math course descriptions
iNFORMATION ABOUT NFC ACADEMY'S ONLINE HIGH SCHOOL math COURSES
mathematics courses online (High School)
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STUDYING MATH
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MATH COURSES
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Mathematics builds logic and pattern recognition in the brain. The structure of math helps with organizational and problem-solving skills. By learning basic math skills, students learn to look at an entire problem before attempting to solve it. They learn to state the problem, come up with possible equations or possible ways to solve it, move step by step to come to a conclusion, and lastly, evaluate the final answer.
The philosopher Santayana famously said that "those who cannot learn from history are doomed to repeat it." This doesn't mean that you'd better memorize all those names and dates, but it means that you need to learn the patterns and lessons of history. The lessons and patterns of mathematics are important, too. If all you take from algebra is a comfort with variables and formulas, an ability to interpret graphs and to think logically, and a willingness to use abstraction when you try to solve problems, then you have gained some incredibly useful life skills |
*One semester course **Required for graduation |
ALGEBRA I & ALGEBRA I HONORS
Algebra I and Algebra I Honors are full year, high school credit courses that are intended for the student who has successfully mastered the core algebraic concepts covered in the prerequisite course, Pre-Algebra. Within the Algebra I course, the student will explore basic algebraic fundamentals such as evaluating, creating, solving and graphing linear, quadratic, and polynomial functions. Upon completion of the course the student’s goals are to successfully,solve single variable, absolute value, and linear systems of equations; solve and graph single variable, absolute value, and linear inequalities; evaluate, solve, and graph linear and quadratic functions as well as conceptualize the relationship between the independent and dependent variable of a function; understand and know how to apply the distance, midpoint, and slope formulas as well as the Pythagorean theorem; form an equation of a line using the slope-intercept, point-slope and standard forms of a line; organize data in the form of a table or matrix; perform complex matrix operations such as multiplication, evaluating the determinant, and solving a system of linear equations using Cramer's Rule; apply basic fundamental rules of exponents; be able to construct a formula or equation necessary to solve algebraic word problems involving area, perimeter, and linear systems of equations, basic probability and statistical reasoning, distance, and compounding interest; evaluate rational expressions and solve equations with rational expressions; and, simplify and perform operations with radical expressions and polynomials.
GEOMETRY & GEOMETRY HONORS
Geometry is a full year, high school math course for the student who has successfully completed the prerequisite course, Algebra I. The course focuses on the skills and methods of linear, coordinate, and plane geometry. In it, students will gain solid experience with geometric calculations and coordinate plane graphing, methods of formal proof, and techniques of construction. This comprehensive course guides students through interactive lessons that cover terminology, postulates and theorems, angles and shapes, and equations for measuring the dimensions and spatial attributes of shapes.
Students enrolled in this online geometry course are guided by a teacher in lessons that discuss simple points, lines, and ultimately complex shapes. Study includes coordinate geometry and isometry. Students will be encouraged to look beyond the obvious and focus on visualization, spatial reasoning, and problem solving from a Christ-centered perspective. The course units include text-based lessons, on and off-computer exercises, special projects, learning games, quizzes, and tests that appeal to today's digital generation and help teachers to evaluate progress and mastery of the materials. Ignitia Geometry enriches the educational experience for homeschool Christian school students and sparks a passion for learning.
Students enrolled in this online geometry course are guided by a teacher in lessons that discuss simple points, lines, and ultimately complex shapes. Study includes coordinate geometry and isometry. Students will be encouraged to look beyond the obvious and focus on visualization, spatial reasoning, and problem solving from a Christ-centered perspective. The course units include text-based lessons, on and off-computer exercises, special projects, learning games, quizzes, and tests that appeal to today's digital generation and help teachers to evaluate progress and mastery of the materials. Ignitia Geometry enriches the educational experience for homeschool Christian school students and sparks a passion for learning.
ALGEBRA II & ALGEBRA II HONORS
Algebra II is a full-year, high school math course intended for the student who has successfully completed the prerequisite course Algebra I. This course focuses on algebraic techniques and methods in order to develop student understanding of advanced number theory, concepts involving linear, quadratic and polynomial functions, and pre-calculus theories. This course also integrates geometric concepts and skills throughout the units, as well as introducing students to basic trigonometric identities and problem solving.
