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# Mathematics

The goal of the mathematics curriculum is to develop a sound understanding of mathematical concepts and foster the ability to apply them creatively to new situations. A major objective is for all students to gain confidence in their mathematical abilities and develop them to the fullest.

Courses are designed to provide students with a solid foundation in mathematical principles. By applying these principles in a variety of problem-solving situations, students become comfortable with mathematical techniques for evaluating problems presented in both practical and theoretical contexts. The department recognizes that the ability to reason logically and analytically is a skill valued beyond the confines of the mathematics classroom. To support critical thinking skills, teachers emphasize the ability to assess new problems and to determine how to proceed through a logical and organized path to a solution.

The use of technology, including the graphing calculator, is integrated throughout the curriculum. All Upper School students are required to own a TI-83 Plus or TI-84 Plus graphing calculator.
• ## Algebra I

2 semesters, 1 credit
Prerequisite: Department recommendation

This course develops a students’ computational, procedural and problem-solving skills in order to provide a solid foundation in algebraic concepts. The course gives students a working understanding of the properties of the real number system and the skills to simplify expressions, solve equations and inequalities, and solve systems of linear equations. Students will understand multiple representations of linear functions. Students learn to evaluate and graph exponential functions using the properties of exponents. They learn to perform operations on polynomials, including learning to solve using different strategies with an emphasis on factoring. Students learn to graph quadratic functions in different forms and understand the important aspects of the graphs. Students are introduced to counting and probability. Math language and vocabulary are developed along with problem-solving strategies applied through the use of tables, charts and graphs.

• ## Algebra II

2 semesters, 1 credit
Prerequisite: Geometry with a minimum grade of C-

In this course, students explore the topics of quadratic and higher-degree polynomial functions, their graphs, and their applications. Students are introduced to complex numbers and basic matrix operations. Other functions introduced in this course include radical functions, exponential functions, logarithmic functions and rational functions. Students also learn to identify and write general rules for sequences and to evaluate series. This course allows students to solidify their algebraic skills and prepares students for the appropriate level of Precalculus.
• ## Algebra II with Trigonometry

2 semesters, 1 credit
Prerequisite: Geometry with a minimum grade of B-, and department recommendation

In this course, students will expand their foundational knowledge from Algebra I to explore complex numbers, quadratics and higher degree polynomial functions, logarithmic functions, exponential functions, and rational functions. Using the aforementioned functions, students will solve equations, graph functions and explore their applications. Additionally, students will learn about sequences and series, conic sections, and trigonometric functions.
• ## Algebra II with Trigonometry Honors

2 semesters, 1 credit
Prerequisite: Geometry Honors with a minimum grade of B, and department recommendation

This course covers the same material as Algebra II with Trigonometry but at a faster pace and in a more rigorous manner. Additionally, students will explore probability and statistics, learn the binomial theorem, and verify trigonometric identities.
• ## AP Calculus AB

2 semesters, 1 credit
Prerequisite: Precalculus AB with a minimum grade of B-, and department recommendation

This rigorous course follows the College Board Advanced Placement syllabus. It is equivalent to the first semester of a college-level calculus course. It begins with a study of limit theory and quickly moves on to differential calculus. The concept of the derivative is applied to related rates, extrema, optimization and curve-sketching problems. The second half of the year is an in-depth study of integral calculus, which includes calculating area under the curve, volume of solids, and using differential equations in mathematical modeling problems. All students will sit for the AP Calculus AB exam in May.
• ## AP Calculus BC

2 semesters, 1 credit
Prerequisite: Precalculus BC Honors with a minimum grade of B, and department recommendation

This rigorous, fast-paced course follows the College Board Advanced Placement syllabus. It is the equivalent of two semesters of college calculus. In addition to the work covered in the AP Calculus AB course, the following topics are included: additional techniques and applications of integration, differential equations, the calculus of polar coordinates and vector-valued functions, the convergence and divergence of infinite series of constants, and Taylor polynomials. All students will sit for the AP Calculus BC exam in May.
• ## AP Statistics

2 semesters, 1 credit
Prerequisite: Algebra II with Trigonometry with a minimum grade of A-, and department recommendation

This course follows the College Board Advanced Placement syllabus and is equivalent to a one-semester, introductory, non-calculus-based college course in statistics. It is an introduction to statistical methods for business, health science, and social science statistics. The course introduces students to the major concepts and tools for collecting, summarizing, analyzing, and drawing conclusions from data. There are four broad themes in the AP Statistics course: collecting data by sampling and experimentation, summarizing quantitative and categorical data, an introduction to probability, and statistical inference. Students use technology, investigations, problem solving, and writing as they build conceptual understanding. All students who take AP Statistics will sit for the AP exam given in May.
• ## Calculus

1 semester, 1/2 credit; 1st semester only
Prerequisite: Precalculus with a minimum grade of C

In this semester elective, students are introduced to limits through graphical analysis. Students focus on derivatives, both graphically and algorithmically, with an emphasis on the general power rule and the chain rule, including the derivative of exponential functions. Students develop skills to understand applications of derivatives and their interpretations in context. Students apply derivatives to maximization and minimization problems in a variety of fields, including business and science.
• ## Geometry

