepts and problems that are related to questions on the SAT.
  • Algebra 2

    Grades 10, 11; full-year course; 1 credit
    Prerequisites: Competence on the Algebra 1diagnostic test along with departmental approval or completion of the Advanced Algebra 1 course.
    This course begins with a review and extension of topics presented in Algebra 1. Topics include linear, quadratic, and other polynomial functions, with an introduction to exponential and logarithmic functions. Students will investigate the complex number system and be introduced to matrices. Rational functions will be included as time permits. The numeric, graphing, and other features of the graphing calculator are used to explore and extend the skills and concepts covered. As students move through the curriculum, they see concepts and problems that are related to questions on the SAT.
  • AP Calculus (AB)

    Grade 12; full-year course; 1 credit
    Prerequisites: B or better in Pre-AB Calculus and departmental approval
    AP Calculus AB includes both the theory of elementary functions and real-world applications. Differential and integral calculus plus their applications will be studied in preparation for the Calculus AB exam. In addition to polynomial, rational, power, exponential, and logarithmic functions, this course also includes work with trigonometric functions. Students are expected to take the AB level of the AP Exam at year’s end. Students are required to have a graphing calculator. (TI-84 Plus is recommended.)
  • AP Calculus (BC)

    Grade 12; full-year course; 1 credit
    Prerequisites: Departmental approval and successful completion of Pre-BC Calculus H
    BC Calculus picks up where Pre-BC Calculus left off. It is a yearlong course that rigorously develops differential and integral calculus for all piecewise-smooth functions of a single real variable, including Cauchy limits, the derivative and its applications, and the Riemann integral and its applications. In addition, several topics in real analysis, including the completeness of the real line, are introduced as time allows. Participation in this class requires an excellent mastery of algebraic and transcendental functions and a formal notion of limits, continuity, and derivatives of algebraic functions. Students without the correct prerequisites will require extensive independent summer work and the special permission of the department. Students are expected to take the BC level of the AP Exam at year’s end. Students are required to have a graphing calculator. (TI-84 Plus is recommended.)
  • AP Statistics

    Grades 11, 12; elective; full-year course; 1 credit
    Prerequisites:  Successful completion of Algebra 2/Trig H or Pre-Calculus H
    Summer work required
    AP Statistics introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: 1) exploring data: describing patterns and departures from patterns; 2) sampling and experimentation: planning and conducting a study; 3) anticipating patterns: exploring random phenomena using probability and simulation; and 4) statistical inference: estimating population parameters and testing hypotheses. Students interested in AP Statistics should possess a strong work ethic, as substantial new vocabulary and calculator procedures will be introduced; the ability to work collaboratively as well as independently, and a desire to master the AP curriculum to succeed on the AP examination in May. Students are expected to take the AP exam at the end of the year. Students are required to have a graphing calculator. (TI-84 Plus is recommended.)
  • Differential Calculus

    Grade 12; full-year course; 1 credit
    Prerequisite: Pre-Calculus
    Summer work required
    Differential Calculus begins with a review of linear, absolute value, non-linear, rational, and piecewise defined functions. Calculus topics include limits, derivatives, and applications of the derivative. A variety of real-life applications taken from fields such as business, life sciences, economics, and physics are used throughout this course. As students move through the curriculum, they see concepts and problems that are related to questions on the SAT.
  • Geometry

    Grade 9, 10; full-year course; 1 credit
    This yearlong study of geometry will include such fundamental concepts as points, lines, planes, angles, polygons, and perpendicular and parallel lines. The properties of triangles and triangle inequalities will be studied in depth. Right triangles, congruent and similar polygons, properties of quadrilaterals, coordinate geometry, right triangle trigonometry, circles, and angles within the circles will also be studied extensively. Students use inductive reasoning to explore and discover geometric ideas via computer software and hands-on experiences. Students will use deductive reasoning, including formal proofs, to solve various kinds of problems. As students move through the curriculum, they see concepts and problems that are related to questions on the SAT. Students will end the year with a short unit on geometric probability.
  • H Accelerated Algebra 2/Trigonometry

    Grade 10; full-year course; 1 credit
    Prerequisite: Departmental approval
    This course covers the same curriculum as the Algebra 2/Trig Honors above; however, students will be expected to analyze concepts at a more abstract level and move through the material at a faster pace. Students will analyze functions numerically, symbolically, and graphically. As students move through the curriculum, they see concepts and problems that are related to questions on the SAT. The numeric, graphing, and programming features of the graphing calculator are used to explore and extend the skills and concepts covered. Students are required to have a graphing calculator. (TI-84 Plus is recommended.)
  • H Algebra 2/Trigonometry

