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# Mathematics

Mathematics is a creative, dynamic system that we use to model and understand our environment. Pacifica teaches its math students to appreciate the aesthetics and beauty of mathematics and gives them a deep understanding of how it enriches their lives. We challenge them to gain not only a conceptual understanding of mathematical skills and principles, but also knowledge of, and experience with, pure reasoning. This logical reasoning will prepare the students for a broad range of situations in which answers to real life problems can be found with accuracy. The students will see the interdependence of mathematics to music, art, architecture, science, and philosophy and are encouraged to be lifelong students of mathematics regardless of the career they pursue.

## Math Courses

**Graduation Requirement: 3 Years**

### Algebra I

**(Year Course)**

Algebra I develops students’ fluency with linear, quadratic, and exponential functions. The critical areas of instruction involve deepening and extending students’ understanding of linear and exponential relationships by comparing and contrasting those relationships and by applying linear models to data that exhibit a linear trend. In addition, students engage in methods for analyzing, solving, and using exponential and quadratic functions. Some of the overarching elements of this course include the notion of function, solving equations, rates of change and growth patterns, graphs as representations of functions, and modeling.

### Geometry

**(Year Course)*** Prerequisite: Completion of Algebra 1*

This course presents geometry as a topic of importance for daily living, for career development, and for the future study of mathematics. It applies the skills of drawing, measurement, visualization and deductive logic to the study of triangles, quadrilaterals, general polygons, and circles. It analyzes concepts of similarity, congruence, and isometric transformations of figures. Emphasis is placed upon the analysis of right triangle and the area and volume of plane and solid figures. Trigonometry of right triangles is introduced. Techniques of coordinate geometry are developed. Algebraic representation and deductive analysis of geometric relations are stressed throughout the course. A TI-84PLUS graphing calculator is required for this course.

### Honors Geometry

**(Year Course)***Prerequisite: Completion of Algebra 1 with a grade of an A*

The fundamental purpose of the Geometry process is to learn how to think more clearly in a formal system, starting with axioms and logic, and continuing with properties and further definitions. This course includes standards from the conceptual categories of Geometry and Statistics and Probability. In this Geometry course, students explore more complex geometric situations and deepen their explanations of geometric relationships, presenting and hearing formal mathematical arguments. This course focuses on six critical areas: (1) establish criteria for congruence of triangles based on rigid motions; (2) establish criteria for similarity of triangles based on dilations and proportional reasoning; (3) informally develop explanations of circumference, area, and volume formulas; (4) apply the Pythagorean Theorem to the coordinate plane; (5) prove basic geometric theorems; and (6) extend work with probability. Underlying all of this will be the continual attention to sound reasoning and a further cultivating proper rationality.

### Algebra II

**(Year Course)*** Prerequisite: Completion of Geometry*

Algebra is the study of generalized arithmetical operations. The Algebra 2 course is an extension of the Algebra 1 curriculum. Topics that were first introduced in Algebra 1 will be built upon and applied to problems that require higher order thinking skills. A primary goal of Algebra 2 is for students to conceptualize, analyze, and understand functions. Students will investigate and learn about linear, absolute value, radical, quadratic, exponential, and logarithmic functions. Students will be required to think and communicate verbally, algebraically, numerically, and graphically. Students will be challenged to develop conceptual understanding, quantitative reasoning, and problem-solving skills in addition to mathematical procedural skills. Students will use technology such as graphing calculators and computers. A TI-84PLUS graphing calculator is required for this course.

### Honors Algebra II

**(Year Course)***Prerequisite: Minimum grade of an A in Geometry or a B or better in Honors Geometry*

Building on their work with linear, quadratic, and exponential functions, students extend their repertoire of functions to include logarithmic, polynomial, rational, and radical functions in the Algebra II course. This course includes standards from the conceptual categories of Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability. For the Algebra II course, instructional time focuses on four critical areas: (1) relate arithmetic of rational expressions to arithmetic of rational numbers; (2) expand understandings of functions and graphing to include trigonometric functions; (3) synthesize and generalize functions and extend understanding of exponential functions to logarithmic functions; and (4) relate data display and summary statistics to probability and explore a variety of data collection methods.

### Pre-calculus

**(Year Course)*** Prerequisite: Completion of Algebra 2 with a grade of C or better*

The first semester of Pre-calculus is devoted to the study of Math Analysis. This part of the course lays the foundation for Calculus by surveying the behavior of the most common functions and relations and their inverses, including conics, powers, exponential, logarithmic and trigonometric functions. The course explores ways of handling the graphs, tables, and formulas that represent the functions. Students are expected to read graphs and think graphically, and to read tables and think numerically. They have the opportunity to apply these skills along with their algebraic skills to many applications and to modeling real-world problems, including data analysis and regression equations. Graphing utilities are used extensively. Second semester is devoted to the study of Trigonometry. Trigonometry uses the techniques that students have previously learned from the study of algebra and geometry. The trigonometric functions studied are defined geometrically rather than in terms of algebraic equations. Facility with these functions as well as the ability to prove basic identities regarding them is especially important for students intending to study calculus, more advanced mathematics, physics and other sciences, and engineering in college. A TI-84PLUS graphing calculator is required for this course.

### Honors Pre-Calculus

**(Year Course)*** Prerequisite: Completion of Algebra 2 with a grade of an A*

Students will build off of a basis of Geometry and Algebra II to further their understandings and fluency with functions, polynomials, and trigonometry. This course includes standards from the conceptual categories of Number and Quantity, Functions, Algebra, Modeling, and Geometry. The Precalculus course has critical components: (1) solving, expressing, and graphing polynomial and rational functions with real and complex roots using the fundamental theorem of algebra; (2) building off simple trigonometry from geometry to numerically and algebraically handle more complex expressions containing trigonometric functions, and relating these back to graphs and solutions of real and complex numbers; and (3) relate the polynomial and trigonometric understanding of the first two components to graphing in the polar coordinate system and better understanding conic sections and sequences and series as a part of broader mathematical goals. Worth noting is that Honors Pre-Calculus will labor in content that is intentionally preparatory for AP Calculus.

### AP Calculus AB

**(Year Course)*** Prerequisite: Minimum grade of an A in Pre-calculus or a B or better in Honors Pre-calculus and instructor approval*

This course is designed to prepare the student to take the Advanced Placement Calculus AB Examination. Topics covered in AP Calculus AB include: algebraic, trigonometric, exponential and logarithmic functions, limits and continuity, the derivative and applications of the derivative, the antiderivative, the definite integral and applications and techniques of integrals. A TI-84PLUS graphing calculator is required for this course.