# Upper School Curriculum Guide

## Overview

The mathematics curriculum is characterized by depth, breadth, and flexibility. These qualities enable students to pursue the study of mathematics as far as they are able while also enjoying the process.

Algebra 1, Geometry, and Algebra 2 & Trigonometry are required of all students. These courses encourage students to be creative, precise, and rigorous when dealing with abstract concepts. For students who have acquired the necessary concepts and skills, various elective courses are offered. Most students follow the traditional analysis sequence through Precalculus and Calculus.

## Policies

**COURSE SELECTION GUIDELINES**

Students selecting the appropriate math course for next year should consult the handbook for the prerequisites and MUST obtain the signature for approval from their current math teacher. Students wishing to take 2 or more math classes in one year MUST obtain a signature from the Department Chair. Students wishing to sign up for AP Statistics or Linear Algebra MUST sign up on the sheets posted outside room 330.

**AP HOMEWORK GUIDELINES**

- AP Calculus AB: Students should expect to spend about 45 minutes of focused time on daily homework preparation.
- BC Calculus: Homework (non-graded) 45 minutes of focused time (+/- 15 minutes) each night.
- AP Stats: 30-45 minutes of focused homework time 5 days per cycle, excluding assessment prep or projects.

**DEPARTMENTAL POLICIES REGARDING ENTRY INTO HONORS/AP COURSES**

A graphing calculator (a Texas Instruments TI-84 Plus or TI-83 Plus) is required in the second semester of the Geometry course and the subsequent courses to enhance the study of the algebraic, geometric, and numeric representations of problems.

- Admissions into an Honors Math class is dependent upon all three of the following:

- Recommendation from the teacher of the previous course
- Year-end grade of A+ from a regular section;

Year-end grade of B from an Honors Geometry section;

Year-end grade of B+ from an Honors Algebra 2 & Trigonometry section;

An equivalent year-end grade from the Middle School - Signature of the department chair, who may require a placement test

- For entry to AP Calculus AB courses, a student must have:

- Recommendation of the current Advanced Precalculus teacher and the math department
- Minimum grade of 85 on the March exam in Advanced Precalculus
- Minimum average of 85 for the second semester in Advanced Precalculus

- A student in Honors Precalculus needs a B or better to continue into AP Calculus BC
- Any accelerated student in Honors Precalculus needs an A- or better to continue directly to AP Calculus BC
- For entry to AP Statistics, a student must have:

- Approval of the math department
- Minimum year grade of:

B in Advanced Precalculus or A in Advanced Algebra 2 & Trigonometry;

B- in Honors Precalculus or Honors Algebra 2 & Trigonometry;

A- in Precalculus

- For entry into Linear Algebra, a student must have:

- Approval of the math department
- Concurrent enrollment in AP Calculus AB or BC or completion of AP Calculus AB or BC
- Minimum year grade of A- in Advanced Precalculus

- For entry into Multivariable Calculus, a student must have:

- Approval of the math department
- Completion of AP Calculus BC or an equivalent college-level course

- A student who takes Advanced Algebra 2 & Trigonometry in the 11th grade and who wishes to take non-AP Calculus in the senior year may do so if the student meets the following criteria:

- Minimum grade of B in Advanced Algebra 2 & Trigonometry
- Prior approval as obtained in a meeting with the math department chair
- Completion of a pre-approved summer precalculus course

- Entrance into 9th grade Geometry from the Middle School requires a minimum year grade equivalent to C+

For maintenance of placement in an honors or AP course during the school year, the policy is as follows: If any honors or AP student receives a grade below B- at the end of the first quarter or first semester, the course teacher, in consultation with the Department Chair, will review the placement. The decision to transfer a student from an AP or honors course will be made jointly by the Principal, the Department Chair, the section teacher, the advisor, and the student.

**MATHEMATICS COURSE BYPASS POLICY**

Mathematics skills build sequentially upon each other, and the mathematics courses offered at RCDS are designed to span an academic year so that students can fully develop those skills alongside their peers. **The Mathematics Department does not consider it appropriate for students to bypass any of the courses in the Upper School sequence**; however, qualified students who wish to accelerate may take our Geometry and Algebra 2 courses concurrently. This acceleration requires the approval of the Department.

There are rare times when a student is prepared and chooses to focus intensively on a course and is able to develop the skills covered in a math course over a condensed period of time in order to bypass a year-long mathematics course in RCDS’s sequence. Bypassing a course in RCDS’s mathematics sequence can only be done with the approval of the Department, and courses can only be bypassed at the Honors level. Students may not bypass any course beyond Algebra 2/Trigonometry.

Students wishing to be considered for a possible move ahead must complete, by April 15, a request form (available from the Mathematics Department) that includes the proposed summer course work/tutoring plans. The form will be reviewed by the Department, and a decision to approve or not will be shared by May 15. Requests after April 15 will not be considered.

