Math

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.

  • AP Calculus AB

    2 semesters, 1 credit 
    Prerequisite: Math III Accelerated 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 the area under the curve and the volume of solids, as well as using differential equations in mathematical modeling problems. All students will sit for the Advanced Placement Calculus AB exam in May.

  • AP Calculus BC

    2 semesters, 1 credit
    Prerequisite: Math III 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 Advanced Placement Calculus BC exam in May.

  • AP Statistics

    2 semesters, 1 credit
    Prerequisite: Math III with a minimum grade of A- or Math III Accelerated with B 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 introduces 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 this 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 to build conceptual understanding. All students will sit for the Advanced Placement Statistics exam in May.

  • Calculus

    2 semesters, 1 credit
    Prerequisite: Math III with a minimum grade of A- or Accelerated Math III with a minimum grade of C+ and department recommendation

    Students will begin this year-long class by reviewing precalculus concepts, including polynomial functions, trigonometric functions, inverses of functions, graphs of functions, and trigonometric identities. Students will go on to learn about limits, rates of change, the definition of a derivative, and the basic differentiation rules, including the product, quotient, and chain rules. Next, students will explore the various applications of derivatives, namely tangent lines, linear approximation, velocity and acceleration, related rates, and optimization. Students will then turn their attention to integral calculus, including antiderivatives, indefinite integrals, the basic integration rules, u-substitution, definite integrals, and the fundamental theorems of calculus. Students will close out the year with a study of the applications of integrals, including areas of irregular regions in the coordinate plane, the average value of a function on a closed interval, displacement, and separable differential equations.

  • Data Science and Statistics

    Prerequisite: Math III with a minimum grade of C. Concurrent enrollment in Math III AB or Math III BC Honors may be considered.

    This introductory data science course emphasizes a modeling approach with the General Linear Model. Students work with authentic datasets, investigate relevant and timely questions, and build coding skills. Throughout the course, data analyses and visualizations will be completed using the statistical programming language R, a programming language used in college and industry for data science applications. Additionally, students learn to find and clean data sets, store their work in Jupyter notebooks, apply critical thinking to interpret their observations, and provide statistical support for their conclusions. No prior experience with coding is necessary.

  • Linear Algebra (Honors)

     2 semesters, 1 credit, offered in academic years with an even start (e.g., 2026–27)
    Prerequisite: AP Calculus BC with a minimum grade of B and department recommendation  by current math teacher or teacher approval  
    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. Students are also introduced to computer programming in C++.

  • Math I

    2 semesters, 1 credit
    Prerequisite: Math B or Math 8

    Math I is the first of a three-year sequence of courses. Students solidify and extend their understanding of functions, solving equations, geometric relationships, and data analysis. Students continue to establish their understanding of linear and exponential sequences and functions. They expand their algebraic skills with a focus on solving equations and inequalities, including systems of linear equations and inequalities. Students develop explanations of geometric relationships of similarity and congruence through transformations and formal constructions. Students formulate and present mathematical arguments. Students extend their work from eighth grade, working with linear models and linear regression equations. Additionally, students employ histograms, dot plots, and box plots to describe and compare the shape, center, and spread of univariate data. Students will be introduced to strategies to recognize quadratic relationships and skills needed to solve quadratic equations.

  • Math I (Honors)

    2 semesters, 1 credit
    Prerequisite: Department recommendation by current math teacher

    Math I Honors is the first of a three-year sequence of compacted courses. The Math I curriculum is regularly extended through enrichment topics in each unit in this class. Students expand their knowledge of sequences to series formulas and sigma notation. Additionally, students in this course will focus on topics related to matrices. Students explore matrix addition and multiplication and use matrices to solve systems of linear equations with elementary row operations and the multiplicative inverse. Matrices are also used to represent vector transformations. Students build proficiency in moving between different forms of quadratic equations and identifying characteristics of the function from its equation, as well as factoring and completing the square techniques. Students develop strategies to solve quadratic equations using various methods and are introduced to complex numbers as solutions.

  • Math II

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

    Math II is the second of a three-year sequence of courses. Students expand their knowledge of functions to include in-depth work with quadratics. Students build proficiency in moving between different forms of quadratic equations and identifying characteristics of the function from its equation. Students develop strategies to solve quadratic equations using various methods and are introduced to complex numbers as solutions. They learn to distinguish between linear, exponential, absolute value, and quadratic functions and apply transformations to the graphs of each. Students explore inverse relationships, including domain restriction and logarithmic functions. Students extend their work with transformations to include dilations. They write formal proofs for similarity and congruence. Additional topics in geometry include angle-arc relationships, the development of formulas related to regular polygons, volume, radian measure, and parabolas as conic sections. Students broaden their understanding of probability by studying conditional probability using tree diagrams, Venn diagrams, and two-way tables.