2 semesters, 1 credit
Prerequisite: Algebra I or equivalent with a minimum grade of C-

Students complete a thorough study of Euclidean geometry and gain exposure to methods of mathematical proof and coordinate geometry. Main topics include angle relationships, polygons, congruent and similar triangles, circles, area, volume and right triangle trigonometry.
• ## Geometry Honors

2 semesters, 1 credit
Prerequisite: Department recommendation

This course covers the same topics of Euclidean geometry with a greater emphasis on methods of proof, coordinate geometry and trigonometry.
• ## Linear Algebra Honors

2 semesters, 1 credit
Prerequisite: AP Calculus with a minimum grade of B, and department recommendation

This rigorous, college-level course explores various matrix methods of solving systems of equations in addition to covering matrix algebra, determinants, vector geometry, vector spaces, eigenvalues and linear transformations. Students examine the proofs of theorems and apply the theorems in solving problems and creating their own proofs. Proof technique is emphasized. Students are also introduced to computer programming in C++.
• ## Math of Finance

2 semesters, 1 credit
Prerequisite: Algebra II with a minimum grade of C-

This course is a senior elective, covering a wide variety of mathematical concepts with an emphasis on finance. Over the first quarter, the course will provide a review of algebraic and geometric concepts in preparation for standardized testing while providing a firm foundation for the finance segment. During the remaining three-quarters of the year, students will cover the basics of investment in stocks and bonds, business modeling, loans (especially car loans and mortgages), tax calculations and retirement planning, all with an emphasis on the underlying mathematics. The year concludes with students preparing a budget using an Excel spreadsheet, which incorporates many of the concepts covered in the previous segments of the course.
• ## Multivariable Calculus (Honors)

2 semesters, 1 credit
Prerequisite: AP Calculus BC with a minimum grade of B, and department recommendation

This advanced course begins with an investigation of vectors in XYZ space, their dot and cross products, and the use of vectors in determining equations for lines and planes in space. Students then study vector-valued functions, their derivatives, velocity and acceleration vectors, tangent and normal vectors, and the use of vector valued functions in calculating arc length and curvature. Students explore multivariable functions, including limits and continuity, partial derivatives, differentiability, total differentials, the generalized chain rule, directional derivatives, tangent and normal lines, tangent planes, extrema, and optimization. Students then turn their attention to multivariable integral calculus with a study of iterated integrals, double integrals and volume, double integrals with polar coordinates, centers of mass, and surface area. They investigate triple integrals and the volume bounded by surface curves. They study cylindrical and spherical coordinates and delve into how cylindrical and/or spherical coordinates make the computation of some triple integrals much more manageable. Lastly, students turn their attention to vector analysis, line integrals, vector fields, flow and flux, Green's Theorem, the Divergence Theorem, parameterized surfaces, and Stokes' Theorem.
• ## Precalculus

2 semesters, 1 credit
Prerequisite: Algebra II with a minimum grade of B-, and department recommendation

This course is designed to provide students with a foundation that will enable them to enroll in the Calculus elective. Students will devote a large portion of the year to the study of trigonometric functions, analytic trigonometry, and applications of trigonometry. Students will also study counting principles, vectors, probability, and simple matrix theory. The course also elaborates on topics covered in Algebra II, with an emphasis on exponential functions, logarithmic functions, and sequences and series.
• ## Precalculus AB

2 semesters, 1 credit
Prerequisite: Algebra II with Trigonometry with a minimum grade of B-, and department recommendation

This course is designed to prepare students for AP Calculus AB or a calculus course in college. Students enrolling in this course should have a solid background in algebra and geometry. Students review polynomial and rational functions as well as applications and equations involving logarithms. This course extends the study of trigonometric relationships introduced in Algebra II with Trig by emphasizing graphing functions, solving equations and verifying identities. Additionally, students are introduced to vectors and basic matrix operations.
• ## Precalculus BC Honors

2 semesters, 1 credit
Prerequisite: Algebra II Honors with a minimum grade of B, and department recommendation
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This course is designed to prepare students for AP Calculus BC. It will build upon the students’ understanding and facility working with polynomial, rational, logarithmic and exponential functions by exploring those topics at a deeper level. Integration of ideas from previous mathematics courses is stressed, and students are given the chance to expand their abstract reasoning and spatial visualization skills while working in two- and three-dimensions. Topics of study include trigonometry, analytic geometry, vectors, polar and parametric equations, limit theory, differentiation rules, sequences, series and probability.
• ## Statistics

1 semester, 1/2 credit; 2nd semester only
Prerequisite: Algebra II with a minimum grade of C

This application-based elective exposes students to methods of data collection, display, and analysis. Students explore regression models and gain the skills to test hypotheses using statistical inference related to means and proportions. Graphing calculators, Excel and R-studio are tools students use to display and analyze data. Students become critical consumers of data as they apply their knowledge to analyze how data and statistics are portrayed in the media.

## La Jolla Country Day School

9490 Genesee Avenue
La Jolla, CA 92037
858-453-3440

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