    Grade 10; full-year course; 1 credit
    Prerequisite: Departmental approval
    This course covers linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions. In addition, students study complex numbers, radicals, and an introduction to matrices. To be successful, students must be able to analyze functions numerically, symbolically, and graphically. The numeric, graphing, and programming features of the graphing calculator are used to explore and extend the skills and concepts covered. As students move through the curriculum, they see concepts and problems that are related to questions on the SAT. Students are required to have a graphing calculator. (TI-84 Plus is recommended.)
  • H Calculus

    Grade 12; full-year course; 1 credit
    Prerequisite: B or better in Pre-Calculus Honors and departmental approval
    In Calculus Honors, the theory of elementary functions and real-world applications of mathematics will be studied. Differential calculus and an introduction to integral calculus plus the applications of each will be explored. The course focuses on polynomial, rational, power, exponential, and logarithmic functions. Students are required to have a graphing calculator. (TI-84 Plus is recommended.)
  • H Geometry

    Grade 9, 10; full-year course; 1 credit
    Prerequisite: Departmental approval
    The main topics in this geometry course are points, lines, planes, angles, polygons, perpendicular and parallel lines, and the fundamental axioms of geometry. In addition, topics include right triangles, congruent and similar polygons, properties of quadrilaterals, coordinate geometry, special right triangles, circles, triangle trigonometry, and properties of three-dimensional figures. Students use geometric ideas to solve problems, to find relationships in complex drawings, and to construct formal proofs. The ultimate goal is for students to think deductively. To be successful in the course, students must gain a mastery of the facts, see the connections among concepts, and synthesize interrelated ideas to present cogent arguments for their solutions to problems. As students move through the curriculum, they see concepts and problems that are related to questions on the SAT.
  • H Multivariable Calculus

    Grades 11, 12; elective; full-year course; 1 credit
    Prerequisites: Departmental approval as well as a grade of A– or higher in the first semester of BC Calculus, as well as successful completion of a full-year physics course. This class MAY be taken concurrently with BC Calculus.
    Multivariable Calculus is a full year course in differential and integral calculus for vector-valued functions of several real variables. Topics include three-dimensional vector fields, partial and directional derivatives and their applications, and multiple integrals. Line and surface integrals (including Green and Stoke’s Theorems) are introduced. Students are required to have a graphing calculator. (TI-84 Plus is recommended.)
  • H Pre-AB Calculus

    Grade 11; full-year course; 1 credit
    Prerequisite: A or better in Algebra 2/Trig Honors and departmental approval
    This course is a rigorous preparation for AP Calculus AB. In this course, functional analysis will be stressed. Topics include polynomial, exponential, logarithmic, and trigonometric functions, and polar coordinates. The year concludes with units on matrices/systems of equations and conic sections. Students are required to have a graphing calculator. (TI-84 Plus is recommended.)
  • H Pre-BC Calculus

    Grade 11; full-year course; 1 credit
    Prerequisite: Departmental approval
    Pre-BC Calculus is a yearlong course in functions and limits that develops the theoretical underpinnings of calculus. The first semester explores the algebraic and transcendental functions students learned in Algebra 2/Trig Honors in greater detail and depth. The second semester rigorously develops formal notions of limits of sequences and functions, as well as the theory of continuous functions (functional analysis). Differential calculus for single-valued functions of real variables rounds out the second semester. Participation in this class requires an excellent mastery of Accelerated Algebra 2 and Trigonometry, a passion for solving problems, and the recommendation of the Mathematics Department. Students are required to have a graphing calculator. (TI-84 Plus is recommended.)
  • H Pre-Calculus

    Grade 11, 12; full-year course; 1 credit
    Prerequisite: B or better in Algebra 2/Trig Honors and departmental approval
    Pre-Calculus Honors is a thorough preparation for Calculus Honors. Topics include polynomial, rational, exponential, logarithmic, and trigonometric functions, and conic sections. As students move through the curriculum, they see concepts and problems that are related to questions on the SAT. The numeric, graphing, and other features of the graphing calculator are used to explore and extend the skills and concepts covered. Students are required to have a graphing calculator. (TI-84 Plus is recommended.)
  • Statistics

    Grades 11, 12; elective; full-year course; 1 credit
    Prerequisites: Algebra 2
    In this course, students will master the art and science of making decisions with data. Topics to be explored are descriptive statistics, inferential statistics, and probability. How do statisticians establish truth? They produce data through observation and experiments. Individual measurements vary, even in seemingly identical conditions. Descriptive statistics provides graphical and numerical tools for modeling variation in data. Descriptive statistics includes visual representation of data and describing the data with summary statistics, such as mean, median, standard deviation, and interquartile range. Inferential statistics includes drawing conclusions based on data collected from various sources.Probability answers the critical question “What are the chances?” Students are required to have a graphing calculator. (TI-84 Plus is recommended.)

Curriculum