Mathematics Department

MATHEMATICS

DEPARTMENT

Note: Math classes are listed sequentially.  There is more than one option for Algebra I, Algebra II and Geometry.

101            PREPARATORY ALGEBRA                                                       1 CREDIT

Course Description:  This course would be designed to assist students who are determined to lack a sufficient background to be successful in a high school graduation credit Algebra 1 course to develop the skills and concepts necessary to be successful for high school credit Algebra 1.  This course could serve as the third credit for high school graduation.

***For a freshman to schedule into Algebra I they must meet benchmarks on MAP, Explore, & Teacher recommendation.

121          ALGEBRA I                                                                     1 CREDIT

Grade Level:  9-12     Prerequisite:  Required of all freshman taking Algebra I in 8th grade with a grade of C/D/F.

Student Expectations and Experience

1. Demonstrate an understanding of number theory and the application on problem-solving.

2. Write and solve linear equations and inequalities and their applications.

3. Solve non-linear functions such as quadratic, exponential and absolute value equations and their application.

4. Collect, organize, and display two-variable data.

5. Use proportional reasoning to write and solve real-world problems.

6. See patterns in arithmetic, geometric, quadratic, cubic sequences and relate to equations.

7. Use combinations, permutations, and conduct probability experiments and interpret the results.

8. Explore linear data and use of graphs to display data in an appropriate manner.

106   GEOMETRY    1 CREDIT

Prerequisite:  Algebra I (121)

This course is designed for college-bound students who had difficulty mastering the concepts in Algebra I or do not intend to pursue post-secondary mathematics or science programs.  Fundamentals are thoroughly introduced so that students develop basic geometric concepts and learn to apply geometric principles.  Manipulative such as geoboards, three-dimensional models, and tools for paper-folding should be incorporated in the course.  Topics will include points, lines, planes, plane figures, area and perimeter of plane figures, congruence, similarity, ratio and proportion, volume and surface area of solids, constructions and congruence, and measurements.  This course meets our state guidelines for pre-college curriculum requirements.

Student Expectations and Experiences

1.  Deduce properties of, and relationships between figures from given assumptions

2.  Classify figures (angles) in terms of congruence, similarity and apply these relationships

3.  Classify figures (triangles) in terms of congruencies, similarities and apply these relationships

4.  Represent problem situations (polygon relationships) with geometric models and apply properties of figures

5.  Use of formulas to determine area, perimeter, and volumes of two and three-dimensional figures

6.  Represent problem situations with geometric models and apply properties of figures.

.*** Must have an “A” or “B” in Algebra I or “A”, “B” or “C” in Algebra II to take Honors Geometry.

109   HONORS GEOMETRY    1 CREDIT

Prerequisite:  Algebra I (121), Algebra II (113)

This course is designed for college-bound students who had little difficulty with the concepts in Algebra I and/or Algebra II.  Focus should be on the discovery and realistic applications of geometric relationships and principles.  Topics include constructions, inductive and deductive reasoning, points, lines, planes, angles, triangles, planar figures, similarity and congruence, circles, three-dimensional geometry, area, volume, locus, coordinate geometry, and transformations.  The vocabulary, axioms, and theorems of Euclidean geometry are presented and students are required to write inductive and intuitive proofs in paragraph form, and deductive proofs in short two-column form.  This course meets our state guidelines for pre-college curriculum requirements.

Student Expectations and Experiences

1.  Classify figures (angles) in terms of congruence, similarity and apply these relationships

2.  Deduce properties of and relationships between figures (quadrilaterals) from given assumptions

3.  Classify figures (triangles) in terms of congruence, similarity and apply these relationships

4.  Translate between synthetic and coordinate representations and use reflections, translations, rotations, and dilation’s

5.  Deduce properties of, and relationships between figures from given assumptions

6.  Represent problem situations with geometric models and apply properties of figures (polygons)

7.  Represent problem situations with geometric models and apply properties of figures (Pythagorean Theorem)

8.  Deduce properties of figures (circles)

113___ ALGEBRA II

Prerequisite: Algebra I

In addition to expanding the mathematical concepts of Algebra I, emphasis should be placed on preparation of study of higher mathematics/abstract thinking skills, the function concept, and the algebraic solution of problems in various content areas.  Topics include the complex number system and matrices, quadratic equations and inequalities, graphs of functions and relations, and introductory work in conic sections

### Student Expectations and Experience

1. Demonstrate an understanding of number theory concepts and their applications

2. Perform operations on algebraic expressions, solve equalities, and inequalities

3. Simplify rational algebraic expressions

4. Explore nonlinear data and use of graphs to display data in an appropriate manner

5. Simplify radicals, rational number exponents, radical equations

6. Understand and use complex numbers

7. Demonstrate an understanding of coordinate geometry

.*** Must have an “A” or “B” in Algebra I or “A”, “B” or “C” in Algebra II to take Honors Geometry.

