Mathematics

**Overview**

All students are required to take at least three years of math. A fourth year of mathematics is highly recommended by the faculty and administration. A fourth year is also required for admission to some universities and colleges.

All new students are required to take a mathematics placement test prior to registering for a math course. SJCHS math classes follow a traditional track while encompassing and adhering to all standards required for common core math. In addition, the SJCHS math curriculum prepares students for standardized tests such as the ACT and SAT as well for rigorous college level courses.

Placement in the Honors Math Track depends upon the previous math class taken, the results of a placement test, and teacher approval. Honors math classes are taught at a fast pace. They require proper background, enthusiasm for the subject, at least .75 - 1 hours of daily homework, and extra study time to prepare for more challenging exams.

**General Track Mathematics Courses: **

Algebra I, Geometry/Statistics, Intermediate Algebra II, College Algebra, Trigonometry

**Honor Track Mathematics Courses:**

Intermediate Algebra II Honors, College Algebra Honors, Trigonometry Honors with Advanced Precalculus Topics, AP Calculus AB, AP Calculus BC

**Basic Algebra **

This course establishes a foundation in algebra and problem solving. Topics include the concepts of signed numbers, exponents, order of operations, simplifying expressions, ratio, percent, and word problems. Additionally, students will be introduced to linear equations and inequalities, graphing, formulas, polynomials, factoring, and elements of geometry. Upon completion, students should be able to apply the above concepts in problem solving.

**Algebra 1**

This course in introductory algebra is designed to develop the manipulative skills of algebra. Topics include the fundamental concepts of operating within the real number system, working with first degree equations in one unknown, identifying and evaluating functions, factoring of and multiplication of polynomials, and working with algebraic fractions. Students will also cover linear equations and graphs, systems of linear equations, exponents and radicals, quadratic equations, and applications. In order to establish a strong foundation, a pre-algebra review of ratios and percentages will also be included. All topics include word problems and modeling.

**Geometry/Statistics | Core | Prerequisites: Algebra I**

Topics from geometry with an emphasis on geometric concepts necessary for standardized tests such as the ACT/SAT. Notation, measurements, and basic constructions will be covered. Also included will be in-depth study of congruence and similarity, properties of geometric figures including triangles, quadrilaterals, and polygons with n number of sides, as well as study of 3 dimensional solids and their surface area and volume.

The statistics portion of the course will cover basic definitions, descriptive statistics, graphs and histograms, central tendencies and measure of spread, probability distributions, linear regression and curve fitting.

**Intermediate Algebra II | Core | Prerequisites: Algebra I and Geometry, appropriate score on placement exam**

This course emphasizes concepts, techniques, and applications of the following major topics: factoring, algebraic fractions, radicals and rational exponents, complex numbers, quadratic equations, rational equations, two-variable linear equations/inequalities and their graphs, systems of linear equations and inequalities and their graphs, systems of linear equations and inequalities, and an introduction to functions, including quadratic, rational, exponential, logarithmic functions. Through the course, word problems and problem solving techniques are emphasized. To succeed in the course, students need to have a mastery of Arithmetic, Geometry, and Algebra I topics.

**Intermediate Algebra II | Honors | Prerequisites: Mastery of Algebra I and Geometry, appropriate score on placement exam, departmental approval, recommendation from previous mathematics instructor**

This course emphasizes concepts, techniques, and applications of the following major topics: factoring, algebraic fractions, radials and rational exponents, complex numbers, quadratic equations, rational equations, two-variable linear equations/inequalities and their graphs, systems of linear equations and inequalities and their graphs, and an introduction to functions, including quadratic, rational, exponential, logarithmic functions, introductions to discrete mathematics (time permitting). Through the course, word problems and problem solving techniques are emphasized. In addition to learning specific procedures, students study math theory.

Intermediate Algebra II Honors is a fast paced college level course with emphasis on mathematical theory, critical thinking skills, and problem solving. Students who wish to take Intermediate Algebra II Honors must have strong study skills and a deep commitment to the subject. Comprehensive final exams are required at the end of each semester.

