# Mathematics

Students today require more rigorous mathematical knowledge and skills to pursue higher education, to compete in a technologically sophisticated and connected workforce, and to be informed citizens. By taking a concept-centered approach to instruction and utilizing our K-12 essential standards, teachers help build capacity in students to make connections across content areas. This approach will help students gain an understanding of fundamental ideas in arithmetic, measurement, geometry, probability, data analysis and statistics, and algebra and functions while developing proficiency in mathematical skills.

Students also will learn to use a variety of methods and tools to compute, including paper and pencil, mental arithmetic, estimation, and calculators. Graphing utilities, spreadsheets, calculators, computers, and other forms of electronic information technology are now standard tools for mathematical problem-solving in science, engineering, business and industry, government, and practical everyday affairs; therefore, the use of technology must be an integral part of teaching, learning, and assessment.

Courses in mathematics are designed to build students’ ability to:

• Analyze situations in mathematical terms, and pose and solve problems based on observed situations.
• Select and use various types of reasoning to develop and evaluate mathematical arguments and proof.
• Organize and consolidate mathematical thinking through precise verbal, written and graphical communication.
• Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
• Use representations to model and interpret physical, social and mathematical phenomena.
• Evaluate and use technology appropriately as a tool to support and apply the problem-solving process.

## Mathematics Course Descriptions

Algebra 1, 2, 3

Algebra 1 includes the study of properties and operations of the real number system; evaluating rational algebraic expressions; solving and graphing first-degree equations and inequalities; translating word problems into equations; operations with and factoring of polynomials; and solving simple quadratic equations.

Algebra 2 topics typically include field properties and theorems; set theory; operations with rational and irrational expressions; factoring of rational expressions; in-depth study of linear equations and inequalities; quadratic equations; solving systems of linear and quadratic equations; graphing of constant, linear, and quadratic equations; properties of higher-degree equations; and operations with rational and irrational exponents.

Algebra 3 courses review and extend algebraic concepts for students who have already taken Algebra 2. Course topics include, but are not limited to, operations with rational and irrational expressions; factoring of rational expressions; linear equations and inequalities; quadratic equations; solving systems of linear and quadratic equations; properties of higher-degree equations; and operations with rational and irrational exponents. The courses may introduce topics in discrete mathematics, elementary probability and statistics, matrices and determinants, and sequences and series.

Algebra 1: Part 1, Part 2

Algebra 1, Part 1 is the first part in a multipart sequence of Algebra 1. This course generally covers the same topics as the first semester of Algebra 1, including the study of properties of rational numbers (i.e., number theory), ratio, proportion, and estimation, exponents and radicals, the rectangular coordinate system, sets and logic, formulas, and solving first-degree equations and inequalities.

Algebra 1, Part 2 is the second part in a multipart sequence of Algebra 1. This course generally covers the same topics as the second semester of Algebra 1, including the study of properties of the real number system and operations, evaluating rational algebraic expressions, solving and graphing first-degree equations and inequalities, translating word problems into equations, operations with and factoring of polynomials, and solving simple quadratics.​

Algebra 2/Trigonometry

Algebra 2/Trigonometry courses combine trigonometry and advanced algebra topics and are usually intended for students who have attained Algebra 1 and Geometry objectives. Topics typically include right trigonometric and circular functions, inverses, and graphs; trigonometric identities and equations; solutions of right and oblique triangles; complex numbers; numerical tables; field properties and theorems; set theory; operations with rational and irrational expressions; factoring of rational expressions; in-depth study of linear equations and inequalities; quadratic equations; solving systems of linear and quadratic equations; graphing of constant, linear and quadratic equations; and properties of higher-degree equations.​

Algebra Functions Data Analysis

​Within the context of mathematical modeling and data analysis, students will study functions and their behaviors, systems of inequalities, probability, experimental design and implementation, and analysis of data.

AP Calculus AB

Following the College Board’s suggested curriculum designed to parallel college-level calculus courses, AP Calculus AB provides students with an understanding of the concepts of calculus and experience with its methods and applications. These courses introduce calculus and include the following topics: functions, graphs, limits, and continuity; differential calculus (including definition, application, and computation of the derivative; derivative at a point; derivative as a function; and second derivatives); and integral calculus (including definite integrals and antidifferentiation).

AP Calculus BC

AP Calculus BC applies the content and skills learned in AP Calculus AB to parametrically defined curves, polar curves, and vector-valued functions; develops additional integration techniques and applications; and introduces the topics of sequences and series.

AP Statistics

AP Statistics is an introductory college-level statistics course that introduces students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students cultivate their understanding of statistics using technology, investigations, problem solving, and writing as they explore concepts like variation and distribution; patterns and uncertainty; and data-based predictions, decisions and conclusions.

Computer Mathematics

This course is intended to provide students with experiences using computer programming techniques and skills to solve problems that can be set up as mathematical models. Students enrolled in Computer Mathematics are assumed to have studied the concepts and skills in Algebra 1 and beginning geometry.

Prerequisite: Algebra 1

Consumer Math

Consumer Mathematics courses reinforce general mathematics topics (such as arithmetic using rational numbers, measurement, ratio and proportion, and basic statistics) and apply these skills to consumer problems and situations. Applications typically include budgeting, taxation, credit, banking services, insurance, buying and selling products and services, home and/or car ownership and rental, managing personal income, and investment.