115  HONORS ALGEBRA II      1 CREDIT

Prerequisite: Algebra & teacher recommendation

This course is designed for students who plan to take upper-level math and are college bound.  In addition to all the topics for Algebra II, this course will expand on topics such as logarithms, rational functions and more.

Student Expectations and Experience

1.  Demonstrate an understanding of number theory concepts and their applications

2.  Perform operations on algebraic expressions, solve equalities, and inequalities

3.  Simplify rational algebraic expressions

4.  Simplify radicals, rational number exponents, and radical equations

5.  Understand and use complex numbers

6.  Demonstrate an understanding of coordinate geometry

120   ADVANCED TOPICS IN MATHEMATICS    1 CREDIT

Prerequisite:  Algebra I (121), Algebra II (113)

The purpose of the course is to provide for exploration and enrichment, maintenance of and improvement of previously acquired pre-college skills.  A wide variety of topics are offered in this course.  Among these are:  analytic geometry, space geometry, non-Euclidean geometry, transformational geometry, relations and functions including trigonometry, complex fields, matrices, vectors, sequences, series, and probability.

Students Expectations and Experiences

1.  Use matrices and determinants and apply to real-world situations

2.  Recognize conic sections and their characteristics

3.  Use Pascal’s Triangle and the Binomial Theorem to expand binomials

4.  Learn the concept of function, domain, range, and appropriate notation

5.  Recognize sequences and series and their applications

6.  Use probability, combinations, and permutations to represent and solve problems involving uncertainty

7.  Be introduced to concepts of topology and fractals

110   PRE-CALCULUS    1 CREDIT

Prerequisite:  Algebra I (121), Algebra II (13, Geometry (109), Advanced Topics in  Mathematics (120)

A or B in Advanced Topics strongly recommended!

This course is intended for students who plan to take a calculus course in high school and college.  It includes the topics traditionally taught as trigonometry and analytic geometry and integrates additional work with other functions.  Topics include:  functions, the inverse, graphs and their applications including polynomial, rational, exponential, logarithmic, circular, trigonometric, absolute value and natural number (sequences and series).

111 STATISTICS & PROBABILITY             1 CREDIT

Prerequisite: A or B in Algebra I

Students Expectations and Experience

1. Recall various mathematical operations and utilize the complex number system, demonstrating proficiency with the operations.
2. Interpret the graphs of functional relationships.
3. Use and apply exponential and logarithmic functions.
4. Recognize trigonometric functions and their applications
5. Demonstrate an understanding of polar coordinates and graphs of polar equations.

The purpose of this course in statistics is to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data.  Students are exposed to four broad conceptual themes:

1. Exploring Data: Describing patterns and departures from patterns
2. Sampling and Experimentation: Planning and conducting a study
3. Anticipating Patterns: Exploring random phenomena using probability and simulation.
4. Statistical Inference:  Estimating population parameters and testing hypotheses.

Students who successfully complete the course and exam may receive credit, advanced placement or both for a one-semester introductory college statistics course.  This does not necessarily imply that the high school course should be one semester long.  Each high school needs to determine the length of its Statistics course to best serve the needs of its students.  Statistics, like some other courses, could be effectively studied in a one-semester, a two-trimester or a one-year course.  Most schools, however, offer it as a one-year course.

112   CALCULUS            1 CREDIT

Grade Level:  12 or instructor permission

Prerequisite:  Pre-Calculus or ACT Math Score of 27 or Qualifying PSAT Math Score

A or B in Pre-Cal strongly recommended

Calculus is designed for students that are talented mathematically and highly motivated.  Students who successfully complete the course will have the opportunity to take a standardized comprehensive exam (a fee must be paid to take the exam); any student that passes this exam will be awarded collegiate credit by most colleges and universities.

