Course | Madison College Outline of Instruction

10-804-118Intermediate Algebra w Apps

Course Information

Description

This course offers algebra content with applications. Topics include properties of real numbers, order of operations, algebraic solution for linear equations and inequalities, operations with polynomial and rational expressions, operations with rational exponents and radicals, algebra of inverse, logarithmic and exponential functions.

Total Credits

Prior Learning Assessment

Exam-College Developed Challenge Exam

Course Competencies

Use linear equations to solve applied problems

Assessment Strategies

Oral, Written, Graphic and/or Skill Assessment

Criteria

evaluate a given formula for specified values

solve a given formula for a specified variable

create a linear equation to model a given scenario

solve a linear equation that models an applied problem

interpret the solution of a linear equation in context
Solve linear inequalities

Assessment Strategies

Oral, Written, Graphic and/or Skill Assessment

Criteria

solve simple linear inequalities

solve compound linear inequalities

solve absolute value equations

solve absolute value inequalities

represent a solution using set builder notation

represent a solution using interval notation

represent a solution using a graph
Analyze relationships on the Cartesian plane

Assessment Strategies

Oral, Written, Graphic and/or Skill Assessment

Criteria

graph a line, given its slope and point on the line

graph linear equations

find the distance between two points

find the midpoint of two points

identify one-to-one functions

graph an inverse function

graph the square root function

graph the absolute value function

graph the reciprocal function
Analyze linear equations

Assessment Strategies

Oral, Written, Graphic and/or Skill Assessment

Criteria

compare slopes to determine if two lines are parallel, perpendicular, or neither

find the equation of a line, given two points on the line

write the equation of a line in standard form

write the equation of a line in slope-intercept form

write the equation of a line in point-slope form

find the slope given two points or the equation of the line

identify x- and y- intercepts
Apply properties of functions

Assessment Strategies

Oral, Written, Graphic and/or Skill Assessment

Criteria

distinguish the differences between relations and functions

find the domain and range of a relation

use function notation

solve applications involving functions

perform arithmetic operations with functions

identify the domain of a function algebraically

write a composite function

evaluate a composite function for a specified value

determine the inverse of a function algebraically
Solve systems of equations

Assessment Strategies

Oral, Written, Graphic and/or Skill Assessment

Criteria

create a system of linear equations to model a given scenario

solve a system of linear equations that models an applied problem

interpret a solution of a system of linear equations in context

solve a system of two linear equations by graphing

solve a system of two linear equations by the elimination method

solve a system of two linear equations by the substitution method

identify inconsistent or dependent systems
Solve polynomial equations

Assessment Strategies

Oral, Written, Graphic and/or Skill Assessment

Criteria

factor using the greatest common factor

factor binomials

factor by grouping

factor trinomials

perform arithmetic operations with polynomials

factor the difference of two squares

factor the sum or difference of two cubes

use the zero product property of real numbers to solve polynomial equations

evaluate a polynomial function for a specified value
Use quadratic equations to solve applied problems

Assessment Strategies

Oral, Written, Graphic and/or Skill Assessment

Criteria

apply the square root principle

apply the quadratic formula

graph a quadratic function written in standard form or vertex form

perform transformations on a quadratic function

identify the domain and range of a quadratic function

interpret the solution of a quadratic equation in context

use the Pythagorean Theorem to solve an applied problem

use a quadratic equation to solve an applied problem
Use rational equations to solve applied problems

Assessment Strategies

Oral, Written, Graphic and/or Skill Assessment

Criteria

simplify rational expressions

find the domain of rational functions

perform arithmetic operations with rational expressions

simplify complex fractions

use a rational equation to solve an applied problem

interpret the solution of a rational equation in context

identify extraneous solutions

solve rational equations
Solve radical equations

Assessment Strategies

Oral, Written, Graphic and/or Skill Assessment

Criteria

convert between radical and exponential notation

simplify radicals

apply rules of exponents with positive and negative rational exponents

perform arithmetic operations with radical expressions

evaluate a radical function for a specified value

find the domain of a radical function

solve equations containing radical expressions or rational exponents
Operate within the complex number system

Assessment Strategies

Oral, Written, Graphic and/or Skill Assessment

Criteria

simplify radicals that include complex numbers

perform arithmetic operations with complex numbers

solve equations with complex solutions

determine a complex conjugate
Use exponential equations to solve applied problems

Assessment Strategies

Oral, Written, Graphic and/or Skill Assessment

Criteria

identify an exponential function or relation

graph an exponential function

evaluate an exponential function for specified values

create an exponential function to model a given scenario

interpret the solution of an exponential equation in context

apply the definition of a logarithm to transform exponential equations

solve an exponential equation that models an applied problem

use properties of logarithms