Upper School Mathematics

Mathematics

Department Philosophy

TVT mathematics department aims to instill habits of mathematical thinking that will prepare students for further inquiry in math and to attain the computational skills needed for everyday life. Students are taught to approach mathematics from multiple perspectives, including numerical, graphical, and symbolic. In addition to simply satisfying the metrics of each course, the teachers focus on student discovery through individual explorations. Students are encouraged to form learning groups that offer a natural context for practicing mathematical communication. Our students are not just highly skilled, but also demonstrate enthusiasm and clear understanding.

The goal of TVT Mathematics is for all students to study mathematics successfully at a pace and depth appropriate to their individual needs. The program is flexible in that it provides the challenge and interest necessary for those who want a sound mathematical background on which to base further study while satisfying the needs of students for whom mathematics is not their primary orientation. To this end, TVT Mathematics offers different tracks of courses to its students.

The chart below shows the anticipated sequencing of mathematics at the high school level. Some students may follow slightly different paths. For those that do, the student and the department chair meet to create an individualized plan of study which may include courses taken at both TVT and area colleges.

College Preparatory
Track 1
College Preparatory
Track 2
College Preparatory
Track 3
Honors Track
Grade 9 Algebra 1 Geometry Geometry Geometry Honors
Grade 10 Geometry Algebra 2 Algebra 2
Trig
Algebra 2
Trig Honors
Grade 11 Algebra 2 FST* or
Financial Math*
Pre-calculus Pre-calculus Honors
Grade 12 FST* or
Financial Math*
Pre-calculus Calculus,
AP Calculus AB, or
AP Statistics
AP Calculus AB,
AP Calculus BC, or
AP Statistics

*Offered every other year

Mathematics Placement

Because success in mathematics depends on students sequentially mastering material, TVT Mathematics takes course placement very seriously. Placements are decided in concert with the department using the prerequisites for each course and teacher recommendation.

Placements for students are completed during the Semester 2 preceding each academic year. All placements are provisional and require that students maintain their level of work through the end of the school year.

Courses at the level of Algebra 2 and above require graphing calculator. Students may purchase any device that is approved for use by the College Board (generally these devices are standalone calculation devices that do not have QWERTY keyboards). The department recommends the Texas Instruments TI-83 Plus.

List of 5 frequently asked questions.

  • Grade 9

    Algebra 1*
    Algebra 1 develops the mathematical background necessary for all subsequent mathematics courses. Students build on their numerical proficiency as they encounter symbolic manipulation and polynomial arithmetic. Substantial units include linear and quadratic equations, factoring, algebraic fractions and radicals. Basic graphing in the Cartesian plane is also covered.
    Grade Level: 9
    Prerequisite: Pre-Algebra, Accelerated Pre-Algebra, or AoPS Pre-Algebra
    Geometry*
    The emphasis in this course is problem solving strategies, graphing, conjecturing, explaining, proving and spatial visualization. Students encounter polygons and three-dimensional figures, elementary trigonometry, circles, congruence, similarity, perimeter, area, and volume. The course is built around problems that help students understand ideas and relationships, develop practical skills, and extend ideas through challenging applications. The integration of algebra in the course maintains and continues the development of necessary algebraic skills.
    Grade Level: 9-10
    Prerequisite: Algebra 1 or Algebra 1 Honors
    Geometry Honors*
    Geometry Honors includes the study of logical arguments along with a study of axioms, logical reasoning, statement-reason proofs, paragraph proofs, and coordinate proofs. In the development of geometric concepts, students are introduced to challenging problems and right triangle trigonometry. The course uses algebra where appropriate to reinforce the skills and concepts necessary for subsequent honors level mathematics courses.
    Grade Level: 9
    Prerequisite: Two of the following:
    1. teacher recommendation,
    2. pass Geometry placement exam with distinction, or
    3. grade of 90% or better in Algebra 1 or 77% or better in Algebra 1 Honors
    Algebra 2/Trigonometry Honors*
    Algebra 2/Trig Honors reinforces a student's algebra skills from a standpoint of functions. Students work toward understanding polynomial, rational and transcendental functions from both algebraic and graphical standpoints. The course ends with a substantial unit on trigonometry that includes proving identities. Graphing calculators are required for this course. The department recommends the Texas Instruments TI-83 Plus calculator.
    Grade Level: 9-10
    Prerequisite: Teacher recommendation and grade of 90% or better in Geometry or 77% or better in Geometry Honors
  • Grade 10