Data Science

The Data Science Standards of Learning provide an introduction to the learning principles associated with analyzing big data. Through the use of open source technology tools, students will identify and explore problems that involve the use of relational database concepts and data-intensive computing to find solutions and make generalizations. Students will engage in a data science problem-solving structure to interact with large data sets as a means to formulate problems, collect and clean data, visualize data, model using data, and communicate effectively about data formulated solutions. For students considering math, science or engineering pathways, this course will provide useful experiences and help build important skills.

Geometry

Geometry courses, emphasizing an abstract, formal approach to the study of geometry, typically include topics such as properties of plane and solid figures; deductive methods of reasoning and use of logic; geometry as an axiomatic system including the study of postulates, theorems, and formal proofs; concepts of congruence, similarity, parallelism, perpendicularity, and proportion; and rules of angle measurement in triangles.

Geometry and the Visual Arts

Students will discover how mathematics is related to art by studying examples of works of art from cultures around the world, examining the mathematical concepts and techniques underlying these works, and using graphic design software and other software tools to create original works of art employing these ideas and techniques. A tentative list of topics to be covered includes: recursion, symmetry transformations, perspective and projections, color mixing, the golden ratio, and sequences. Examples will be drawn from Asian, African and Arabic art, as well as European art.

IB Math: Analysis and Approaches I

This course focuses on developing important mathematical concepts in a coherent and rigorous way, with an emphasis on communication and independent inquiry. The course reviews the fundamentals of algebra, geometry and trigonometry, before delving into an in-depth investigation of statistics and single-variable calculus.

IB Math: Applications and Interpretation I, II

IB Math: Applications and Interpretation I focuses on introducing important mathematical concepts with an emphasis on statistics and introductory calculus. Instruction will focus on the application of mathematics to real-world phenomena and the interpretation of advanced mathematical notions in terms of concrete scenarios.

IB Math: Applications and Interpretation II focuses on introducing important mathematical concepts with an emphasis on statistics and introductory calculus. Instruction will focus on the application of mathematics to real-world phenomena and the interpretation of advanced mathematical notions in terms of concrete scenarios.

Prerequisites: Geometry and Algebra 2

Mathematical Analysis

Students enrolled in Mathematical Analysis are assumed to have mastered geometry and Algebra 2 concepts. Mathematical Analysis develops students’ understanding of algebraic and transcendental functions, parametric and polar equations, sequences and series, and vectors. The content of this course serves as appropriate preparation for a calculus course.

Probability & Statistics

Probability and Statistics courses introduce the study of likely events and the analysis, interpretation, and presentation of quantitative data. Course topics generally include basic probability and statistics: discrete probability theory, odds and probabilities, probability trees, populations and samples, frequency tables, measures of central tendency, and presentation of data (including graphs). Course topics may also include normal distribution and measures of variability.

PVCC MTH 154/155 Quantitative Reasoning/Statistics

PVCC MTH 154 Quantitative Reasoning​ presents topics in proportional reasoning, modeling, financial literacy, and validity studies (logic and set theory). Focuses on the process of taking a real-world situation, identifying the mathematical foundation needed to address the problem, solving the problem, and applying what is learned to the original situation. This is a Passport Transfer course.

PVCC MTH 155 Statistics presents elementary statistical methods and concepts including visual data presentation, descriptive statistics, probability, estimation, hypothesis testing, correlation, and linear regression. Emphasis is placed on the development of statistical thinking, simulation, and the use of statistical software. This is a Passport Transfer course.

Prerequisite: Algebra 2

PVCC MTH 161/261 PreCalculus I/Applied Calculus I

MTH 161 PreCalculus I presents topics in power, polynomial, rational, exponential, and logarithmic functions, and systems of equations and inequalities. Credit will not be awarded for both MTH 161: Precalculus I and MTH 167: Precalculus with Trigonometry or equivalent. This is a Passport Transfer course.

MTH 261 Applied Calculus I introduces limits, continuity, differentiation and integration of algebraic, exponential and logarithmic functions, and techniques of integration with an emphasis on applications in business, social sciences and life sciences. This is a Passport Transfer course.

PVCC MTH 167 PreCalculus with Trigonometry

This course presents topics in power, polynomial, rational, exponential, and logarithmic functions; systems of equations; trigonometry; trigonometric applications, including Law of Sines and Cosines; and an introduction to conics.

Note: Credit will not be awarded for both MTH 167 PreCalculus with Trigonometry and MTH 161/162 PreCalculus I/II, or equivalent.

Prerequisite: Algebra 2

PVCC MTH 265/267 Calculus III/Differential Equations

MTH 265 Calculus III focuses on extending the concepts of function, limit, continuity, derivative, integral and vector from the plane to the three-dimensional space. Topics include vector functions, multivariate functions, partial derivatives, multiple integrals, and an introduction to vector calculus. Designed for mathematical, physical and engineering science programs.

MTH 267 Differential Equations introduces ordinary differential equations. Includes first order differential equations, second and higher order ordinary differential equations with applications, and numerical methods.

Skills Development Math 1, 2, 3

​This is an individualized and comprehensive course that covers the concepts and skills necessary to be successful in Algebra 1.