Mathematics

Math Sequence

In an effort to meet all students’ needs and raise the rigor for all students, the math department has developed the following sequences, based upon a student’s skill level and problem solving ability as evidenced by test scores such as the MAP, ACT, and grades in previous math classes.

Students must have Algebra 1, Geometry, and Algebra 2 in combination with a math course each year of high school according to the KDE Graduation Requirements.

• **Students wanting to move into the advanced sequence their 10th grade may take Advanced Geometry and Advanced Algebra 2 courses concurrently, and then take Algebra 3, JCTC Mat 150 & JCC Sta 220 or Advanced Precalculus their 11th grade year.
• JCTC Mat 150 is not recommended as an option for students who successfully complete Advanced Precalculus.
• Students interested in taking JCTC Dual Credit math courses must meet the ACT requirement prior to acceptance into the course.

ALGEBRA 1

Graduation Requirement

Suggested Grade Level: 9

Prerequisites: Teacher Recommendation

Max GPA: 4.0 Credits: 1.0

Course Description: This course is the study of high school Algebra 1 content. Upon completion of the course, students should be able to represent relationships mathematically, develop fluency in writing, interpret expressions and equations, translate between various forms of linear equations and inequalities and use them to solve problems including those that require a system of equations, solve linear equations, apply related solution techniques and the laws of exponents to solve simple exponential equations, understand function definition and notation, contrast linear and exponential graphical representations, make judgments about the appropriateness of linear models, perform arithmetic operations on inequalities, interpret functions and fluently use function notation, construct and compare linear and exponential models and solve related problems, factor quadratic and cubic expressions solve quadratic equations to interpret related quadratic functions and explore non-linear relationships. This course should be designed to meet the high school graduation credit for Algebra 1 and to build a solid foundation necessary for future high school math courses.

GEOMETRY

Graduation Requirement

Suggested Grade Level: 10

Prerequisites: Algebra 1

Max. GPA: 4.0 Credits: 1.0

Course Description: This course is the study of high school Geometry content. Upon completion of the course, students should be able to prove theorems and solve problems about triangles, quadrilaterals, and other polygons, apply reasoning to complete geometric constructions and explanations, establish triangle congruence criteria based on analyses of rigid motions and formal constructions, use similarity to solve problems and apply similarity in right triangles to understand right triangle trigonometry (with particular attention to special right triangles and the Pythagorean theorem), develop the Law of Sines and Cosines from understanding relationships in right triangles, apply knowledge of two-dimensional shapes to consider the shapes of cross-sections and the result of rotating a two-dimensional object about a line, connect algebraic concepts to geometric concepts through the rectangular coordinate system (such as deriving the equation of a circle given the center and radius length using the distance formula or Pythagorean Theorem) and prove basic theorems about circles, chords, secants, and tangents.

ADVANCED GEOMETRY

Graduation Requirement if not taking Geometry

Suggested Grade Level: 9 – 10

Prerequisites: "A" in Algebra 1 and Teacher Recommendation

Max. GPA: 4.0 Credits: 1.0

Course Description: This course is designed for students with a high degree of proficiency in abstract mathematical ideas. It prepares students for Advanced Algebra 2. This course is the study of high school Geometry content. Upon completion of the course, students should be able to prove theorems and solve problems about triangles, quadrilaterals, and other polygons, apply reasoning to complete geometric constructions and explanations, establish triangle congruence criteria based on analyses of rigid motions and formal constructions, use similarity to solve problems and apply similarity in right triangles to understand right triangle trigonometry (with particular attention to special right triangles and the Pythagorean theorem), develop the Law of Sines and Cosines from understanding relationships in right triangles, apply knowledge of two-dimensional shapes to consider the shapes of cross-sections and the result of rotating a two-dimensional object about a line, connect algebraic concepts to geometric concepts through the rectangular coordinate system (such as deriving the equation of a circle given the center and radius length using the distance formula or Pythagorean Theorem) and prove basic theorems about circles, chords, secants, and tangents.

ALGEBRA 2

Graduation Requirement

Suggested Grade Level: 10-11

Prerequisites: Algebra 1 and Geometry

Max. G.P.A.: 4.0 Credits: 1.0

Course Description: This course is the study of high school Algebra 2 content. Upon completion of the course, students should be able to use properties of numerical operations to perform calculations involving polynomials,, identify zeros of polynomials and make connections between zeros of polynomials and solutions of geometry to extend trigonometry to model periodic phenomena, work with a variety of function families exploring the effects of transformations, analyze functions using different representations, build, interpret and compare functions including square root, cube root, piecewise, trigonometric and logarithmic functions, identify appropriate functions to model situations, adjust parameters to improve the models, and compare models by analyzing appropriateness of fit.

