## Math Course Descriptions

California Common Core State Content Standards

**Algebra 1 **

Topics taught in this course will emphasize functions, polynomials & factoring, quadratic equations and statistics, with a brief review of graphing linear equations and solving systems.

**Geometry**

This course is designed to teach the fundamentals of both plane and solid geometry, with a strong emphasis on transformation and constructions.. Geometry is the study of the measurements, properties and relationships of points, lines, angles, triangles, quadrilaterals, circles, and the nature of deductive and inductive proofs.

**Algebra 2**

This course is designed to teach higher level Algebra topics including rational exponents, quadratic inequalities, binomial theorem, functions, exponential and logarithmic equations, complex numbers, and probability. This course meets the UC/CSU math requirement.

**Algebra 2 Plus**

This course is intended to give students additional content needed to succeed in upper level math courses. It includes all standards from Algebra 2, plus matrices and vectors.

**Modern Math**

This course is designed to provide an alternative for college bound students who do not want to pursue Pre-Calculus and Calculus in high school, yet want to supplement their math education. The course includes applications of mathematical concepts in business, government, art, nature and statistics used by decision makers in our modern society.

**Trigonometry**

This course was developed as an option for students who wish to take more math classes but do not need Pre-Calculus. The purpose of the course is to introduce you to the uses of trigonometry both in its own right, and as a tool for more advanced math courses. Because the course is preparatory for the college-bound student, it provides depth but without the rigor of more advanced courses. Topics include: trigonometric functions, right triangle trigonometry, radian measure, graphing trigonometric functions, trigonometric identities and formulas, solving trigonometric equations, law of sines and cosines.

**Probability & Statistics**

This course is designed to provide an alternative for college prep students who do not want to pursue Pre-Calculus and Calculus in high school, yet want to supplement their math education. The topics to be covered include probability and statistics, collecting data, sorting data, analyzing data, binomial distribution and probability, linear regression, combinations, permutations, and normal distributions.

**AP Statistics**

Statistics is the science (and art) of learning from data. Data are numbers, but not “just numbers”, they are numbers with context. We will explore four general themes throughout this course: Exploring Data, Sampling and Experimentation, Anticipating patterns and Statistical Inference. AP Statistics is a math class not calculation intensive, but will challenge the intellect. A graphing calculator is heavily relied upon, so it important to feel at ease with technology.

**Pre-Calculus**

Students will be reintroduced to conic sections, factoring, polynomials, functions, and inequalities. Trigonometry will be studied as curricular functions and as ratios of sides of a triangle. Related topics include radian and degree measure, graphs of trigonometric functions. Methods for solving trigonometric equations will be explored. Exponential and logarithmic functions will be reintroduced. Vectors and vector properties will be examined.

**Accelerated Pre-Calculus**

This is an accelerated course, combining Pre-Calculus and Calculus A, so that a student may complete the Caclculus BC course in the second year. In the first semester, students study Trigonometric functions, equations and applications as well as identities and an introduction to polar coordinates and complex numbers, 2-dimensional and 3-dimensional vectors are studied in a manner to prepare the student for the study of Calculus. In the second semester, students will study differential calculus and part of integral calculus. In differential calculus the topics include: curve sketching, related rates, optimization, and implicit differentiation. In integral calculus the topics will include: indefinite integral, definite integral, the area under a curve, and volumes of revolutions and cross sections.

**Calculus AB**

Calculus AB is a college level course in beginning Calculus. Topics include limits, derivatives, and integration concepts; techniques and application of derivatives, techniques and applications of integration and an introduction to differential equations. Students will work with functions graphically, analytically, numerically, and through writing. AP requires the use of a graphing calculator for part of the course.

**Calculus BC**

Calculus BC is a college level course continuing the study of Calculus beyond Calculus AB. Topics include limits, derivatives and integration concepts; techniques and applications of derivatives, techniques and applications of integration, including the study of Calculus with Polar, Parametric, and Vector functions. Also included will be a study of the Calculus in Series and Taylor polynomials and an introduction to differential equations. Students will work with functions graphically, analytically, numerically, and through writing. AP requires a graphing calculator for part of the course.

**Calculus D**

CSUSM: MATH 260 (4 units): Calculus with Applications III Differential and integral calculus of functions of several variables: three dimensional analytic geometry, vector calculus, partial derivatives, multiple integrals, line integrals, applications, and historical perspectives.

*IB Mathematics*

**SL Studies**

Mathematical Studies SL is designed for the student that does not have a rigorous background in mathematics and does not plan on pursuing a career that requires a heavy concentration of mathematics. Focusing on the areas of statistics, sets, logic, probability, geometry, trigonometry, and functions is intended to expose the students to the topics of mathematics they can readily apply in a wide variety of fields. This concentration does not preclude the work they will also do in financial mathematics, number, algebra, and basic calculus. The goal is to produce a student that is well rounded in their mathematical knowledge and prepare them for further work in any of the topics they may pursue in college.

**SL(Standard Level)**

Mathematics SL is designed for the individual that does not have a strong interest in going into a field having a heavy concentration in mathematics (such as engineering), but rather into fields requiring knowledge of mathematics but not a theoretical basis of knowledge. Such fields are chemistry, psychology, economics, and business administration . Topics include statistics & probability, circular functions, trigonometry, vectors, matrices and calculus. Students going into the SL program still should have a proficient background in basic mathematical concepts, and should possess skills needed to apply simple mathematical techniques correctly. They should also be more independent and responsible than the typical student so that success will be more probable when confronted with the portfolio problems (Type 1 and 2).

**HL (Higher Level)**

Mathematical HL is designed for the student that plans on pursuing a career in mathematics or a field that requires a heavy concentration of mathematics. The emphasis of the course is on developing a deep understanding of mathematical concepts enabling the student to use the skills proficiently, develop links between various concepts, and justify their mathematics in proofs. A student leaving this course should be equipped to pursue further work in many areas of mathematics. The various topics that are covered in Mathematics HL are: algebra, functions and equations, circular functions and trigonometry, matrices, vectors, statistics and probability, calculus, sets, relations, and groups, series and differential equations, and discrete mathematics. The topics listed by the IBO for Mathematics HL are actually covered over a 4 year span in the courses of Pre IB Algebra 2, Pre IB Pre Calculus, Calculus BC, and Mathematics HL.The goal is to allow students to develop a strong background in mathematics so that they are prepared to pursue a degree in mathematics or start work in a field that relies heavily on mathematics.