If the student’s request is approved, the student is responsible for completing the summer work by mid-August. The student will then be required to take a placement test at RCDS on the testing date assigned for the week of August 15. The student must pass the appropriate placement test with a grade of 90% or better in order to bypass the course and demonstrate preparedness to enter the successive honors level math course. Placement tests will not be given prior to the mid-August date, and students may only take the placement test once.

If the student does not pass the placement test at the Honors level, then the student will continue to be enrolled in the course that the student was assigned during course selection.

## Curricular Sequence

Grade 9 | Grade 10 | Grade 11 | Grade 12 |
---|---|---|---|

Algebra 1 | Geometry | Algebra 2/Trig | Statistics Precalculus |

Algebra 1 | Adv Geometry | Adv Algebra 2/Trig | Adv Precalculus |

Algebra 1 | Adv Geometry Adv Algebra 2/Trig |
Adv Precalculus | AB Calculus AP Statistics |

Geometry Adv Geometry |
Algebra 2/Trig Adv Algebra 2/Trig |
Precalculus* Adv Precalculus |
Calculus AP Calculus AB AP Statistics |

Honors Geometry | Honors Algebra 2/Trig Adv Algebra 2/Trig |
Honors Precalculus Adv Precalculus AP Statistics |
AP Calculus BC** AP Calculus AB AP Statistics |

Honors Algebra 2/Trig | Honors Precalculus | AP Calculus BC** AP Statistics |
Multivariable Calculus Linear Algebra AP Statistics |

* Precalculus does not lead students to AB Calculus in the following year, but it may lead students to regular Calculus, with departmental approval.

** Students may enter BC Calculus from Honors Precalculus with departmental approval.

- AP Statistics is another advanced offering, to be taken upon completion of Adv Algebra 2/Trig, with department approval.
- Students taking AP Calculus AB or BC may concurrently take Linear Algebra in grade 12.
- AP Statistics is offered for juniors and seniors only, Statistics and Linear Algebra are only offered for seniors.

## Courses

**ALGEBRA 1**

This course includes the following topics: properties of real numbers and their applications, linear equations and inequalities in one and two variables, exponents, radicals, factoring, rational expressions, solving quadratic equations including the quadratic formula, and graphing in the coordinate plane. Emphasis is placed on developing strong skills and independent thinking. (1 unit; Grades 9, 10; prerequisite: simplification, evaluation, solving and graphing linear equations and inequalities in one variable, factoring a common monomial, and verbal applications)

**GEOMETRY**

This course studies the properties of plane figures including parallel and perpendicular lines, congruent and similar triangles, polygons, circles, right triangle trigonometry, areas, and volumes, as well as introductions to solid and coordinate geometry. This course provides a thorough study of the topics in geometry that will be necessary for the successful study of Advanced Algebra 2/Trigonometry and future courses, as well as the SAT and ACT exams. The emphasis is to apply geometric postulates and theorems to the numerical solution of problems. Students will also learn to develop proofs by working with modified proofs. The Geometer's Sketchpad software is used throughout the course as a discovery tool and supports the material covered. The course will stress the importance of developing strong algebraic skills. (1 unit; Grades 9, 10)

**ADVANCED GEOMETRY**

This course studies the properties of plane figures including parallel and perpendicular lines, congruent and similar triangles, polygons, circles, right triangle trigonometry, areas, and volumes, as well as introductions to solid and coordinate geometry. Throughout the course, the student's ability to develop and present formal proofs is systematically strengthened and expanded through the use of deductive reasoning. The Geometer's Sketchpad software is used throughout the course as a discovery tool and supports the material covered. A review of Algebra 1 is included using equations based on geometric theorems. (1 unit; Grades 9, 10; department approval required)

**HONORS GEOMETRY**

This course presents a more sophisticated and in-depth study of plane geometry. Additional topics include locus and geometric inequalities. Emphasis is placed on original proofs (direct and indirect), abstract reasoning, and synthesis. (1 unit; Grades 9, 10; department approval required)

**ALGEBRA 2 AND TRIGONOMETRY**

This course includes a study of linear, quadratic, and polynomial functions, systems of equations in two and three variables, inequalities, complex numbers, variation, conic sections, exponential and logarithmic functions, and trigonometric functions, including applications. (1 unit; Grades 10, 11)

**ADVANCED ALGEBRA 2 AND TRIGONOMETRY**

This course includes a study of linear, quadratic, and polynomial functions, systems of equations in two and three variables, inequalities, complex numbers, variation, conic sections, exponential and logarithmic functions, and trigonometric functions. The focus is on the representation of problems algebraically, numerically, and graphically. Applications include an introduction to data analysis, regression and modelling. (1 unit; Grades 10, 11; department approval required)

