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SAT/ACT

Mathematics Courses

Mathematics Department Chair

Suzan Pham :: spham@sileducation.com

Mathematics Teachers

Courses marked with an asterix are pending UC approval.

'c' Category College Prep Courses

Algebra 1

Algebra 1 serves as an introductory course into the language and fundamental operations of mathematics. Students solidify skills in distinguishing classes of numbers and their properties, simplifying expressions, equation and inequality solving, and function applications. An exploration into linear, quadratic, exponential, rational, and radical equations and functions begins by cementing operational techniques and then developing graphing skills. In addition, methods such as factoring, completing the square, and the quadratic formula are introduced. This course will serve as the key basis of any future math course.

Prerequisites: Completion of Pre-Algebra with a grade of C or higher.

Algebra 1/Geometry

Algebra 1/Geometry is an accelerated course, combining crucial algebraic concepts with a full year analysis of introductory Euclidean geometry. Students first begin by reviewing algebra, with an emphasis on factoring, simplifying radicals, linear and non linear equation solving, graphing, and word problem solving. Students then explore geometrical concepts such as planes, lines, triangles, circles, area, and volume. In addition, students are exposed to introductory trigonometry and coordinate geometry. Students engage heavily in geometrical proofs, which involve both deductive and inductive reasoning using theorems, definitions, and properties.

Prerequisites: Completion of 8th grade Algebra 1 with a grade of B or higher.

Geometry

Geometry is an introductory course of theoretical and analytical Euclidean geometry. Students advance his or her knowledge about geometric concepts such as planes, lines, triangles, circles, area, and volume. In addition, students engage in basic trigonometry as well as coordinate geometry. Students engage heavily in geometrical proofs, which involve both deductive and inductive reasoning using theorems, definitions, and properties. Students also use algebraic techniques in equation solving, simplifying radicals, graphing, and formula based operations.

Prerequisites: Completion of Algebra 1 with a grade of C or higher.

Algebra 2

Algebra 2 is a continuation of concepts introduced in Algebra 1, with the advancement in applications. Great emphasis is placed on analyzing linear and nonlinear functions, equations, and inequalities. Students engage not only in the real number system, but also extend into the complex number system. Students refine their abilities in solving system of equations and inequalities, polynomial, rational, exponential, and radical equations and functions. In addition, the course exposes students to newer concepts such as conic sections and logarithms and takes an in-depth approach to sequences, series, and probability.

Prerequisites: Completion of Algebra 1 and Geometry with a grade of C or higher.

Algebra 2/Trigonometry

Algebra 2/Trigonometry is an accelerated course which advances concepts from Algebra 1 as well as the trigonometric properties initially introduced in Geometry. There is a greater emphasis in analyzing linear and nonlinear functions, equations, and inequalities than in College Prep. Algebra 2. Students engage not only in the real number system, but also examine the complex number system. Students refine their abilities in solving systems of equations and inequalities, polynomial, rational, exponential, and radical equations and functions. In addition, the course exposes students to newer algebraic concepts such as conic sections, matrices, and logarithms as well as a deeper approach into sequences, series, and probability. Students thoroughly investigate trigonometry by first comprehending the significance of the ratios initially gained from the special triangles in Geometry. From there, students engage in applications and graphs of sine, cosine, tangent, secant, cosecant, and cotangent functions in both degree and radian measurements. Students will also work in rectangular, polar, and parametric forms. Trigonometric identities and non-right triangle applications are also introduced.

Prerequisites: Completion of Algebra 1 and Geometry or Algebra 1/Geometry with a grade of B- or higher.

Pre-Calculus

Pre-Calculus is a continuation in exploring concepts introduced in Algebra 2 as well as a formal introduction to trigonometry. Students initially review concepts such as linear and nonlinear applications, solving systems of equations and inequalities, and number properties. Students engage in a deeper analysis of varying functions, emphasizing continuity, critical points, asymptotes, end behavior, domain, range, intervals of increasing and decreasing, and roots. Additionally, students investigate a great range of trigonometric concepts that includes solving non-right triangles as well as using other trigonometric functions such as secant, cosecant, and cotangent. Graphing is heavily emphasized and even further extended into inverse functions. Not only will students work within the Cartesian coordinate system, but also within the complex and polar system. Vectors, parametric equations, logarithms, conic sections, sequences, and series are also included. At the end, students begin to handle introductory calculus concepts through initial exposure to limits and basic differentiation.

