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Math Competency

Purpose:

 • Develop critical and analytical thinking skills Engage students in sound mathematical thinking and reasoning.
 • Enhance and reinforce students’ understanding of concepts through the use of technology when appropriate.
 EX: graphing calculators, computers, software such as MyMathLab, students’ response system, etc.
 • Develop mathematical fluency to improve written and verbal communication.
 • Analyze the structure of real world problems and plan solutions, and solve the problem using appropriate tools.
 EX: Use functions to model real world applications.
 • Explore multiple representation of topics (graphical, numerical , symbolic, verbal)

Why:

 • Prerequisite for calculus and pre-calculus
 • Have not learned, a review of topics of high school
 • Prerequisite for other programs such as science, nursing
 • To satisfy state requirements and accreditation, for graduation in some programs
 • Gateway course for higher mathematics and sciences

FUTURE NOTE:

course should be more rigorous (more depth, not more topics?)

Population:

• Students who need the future sequences for prerequisites.

EX: Math, science, engineering, business, accounting majors.

Part of sequence: Yes

General education course: Yes (get clarification)

21st century redefinition:

 • As students enter college more prepared, this class in 10 – 15 years might have fewer sections.
 • Emphasis more depth, might be too many topics right now.
 • Change in ways of teaching (more hands-on, activities based, collaboration, cooperation, technological (with
more on- line sources , interaction could go beyond meeting times of the class),
 • More abstract and formal coverage
 • Focus on concepts rather than just rote skills
 • Higher expectation of students knowing well their foundational and arithmetic skills rather than promoting a total dependency on calculators

Course Content:

 • The basic content of this course focuses on functions:
  -definition of functions
  -domain and range
  -function notation
  -types of functions (EX: linear, quadratic, exponential, absolute value, logarithmic, power with rational exponents, piece-wised defined functions)
  -transformations
  - graphs and their properties (EX: extrema, symmetry, even/odd, etc.)
  -solving non-linear inequalities graphically
  -intersection of graphs (non- linear of 2 variables )
  - difference quotients
  -real world applications (EX: average rate of change)
  - operations including composition
  -inverse functions
  -piece-wise defined linear & non-linear functions (evaluate and graphing)
  -asymptotes
  - exponential and logarithmic functions including applications of interest (graph, properties,
domain, range, solve simple exponential and logarithmic equations )
EX: ln x = 3, ekt = 45

 • Coordinate geometry
  - circles (equations, completing the squares , distance, midpoint)

Suggested Delivery and methodologies:

 • students should graph by hand and use the calculator
 • More focus on analyzing graphs over making graphs

Side Notes:

 • Use classroom set of calculator to prevent cheating.
 • Students don’t get much about functions before college algebra. Students should demonstrate applications of math more heavily than previous course (such as Intermediate algebra)
 • In the future, maybe create an alternative, less rigorous college algebra course for students who do not go on!
 • Consult with chemistry on depth of logarithmic functions and properties

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