Students Expectations and Experience

1. Students should be able to model a description of a physical situation with a function, a differential equation, or an integral.

2. Students should be able to use technology to solve problems, experiments, interpret results, and verify conclusions.

3. Students should be able to determine the reasonableness of solutions, including sign, size, relative accuracy, units of measurement

4. Students should be able to work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal.

5. Students should understand the meaning of the derivative and be able to use it to solve a variety of problems

6. Students should understand the meaning of the definite integral and be able to use it to solve a variety of problems.

7. Students should understand the relationship between the derivative and the definite integral.

8. Students should develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.

MT 065   BASIC ALGEBRA

OCTC would COMPASS test our seniors whose ACT scores are less than 18 to see if they qualify for this class (MT 065).  If a student passes the course and exit exam given by OCTC, they would be ready for MT 122 (Intermediate Algebra).  MT 122 is a credit bearing class at OCTC.

Course Description:

Basic algebra course covering variable expressions, linear equations and inequalities, exponents, polynomials, factoring, square and cube roots, scientific and engineering notation, elementary graphing, and measurement unit and conversions.

Course Outline/Objectives/Competencies:

1. Apply properties of real numbers
2. Perform conversions within and between U.S. Customary and the International System (SI-metric) of units.
3. Simplify and evaluate algebraic expressions using the order of operations.
4. Use the properties of integer exponents.
5. Perform operations with powers of 10, scientific and engineering notations, and units of measurement.
6. Simplify and evaluate square and cube roots.
7. Add, subtract, and multiply polynomials.
8. Divide a polynomial by a monomial.
9. Solve linear equations and inequalities.
10. Solve literal equations for variables of power 1.
11. Solve problems using direct and inverse variations.
12. Plot points in the rectangular coordinate system and graph linear equations using slope and y – intercept.
13. Calculate the third side of a right triangle using the Pythagorean Theorem.
14. Translate verbal statements into mathematical equations and solve.
15. Calculate and solve applied problems of the perimeter, circumference, area, volume and surface area.
16. Factor the greatest common factor from a polynomial; factor simple trinomial of the form x2 + bx + c; factor difference of two squares.
17. Solve applied problems using these competencies with real world applications.

MAT 150 College Algebra ( 3 credit hours)  Dual Credit

Description:

Selected topics in algebra and analytic geometry.  Develops manipulative skills and concepts required for further study in mathematics.  Includes linear, quadratic, polynomial, rational, exponential, logarithmic and piecewise functions; systems of equations and inequalities; and introduction to analytic geometry.  Students may not receive credit for both MAT 150 and MA 109 or for both MAT 150 and MA 110.  Credit not available on the basis of special exam.

Topics include:

• linear functions
• polynomial functions
• rational functions
• exponential functions
• logarithmic functions
• piecewise functions
• systems of equations and inequalities
• introduction to analytical geometry

Pre-requisites:   ACT score of 22 or above, Algebra I, Algebra II & Geometry

Upon completion of this course, the student can:

1.                   Recognize functions and specify the domain and the range of a given function;

2.                   Graph linear, quadratic, polynomial, rational, exponential, logarithmic, and piecewise functions;

3.                   Write function expressions and equations of conic sections from data, verbal description, or graph;

4.                   Solve applications using linear, quadratic, exponential, logarithmic, and piecewise functions;

5.                   Perform operations with functions;

6.                   Find inverse functions;

7.                   Solve linear and nonlinear systems of equations and inequalities;

8.                   Graph parabolas, ellipses, circles, and hyperbolas;

9.                   Recognize the equations and important features of the conic sections.

Outline:

I.             Review of Intermediate Algebra Topics

A.            Real and Complex Number Systems

B.            Exponents and Radicals

C.            Polynomials:  Factoring and Simplification

D.            Solution of Linear Equations & Inequalities

E.            Solution of Quadratic Equations

II.            Functions, Models,  & Applications

A.            Functions, Relations, Domain, and Range

B.            Linear Functions

D.            Exponential Functions

E.           Logarithmic Functions

F.             Polynomial and Rational Functions

G.            Operations with Functions

H.            Piecewise-Defined and Inverse Functions

III.          Systems of Equations & Inequalities

A.            Linear

B.            Nonlinear

IV.          Analytic Geometry

A.      Circles and Ellipses

B.      Parabolas

C.      Hyperbolas