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Department Chair

Jeremy Dybdahl
jeremy_dybdahl@fuhsd.org

Mathematics

Algebra

Algebra (10 credits)
Grade level: 9-12
College eligibility: UC and CSU approve math course, subject area C
Recommended Coursework: none

Algebra1 is imperative for success in subsequent math courses, and transitions students from arithmetic to symbolic reasoning.  The key content, which follows the state standards for Algebra 1, involves understanding, writing, solving, and graphing linear and quadratic equations and inequalities.  When graphing linear equations, emphasis will be placed on understanding the slope-intercept formula and slope in general as it relates to parallel and perpendicular lines.  Solving systems of two linear equations in two unknowns is also emphasized.  Quadratic equations will be solved by factoring, using graphs, and applying the quadratic formula.  Students should also become comfortable with operations on monomial and polynomial expressions.  They learn to solve problems employing all of these techniques.  Algebra 1 meets the graduation requirement.  This is a one period course that covers all the district standards.

Geometry or Geometry Enriched

Geometry (10 credits)
Grade level: 9-12
College eligibility: UC and CSU approve math course, subject area C
Recommended Coursework: C or better in Algebra 1 

The key content, which follows the state standards for Geometry, includes a formal development of geometric skills and concepts.  This course introduces plane and solid geometry.  They will develop the ability to construct formal logical arguments and proofs in a geometric setting.   Students will build their reasoning skills through studying the following topics:  properties of triangles, quadrilaterals, circles, compass constructions, transformations, volume, area, similarity, the Pythagorean Theorem, coordinate geometry, and an introduction to basic trigonometric functions.  Geometry meets the graduation requirement.    This course covers all state standards and prepares a student for Algebra 2.

 

Geometry Enriched (10 credits)
Grade level: 9-12
College eligibility: UC and CSU approve math course, subject area C
Recommended Coursework:
B or better in Algebra I or Algebra 1B with teacher recommendation

The key content, which follows the state standards for Geometry, includes a formal development of geometric skills and concepts.  This course introduces plane and solid geometry.  They will develop the ability to construct formal logical arguments and proofs in a geometric setting.   Students will build their reasoning skills through studying the following topics:  properties of triangles, quadrilaterals, circles, compass constructions, transformations, volume, area, similarity, the Pythagorean Theorem, coordinate geometry, and an introduction to basic trigonometric functions.  Geometry Enriched meets the graduation requirement.  Emphasis will be placed on formal proofs and students are expected to have a firm grasp of Algebra 1 concepts.  This course covers the state standards and prepares students for the rigor of the accelerated course that follows:  Algebra 2/Trigonometry.

Algebra 2 or Algebra 2/Trigonometry

Algebra 2 (10 credits)
Grade level: 9-12
College eligibility: UC and CSU approve math course, subject area C
Recommended Coursework: C or better in Geometry

This course expands and reviews the mathematical content of Algebra 1 and Geometry.  Emphasis is placed on abstract thinking skills, the function concept including domain and range, extension from the real to the complex number system, and the algebraic solution of problems in various content areas. Polynomial, logarithmic, exponential, rational, and conic functions and relations comprise the core material through which equations and graphs are studied and applied.  Additional topics include combinatorics, probability, basic statistics, sequences, and series.  Calculators are used to aid in the solution of problems and in making estimates for realistic solutions.

 

Algebra 2/Trigonometry (10 credits)
Grade level: 9-12
College eligibility: UC and CSU approve math course, subject area C
Recommended Coursework: Recommended: B or better in Geometry (Enriched) with teacher recommendation.

Algebra 2/Trig is for accelerated students who plan to maximize the amount of mathematics studied in high school. Course content includes a more rigorous study of all topics taught in the Algebra 2 course. Students will study, in depth, the 6 trigonometric functions as they relate to the unit circle using radians and degrees to simplify expressions, solve equations and applications, and graph basic and translated trigonometric functions.  Additional topics include solving triangles, defining and solving equations with inverse trigonometric functions, and proving and applying trigonometric identities.

Math Analysis

Math Analysis (10 credits)
Grade level: 9-12
College eligibility: UC and CSU approve math course, subject area C
Recommended Coursework: C or better in Algebra 2

This course is recommended for those students planning to take Calculus. Topics covered include trigonometric functions of ratios of lengths of sides of triangles, circular functions, graphical characteristics of trigonometric functions, solution of right triangles, radian and degree measure, trigonometric identities, laws of sines and cosines, solution of oblique triangles, reinforcement of function concept, inverse trigonometric functions and their graphs, polar coordinates and vectors and their graphs, trigonometric form of complex numbers, de Moivre's Theorem, coordinate geometry, conic sections, rational functions and their graphs, elementary functions and their inverses, introduction to linear algebra, parametric equations and their graphs, lines and planes in space, three-dimensional coordinate geometry and vectors in space.