Prerequisites: Completion of Algebra 1, Geometry, and Algebra 2 with a grade of C or higher or Algebra2/Trigonometry with a grade of C or higher.

Calculus

Calculus introduces basic differential and integral applications, emphasizing more of a computational than theoretical approach. This class is designed to give students a less rigorous exposure to Calculus, in preparation for future encounters of the college level based course. Students are required to have a firm understanding of varying functions and behaviors, with crucial emphasis on domain, range, critical values, and graphing techniques. Furthermore, students learn to evaluate limits, implement differentiation techniques using the power, chain, quotient, and product rules, and integrate definite and indefinite functions. Real world correlations are dominant, requiring students to engage in a greater analysis of word-based problems. Students delve into the differential and integral applications such as optimization, related rates, motion, and area.

Prerequisites: Completion of Pre-Calculus, Trigonometry/Math Analysis with a grade of C or highe.

Linear Algebra

Linear Algebra is a full year, elective course that introduces students to the basic theory of linear equations and matrices, real vector spaces, bases and dimension, rank, nullity, linear transformations as matrices, determinants, eigenvalues and eigenvectors, inner product spaces, and the diagonalization of symmetric matrices. This course enables high-school students to enter college with an advantage, as Linear Algebra is a requirement for mathematics and physics majors, and is highly recommended for majors in other applied sciences, such as computer science.

Prerequisites: AP Calculus BC with a grade of C or higher

'c' Category Honors & AP Courses

Honors Trigonometry/Math Analysis

Honors Trigonometry/Math Analysis is a continuation of concepts first introduced in Algebra 2 as well as a formal introduction to trigonometry. Students initially review concepts such as linear and nonlinear applications, solving systems of equations and inequalities, matrices, and number properties. Students engage in a deeper analysis of varying functions, emphasizing continuity, critical points, asymptotes, end behavior, domain, range, intervals of increasing and decreasing length, and roots. Students further investigate a great range of trigonometric concepts that include solving non-right triangles as well as using other trigonometric functions such as secant, cosecant, and cotangent. Graphing is heavily emphasized and even further extended into inverse functions. Not only will students work within the Cartesian coordinate system, but also within the complex and polar system. Vectors, parametric equations, logarithms, conic sections, sequences, series, and probability are also included. At the end, students begin to handle introductory calculus concepts through initial exposure to limits, basic differentiation, and integrals. Students are responsible for the presentation of a project at the end of each semester. Topics vary, but the underlying purpose is to investigate either the history of particular concepts or directly demonstrate the usage of them in real life applications.

Prerequisites: Completion of Algebra 1, Geometry, and Algebra 2 with a grade of C or higher or Algebra2/Trigonometry with a grade of C or higher.

Honors Math Analysis

Honors Math Analysis is an advanced, accelerated course designed to prepare students for Calculus BC. This is the only non-AP mathematics course granted UC-Honors distinction. Students who take this course can earn honors credit towards his or her GPA. This course is a continuation of concepts introduced in Algebra 2 as well as a formal introduction to trigonometry. Students initially review concepts such as linear and nonlinear applications, solving systems of equations and inequalities, matrices, and number properties. Students engage in a deep analysis of varying functions, emphasizing continuity, critical points, asymptotes, end behavior, domain, range, intervals of increasing and decreasing, and roots. Students also investigate a great range of trigonometric concepts that includes solving non-right triangles as well as using other trigonometric functions such as secant, cosecant, and cotangent. Graphing is heavily emphasized and even further extended into inverse functions. Not only will students work within the Cartesian coordinate system, but also within the complex and polar system. Vectors, parametric equations, logarithms, conic sections, sequences, series, and probability are also included. In addition, students begin introductory differential calculus by analyzing limits using both theoretical and computational approaches. In conjunction, students learn various differential techniques from the power, chain, quotient, and product rule and then complete a rigorous study in application of derivatives. Students are required to present a project at the end of each semester. Topics vary, but the underlying purpose is to investigate either the history of particular concepts or directly demonstrate the usage of them in real life applications.

