# Mathematics

## Mathematics Course Offerings

- Foundations of Math I and Math I B Yearlong
- Math I
- Math I Honors
- Math II
- Math II Honors
- Math III
- Math III Honors
- Math IV
- Math IV Honors
- Pre-Calculus Honors
- Calculus Honors
- AP Calculus AB
- AP Calculus BC
- AP Statistics
- AP Precalculus
- NCVPS Online Electives in Mathematics

## Foundations of Math I and Math I B Yearlong

**Grade Level: **9

**Foundations of Math I**

This is a preparatory course for Math I. Students are introduced to algebra, geometry, and other mathematical topics that are integrated in a format that connects mathematics to students’ lives and the world of work. This course is taking in the Fall semester.

**Math I B**

Note: This course should be paired with Foundations of NC Math 1 and is taken in the Spring semester

The purpose of this course is to formalize and extend the mathematics that students learned in the middle grades. This course deepens and extends understanding of linear relationships, in part by contrasting them with exponential and quadratic phenomena, and in part by applying linear models to data that exhibit a linear trend. In addition to studying bivariate data, students also summarize, represent, and interpret data on a single count or measurement variable. The geometry standards that appear in this course formalize and extend students’ geometric experiences to explore more complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments. The Standards for Mathematical Practice apply throughout each course and, together with the content standards, require that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. This course fulfills the North Carolina high school graduation requirement for NC Math 1. The final exam is the North Carolina End-of-Course Test based on the NC Math 1 Standards

## Math I

**Grade Level: **9-10

Recommended prerequisite: Mastery of the middle school mathematics curriculum

Math I provides students the opportunity to study concepts of algebra, geometry, functions, number and operations, statistics and modeling throughout the course. These concepts include expressions in the real number system, creating and reasoning with equations and inequalities, interpreting and building simple functions, expressing geometric properties and interpreting categorical and quantitative data. The final exam is the North Carolina End-of-Course Test based on the Common Core Math 1 Standards.

## Math I Honors

## Math II

**Grade Level: **9-12

**Prerequisite:** ** **Math I

This course continues a progression of the standards established in Math I. In addition to these standards, Math II includes: polynomials, congruence and similarity of figures, trigonometry with triangles, modeling with geometry, probability, making inferences and justifying conclusions.

## Math II Honors

## Math III

**Grade Level: **9-12

**Prerequisite:** ** **Math I & Math II

Progresses from the standards learned in Math I and Math II. In addition to these standards, Math III extends to include algebraic concepts such as: the complex number system, inverse functions, trigonometric functions and the unit circle. Math III also includes the geometric concepts of conics and circles.

## Math III Honors

**Grade Level: **9-12

**Prerequisite:** ** **B in Math II Recommended

Designed for those students who have potential for outstanding performance in mathematics, Math III Honors is an accelerated, expanded, and demanding course. Students will work with real, irrational and imaginary numbers, solving systems of equations, problem solving with logarithms, conic sections and polynomials.

## Math IV

**Grade Level:** 11-12

**Prerequisite:** Math I, Math II, Math III

NC Math 4 focuses on functions and statistical thinking, continuing the study of algebra, functions, trigonometry and statistical concepts previously experienced in NC Math 1-3. The course is designed to be a capstone to introductory statistical concepts. Additionally, the course intentionally integrates concepts from algebra and functions to demonstrate the close relationship between algebraic reasoning as applied to the characteristics and behaviors of more complex functions.

## Math IV Honors

## Pre-Calculus Honors

**Grade Level: **10-12

**Prerequisite: **Math III

This is a survey course of various topics that will prepare the student for calculus and college-level mathematics courses. Emphasis is placed on functions, logarithms, and exponential systems of equations. Graphing calculators will be used on a regular basis. This course satisfies the 4th math requirement for the public universities in the UNC system. Math I, Math II with A or B recommended.

