## Mathematics - Study.com

## Organization

## Descriptions and credit recommendations for all evaluated learning experiences

Various; distance learning format.

30 hours (15 weeks).

February 2012 - Present.

Upon successful completion of the course, students will be able to: define, identify, and construct various geometric figures; calculate geometric values of two- and three-dimensional shapes including perimeter, circumference, area, surface area, and volume; solve problems involving perpendicular lines, parallel lines, and parallel lines with transversals; prove that two triangles are congruent or similar using transformations as well as theorems and postulates; classify different types of polygons including triangles and quadrilaterals; compute values involving circles, chords, arcs, and sectors; recall the basics of conic sections including the parabolas, ellipses, and hyperbolas; apply coordinate geometry to solve problems and calculate values such as distance and midpoint; and explain the basic assumptions of non-euclidean geometry and apply trigonometric ratios to solve right triangles.

The course is self-paced. Instruction is delivered through online video and text lessons. Students are assessed through quizzes and a proctored final exam. Topics include: basics of geometry; logic and proof in mathematics; intro to geometric figures; triangle properties and construction; parallel lines and polygons; triangle congruence; ratios and proportions in geometry; similar polygons; quadrilaterals overview; circles overview; overview of conic sections; 3d geometry; analytical geometry; non-euclidean geometry; and introduction to trigonometry.

In the lower division baccalaureate associate/degree category, 3 semester hours in Business, Mathematics, or as a general business elective (2/17).

Various; distance learning format.

24 hours (6 weeks).

December 2012 - Present.

Upon successful completion of the course, students will be able to: solve and graph linear equations and systems of equations; solve for absolute value; factor polynomials and quadratics; graph parabolas and polynomials; perform operations with functions; perform operations with rational expressions; evaluate logarithms and solve equations; solve exponential equations; solve factorials and binomials; and use summation notation.

Major topics include: linear equations; matrices; absolute value; inequalities; polynomials; complete numbers; factoring; functions; exponents; rational expressions; logarithms; probability mechanics; and sequences and series.

In the lower division baccalaureate degree category, 3 semester hours in College Math, Algebra, or as a general elective (12/16).

Various; distance learning format.

8 hours (6 weeks).

December 2012 - Present.

Upon successful completion of the course, students will be able to: write and graph linear equations; solve and graph inequalities with one or two variables; simplify expressions with exponents and rational exponents; know how to graph cubics, quartics, and quintics; evaluate logarithms and solve logarithmic equations; understand uses of logic in mathematics; understand elements of sets and subsets; calculate percent increase with relative and cumulative frequency tables; calculate probabilities; and find perimeter, area, and circumference in triangles, circles, and rectangles.

Major topics include: linear equations; inequalities; quadratic equations; complex numbers; exponents; polynomials; rational expressions; functions; logarithms; logic; sets; probability; statistics; and geometry.

In the lower division baccalaureate degree category, 3 semester hours in College Math, or as a general elective (12/16).

Various; distance learning format.

24 hours (6 weeks).

December 2012 - Present.

Upon successful completion of the course, students will be able to: determine the domain and range of functions; solve and graph equations with exponential functions and logarithms; evaluate compound inequalities and systems of inequalities; graph 1- and 2- variable inequalities and absolute value inequalities; solve linear equations with one and two variables; factor quadratic equations; evaluate and graph piecewise functions; solve visualizing geometry problems; solve problems with the Pythagorean theorem; and use the double angle formula.

Major topics include: functions; exponential and logarithmic functions; inequalities; linear equations; rational equations; quadratic equations; exponents; polynomials; geometry; and trigonometry.

In the lower division baccalaureate degree category, 3 semester hours in Calculus, College Math, or as a general elective (12/16).

Various; distance learning format.

28 hours (6 weeks).

December 2012 - Present.