ADVANCED ALGEBRA 2

Graduation Requirement if not taking Algebra 2

Suggested Grade Level: 9-12

Prerequisites: An "A" or "B" in Advanced Geometry AND Teacher Recommendation.

Max. GPA: 4.0 Credits: 1.0

Course Description: This course is designed for students with a high degree of proficiency in abstract mathematical ideas. It prepares students for Advanced Pre-Calculus. This course is the study of high school Algebra 2 content. Upon completion of the course, students should be able to use properties of numerical operations to perform calculations involving polynomials,, identify zeros of polynomials and make connections between zeros of polynomials and solutions of geometry to extend trigonometry to model periodic phenomena, work with a variety of function families exploring the effects of transformations, analyze functions using different representations, build, interpret and compare functions including square root, cube root, piecewise, trigonometric and logarithmic functions, identify appropriate functions to model situations, adjust parameters to improve the models, and compare models by analyzing appropriateness of fit.

ALGEBRA 3

Graduation Requirement possibility for 4th math credit

Suggested Grade Level: 11-12

Prerequisite: Geometry, Algebra 2 AND Teacher Recommendation

Max GPA 4.0 Credit: 1.0

Course Description: The content of this course goes beyond a traditional Algebra 2 course and should provide opportunities for students to: solve applied (in context) problems using various types of equations (linear, quadratic, exponential, trigonometric, logarithmic and power functions piecewise), read and analyze real-life problems using mathematical modeling, perform matrix operations, graph and interpret data represented by linear, quadratic, exponential, logarithmic and power functions, use numerical and graphical data to make reasonable and valid conclusions, solve applied problems that can be modeled with equations and inequalities involving absolute value, solve systems of linear equations using several techniques including matrices, use and verify trigonometric identities, solve applied problems that can be modeled with exponential and logarithmic equations, find terms of sequences and find the sum of finite series.

MATHEMATICS CONCEPTS: COLLEGE READINESS

Graduation Requirement possibility for 4th math credit

Does NOT meet Pre College Curriculum Requirement (NCAA/NAIA)

Suggested Grade Level: 12

Prerequisites: Algebra 2 AND Teacher Recommendation

Max GPA: 4.0 Credits 1.0

Course Description: This course is designed to be taken after completion of Algebra 1, Geometry and Algebra 2. Topics include probability and statistics, extension of algebra and geometry concepts, and discrete mathematics. It is primarily intended for students who are not planning on a career path after high school that requires an intensive math background. This math course is intended to provide non-math major students the quantitative literacy needed to be an informed citizen in the 21st century. The course will include a quick review of calculations and then a study of the mathematics behind Consumption, Logic and the Media, Inflation & Depreciation, Taxation, Borrowing & Saving, patterns & Nature, Likelihood, Description of Groups, and Fitness & Sports. This course is mandatory for all seniors who have not met the math college readiness benchmarks by the start of their senior year. Specific instruction will also be included to help students reach college readiness benchmarks in math.

PROBABILITY AND STATISTICS

Graduation Requirement possibility for 4th math credit

Suggested Grade Level: 12

Prerequisite: Algebra 2

Max GPA 4.0 Credit: 1.0

Course Description:This course should focus primarily on the conceptual categories: Statistics & Probability and Modeling to address such concepts as theoretical and experimental probability, independent and conditional probability using them to interpret data, rules of probability to compute probabilities of compound events in a uniform probability model, calculations of expected values, analysis of decisions and strategies using probability concepts, binomial distributions, normal distributions, displaying and describing distributions of data, collecting data, measures of central tendency and spread and methods of inferential statistics. Technology should be an integral part of this course to generate plots, regressions functions and correlation coefficients and to simulate possible outcomes relatively quickly based on a given situation.

ADVANCED PLACEMENT (AP) STATISTICS

Graduation Requirement possibility for 4th math credit

Suggested Grade Level: 10-12

Prerequisites: Advanced Algebra 2 OR an "A" or "B" in Algebra 3 AND Teacher Recommendation

Benchmark scores for JCTC College Dual Credit: ACT Math 22+ and completion of College Algebra or equivalent or AP Calculus AB Exam score of a 3 or higher

Max. GPA: 5.0 Credits 1.0

Course Description: The AP Statistics course is equivalent to a one-semester, introductory, non-calculus based college course in statistics. The course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. There are four themes in the AP Statistics course: exploring data, sampling and experimentation, anticipating patterns, and statistical inference. Students use technology, investigations, problem solving, and writing as they build conceptual understanding. College credit is earned with a qualifying score on an AP exam.Students must meet eligibility requirements and must take the AP exam to receive the weighted GPA and the Advanced Placement course title on the transcript

JCTC MATH 150 (College Algebra) -- 3 hours

Graduation Requirement possibility for 4th math credit

Offered at OCHS and JCTC Carrollton

Suggested Grade Level: 11-12

Prerequisite: Successfully passed Algebra 1, "A" or "B" in Algebra 2, Geometry AND Teacher Recommendation. Must have qualifying ACT to receive dual credit.