Pre-Calculus Honors

Pre-Calculus Honors (10 credits)
Grade level: 10-12 (9th grade by teacher recommendation/approval)
College eligibility: UC and CSU approve math course, subject area C
Recommended Coursework: B or better in Algebra 2/Trigonometry or Math Analysis

This course is recommended for those students planning to take Calculus.  The curriculum includes an in-depth algebraic and graphical analysis of different families of functions and their inverses, including polynomial, exponential, logarithmic, rational and trigonometric functions.  Rectangular, polar, and parametric forms of an equation will be taught in addition to vectors and their graphs.  Further study of topics introduced in earlier courses includes matrices and determinants, coordinate geometry, conic sections, series and sequences, binomial expansion, properties of radical expressions, complex numbers, de Moivre’s Theorem, limits (epsilon-delta), and an introduction to calculus.

AP Calculus AB or BC

AP Calculus AB (10 credits)
Grade level: 10-12 (9th grade by teacher recommendation/approval)
College eligibility: UC and CSU approved math course; subject area C
Recommended: B or better in Math Analysis or C or better in Pre-Calculus Honors with teacher recommendation

This course covers the content of two quarters of a college calculus curriculum, focusing on differentiation with applications and integration with applications. Techniques of integration, indeterminate forms for limits are also covered. Throughout the course, an emphasis is placed on symbolic, graphical, and numeric representations, as well as on clear communication of mathematical thinking. Students successfully completing this course are prepared to take the Calculus AB AP Exam.  A graphing calculator will be necessary for this course.

 

AP Calculus BC (10 credits)
Grade level: 10-12 (9th grade by teacher recommendation/approval)
College eligibility: UC and CSU approved math course; subject area C
Recommended: B or better in Pre-Calculus Honors with teacher recommendation

This course covers the content of three quarters (or two semesters) of a college calculus curriculum, focusing on differentiation with applications and integration with applications. Techniques of integration, indeterminate forms for limits, and Taylor series are also covered, as well as application of calculus techniques to parametric and polar representations. Throughout the course, an emphasis is placed on symbolic, graphical, and numeric representations, as well as on clear communication of mathematical thinking. Students successfully completing this course are prepared to take the Calculus BC AP Exam.  A graphing calculator will be necessary for this course.

AP Statistics

AP Statistics (10 credits)
Grade level: 10-12 (9th grade by teacher recommendation/approval)
College eligibility: UC and CSU approved math course; subject area C
Recommended: C or better in Algebra 2 with teacher recommendation

The Advanced Placement (AP) Program of the College Board offers a course and examination in statistics to high school students who wish to complete studies equivalent to a one semester, introductory, noncalculus-based college course in statistics. Like the college course, the purpose of the AP course in statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. The course is built around four main topics: exploring data, planning a study, probability as it relates to distribution of data, and inferential reasoning. With the possible exception of probability, most of the material in this course has not been a part of the traditional secondary mathematics curriculum. This course is an excellent option for interested students who have successfully completed a second year course in algebra.

Math Electives

Computer Programming JAVA (10 credits)
Grade level: 9-12
College eligibility: UC and CSU approved college preparatory elective; subject area G
Recommended: Algebra 1 and previous computer use or teacher recommendation

The course is designed to introduce the student to the study and writing of computer programs, with an emphasis on understanding and solving problems. Analytical thinking skills and logic are emphasized. The JAVA language is used with an emphasis on programming for the Internet, so structured as well as object-oriented methods of programming are studied. Elementary study of digital computer hardware is included. This course is recommended for the college-bound student planning on a business, math, or science major or for the student preparing for an AP Computer Science course.

 

AP Computer Science (10 credits)
Grade level: 10-12
College eligibility: UC and CSU approved college preparatory elective; subject area G
Recommended: C or better in Algebra 2, or teacher recommendation

Students will learn the language JAVA and use this language to create structured programs. Programming methodology, algorithms and data structures will be taught.

 

AP Computer Science Principles (10 credits)
Grade level: 10-12
College eligibility: UC and CSU approved college preparatory elective; subject area G
Recommended: none

The AP Computer Science Principles course is designed as the equivalent to a first-semester introductory college computing course. In this course, students will develop computational thinking skills vital for success across all disciplines, such as using computational tools to analyze and study data and working with large data sets to analyze, visualize, and draw conclusions from trends. The course is unique in its focus on fostering student creativity. Students are encouraged to apply creative processes when developing computational artifacts and to think creatively while using computer software and other technology to explore questions that interest them. They will also develop effective communication and collaboration skills, working individually and collaboratively to solve problems, and discussing and writing about the importance of these problems and the impacts to their community, society, and the world. Students complete part of the AP Computer Science Principles Exam through course assignments and activities, and take the other part of the exam in May.