Students will learn to combine terms in algebraic expressions and explore compound sentences. Other topics include polynomial functions, data analysis, logarithms, function graphing, joint and combined variation, algorithms, conic sections, and probability. Throughout the course, students will explore the following topics: Sets, Structure, and Function; Numbers, Sentences, and Problems; Linear Equations and Inequalities; Polynomials; Algebraic Fractions; Real and Imaginary Numbers; Quadratic Relations and Systems; Exponential Functions; Counting Principles and Outcomes
Students will learn to combine terms in algebraic expressions and explore compound sentences. Other topics include polynomial functions, data analysis, logarithms, function graphing, joint and combined variation, algorithms, conic sections, and probability. Throughout the course, students will explore the following topics: Sets, Structure, and Function; Numbers, Sentences, and Problems; Linear Equations and Inequalities; Polynomials; Algebraic Fractions; Real and Imaginary Numbers; Quadratic Relations and Systems; Exponential Functions; Counting Principles and Outcomes
PRE-CALCULUS (HONORS)
Pre-Calculus prepares students for calculus and college level math with interactive online lessons and advanced problem solving. Students will explore the purpose of calculus and mathematical analysis while they expand their algebraic knowledge through the realm of trigonometry. With a clear, step-by-step delivery, this online course covers a wide range of mathematical concepts including an in-depth observation of math functions, quadratic inequalities, logarithms, probabilities, and permutation. Lessons are interactive to encourage retention of complex information and provide learning tools to clarify complicated mathematic operations.
Pre-calculus is a full-year, high school credit course that is intended for the student who has successfully mastered the core algebraic and conceptual geometric concepts covered in the prerequisite courses: Algebra I, Geometry, and Algebra II. The course primarily focuses on the skills and methods of analytic geometry and trigonometry while investigating further relationships in functions, probability, number theory, limits, and the introduction of derivatives.
Throughout the course, students will explore the following topics: Relations and Functions; Special Functions; Trigonometric Functions; Circular Functions and Graphs; Identities and Functions of Multiple Angles; Application of Trigonometric Functions; Inverse Trigonometric Functions and Polar Coordinates; Quadratic Equations; Probability; Calculus Basics
Pre-calculus is a full-year, high school credit course that is intended for the student who has successfully mastered the core algebraic and conceptual geometric concepts covered in the prerequisite courses: Algebra I, Geometry, and Algebra II. The course primarily focuses on the skills and methods of analytic geometry and trigonometry while investigating further relationships in functions, probability, number theory, limits, and the introduction of derivatives.
Throughout the course, students will explore the following topics: Relations and Functions; Special Functions; Trigonometric Functions; Circular Functions and Graphs; Identities and Functions of Multiple Angles; Application of Trigonometric Functions; Inverse Trigonometric Functions and Polar Coordinates; Quadratic Equations; Probability; Calculus Basics
ADVANCED CALCULUS (HONORS)
Advanced Calculus is a full-year, high school credit course that is intended for the student who has successfully mastered a minimum of four high school level mathematics courses that cover analytical and conceptual algebra (with heavy emphasis on functions), coordinate and plane geometry, and trigonometric functions. It is highly recommended that the student successfully complete pre-calculus as a prerequisite. The course primarily focuses on the skills and methods of analyzing graphical behavior of functions, the definition of a derivative as well as applications of derivatives, integration and their relationships with the graphical function. Textbook: The textbook for the course is the seventh edition of Calculus of a Single Variable by Ron Larson, Robert Hostetler, and Bruce Edwards (Boston: Houghton Mifflin, 2001; ISBN 0-618-14916-3).
Upon successfully completing the course, the student should have mastered the following concepts: perform operations on functions including composition and inverses; using calculation and estimation to evaluate limits; analyze infinite limits and the correlation between their values and the graph’s behavior; estimate and understand discontinuity and continuous functions; compute the derivative of a function using the power rule, product and quotient rule, chain rule and all trigonometric rules; use the concept of a derivative to interpret a function’s rate of change and continuity; construct the equation of a line tangent to a curve; evaluate the intervals for which a function is increasing or decreasing; interpret the Mean Value Theorem; evaluate the second derivative and find the points of inflection; utilize the derivative through application problems involving area under a curve, velocity, acceleration and speed; evaluate a definite integral using the Fundamental Theorem of Calculus, Riemann Sums, and the rate of change formula.