Upon successful completion of the course, students will be able to: identify continuities and discontinuities in functions and graphs; define and apply the Intermediate Value Theorem; determine the limits of functions and use a graph to define limits; summarize the formal definition of a derivative and appraise graphical representations of derivatives; calculate derivatives of trigonometric functions, polynomial equations, and exponential equations; calculate higher order derivatives; use Newton's Method to find roots of equations; define the Fundamental Theorem of Calculus; calculate integrals of trigonometric and exponential functions; and solve integrals using substitution and trigonometric substitution.

Major topics include: continuity; limits; rate of change; calculating derivatives; graphing derivatives; applications of derivatives; integrals; integration techniques; integration applications; and differential equations.

In the lower division baccalaureate degree category, 4 semester hours in Calculus, College Math, or as a general elective (12/16).

Various; distance learning format.

26 hours (7 weeks).

December 2013 - Present.

Upon successful completion of the course, students will be able to: write and solve mathematical modeling equations, including those pertaining to cost determination, economic equilibrium and relating a 2- dimensional figure's side lengths, perimeter and area; evaluate linear equations, 1- and 2- variable inequalities and systems of equations; factor and solve quadratic equations, including solving by utilizing the quadratic formula; complete operations involving rational expressions and solve rational equations; complete operations involving polynomials, including factoring polynomials using the remainder, factor and rational zero theorems as well as synthetic division; evaluate absolute value expressions and solve and graph absolute value equations and inequalities; complete operations involving complex numbers and graph complex numbers on the complex plane; graph different types of functions, including inverse functions, square root functions, cube root functions and functions of functions; detect symmetry graphically, numerically and algebraically; evaluate logarithms, including rewriting logarithmic equations in exponential form, graphing logarithmic functions and identifying a logarithmic function's vertical asymptote, domain and range; and define and utilize the derivative, including demonstrating its relationship to the rate of change.

Major topics include: mathematical modeling; linear equations and inequalities; quadratic functions; rational expressions and functions; polynomial functions of a higher degree; absolute value equations and inequalities; complex numbers; geometry basics; functions overview; function operations; graph symmetry; exponential and logarithmic functions; and introduction to the derivative.

In the lower division baccalaureate degree category, 4 semester hours in Calculus, College Math, or as a general elective (12/16).

Various; distance learning format.

30 hours (15 weeks).

December 2012 - Present.

Upon successful completion of the course, students will be able to: analyze types of numbers, percentages, fractions, decimals, graphs, and charts; evaluate slope types, inequalities, and various function types (basic, compound, inverse, etc.) and solve them; demonstrate an understanding of mathematical transformations, translations, dilations, rotations, and reflections; compare different units of measurement and convert them from one system to another; discover and compare trigonometry fundamentals; examine and critique statistics, populations, samplings, and the applications for each; develop knowledge of calculating and identifying probability, with dependent and complex events, and in permutations; evaluate and compute mathematical methods used to determine election results; analyze probability distributions, including area under the normal curve using Z-scores; and calculate values regarding financial management such as compound interest, sinking funds, and ROIs (Return on Investments).

Major topics include: basic number sense and operations ratios, proportions and scale factor; estimation and rounding; exponents and square roots; expressions and equations in algebra; linear equations and inequalities; graphing and evaluating functions; quadratic equations and functions; logarithmic and exponential functions; rational expressions and equations; measurement and conversion; transformations in geometry; right triangles and the pythagorean theorem; trigonometry fundamentals; area and perimeter; surface area and volume; lines and angles in geometry; symmetry, similarity and congruence; statistics, populations and sampling; calculating and understanding probability; critical thinking and problem solving in math; and mathematical methods for elections.

In the lower division baccalaurate degree category, 3 semester hours in Calculus, College Math, or as a general elective (12/16).

Various; distance learning format.

Varies; self-paced.

June 2012 - Present.