    Geometry*
    The emphasis in this course is problem solving strategies, graphing, conjecturing, explaining, proving and spatial visualization. Students encounter polygons and three-dimensional figures, elementary trigonometry, circles, congruence, similarity, perimeter, area, and volume. The course is built around problems that help students understand ideas and relationships, develop practical skills, and extend ideas through challenging applications. The integration of algebra in the course maintains and continues the development of necessary algebraic skills.
    Grade Level: 9-10
    Prerequisite: Algebra 1 or Algebra 1 Honors
    Algebra 2/Trigonometry*
    Algebra 2 develops the mathematics background necessary for successful entry into Functions, Statistics & Trigonometry, Financial Algebra, Pre-calculus, or AP Statistics. Students review and extend their mastery of elementary algebra through work with polynomials and rational functions and are introduced to exponential and logarithmic functions and their graphs from both algebraic and graphical perspectives. Students also work with basic trigonometric functions and their graphs. The course is built around problems that help students understand mathematical ideas and relationships through applications. Graphing calculators are required for this course. The department recommends the Texas Instruments TI-83 Plus calculator.
    Grade Level: 10-11
    Prerequisite: Geometry or Geometry Honors
    Algebra 2/Trigonometry Honors*
    Algebra 2/Trig Honors reinforces a student's algebra skills from a standpoint of functions. Students work toward understanding polynomial, rational and transcendental functions from both algebraic and graphical standpoints. The course ends with a substantial unit on trigonometry that includes proving identities. Graphing calculators are required for this course. The department recommends the Texas Instruments TI-83 Plus calculator.
    Grade Level: 9-10
    Prerequisite: Teacher recommendation and grade of 90% or better in Geometry or 77% or better in Geometry Honors
    Pre-calculus*
    This course is taught with an eye toward preparing students to take AP Calculus AB the following school year. As such, students spend extensive time studying polynomial, rational and transcendental functions from algebraic, numerical, graphical and verbal perspectives. Graphs and their transformations receive extensive coverage. Systems of equations and an introduction to sequences and series are also covered. Graphing calculators are required for this course. The department recommends the Texas Instruments TI-83 Plus calculator.
    Grade Level: 10-12
    Prerequisite: Two of the following:
    1. Teacher recommendation,
    2. pass Pre-calculus placement exam, or
    3. grade of 87% or better in Algebra 2 with completion of Trigonometry packet over the summer or passing grade in Algebra 2/Trig Honors
    Functions, Statistics & Trigonometry*
    In this course, offered every other year, students approach functions from a real-life perspective, learn the basics of trigonometry and, are introduced to elementary statistics. The class is taught with an eye toward the student who has had difficulty in mathematics courses that focus heavily on algebraic manipulation. Upon successful completion of this course, students will be ready for either a basic college level course in elementary statistics or AP Statistics at TVT. Graphing calculators are required for this course.
    Grade Level: 10-12
    Prerequisite: Algebra 2
  • Grade 11

    Algebra 2/Trigonometry*
    Algebra 2 develops the mathematics background necessary for successful entry into Functions, Statistics & Trigonometry, Financial Algebra, Pre-calculus, or AP Statistics. Students review and extend their mastery of elementary algebra through work with polynomials and rational functions and are introduced to exponential and logarithmic functions and their graphs from both algebraic and graphical perspectives. Students also work with basic trigonometric functions and their graphs. The course is built around problems that help students understand mathematical ideas and relationships through applications. Graphing calculators are required for this course. The department recommends the Texas Instruments TI-83 Plus calculator.
    Grade Level: 10-11
    Prerequisite: Geometry or Geometry Honors
    Pre-calculus*
    This course is taught with an eye toward preparing students to take AP Calculus AB the following school year. As such, students spend extensive time studying polynomial, rational and transcendental functions from algebraic, numerical, graphical and verbal perspectives. Graphs and their transformations receive extensive coverage. Systems of equations and an introduction to sequences and series are also covered. Graphing calculators are required for this course. The department recommends the Texas Instruments TI-83 Plus calculator.
    Grade Level: 10-12
    Prerequisite: Two of the following:
    1. Teacher recommendation,
    2. pass Pre-calculus placement exam, or
    3. grade of 87% or better in Algebra 2 with completion of Trigonometry packet over the summer or passing grade in Algebra 2/Trig Honors
    Functions, Statistics & Trigonometry*
    In this course, offered every other year, students approach functions from a real-life perspective, learn the basics of trigonometry and, are introduced to elementary statistics. The class is taught with an eye toward the student who has had difficulty in mathematics courses that focus heavily on algebraic manipulation. Upon successful completion of this course, students will be ready for either a basic college level course in elementary statistics or AP Statistics at TVT. Graphing calculators are required for this course.
    Grade Level: 10-12
    Prerequisite: Algebra 2
    Pre-calculus Honors*
    This course is required for the student who wishes to take AP Calculus BC the following school year. Polynomials and rational functions are studied in-depth from both a mechanical and theoretical standpoint. The concept of a limit is breached early on in the course. From there, students complete a rigorous treatment of exponential, logarithmic and trigonometric functions. Sequences, series, and analytic geometry receive substantial treatment as well. Students receive extensive exposure to parametric curves and polar coordinates. Finally, students begin the study of differential calculus from limits to derivatives of polynomial, rational, trigonometric and exponential functions. Derivative applications such as optimization and curve sketching are also covered. Graphing calculators are required for this course. The department recommends the Texas Instruments TI-83 Plus calculator.
    Grade Level: 11
    Prerequisite: Two of the following:
    1. Teacher recommendation,
    2. pass Pre-calculus placement exam with distinction, or
    3. grade of 90% or better in Algebra 2/Trig or 77% or better in Algebra 2/Trig Honors
  • Grade 12