Upon successfully completing the course, the student should have mastered the following concepts: perform operations on functions including composition and inverses; using calculation and estimation to evaluate limits; analyze infinite limits and the correlation between their values and the graph’s behavior; estimate and understand discontinuity and continuous functions; compute the derivative of a function using the power rule, product and quotient rule, chain rule and all trigonometric rules; use the concept of a derivative to interpret a function’s rate of change and continuity; construct the equation of a line tangent to a curve; evaluate the intervals for which a function is increasing or decreasing; interpret the Mean Value Theorem; evaluate the second derivative and find the points of inflection; utilize the derivative through application problems involving area under a curve, velocity, acceleration and speed; evaluate a definite integral using the Fundamental Theorem of Calculus, Riemann Sums, and the rate of change formula.
TRIGONOMETRY (HONORS)
Trigonometry is a five-unit elective course for high school students who have successfully completed Algebra I, Geometry, and Algebra II. The materials cover a development of trigonometry from right triangle trigonometry to oblique triangles and the polar plane. Throughout the course, students will develop trigonometric formulas and use them in real-world applications, evaluate trigonometric proofs using complex trigonometric identities and solving trigonometric equations with regard to the unit circle. Students will study right triangle trigonometry; graphing and inverse functions; analytic trigonometry; trigonometric applications; polar coordinates
The course seeks to help students expand their knowledge and skills so that they may achieve the following goals: use trigonometry as a tool for indirect measurement; model natural phenomenon with trigonometric functions; perform operations with complex numbers using trigonometry; use trigonometric identities to evaluate trigonometric proofs and solve trigonometric equations with regard to the unit circle; solve for unknown sides and angles of right and oblique triangles using right triangle trigonometry, law of sines and law of cosines.
In attaining these goals, students will begin to see the "big picture" of mathematics and understand how numeric, algebraic, and geometric concepts are woven together to build a foundation for higher mathematical thinking.
The course seeks to help students expand their knowledge and skills so that they may achieve the following goals: use trigonometry as a tool for indirect measurement; model natural phenomenon with trigonometric functions; perform operations with complex numbers using trigonometry; use trigonometric identities to evaluate trigonometric proofs and solve trigonometric equations with regard to the unit circle; solve for unknown sides and angles of right and oblique triangles using right triangle trigonometry, law of sines and law of cosines.
In attaining these goals, students will begin to see the "big picture" of mathematics and understand how numeric, algebraic, and geometric concepts are woven together to build a foundation for higher mathematical thinking.
CONSUMER MATH
Consumer Math is an introduction to the many ways in which math can be used in everyday life. The course gives practical advice on how to handle situations that involve money and math principles. Consumer Math focuses on the basic skills and methods of arithmetic and provides students the opportunity to develop experience with algebraic techniques of evaluating variables and equations, including geometric formulas and interest equations. Students will also be introduced to topics in statistics.
The major areas of study in this course are as follows: Number Skills - number skills lessons consist of basic math review. They emphasize non-algebra-related topics, such as decimals, fractions, and percentages, topics that are typically covered before high school ; Statistics - statistics lessons are fairly advanced, providing instruction on sets and probability; measures of variation and distribution (such as standard deviation and z-scores); accurate sampling and confidence intervals; data interpretation; and graph creation and interpretation; Geometry - geometry lessons teach about measurement, focusing on applying measurement in the construction/building trades. These lessons cover ratio and proportion; perimeter, area, and volume of two- and three-dimensional figures (including pyramids, cones, cylinders, and spheres); and indirect measurement using similarity and right triangle relationships (including sine, cosine, and tangent); Personal Finance - Consumer Math also offers instruction on personal finance, covering topics like job acquisition, payroll deduction, commissions and tips, buying/leasing/renting goods and equipment, health insurance, asset depreciation, vacation and travel costs, retirement, life insurance, and will and estate planning; Taxes - some lessons address the issue of taxes, discussing federal, state, and local taxes, and also FICA and miscellaneous taxes; Banks and Financial Instruments - Consumer Math explores the world of banks and financial instruments, covering topics like savings and checking accounts; interest rates; stocks, bonds, and mutual funds; loan financing; credit cards; and mortgages.
