# Mathematics Program

**Graduation Requirements: A math or math intensive course must be taken each year in high school, including Algebra I.**

### 397-ALGEBRA CONCEPTS

### (2 credits)

This every day course is to review basic math skills and concepts to prepare students for Pre-Algebra. Topics include operations of rational numbers, order of operations, factors/multiples, percentages, decimals, absolute value, graphing basics, general vocabulary and problem solving.

### 398-PRE-ALGEBRA

### (1 credit)

This course builds skills for students weak in algebraic concepts. This will enable students to further their math studies in Algebra and Geometry. Covered topics will include algebraic expressions and integers, one step equations and inequalities, decimals and equations, factors, fractions, and exponents, operations with fractions, ratios, proportions, and percents, solving equations and inequalities with two steps, linear functions and graphing, data analysis and probability.

### 400-ALGEBRA I-Level 1 (1 credit)

### 405-ALGEBRA I (1 credit)

Algebra I courses enable students to develop an understanding of the vocabulary and properties of Algebra. Students are able to communicate mathematically and are able to apply the properties. Students simplify algebraic expressions, solve problems, and equations. Level 1 students extend basic skills to application and continue to quadratic functions.

### 414-ALGEBRA I

### (2 credits)

This every day, year-long course will build a strong foundation necessary to succeed in future math courses. Concepts and topics are developed around the study of the real number system; understanding slope and its applications to linear systems and inequalities; the representations of functions through tables, graphs, and equations; factoring; and becoming fluent with polynomials and related operations. Students will also explore and graph quadratic equations. Learning the fundamentals will be accomplished through application of algebraic techniques to real world scenarios. In addition to the algebra concepts and skills, students will receive instruction on study skills. This course includes a review of pre-algebra. Upon successful completion of the course, 2 credits will be awarded, and the second credit meets the PHS Algebra I graduation requirement

### 421-GEOMETRY-Honors (1 credit)

### 420-GEOMETRY-Level 1 (1 credit)

### 425-GEOMETRY (1 credit)

Students study geometric concepts and applications through a variety of approaches including discovery and inductive/deductive reasoning. Students develop the geometric structure through theorems, postulates, properties, and definitions. They apply these concepts to solve geometric problems. Students formulate concepts through discovery and inductive reasoning. Level 1 students are required to formulate concepts through a formal deductive approach. Honors classes will include more in depth proofs, transformations, and symmetry.

**Prerequisites: **Algebra I For students to select Honors or Level 1, they need to earn a B- or better in the current Honors or Level 1 math course.

### 431-ALGEBRA II-Honors (1 credit)

### 430-ALGEBRA II-Level 1 (1 credit)

### 435-ALGEBRA II (1 credit)

Students review and expand the essential content of Algebra I. Students study properties of real numbers, solve and graph equations and inequalities (including absolute value), solve linear systems using determinants, simplify radical expressions, quadratic terms, study relations and functions, and perform operations on matrices factoring, polynomials, and rational expressions. In addition, Level 1 students examine conic sections, exponential, and quadratic functions. They apply their mathematical skills to problem-solving situations. Honors classes include arithmetic and geometric sequences and series, recursion formulas, infinite geometric series, binomial theorem, Pascal’s Triangle and mathematical induction are also explored. Rigorous intellectual practical applications are studied.

**Prerequisites: **Algebra I For students to select Honors or Level 1, they need to earn a B- or better in the current Honors or Level 1 math course.

### 432-APPLIED ALGEBRA

### (½ credit)

This is a survey course, focusing primarily on algebra skills. Students will develop ease in simplifying and evaluating polynomial and rational expressions, as well as solve linear equations and inequalities, quadratic equations and systems of linear equations. Emphasis will be placed on applying these skills in solving real world problems. Students must take the Accuplacer test prior to entering the class. If you have already taken Trigonometry, please consult with the Dean of the mathematics department.

**Prerequisite: Junior or Senior; Algebra II; Accuplacer test score of at least 45. **

### 443-TRIGONOMETRY

### (1 credit)

In this course students study trigonometric properties, applications, and they apply these skills and concepts to practical applications. Students solve triangular problems, and they learn trigonometric functions, convert radian measures, prove trigonometric identities, graph trigonometric functions, and apply Heron's Formula.