**College Algebra | Core | Prerequisites: Intermediate Algebra or equivalent or placement exam**

Major study units include Set Theory, Algebraic Manipulations, Systems of Equations, Matrices, Problem Analysis, Functions, Graphic techniques, Transformations, Representation, Complex numbers, Polynomials Theory and Fundamental Theorem of Algebra, Rational Functions and their Graphs. Students are expected to excel in problem solving, and in the grasp of mathematical theory. The course will prepare students for an optional College Algebra CLEP exam, for which college credit is granted. *Graphing calculators are required.*

**College Algebra Honors | Core | Prerequisites: Intermediate Algebra and/or Trigonometry,**

**and/or appropriate score on placement exam and department approval**

The Honors section of the College Algebra course will include all topics from the Regular Section. In addition, conic sections will be covered, and, time permitting, selected topics from Discrete Mathematics. The course pace will be much faster, allowing for more in-depth coverage of the material. Problems requiring advanced problem solving skills will be included in the discussion of all topics. The homework assignments will be longer than in the regular section, as it is expected that honors students can complete assignments faster. Honors section will require a serious commitment from students, it is recommended for all students wishing to excel in science and other areas requiring high levels of math proficiency. The course is prerequisite for AP Calculus, and thus all students who plan to take AP Calculus (or calculus in college) should enroll in honors section. The course will prepare students for an optional College Algebra CLEP exam, for which college credit is granted. *Graphing Calculators are required.*

**Trigonometry/Advanced Precalculus Topics Honors Only | Core | Prerequisite: College Algebra or adequate score on placement exam and department approval.**

The study of Trigonometry includes: the definitions and applications of the trigonometric functions for acute and non-acute angles, radiant measure with its applications, the unit circle, definitions and application of the circular functions, graphs of the circular functions, trigonometric identities, solving trigonometric equations, law of sines and cosines, inverse trigonometric functions, vector applications of trigonometry, and trigonometric (polar) form of complex number and their applications.

Other topics are: in-depth coverage of conic sections, nonlinear systems of equations and inequalities, polar coordinates and polar graphs, parametric equations and graphs, advanced theory of complex numbers (including de Moivre’s formula and complex roots), advanced theory of counting and probability (including conditional probability).

During the course many College Algebra topics will be revisited, especially problem analysis, graphing techniques, theory of functions, modeling, and mathematical induction. Students deepen their ability to understand and apply the study of functions and advanced mathematics concepts to solve problems.

If applicable, students will learn how to use graphing calculators to solve problems, but students are expected to master all topics without calculators.

**AP Calculus AB | Core/Elective | Prerequisites: College Algebra, Trigonometry and departmental approval.**

This is a college-level course in differential and integral calculus, equivalent to one or one and a half semester of university calculus. Topics include a review of functions, an introduction to limits and continuity, derivatives and their applications, integrals and their applications, anti-derivatives and the Fundamental Theorem of Calculus, and an introduction to differential equations using slope fields. Course emphasis is on conceptual understanding and working with functions represented graphically, numerically, analytically, and verbally. Graphing calculator is used extensively. The Advanced Placement Calculus AB exam is expected of all students in this course. More information can be found at http://www.collegeboard.com/ap/students/calculus/.

As for all AP courses, students need to work at least .75-1 hour daily outside the class time, and to study extensively for tests. Extra effort is required in April to adequately prepare for AP test.

**AP Statistics | Elective | Prerequisite: Intermediate Algebra and departmental approval.**

The purpose of the AP course in statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. This course draws connections between all aspects of the statistical process, including design, analysis, and conclusions. Additionally, using the vocabulary of statistics this course teaches students how to communicate statistical methods, results and interpretations. Students learn how to use graphing calculators and read computer output in an effort to enhance the development of statistical understanding. More information can be found at http://www.collegeboard.com/ap/students/statistics/.

As for all AP courses, students need to work at least .75-1 hour daily outside the class time, and to study extensively for tests. Extra effort is required in April to adequately prepare for AP test.

**AP Calculus BC | Elective** | **Prerequisite: AP Calculus AB and departmental approval.**

This AP Calculus BC course covers topics in single variable differential and integral calculus typically found in a first-year college Calculus I and Calculus II two semester course sequence. The course prepares students to succeed on the AP Calculus BC exam and subsequent courses that draw on material from this course.

Topics include: Precalculus review, limits and continuity, derivatives & applications, curve sketching, related rates, techniques of integration & applications, applications of integration, L’Hôpital’s rule and improper integrals, applications of integral calculus, parametric equations and polar coordinates, differential equations, sequences and series, applications of series.

The course coverage includes the review and reinforcement of all topics taught in AP Calculus AB, and detailed coverage of topics not included in AP Calculus AB.

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