The major areas of study in this course are as follows: Number Skills - number skills lessons consist of basic math review. They emphasize non-algebra-related topics, such as decimals, fractions, and percentages, topics that are typically covered before high school ; Statistics - statistics lessons are fairly advanced, providing instruction on sets and probability; measures of variation and distribution (such as standard deviation and z-scores); accurate sampling and confidence intervals; data interpretation; and graph creation and interpretation; Geometry - geometry lessons teach about measurement, focusing on applying measurement in the construction/building trades. These lessons cover ratio and proportion; perimeter, area, and volume of two- and three-dimensional figures (including pyramids, cones, cylinders, and spheres); and indirect measurement using similarity and right triangle relationships (including sine, cosine, and tangent); Personal Finance - Consumer Math also offers instruction on personal finance, covering topics like job acquisition, payroll deduction, commissions and tips, buying/leasing/renting goods and equipment, health insurance, asset depreciation, vacation and travel costs, retirement, life insurance, and will and estate planning; Taxes - some lessons address the issue of taxes, discussing federal, state, and local taxes, and also FICA and miscellaneous taxes; Banks and Financial Instruments - Consumer Math explores the world of banks and financial instruments, covering topics like savings and checking accounts; interest rates; stocks, bonds, and mutual funds; loan financing; credit cards; and mortgages.
INTEGRATED MATH
Integrated Math I is a mathematics course for high school students who have successfully completed either general mathematics for grade 8 or pre-algebra. This course is the first in a four-part, integrated high school mathematics curriculum. The materials in this course integrate the topics of algebra, geometry, probability, and statistics. Throughout the course, students will practice algebraic thinking and use algebra to model and solve real world problems. Students are exposed to several branches of mathematics and will explore ways in which each one can be used as a mathematical model in understanding the world.
Beginning with an introduction to algebra, the course leads students through the study of variables and expressions, radicals, exponents, geometry, functions, linear and quadratic equations, graphing, probability, and statistics. Throughout the course, students will explore the following topics: foundations of algebra; the language of algebra; geometry; coordinate geometry; linear systems; equations and inequalities; probability and statistics.
Beginning with an introduction to algebra, the course leads students through the study of variables and expressions, radicals, exponents, geometry, functions, linear and quadratic equations, graphing, probability, and statistics. Throughout the course, students will explore the following topics: foundations of algebra; the language of algebra; geometry; coordinate geometry; linear systems; equations and inequalities; probability and statistics.
ESSENTIALS OF MATH
Essentials of Mathematics is a semester-length review of the fundamentals taught in Pre-Algebra, Algebra I and Geometry courses and is useful at the high school level for basic skill remediation and/or practice necessary to prepare for a state exam. The course highlights basic mathematical skills through multiple review, practice and sample exam questions.
Upon successfully completing the course, the student should have mastered the following concepts: understand and know how to compute and define rational numbers; perform basic operations such as addition, subtraction, multiplication, and division with fractions, decimals, and percents; apply basic fundamental rules of exponents as well as scientific notation; be able to construct basic and complex geometric shapes; solve for perimeter, area, surface area, and volume; use inductive and deductive reasoning, conjectures, and estimation necessary to construct a picture, formula or equation needed for analyzing and solving algebraic and geometric word problems involving basic probability and statistical reasoning, scale factor, graphic representation of quantities, and linear systems of equations; solve single variable, absolute value, and linear systems of equations; evaluate, solve, and graph linear functions as well as conceptualize the relationship between the independent and dependent variable of a function; simplify and perform operations with radical expressions and polynomials; understand and know how to apply the slope-intercept form of a line, slope formula, and Pythagorean theorem
Upon successfully completing the course, the student should have mastered the following concepts: understand and know how to compute and define rational numbers; perform basic operations such as addition, subtraction, multiplication, and division with fractions, decimals, and percents; apply basic fundamental rules of exponents as well as scientific notation; be able to construct basic and complex geometric shapes; solve for perimeter, area, surface area, and volume; use inductive and deductive reasoning, conjectures, and estimation necessary to construct a picture, formula or equation needed for analyzing and solving algebraic and geometric word problems involving basic probability and statistical reasoning, scale factor, graphic representation of quantities, and linear systems of equations; solve single variable, absolute value, and linear systems of equations; evaluate, solve, and graph linear functions as well as conceptualize the relationship between the independent and dependent variable of a function; simplify and perform operations with radical expressions and polynomials; understand and know how to apply the slope-intercept form of a line, slope formula, and Pythagorean theorem
