MTH 095 - Quantitative Reasoning

Credits: 3
Instructional Contact Hours: 3

This course is designed for students who need practice in foundational skills as a preparation for any math gateway course with or without extended hours.

Prerequisite(s): None
Corequisite(s): None
Lecture Hours: 45 Lab Hours: 0
Meets MTA Requirement: None
Pass/NoCredit: Yes

Outcomes and Objectives

1. Compute quantities associated with integers, fractions or decimals
   1. Add, subtract, multiply, and divide integers.
   2. Add, subtract, multiply, and divide fractions.
   3. Add, subtract, multiply, and divide decimals.
   4. Compute the opposite, reciprocal, and absolute value of a number.
   5. Simplify numerical expressions using the order of operations.
2. Demonstrate understanding of basic mathematical operations.
   1. Set up and simplify ratios and rates.
   2. Solve proportions.
   3. Carry out fraction, decimal, and percent conversions.
   4. Solve percent equations.
   5. Evaluate square root expressions.
   6. Evaluate exponential expressions.
3. Perform basic algebraic operations.
   1. Use the Distributive Property.
   2. Combine like terms.
   3. Evaluate algebraic expressions.
   4. Simplify algebraic expressions using the order of operations.
4. Demonstrate skills related to graphs.
   1. Construct and interpret line graphs.
   2. Understand the Cartesian (rectangular) coordinate system.
   3. Construct the graph of a line if given the equation of the line.
   4. Identify an appropriate scale for both axes on a graph.
   5. Approximate one coordinate of a point on a graph given the other coordinate.
   6. Identify graphs as linear or nonlinear.
5. Demonstrate skills related to working with polynomials
   1. Add, subtract, and multiply polynomial expressions.
   2. Compare and contrast terms and factors.
   3. Factor polynomials by factoring out the greatest common factor.
   4. Factor trinomials.
   5. Factor binomials of the form x² – y².
   6. Identify prime polynomials.
   7. Compare and contrast expressions and equations.
6. Produce solutions to a variety of mathematical problems.
   1. Solve a variety of linear, quadratic (using the factoring method and the quadratic formula), and radical equations.
   2. Verify the solution to an equation.
   3. Recognize when an equation has no solution or is an identity.
   4. Solve a variety of linear inequalities.
   5. Recognize when an inequality has no solution or is an identity.Describe sets of numbers using relational symbols (<, >, ≤, ≥,=), a one-dimensional graph, and interval notation.
   6. Solve 2 by 2 systems of equations graphically, by substitution and by elimination.
   7. Verify solutions to systems of linear equations.
   8. Recognize when a system of equations has no solution or infinitely many solutions.