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Mathematics

The Mathematics Department at Cate will encourage you to be a confident and competent mathematician, and, as a result, a better thinker. The coursework is designed to prepare you for tasks in your life in which you will be using mathematics or be required to think mathematically.

You will find yourself using technology in class, studying in groups, competing in contests, and working on the board solving engaging problems. You will take one course a year through your junior year, the final course determined by the initial Cate entry level.

For the last 25 years, Cate has been a leader in local California Mathematics League competitions, winning many county titles and finishing among the top schools in California. Last year, over 150 students and faculty participated – more than half of the School. Students also compete in the Westmont College Mathematics Contest and the American High School Mathematics Contest each winter.

Year course. This course introduces and emphasizes the basic concepts of algebra, including types of numbers and their properties, variables, operations with expressions, exponents, radicals, axioms, working with polynomials, solving linear and quadratic equations, solving inequalities, and working with rational expressions. Emphasis is placed on developing skills needed for future work in math, problem-solving techniques, logic, and applications to real-world situations.

Year course. This course introduces and emphasizes the basic concepts of algebra, including types of numbers and their properties, variables, operations with expressions, exponents, radicals, axioms, working with polynomials, solving linear and quadratic equations, solving inequalities, and working with rational expressions. Emphasis is placed on developing skills needed for future work in math, problem-solving techniques, logic, and applications to real-world situations.

Year course. Students who meet a qualifying standard will have the option of participating in our honors Geometry program. This class is not separately scheduled, instead students will be expected to commit to meeting one flex period a week to pursue additional challenges and greater depth of material. Students will also need to meet a certain competency level in these challenges to earn honors credit.

Year course. Students who meet a qualifying standard will have the option of participating in our honors Geometry program. This class is not separately scheduled, instead students will be expected to commit to meeting one flex period a week to pursue additional challenges and greater depth of material. Students will also need to meet a certain competency level in these challenges to earn honors credit.

Year course. This course builds a strong foundation of algebraic principles and skills by reviewing and extending the topics from previous courses. This is achieved through the study of polynomial, rational, radical, exponential, logarithmic, and trigonometric functions. In addition, discrete topics such as sequences, series, the binomial distribution, and combinatorics are considered. Emphasis is placed on the skills of graphing and analyzing functions, problem-solving, and relating the material to real-world applications.

Year course. This challenging course provides more emphasis on depth, proof, and applications, in addition to studying more topics such as matrices and conic sections. Students are expected to work more independently, with a spirit of inquiry and willingness to seek challenge to investigate why methods work.

Year course. Math 35 is a problem-solving course, which places both the burden and the excitement of investigation on students’ shoulders. Emphasis is placed on the role it plays in mathematical modeling and as a problem-solving tool. Students are expected to be at the very center of the cooperative process, discussing, writing about, and presenting well-reasoned explanations. The pace is swift and requires dedication, but the classroom is also a cooperative environment, one that builds mathematical confidence, understanding, and appreciation of the material.

Year course. This course is designed to prepare students for calculus by providing a thorough study of functions, trigonometry, and applications. Students explore the algebraic, numerical, and graphical representations of these functions and their transformations in a variety of contexts.

Year course. Students in this honors level course should already have a strong background in the various representations of toolkit functions and their transformations. This allows time for exploration of parametric and polar functions, recursion and series, as well as projects in mathematical modeling. Differential and integral calculus, following the Advanced Placement AB syllabus is woven in throughout the first two trimesters and is the main focus of study in the spring term.

Year course. This course is intended as a non-advanced mathematics elective for juniors and seniors who do not choose to pursue one of the advanced options. In the fall and winter trimesters, the course provides an introduction to the discrete math topics of probability and statistics, including the analysis of data, the conducting of surveys, sampling, experiments, and inference. In the spring the major themes of calculus (the limit, derivative, and integral) are introduced in a conceptual approach with applications, with extensive use of the graphing calculator. Financial applications including the use of spreadsheets will be included.

Year course. This college-level course is designed as in introduction to a variety of topics relating to integral and differential calculus including, functions, graphs, and limits, the conception and application of derivatives, the interpretation and application of integrals, and the fundamental theorem of calculus. The course outline focuses on the tools of Calculus for problem solving. Students will be prepared to take the AP examination in the spring.

Year course. This course seeks to challenge students with Calculus topics and a number of topics that prepare students for the Calculus (BC) AP examination but also exceed that syllabus. Emphasis is on theory and more complex problems than those encountered in Calculus 1 and there is emphasis on proof and applications. Topics include a review of differential and integral calculus, advanced integration techniques, applications, infinite series, vector algebra, and vector calculus. Students will be prepared to take the AP examination in the spring.

Year course. This course is equivalent to a college level one-semester introductory course in statistics. Its purpose is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: (1) Exploring data: observing patterns and departures from patterns; (2) Planning a study: deciding what and how to measure; (3) Anticipating patterns in advance: producing models using probability and simulation; and (4) Statistical inference: Confirming models. Students will be prepared to take the Advanced Placement examination in the spring.

Year course. This course explores advanced collegiate math topics beyond Calculus. In the fall, students study descriptive and inferential statistics at an accelerated pace along with calculus applications. Interested students will be prepared to take the AP Statistics exam in the spring. The winter term will expose students to multivariable calculus including partial derivatives, double and triple integrals, and applications. In the spring, students will be introduced to Linear Algebra.

For students who have taken the other math electives offered, independent study is available through our directed studies program. Students can design their own program or follow collegiate online options such as the Stanford EPGY program.