Prerequisites: Completion of Honors Algebra/Trigonometry with a grade A- or higher or completion of Honors Trigonometry/Math Analysis with B+ or higher.

AP Calculus AB

AP Calculus AB is a rigorous, introductory college-level course into single variable differentiation and integral Calculus. Students analyze limits, differentiation, and integrals at a theoretical, conceptual, and computational level. Students investigate the meaning of limits and then proceed into differentiation. Basic techniques such as power, product, quotient, and chain rule are explored. Students then engage in the application of derivatives, learning key concepts such as the Mean Value Theorem and Rolle's Theorem, as well as optimization and related rates. Further analysis of critical values, intervals of increasing/decreasing in functions, as well as concavity are emphasized. In addition, students learn how to evaluate area underneath curves by a geometrical approach using the Midpoint, Upper/Lower, Trapezoidal, and Simpson's Rule. Afterwards, implementation of both the First and Second Fundamental Theorem of Calculus provides students with a direct approach into evaluating integrals. Students continue to learn integration techniques such as varying substitution methods, integration by parts, and partial fraction decomposition. Applications of integration remain to be the latter half of the course, where students explore area between curves, surface area, and volume generated by revolutions.

Prerequisites: Completion of Pre-Calculus, Trigonometry/Math Analysis with a grade of B or higher.

AP Calculus BC

AP Calculus BC is a rigorous, accelerated, introductory college-level course into single variable differentiation and integral Calculus. Students analyze limits, differentiation, and integrals in both a theoretical, conceptual, and computational level. Students investigate the meaning of limits and then proceed into differentiation. Basic techniques such as power, product, quotient, and chain rule are explored. Students then engage in application of derivatives, learning key concepts such as the Mean Value Theorem and Rolle's Theorem, as well as optimization and related rates. Further analysis of critical values, intervals of increasing/decreasing in functions, as well as concavity are emphasized. In addition, students learn how to evaluate area underneath curves by first a geometrical approach using the Midpoint, Upper/Lower, Trapezoidal, and Simpson's Rule. Afterwards, implementation of both the First and Second Fundamental Theorem of Calculus provides students with a direct approach into evaluating integrals. Students continue to learn integration techniques for further applications, where exploration of area between curves, surface area, and volume generated by revolutions are interpreted. In addition, students obtain a deep analysis of sequence and series, heavily investigating convergence and divergence. Parametric equations with emphasis in vector and conic sections are also included.

Prerequisites: Completion of Pre-Calculus, Trigonometry/Math Analysis with a grade of B, or higher or completion of Honors Math Analysis with a B or higher.

AP Statistics

AP Statistics is often times considered to be a different branch of mathematics that allows an alternative outlook into calculating and interpreting uncertainty. Students learn introductory probability, distinguishing population versus sample, translating graphical data, random variables, probability distribution functions, Central Limit Theorem, test statistics, confidence intervals, hypothesis testing, paired sampling, analysis of variance, and regression. By the end of the course, students will have a strong basis in deciphering numerical information and comprehending the importance of real-world applications.

Prerequisites: Completion of Pre-Calculus, Trigonometry/Math Analysis with a grade of B or higher.

'g' Category Honors & AP Courses

AP Computer Science

AP Computer Science A is an elective course for potential computer science majors and a foundation course for students interested in mathematics, engineering and the sciences. The purpose of this course is to introduce the student to the object-oriented programming paradigm using the Java programming language. This course emphasizes programming methodology, procedural abstraction, and in-depth study of algorithms and data structures, and a detailed examination of a large case study program. Students have individual hands-on laboratory work that helps to reinforce new concepts. Instruction includes preparation for the AP Computer Science A exam. At the completion of the course, the student should have a clear understanding of Java and have confidence in approaching and solving challenging problems, and recognizing ethical and social implications of using and developing software.

Prerequisites: Completion of Pre-Calculus or Trigonometry/Math Analysis with a grade of C or higher Additional Recommendation: Completion of a computer science course with a grade of C or higher.