    Pre-calculus*
    This course is taught with an eye toward preparing students to take AP Calculus AB the following school year. As such, students spend extensive time studying polynomial, rational and transcendental functions from algebraic, numerical, graphical and verbal perspectives. Graphs and their transformations receive extensive coverage. Systems of equations and an introduction to sequences and series are also covered. Graphing calculators are required for this course. The department recommends the Texas Instruments TI-83 Plus calculator.
    Grade Level: 10-12
    Prerequisite: Two of the following:
    1. Teacher recommendation,
    2. pass Pre-calculus placement exam, or
    3. grade of 87% or better in Algebra 2 with completion of Trigonometry packet over the summer or passing grade in Algebra 2/Trig Honors
    Functions, Statistics & Trigonometry*
    In this course, offered every other year, students approach functions from a real-life perspective, learn the basics of trigonometry and, are introduced to elementary statistics. The class is taught with an eye toward the student who has had difficulty in mathematics courses that focus heavily on algebraic manipulation. Upon successful completion of this course, students will be ready for either a basic college level course in elementary statistics or AP Statistics at TVT. Graphing calculators are required for this course.
    Grade Level: 10-12
    Prerequisite: Algebra 2
  • Advanced Placement

    AP Calculus AB*
    Students complete the College Board's AB Calculus rubric which is akin to most first semester courses in Calculus offered at the university level. Limits and continuity, derivatives their techniques and applications single variable integration, computation of areas as well as the volumes of solids of revolution are covered. Among the theorems stressed in the course are the Intermediate Value Theorem, Extreme Value Theorem, Squeeze Theorem, Rolle's Lemma, Mean Value Theorem, and The Fundamental Theorem of Calculus. Students in the course also spend about one month reviewing for the AP Exam. Graphing calculators are required for this course. The department recommends the Texas Instruments TI- 83 Plus calculator.
    Grade Level: 12
    Prerequisite: Two of the following:
    1. Teacher recommendation,
    2. pass Calculus placement exam, or
    3. grade of 90% or better in Pre-calculus or 77% or better in Pre-calculus Honors
    AP Calculus BC*
    Students complete the College Board's BC Calculus rubric, which covers roughly the same material as the first two semesters of college calculus. In addition to the material covered in AP Calculus AB (outlined above), the course covers the remaining basic concepts of single variable calculus: techniques of integration, integration in polar coordinates, infinite sequences and series, basic calculus of vector functions and an introduction to differential equations. Students in the course also spend about two weeks reviewing for the AP Exam. Graphing calculators are required for this course. The department recommends the Texas Instruments TI-83 Plus calculator.
    Grade Level: 12
    Prerequisite: Two of the following:
    1. Teacher recommendation,
    2. pass Calculus placement exam with distinction, or
    3. grade of 77% or better in Pre-calculus Honors
    AP Statistics*
    Advanced Placement Statistics is equivalent to a one-semester, introductory, non-calculus-based college course in statistics. Students are introduced to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Topics include exploring data, planning study, anticipating patterns, and statistical inference. Graphing calculators are required for this course. The department recommends the Texas Instruments TI-83 Plus calculator.
    Grade Level: 11-12
    Prerequisite: Teacher recommendation and passing grade in Pre-calculus or grade of 90% or better in Financial Math or FST
*This course is approved by the University of California.
Course Availability: It is important to note that a course may not be offered in a given year due to low course enrollment.
TVT Community Day School is a TK-12 Independent Community Day School in Irvine, CA
Founded in Loving Memory of Naomi Gelman Weiss