# Where limits don’t exist.

## Where limits don’t exist.

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.

Constructing understanding through a problem based learning (PBL) curriculum is challenging, inspires curiosity, and is very rewarding. Each day, our students arrive to class with a handful of problems prepared for sharing and discussion. We sit in a circle, showcasing work on the board using iPads with Apple TV, and talk through specific problem solving strategies, highlight content connections, and seek feedback on alternate methods. Students see the true interconnectedness of math every day and they are also exposed to important life skills like risk-taking, collaboration, and effective written communication. There are a lot of “aha” moments and instances of students taking responsibility for their own learning.

**Click on the following links to learn more about PBL at Cate**

Frequently Asked Questions about Cate PBL

What students and parents say about Cate PBL (link coming)

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. This course also introduces functions algebraically and graphically. Emphasis is placed on developing skills needed for future work in math, problem-solving techniques, logic, and applications to real-world situations. Emphasis is also placed on ability to use technology to emphasize and accentuate the math. Although the course assumes no previous experience with high-school algebra, it is still an excellent choice for students who have had an algebra course, but who feel they need to strengthen their grasp of fundamental skills and ideas.

Year course. Math 15 is a problem-based learning course, which places both the burden and the excitement of investigation on students’ shoulders. We study algebra at the conceptual level, but 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. Intended for students with some algebra and geometry experience.

Year course. This course introduces and stresses the basic topics and concepts of plane and solid geometry, coordinate geometry, including angles, triangles, lines, circles, polygons, area, similarity, congruence, and right angle trigonometry. Emphasis is placed on developing problem-solving skills, logical understanding of theorems and proofs, the deductive reasoning process, and relating the material to realistic applications. Algebra skills and descriptive statistics are integrated into the year to provide depth and connections. Prerequisite: Math 10 or 15.

Year course. Math 21H is a problem-based learning course that provides students with a more rigorous, integrated, and in-depth exposure to geometry in two and three dimensions. Students investigate lines, polygons, vectors, circles, and parabolas while also analyzing right-triangle trigonometry. Through the exploration of linear motion, students are introduced to optimization and transformations. We use a variety of materials, including iPad technology and problems that focus on pattern-building through the integration of algebra and geometry.

Prerequisite: Math 15 and consent of department.

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 problem solving, graphing and analyzing functions in multiple forms, and relating the material to real-world applications. Honors level is offered and selection is made by the department. Prerequisite: Math 20

Year course. Students in this course access the same content described in Math 30 but go more deeply into proof and applications, while also studying more topics such as matrices and conic sections. Students must qualify for this level and are expected to work more independently, with a spirit of inquiry to investigate why methods work, and with a willingness to challenge themselves. Prerequisite: Math 20 or 21H, and consent of department.

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. Entering students should have a strong background in Algebra, usually meaning B or better in Math 30. Prerequisite: Math 30.

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. Students enrolling in the honors course may be eligible to enroll in Math 51H (BC Calculus) in the following year. Prerequisite: Math 30 or 31H and consent of department.

Year course. This course is intended as a 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. Prerequisite: Math 30.

Year course. This college-level mathematics 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. Prerequisite: Math 40 and consent of department.

Year course. This course seeks to challenge our strongest students with Calculus topics and a number of topics that prepare students for the Calculus (BC) Advanced Placement 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 Advanced Placement examination in the spring. Prerequisite: Math 41H or Math 50 and consent of department.

Year course. This course is equivalent to a College level one-semester introductory course in statistics. The purpose of Advanced Statistics 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. Prerequisite: Math 40 or 45, and consent of department.

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. The software program “Mathematica” will be used throughout the winter and spring. These topics also provide a natural connection to the style of proof common to higher-level mathematics. The course is intended for students who have completed calculus and have an interest in further work in mathematics. Prerequisite: Math 50 or 51H.

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.