**HONORS ALGEBRA 2 AND TRIGONOMETRY**

This course consists of a thorough and fast-paced study of algebra and an extensive study of trigonometry. Its emphasis is on the structure of mathematical systems and their underlying concepts. The focus is on the representation of problems algebraically and graphically. Applications include an introduction to data analysis. Strong algebraic skills are presumed. (1 unit; Grades 10, 11; department approval required)

**PRECALCULUS**

The central theme of this course is functions as models of change. Functions can be grouped into families (linear, exponential, power, and periodic, polynomial, and rational) and used as models for real-world behavior. Providing numerical and graphical approaches, in addition to the algebraic, gives students several ways of mastering the material. This is a Precalculus course at a less rigorous level and does not constitute preparation for Advanced Placement Calculus or Advanced Placement Statistics. (1 unit; Grades 11, 12; department approval required)

**ADVANCED PRECALCULUS**

This course extends the content of algebra through advanced-level consideration of various functions and develops skill in mathematical analysis. Polynomial, rational, exponential, logarithmic, and circular functions are considered along with the study of analytic geometry, polar coordinates, and sequences and series. This course is specifically designed as a preparation for AB Calculus and is a prerequisite for AB Calculus. (1 unit; Grades 11, 12; department approval required)

**HONORS PRECALCULUS**

This course is a highly theoretical, rigorous, and integrated approach to the study of the algebraic and transcendental functions. The functions studied include the polynomial, rational, linear and quadratic, trigonometric and inverse trigonometric, logarithmic and exponential, and sequence functions. The course is specifically designed as a preparation for BC Calculus; therefore, the concepts and notation needed in BC Calculus are developed and stressed throughout the year. The course demands independence, creativity, and highly developed algebra skills. (1 unit; Grades 10, 11; department approval required)

**STATISTICS**

This course is an introduction to the fundamental concepts of statistics involved in collecting, displaying, summarizing, and drawing inferences from data. Topics include exploratory data analysis, design of surveys and experiments, sampling distributions, estimation, and significance testing. Students frequently work on projects involving the hands-on gathering and analysis of data that are applicable to their daily lives and real-world events. In the spring, students apply what they have learned in the course by designing, conducting, and analyzing their own studies. Calculators and computers are used to assist in understanding the major concepts of the course. Open only to seniors. (1 unit; Grade 12)

**AP STATISTICS**

Today's society places increasing importance on data analysis using computers, calculators, graphs and charts in many areas, ranging from the sciences to business. This is a mathematics course with an interdisciplinary approach. The course is divided into four major themes: exploratory analysis, planning considerations, probability, and statistical inference. Students, individually or in small groups, plan and perform data collection and analyses with opportunities to share questions and conclusions. Projects that include writing a statistical report encourage interdisciplinary connections and real-world applications. The graphing calculator and computer software will facilitate the production of graphs and statistical computations. This course will prepare students for the Advanced Placement Statistics examination. (1 unit; Grades 11, 12; department approval required; students in Grade 11 must concurrently take Precalculus)

**CALCULUS**

This is a study of elementary calculus without the pressure of adhering to the Advanced Placement Calculus curriculum. The course focuses on working with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. Topics include analysis of graphs, limits, the concept and applications of the derivative, the Fundamental Theorem, and interpretations and applications of integrals. (1 unit; Grades 11, 12; department approval required)

**AP CALCULUS AB**

This is an Advanced Placement course in preparation for the AP Calculus AB examination. The course focuses on working with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. Topics include analysis of graphs, limits, the concept and applications of the derivative, the Fundamental Theorem, and interpretations and applications of integrals. (1 unit; Grades 11, 12; department approval required)

**AP CALCULUS BC**

This is an Advanced Placement course in preparation for the AP Calculus BC examination. In addition to those listed under AP Calculus AB, the following topics are covered: numerical and graphical solutions of differential equations; parametric, polar and vector functions; improper integrals; polynomial approximations; and series. (1 unit; Grades 11, 12; department approval required)

**LINEAR ALGEBRA**

Linear Algebra is a rigorous study of vectors, matrices, and linear systems in two and three dimensions from both a practical and an abstract point of view. Topics include Gauss-Jordan elimination, determinants, Euclidean, general and complex vector spaces, eigenvalues, eigenvectors and QR decomposition. Open only to seniors. (1 unit; Grade 12; department approval required)

**MULTIVARIABLE CALCULUS**

Multivariable Calculus involves the calculus of functions of more than one variable: vector algebra and vector calculus; lines and hyperplanes in n-dimensional space; partial derivatives and optimization; multiple integrals, and coordinate transformations; line and surface integrals; Green's Theorem, Stokes' Theorem, and Gauss' Divergence Theorem. This course lays the groundwork for a variety of applications in physics, engineering, probability, and statistics, which will be included as time and scheduling permit. (1 unit; Grade 12; department approval required)