*Benchmark scores for JCTC College Dual Credit: ACT Math 22+ OR SAT Math 510+

*Can take course if ACT is 19-21 with a supplemental Math Lab

Max. GPA: 4.0 Credits: 1.0 semester long course.

Course Description: This course includes selected topics in algebra and analytic geometry. Develops manipulative algebraic skills required for successful calculus study. Course includes linear, quadratic, polynomial, rational, exponential, logarithmic and piecewise functions, systems of equations and inequalities and introduction to analytic geometry.

JCTC STA 220 (Introduction to Statistics) – 3 Hours

Math Elective/Graduation Requirement possibility for 4th math credit

Suggested Grade Level: 12

Pre-requisite: Successful completion of MAT 150 AND Teacher Recommendation

Max. GPA: 4.0 Credits: 1.0 semester long course.

Course Description: Examines statistical description of sample data including frequency distributions, measures of central tendency, and measures of dispersion. Includes theoretical distributions, statistical estimation, and hypothesis testing. Introduces simple linear regression and correlation.

ADVANCED PRECALCULUS

Graduation Requirement possibility for 4th math credit

Suggested Grade Level: 11-12

Prerequisite: At least a "B" in Advanced Algebra 2 OR an A in Algebra 3 AND Teacher Recommendation.

Max. GPA: 4.0 Credits 1.0

Course Description: This course is designed for students to attain the concepts necessary to be successful in a Calculus course, an AP Calculus course or a College Calculus course. Objectives for this course should include, but are not limited to: solve equations and inequalities involving polynomial, rational, exponential, logarithmic and trigonometric functions, understand and apply the behavior and properties of polynomial, rational, exponential, logarithmic, and trigonometric functions, graph polynomial, rational, exponential, logarithmic, and trigonometric functions, use technology to solve and graph various types of equations and inequalities and prove trigonometric identities.

ADVANCED PLACEMENT (AP) CALCULUS AB - JCTC MAT 175 – 5 hours

Graduation Requirement possibility for 4th math credit

Suggested Grade Level: 11-12

Prerequisite: At least a "B" in Advanced Pre-calculus AND Teacher Recommendation.

Benchmark scores for JCTC College Dual Credit: ACT Math 27+

Max GPA: 5.0 Credits: 1.0

Course Description: AP Calculus AB is roughly equivalent to a first semester college calculus course devoted to topics in differential and integral calculus. The AP course covers topics in these areas, including concepts and skills of limits, derivatives, definite integrals, and the Fundamental Theorem of Calculus. The course teaches students to approach calculus concepts and problems when they are represented graphically, numerically, analytically, and verbally, and to make connections among these representations. Students learn how to use technology to help solve problems, experiment, interpret results, and support conclusions. College credit is earned with a qualifying score on an AP exam. Students must meet eligibility requirements and must take the AP exam to receive the weighted GPA and the Advanced Placement course title on the transcript.

ADVANCED PLACEMENT (AP) CALCULUS BC

Math Elective/Graduation Requirement possibility for 4th math credit

Suggested Grade Level: 12

Prerequisite: AP Calculus AB AND Teacher Recommendation.

Max GPA: 5.0 Credit: 1.0

Course Description: AP Calculus BC is roughly equivalent to both first and second semester college calculus courses. It extends the content learned in AB to different types of equations (polar, parametric, vector-valued) and new topics (such as Euler's method, integration by parts, partial fraction decomposition, and improper integrals), and introduces the topic of sequences and series. The AP course covers topics in differential and integral calculus, including concepts and skills of limits, derivatives, definite integrals, the Fundamental Theorem of Calculus, and series. The course teaches Version 1.0 191 students to approach calculus concepts and problems when they are represented graphically, numerically, analytically, and verbally, and to make connections amongst these representations. Students learn how to use technology to help solve problems, experiment, interpret results, and support conclusions. College credit is earned with a qualifying score on an AP exam. Students must meet eligibility requirements and must take the AP exam to receive the weighted GPA and the Advanced Placement course title on the transcript.