## Calculus Honors

**Grade Level: **11-12

**Prerequisite:** Honors Pre-calculus

Calculus focuses on the solution of problems which cannot be solved by algebra or trigonometry. Finding the slope of the tangent to a curve, areas of planar and spatial surfaces, the volume of solids, and the mathematics of speed and acceleration are examples. The ability to construct and interpret graphs is a necessary component of many solutions. Calculus is intended for students with a high aptitude in mathematics who intend to pursue fields related to mathematics, physics, and engineering while in college. Graphing calculators are used on a regular basis.

## AP Calculus AB

**Grade Level: **11-12

**(Offered at LHS, FHS)**

Recommended prerequisite(s): Mastery of the Precalculus curriculum

This is a college level course and is offered for students who will take the Calculus AB AP exam. Course is intended to be challenging and demanding. Calculus AB is primarily concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The connections among these representations are also important.

## AP Calculus BC

**Grade Level: **11-12

**(Offered through the North Carolina School of Science and Mathematics Connect Online Program at FHS)**

Recommended prerequisite(s): AP Calculus AB

This is a college level course and is offered for students who will take the Calculus BC AP exam. Calculus BC is an extension of Calculus AB rather than an enhancement; common topics require a similar depth of understanding. The course is intended to be challenging and demanding. Calculus BC is primarily concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The connections among these representations are also important.

## AP Statistics

**(Offered at FHS)**

**Grade Level: **11-12

Recommended prerequisite(s): Honors NC Math 3, NC Math 4, NC Math 4 Honors or Honors Precalculus

Advanced Placement Statistics introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students will observe patterns and departures from patterns, decide what and how to measure, produce models using probability and simulation, and confirm models. Appropriate technology, from manipulatives to calculators and application software, should be used regularly for instruction and assessment.

## AP Precalculus

**Grade Level: **11-12

Recommended prerequisite: Honors NC Math 3

AP Precalculus is designed to be the equivalent of a first semester college precalculus course. AP Precalculus provides students with an understanding of the concepts of college algebra, trigonometry, and additional topics that prepare students for further college-level mathematics courses. This course explores a variety of function types and their applications—polynomial, rational, exponential, logarithmic, trigonometric, polar, parametric, vector-valued, implicitly defined, and linear transformation functions using matrices.

Before studying precalculus, all students should develop proficiency in topics typically found in Math I, Math II, and Math III. Students should have developed the following:

- Proficiency with the skills and concepts related to linear and quadratic functions, including algebraic manipulation, solving equations, and solving inequalities
- Proficiency in manipulating algebraic expressions related to polynomial functions, including polynomial addition and multiplication, factoring quadratic trinomials, and using the quadratic formula
- Proficiency in solving right triangle problems involving trigonometry
- Proficiency in solving systems of equations in two and three variables
- Familiarity with piecewise-defined functions
- Familiarity with exponential functions and rules for exponents
- Familiarity with radicals (e.g., square roots, cube roots)
- Familiarity with complex numbers
- Familiarity with communicating and reasoning among graphical numerical, analytical, and verbal representations of functions

## NCVPS Online Electives in Mathematics

North Carolina Virtual Public School is an initiative by the State of North Carolina through which certified teachers provide online instruction in courses that meet the objectives of the North Carolina Standard Course of Study. * NCVPS course availability is based upon funding that high schools receive each school year for online courses and the number of course sections offered by NCVPS*, so students need to plan their course of studies carefully with the assistance of their school counselor.

*Details about NCVPS are found at www.ncvps.org.*

**FCS high schools may restrict enrollment in online classes to courses not already being provided face-to-face.****Prerequisite:** 3.0 GPA Recommended

**Note: ** Students should see their school counselor for online course availability and enrollment deadlines.

**Grade Level:** 10-12

Course Descriptions for NCVPS Online Electives in Mathematics

**These are online electives in Mathematics that are not available face-to-face at some FCS high schools.**

**AP Calculus AB (Yearlong - 1 credit)****AP Calculus AB (Block- 1 credit)****AP Calculus BC (Block - 1 credit)****Pre-Calculus Honors****Discrete Math**