**Prerequisite: **Algebra II and Geometry

### 448-PRE-CALCULUS-HONORS (1credit)

### 447-PRE-CALCULUS-Level 1 (1 credit)

We will explore the twelve basic functions and their algebraic properties; reinforce connections among algebraic, graphical, and numeric representations. Included are quantitative literacy topics probability, statistics, and the mathematics of finance, exponential growth, exponential decay, and Newton’s Law of Cooling. Students will study the basic functions including: identity, squaring, cubing, reciprocal, square root, exponential, natural logarithm, absolute value, greatest integer, logistic, circular trigonometry functions and identities and a conic sections including: parabolas, circles, ellipses, and hyperbolas. We connect the algebra of functions to the visualization of their graphs, introduce parametric equations, piecewise defined functions, limit notation, continuity, bounded-ness, end behavior, domain, and range. In addition, the concept and application of a derivative is explored if time allows. This course integrates graphing technology throughout the course, not as an additional topic, but rather as an essential tool for both mathematical discovery and effective problem solving. Technology enables students to study many basic functions that allow insight into the properties of functions at an earlier time than most courses.

Honors Prerequisite: For students to select Honors, they need to earn a B- or better in Algebra II Honors and Geometry Honors.

Level 1 Prerequisite: For students to select Level 1, they need to earn a B- or better in Algebra II Level 1 and Geometry L1 or a B- in Trigonometry and Algebra II.

### 455-CALCULUS-AP (1 credit)

### 450-CALCULUS-CC (1 credit)

The Calculus course emphasizes broad concepts and focuses on understanding and manipulating functions, curves, theorems, and problem types. Students should understand the meaning of the derivative in terms of a rate of change and local linear approximation and should be able to use derivatives to solve a variety of problems. With the unifying themes of derivatives, integrals, limits, approximation, and applications and modeling, students should be able to communicate mathematics in well-written sentences and should be able to explain solutions to problems (APcentral.collegeboard.com). Students learn to use the graphing calculator. It is recommended that students purchase their own graphing calculator for home use.

The AP Calculus part of the course engages students to be able to work with functions represented in various ways, understand the meaning of derivatives and integrals to solve a variety of problems, communicate mathematics and explain solutions, model written descriptions of physical situations with a function, a differential equation, or an integral, use technology, and develop an appreciation of Calculus as a coherent body of knowledge (APcentral.collegeboard.com). Students are able to take the AP Calculus exam as administered by the College Board. Test fees are the responsibility of the student. Students desiring to take the AP portion will be required to meet with the teacher once a week outside of class with additional assignments weekly.

**Prerequisite: **Pre-Calculus

### 462-STATISTICS (½ credit)

Students learn the fundamental concepts of probability: graphs and tables, random sampling, measures of central tendency, probability and probability distributions, confidence interval, linear correlation, regression analysis and prediction. This Statistics course is for the student who plans to enter such fields as biology, business, economics, education, medicine, psychology, and sociology and is not yet ready for the college Statistics course.

**Prerequisite: **Algebra II

### 456-STATISTICS-AP (1 credit)

### 463-STATISTICS-CC (1 credit)

Students learn the fundamental concepts of probability: graphs and tables, random sampling, measures of central tendency, probability and probability distributions, confidence interval, error and sample size estimation, hypothesis testing, linear correlation, regression analysis and prediction. Statistics is a course for the student who plans to enter such fields as biology, business, economics, education, medicine, psychology, and sociology. It is recommended that students purchase their own graphing calculator for home use.

The Statistics AP part of the course introduces students to the major concepts and tools for collecting, organizing, analyzing, and drawing conclusions from data. Students design, administer, and tabulate results from surveys and experiments. Probability and simulations aid students in constructing models for chance phenomena. Sampling distributions provide the logical structure for confidence intervals and hypothesis tests. Students use a TI 84+ graphing calculator to investigate statistical concepts. To develop effective statistical communication skills, students are required to prepare frequent written and oral analysis of real data. Students are able to take the AP Statistics exam as administered by the College Board. Test fees are the responsibility of the student.

**Prerequisite: **Algebra II or Geometry

### 467-INTRODUCTION TO PROGRAMMING WITH PYTHON

### (½ credit)

This course is intended as an introduction to programming which will provide students with a strong foundation using the programming language Python, as well as general computer science theory. It is assumed that students taking this course have no formal programming experience. Therefore, the course focuses on basic programming concepts such as commands for performing calculations, receiving input and displaying output, basic flow control structures, and functions / methods. The class will also begin looking at the object-oriented programming concepts of classes and objects. This course requires mathematical problem solving skills, as students will be examining complex problems that computers can solve more effectively than humans can.

**This course qualifies as a Math Intensive course. **

**Prerequisite:** Junior or Senior; Algebra II or taking concurrently