Upon successful completion of the course, students will be able to: solve basic logic problems and mathematical proofs, explaining the reasoning behind the solution; identify and compare different types of sets and their representation, including finite, infinite, countable, and uncountable sets; demonstrate techniques for performing operations and solving equations with rational and irrational numbers; differentiate between relations and functions, and determine if a function is an injection, surjection, or bijection; write equations to calculate combinations and permutations and use those equations to solve problems; measure the angles of a triangle and use indirect proofs to prove two lines are parallel; construct a geometric proof to determine the validity of a statement; calculate the area of basic geometric shapes such as triangles, quadrilaterals, polygons, and circles; compare figures to determine if they are symmetrical.

The course is self-paced. Instruction is delivered through online video and text lessons. Students are assessed through quizzes and a proctored final exam. Topics include: introduction to logic in math; mathematic inductions; types of proofs in math; numerical problem solving skills; principles of mathematical sets; groups and sets in algebra; number theory overview; rational and irrational numbers overview; order relations and functions; mathematical combinations; informal geometry and measurement; acute, obtuse and right angles; parallel lines in geometry; geometric postulates and proofs; triangle types and theorems; proportions and similar triangles; types of quadrilaterals; introduction to circles; area of polygons and circles; surfaces and solids; symmetry and transformations.

In the associate/certificate degree category, 4 semester hours in General Math or as a general elective (6/17).

Various; distance learning format.

Varies; self-paced.

June 2012 - Present.

Upon successful completion of the course, students will be able to: outline methods of problem solving using models, estimations and word problems; demonstrate how to use a variety of mathematical operations with integers, decimals, fractions, mixed numbers and exponents; solve basic mathematical expressions and problems using proportions, ratios and averages, and unit conversions within and between systems; show how to write, solve, notate and graph linear equations and basic functions as well as basic transformations using graphs; describe systems of equations and basic inequalities as well as how to solve inequalities and systems of equations; examine mathematical sequences including classifying arithmetic and geometrics sequences and writing variable expressions; explain the basic characteristics and relationships of angles, lines, geometric shapes and how to calculate perimeter, area and volume for geometric shapes; apply basic statistical concepts such as probability and Bayes’ theorem to everyday life; compare and contrast different types of charts and graphs including pie charts, bar graphs, whisker plots, and line graphs; and interpret and use written data with the following methods: spreading data, ranking and weighting data, evaluating instruments, and interpreting relationships.

The course is self-paced. Instruction is delivered through online video and text lessons. Students are assessed through quizzes and a proctored final exam. Topics include: problem solving and math models; working with integers and exponents; working with rational numbers; mathematical operations; unit conversion and measurement; proportions, ratios and averages; basic equations and expressions; solving and graphing linear equations; understanding inequalities; systems of equations; working with functions; sequences in math; transformations in math; points, lines and angles; triangles and their properties; measuring perimeter, area and volume; congruency in math; probability basics; statistics in daily life; understanding graphs and charts; interpreting and analyzing data sets.

In the associate/certificate degree category, 4 semester hours in General Math or as a general elective (6/17).

Various; distance learning format.

20 hours (15 weeks).

December 2013 - Present.

Upon successful completion of the course, students will be able to: identify the differences between various types of data and statistics; calculate values including mean, median, mode, and standard deviation; interpret data displays such as stem and leaf plots, histograms, box plots, bar graphs, two-way tables, and others; use basic set theory to answer questions about the probability of events; understand, interpret, and graph discrete and continuous probability distributions; recognize properties of binomial probabilities and normal distributions; identify relationships between confidence intervals, sample size, and sample means; follow steps in hypothesis testing for small and large independent samples, matched pairs, and proportions; and create and interpret scatter plots and solve problems using linear regression and the correlation coefficient.

Major topics include: overview of statistics; summarizing data; tables and plots; probability; discrete probability distributions; continuous probability distributions; sampling; regression and correlation; statistical estimation; and hypothesis testing .

In the lower division baccalaureate/associate degree category, 4 semester hours in Mathematics or Statistics (12/16).