I. General Information
1. Course Title:
Mathematical Reasoning
2. Course Prefix & Number:
MATH 1442
3. Course Credits and Contact Hours:
Credits: 3
Lecture Hours: 3
4. Course Description:
This is a college level math course that satisfies MN Transfer Curriculum Goals 2 and 4 and is intended to increase students' problemsolving and mathematical reasoning skills. Topics include geometry, right triangle trigonometry, set theory, probability, statistics, and finance. Solving real world applications problems in each of these areas and communicating mathematically will be emphasized.
5. Placement Tests Required:
Accuplacer (specify test): 
Math Introductory College Level or Algebra College Level or PreCalculus College Level or Calculus College Level 
Score: 

Other (specify test): 
NGA AAF 
Score: 
236

6. Prerequisite Courses:
MATH 1442  Mathematical Reasoning
There are no prerequisites for this course.
8. Prerequisite (Entry) Skills:
Fundamental algebra background and familiarity with a graphing calculator
9. Corequisite Courses:
MATH 1442  Mathematical Reasoning
There are no corequisites for this course.
II. Transfer and Articulation
1. Course Equivalency  similar course from other regional institutions:
Alexandria Technical & Community College, MATH 1415 Mathematical Reasoning, 3 credits
Itasca Community College, MATH 1101 Contemporary Mathematics, 3 credits
Lake Superior College, MATH 1105, Mathematical Reasoning, 3 credits
St. Cloud Technical & Community College, MATH 1331, Applications of Mathematical Reasoning, 3 credits
III. Course Purpose
2. MN Transfer Curriculum (General Education) Courses  This course fulfills the following goal area(s) of the MN Transfer Curriculum:
 Goal 2 – Critical Thinking
 Goal 4 – Mathematical/Logical Reasoning
IV. Learning Outcomes
1. CollegeWide Outcomes
CollegeWide Outcomes/Competencies 
Students will be able to: 
Analyze and follow a sequence of operations 
Justify the steps used in solving a mathematical problem. 
Apply abstract ideas to concrete situations 
Apply appropriate mathematical formulas to solve problems in geometry, set theory, probability, statistics, and finance. 
Utilize appropriate technology 
Utilize technology to solve mathematical application problems. 
2. Course Specific Outcomes  Students will be able to achieve the following measurable goals upon completion of
the course:
 Express mathematical ideas clearly in writing (Goal 4);
 Apply logic in analyzing arguments (Goals 2 & 4);
 Apply higherorder problemsolving strategies (Goals 2 & 4);
 Solve applied financial problems involving simple and compound interest, annuities, and loans (Goal 4);
 Solve realworld problems that can be modeled with sets, permutations, and combinations (Goal 4);
 Display data graphically, calculate and interpret descriptive statistics, and assess possible bias in statistics (Goals 2 & 4);
 Apply the rules of probability in calculating expected values and conditional probabilities ( Goal 4);
 Solve realworld problems using two and threedimensional geometry (Goal 4); and
 Solve application problems that can be modeled by right triangles and solved using right triangle trigonometry (Goal 4).
V. Topical Outline
Listed below are major areas of content typically covered in this course.
1. Lecture Sessions
 Sets and Counting
 Intersection, union, complement of sets
 Cardinal number formulas for union and complement
 Venn diagrams
 The Fundamental Theorem of Counting
 Permutations
 Combinations
 Using the correct counting principle for a given situation
 DeMorgan’s laws
 Probability
 The history of the development of probability theory
 The terminology of probability: experiment, sample space, event, outcome, relative frequency, odds
 Basic rules of probability
 Using counting principles (permutations, combinations) to calculate probabilities
 Expected value
 Conditional probabilities and the product rule
 Punnett squares and basic probability in genetics
 Independence of events
 Statistics
 Frequency distributions and histograms
 Measures of central tendency for raw data and grouped data
 Range and standard deviation for a set of raw data and for grouped data
 The standard normal (z) distribution
 Margin of error and level of confidence
 Terminology of statistics: population, sample, data, frequency distribution, histogram, measures of central tendency, measures of dispersion, etc.
 Finance
 Terminology of finance: principal, simple and compound interest, future value, present value, annuity, amortization, etc.
 Simple and compound interest formulas
 Credit card finance charges, bank deposits, and loans
 Ordinary annuities and annuities due
 Payout annuities
 Simple interest amortized loan formula, payment amounts, amortization schedules
 Geometry
 Perimeter and circumference of twodimensional figures
 Area formulas for triangles, rectangles, trapezoids, parallelograms, and circles
 Volume and surface area of rectangular prisms, cylinders, cones, pyramids, and spheres
 The use of geometry in one or more ancient civilizations
 Basic twocolumn proofs
 Fibonacci numbers and the golden ratio
 Similar triangles and their applications
 Identification of conic sections by their graphs
 Reflective properties of parabolas, ellipses, and hyperbolas
 Center and radius of a circle from its equation
 Arcs of circles
 Trigonometric ratios of sine, cosine, and tangent for acute angles of a right triangle
 Sine, cosine, and tangent for the special angles (30, 45, 60 degrees) of a right triangle
 Using inverse trigonometric functions to find angles
 Applications of right triangle trigonometry