  • Math II (Honors)

    2 semesters, 1 credit 
    Prerequisite: Math I Honors with a minimum grade of B+ and department recommendation
    Math II Honors is the second of a three-year sequence of compacted courses. Students will apply their existing knowledge to new and challenging situations. Students will build upon their fluency with linear, exponential, and quadratic functions at the start of the course and quickly move on to a study of piecewise, inverse, and logarithmic functions. Throughout the course, students will apply algebraic thinking and function transformations. They will deepen their understanding of deductive reasoning and writing two-column proofs in their study of geometry topics, including triangle congruence and similarity, special angle pairs, parallel lines and transversals, characteristics of special polygons, right triangles, and circles. Students will return to algebra topics, including conic sections, polynomials, and rational functions.

  • Math III

    2 semesters, 1 credit 
    Prerequisite: Math II with a minimum grade of C each semester
    Math III is the third course of a three-year sequence of courses. Students continue to develop skills working with linear, exponential, and quadratic functions while beginning to work with higher-order polynomial functions. They learn the Fundamental Theorem of Algebra, apply strategies of factoring and polynomial division for finding roots, and learn to graph polynomials. Students visualize 3-dimensional solids of revolution and practice using areas of cross sections to find an object’s volume. Students extend their skills with trigonometry by deriving and applying the Law of Sines and the Law of Cosines. Then, they learn to apply the sine, cosine, and tangent functions to any angle, use sine and cosine to model periodic behavior, and explore fundamental trigonometric identities. Students also explore statistics with the Central Limit Theorem, the normal distribution, and basic inferences related to means and proportions.

  • Math III AB

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


    Math III AB is the third of a three-year sequence of courses. This course is designed to prepare students for AP Calculus AB. Integration of ideas from previous mathematics courses is stressed. This course covers the content of Math III at a faster pace and with more depth on some topics, including a strong emphasis on algebraic manipulation, polynomials, inverses, and trigonometry. Additionally, students complete extensive work with trigonometric functions and identities important to calculus and are introduced to the concept of limits.

  • Math III BC (Honors)

    2 semesters, 1 credit 
    Prerequisite: Math II Honors with a minimum grade of B+ and department recommendation
    Math III BC Honors is the third course of a three-year compacted curriculum and is designed to prepare students for AP Calculus BC. Students build upon their 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, including work with matrices and vectors. Students are given the chance to expand their abstract reasoning. Students visualize 3-dimensional solids of revolution and practice using areas of cross sections to find an object’s volume. Students extend their skills with trigonometry by exploring and applying trigonometric identities important to calculus. Additionally, students study polar and parametric equations, limit theory, differentiation rules, applications of derivatives, sequences, series, and probability.

  • Math IV: Topics in Precalculus

    2 semesters, 1 credit 
    Prerequisite: Math III with a minimum grade of C+ and department recommendation
     
    This course is designed to prepare students for a calculus course in college. Students will review, expand upon, and apply their knowledge of polynomial, rational, exponential, and logarithmic functions, sequences and series, and probability. This course deepens and extends the study of trigonometric relationships introduced in Math III by emphasizing graphing functions, solving equations, and verifying identities. Students are introduced to vectors and their applications, matrix operations, and limits.

  • Mathematics of Finance

    2 semesters, 1 credit 
    Prerequisite: Math III with a minimum grade of C. Grade 12 only. 

    This course is a 12th-grade elective covering a wide variety of mathematical concepts with an     emphasis on finance. Over the first quarter, the course will review algebraic and geometric concepts in preparation for standardized testing while providing a firm foundation for the finance segment. During the remainder 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 emphasizing 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, offered in academic years with an odd start (e.g., 2025-26)
    Prerequisite: AP Calculus BC with a minimum grade of B and department recommendation

    This advanced course begins with investigating vectors in XYZ space, their dot and cross products, and the use of vectors in determining equations for lines and planes in space. Next, students 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 then 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 will then turn their attention to multivariable integral calculus by studying iterated integrals, double integrals, and volume, double integrals with polar coordinates, centers of mass, and surface area. They will close the year by investigating triple integrals and volumes bounded by surface curves.

La Jolla Country Day School

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

© 2025 La Jolla Country Day School 

Privacy Policy

Country Day Connection Newsletter

Accredited by: