Introduction to College Math | Madison College Outline of Instruction

10804129 Introduction to College Math

Course Information

Description

Basic computational skills are reviewed and fundamental mathematical concepts from algebra, geometry, trigonometry, and statistics are developed. The topics covered in this course are fractions, decimals, ratios and proportions, percent, geometry and measurement systems, data interpretation and presentation, basic algebraic concepts, and right angle trigonometry. Additionally, how-to study mathematics, how-to approach problem solving, and the use of calculators as mathematical tools will be addressed.

Total Credits

Course Competencies (Course Outcomes)

Perform basic mathematical operations

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you add whole numbers

you subtract to whole numbers

you multiply whole numbers

you divide whole numbers

you use exponents correctly with whole numbers

you combine these operations applied to whole numbers according to the standard order of operation rules

you recognize explicit grouping symbols in performing calculations

you correctly use explicit grouping symbols in performing calculations

you recognize implicit grouping symbols (fraction bar, radical symbol, etc) in performing calculations

you correctly use implicit grouping symbols (fraction bar, radical symbol, etc) in performing calculations

you correctly use a scientific calculator to compute expressions that involve addition, subtraction, multiplication, division, exponentiation or combinations of these according to the standard order of operation rules
Apply mathematical problem solving skills

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you show work in a clear and logical manner

you verify solution

you verify that solution is within stated range and reflects appropriate accuracy or precision

you label solution with appropriate unit(s)
Perform basic mathematical operations with fractions

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you determine if fractions are equivalent

you compare the magnitude of different fractions

you express improper fractions as mixed numbers

you express mixed numbers as improper fractions

you reduce fractions to lowest terms

you perform multiplication, division, addition, subtraction, or combinations of these operations with fractions according to the standard order of operations

you use a scientific calculator to check calculations involving fractions

you use a scientific calculator to check calculations involving fractions
Perform basic mathematical operations with decimal numbers

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you convert fractions into decimals

you convert terminating decimals into fractions

you perform addition, subtraction, multiplication, division, exponentiation, root taking or combinations of these operations with decimal numbers according to the standard order of operation rules

you recognize signed decimal numbers

you correct use signed decimal numbers

you recognize decimal numbers expressed in scientific notation

you correctly use decimal numbers expressed in scientific notation

you correctly use a scientific calculator to compute expressions that involve addition, subtraction, multiplication, division, exponentiation, root taking or combinations of these with decimal numbers according to the standard order of operations

you round a decimal to a required place
Perform basic mathematical operations with numbers expressed as percents

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you explore the definition of percent

you convert fractions or decimals into percentages and vice versa

you convert fractions or decimals into percentages

you convert percents into fractions or decimals into percentages

you solve percent problems for amount

you solve percent problems for base

you solve percent problems for percentage

you correctly use a scientific calculator to compute the answer to percent problems

you correctly translate a verbally stated application involving percentages into performing an equivalent computation

you solve percent problems that arise in personal finance

you correctly interpret the computer answer to a word problem

you check the reasonableness of a computed answer to a word problem
Create and interpret graphs

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you determine the coordinates of a point from a graph

you extract quantitative information from graphs

you summarize the relationships between variables represented in a graph

you interpret the information represented in a graph

you generate a graph with appropriate scales, labels and dimensions from a table of values

you generate a graph with appropriate scales, labels and dimensions from an equation relating two variables

you create and interpret line graphs

you create and interpret bar graphs and histograms

you create and interpret pie graphs

you create and interpret box and whiskers graphs
Calculate statistical measures from data sets

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you compute the mean

you compute the median

you compute the mode

you compute the midrange

you compute the range

you compute the variance of a sample and population

you compute the standard deviation of a sample and population

you compute various quartiles
Perform basic mathematical operations with signed numbers

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you perform multiplication with signed numbers according to the standard order of operations

you perform division with signed numbers according to the standard order of operations

you perform addition with signed numbers according to the standard order of operations

you perform subtraction with signed numbers according to the standard order of operations

you perform combinations of these operations with signed numbers according to the standard order of operations
Apply the rules of exponents

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you use the roles of exponents to simplify expressions with whole number exponents

you use the rules of exponents to simplify expressions with integer exponents

you recognize numbers expressed in scientific notation

you correctly interpret numbers expressed in scientific notation

you simplify numbers expressed in scientific notation

you perform calculations on numbers expressed in scientific notation

you use a scientific calculator to compute expressions with exponents

you use a scientific calculator to compute expressions with numbers expressed in scientific notation
Simplify algebraic expressions

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you recognize "like terms"

you distinguish between "like terms" and "unlike terms"

you use the distributive property to correctly combine "like terms"

you correctly distribute a minus sign across a sum or difference of terms

you correctly distribute a single term denominator across a numerator expressed as a sum

you distinguish the simplification of a fraction with a numerator expressed as a sum from the simplification of a fraction with a numerator expressed as a product

you use the distributive property to simplify linear combinations of polynomials

you use a scientific calculator to numerically check the result of an algebraic simplification
Simplify and rearrange formulas

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you use the rules of equivalence to solve linear equations in a single variable

you use the rules of equivalence to rearrange formulas
Perform calculations with quantities having units of measure

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you perform addition, subtraction, multiplication, division, exponentiation, root taking or combinations of these operations for quantities expressed as measurements

you express the answer with the appropriate units

you correctly use a scientific calculator to compute the answer to problems involving measured quantities

you set up unit fractions to convert measurements from one unit to another
Convert measurements within the English system of units

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you set up unit fractions to convert measurements from one unit to another

you use unit fractions to convert measurements from one unit to another

you convert area measurements to different square and cubic units of length measure

you convert volume measurements to different square and cubic units of length measure
Convert measurements within the metric system of units

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you use the prefixes in the metric system to convert measurements within the metric system

you set up unit fractions to convert measurements from one unit to another

you use unit fractions to convert measurements from one unit to another

you convert metric area measurements to different metric square and cubic units of length measure

you convert volume measurements to different metric square and cubic units of length measure
Convert measurements between the metric and English systems

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you set up unit fractions to convert measurements from specified English units to specified metric units

you use unit fractions to convert measurements from specified English units to specified metric units

you set up unit fractions to convert measurements from specified metric units to specified English units

you use unit fractions to convert measurements from specified metric units to specified English units
Solve applied problems

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you translate a verbally stated problem into solving an equivalent equation

you solve the equation extracted from a verbally stated problem

you interpret the computed answer to a word problem

you check the reasonableness of a computed answer to a word problem
Solve ratio and proportion problems

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you rearrange a proportion to solve for an unknown quantity

you translate a relationship stated in the language of variation ("varies directly as", "varies inversely as", etc) into a proportion

you solve the proportion extracted from a verbally stated variation problem

you interpret the computed answer to a variation word problem

you check the reasonableness of a computed answer to a word problem
Solve variation problems

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you identify types of ratio and proportion

you write variation equations

you solve direct variation problems

you solve indirect variation problems

you solve inverse variation problems

you solve joint and combined variation problems

you apply skill to applied technical problems

you apply the process for solving technical problems according to the problem solving criteria
Use and compute angle measurements

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you label angles in a diagram

you interpret diagrams with labeled angles

you convert decimal degrees into DMS notation

you convert DMS notation into decimal degrees

you perform DMS to DD conversions on a scientific calculator

you perform DD to DMS conversions on a scientific calculator

you use properties of parallel and intersecting lines and polygons to solve for missing angles in a figure
Use properties of triangles and other polygons

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you identify polygons (triangles, quadrilaterals and hexagons)

you identify special cases of triangles (isosceles, equilateral, right)

you identify quadrilaterals (rectangles, squares, parallelograms, trapezoids)

you solve for missing angles in a triangle and polygon

you solve for missing sides in a triangle and polygon

you recognize the rules of congruence (SAS, ASA, SSS) for triangles

you use the rules of congruence (SAS, ASA, SSS) for triangles
Perform calculations using the Pythagorean Theorem

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you use the Pythagorean Theorem to solve for any missing side of a right triangle

you determine the height of an isosceles triangle with given sides by dropping a perpendicular and using the Pythagorean Theorem

you correctly use a scientific calculator to perform calculations involving the Pythagorean Theorem
Calculate perimeters and areas of closed planar figures

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you compute (given sufficient data) the perimeters and areas of rectangles

you compute (given sufficient data) the perimeters and areas of triangles

you compute (given sufficient data) the perimeters and areas of parallelograms

you compute (given sufficient data) the perimeters and areas of trapezoids

you compute (given sufficient data) the perimeters and areas of regular hexagons

you correctly use a scientific calculator to compute the area of a triangle (given the lengths of its sides) from Heron's formula

you compute the area of a circle given its radius or diameter

you compute the circumference of a circle given its radius or diameter
Calculate the volume and surface area of a three-dimensional solid

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you compute (given sufficient data) the lateral surface area of a right prism

you compute (given sufficient data) the total surface area of a right prism

you compute (given sufficient data) the volume of a right prism

you compute (given sufficient data) the volumes of cones

you compute (given sufficient data) the volumes of right pyramids

you compute the total surface area of a sphere from its radius or diameter

you recognize the geometric solid (prism, cone, cylinder, sphere, etc) necessary to compute a surface area or volume required in an application

you compute a surface area or volume required in an application

you check the reasonableness of a computer answer to an area or volume problem
Convert angle measurements from degrees to radians and vice versa

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you convert angles measured in radians to DD (decimal degrees)

you convert angles measured in radians to DMS (degrees, minutes, seconds)

you convert angles measured in DD to radians

you convert angles measured in DMS to radians

you compute the arc length subtended by a central angle
Use radian measure to solve applied problems

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you use radian measure to solve a verbally stated application

you check the reasonableness of a verbally stated application of radian measure
Perform computations with the sine, cosine, tangent functions and their inverses

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you distinguish between the opposite and adjacent sides to an acute angle in a right triangle

you identify the correct ratio of sides for the sine function of an acute angle in a right triangle

you identify the correct ratio of sides for the cosine function of an acute angle in a right triangle

you identify the correct ratio of sides for the tangent function of an acute angle in a right triangle

you use a scientific calculator to compute the sine function for an acute angle expressed either in DD or DMS notation

you use a scientific calculator to compute the cosine function for an acute angle expressed either in DD or DMS notation

you use a scientific calculator to compute the tangent function for an acute angle expressed either in DD or DMS notation

you use a scientific calculator and the appropriate inverse trigonometric function to compute an acute angle for a given value of a trigonometric function and express the answer in either DD or DMS notation

you identify the correct relationship between the coordinates of a point on the standard unit circle and the sine, cosine, and tangent functions of a central angle measured from the positive x axis

you, for a given value of a trigonometric function and a specified quadrant, use a scientific calculator and the appropriate inverse trigonometric function to compute the measure of the angle and express the answer in either DD or DMS notation

you use a scientific calculator to compute the sine function for any angle expressed either in DD or DMS notation

you use a scientific calculator to compute the cosine function for any angle expressed either in DD or DMS notation

you use a scientific calculator to compute the tangent function for any angle expressed either in DD or DMS notation
Solve for the missing information in a right triangle

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you solve for the length of the missing side and the measure of the two missing acute angles given the lengths of two sides in a right triangle

you solve for the measure of the missing acute angle and the lengths of the two missing sides given the length of one side and the measure of one acute angle in a right triangle

you check the reasonableness of the answers for the missing information in a right triangle
Solve for the missing information in an oblique triangle

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you use the law of cosines to find the length of the missing side and then use either the law of sines or the law of cosines to find the measure of the two missing angles given the lengths of two sides and the included angle (SAS)

you computes the measure of the missing angle and then use the law of sines to find the lengths of the two missing sides given the measures of two angles and the length of the included side (ASA)

you use the law of cosines to compute the measure of the largest missing angle and then use either the law of sines or the law of cosines to find the measure of the two missing acute angles given the lengths of all three sides (SSS)

you check the reasonableness of the answers for the missing information in an oblique triangle
Solve applications of trigonometry

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you translate a verbally stated problem in solving for the missing information of a triangle

you solve for the missing information of a triangle extracted from a verbally stated problem

you interpret the computed answer to a word problem

you check the reasonableness of a computed answer to a word problem