Friday, August 31, 2012

Math 30-2 Course Outline

Unit I:  Counting Methods & Probability 15%
-solve problems involving the following:
                -fundamental counting principle
-interpret and assess validity of odds and probability statements
-solve problems involving mutually exclusive and non-mutually exclusive events
-solve problems involving the probability of two events

Unit II:  Rational Expressions & Equations 25%
-determine equivalent forms of rational expressions (limited to monomials & binomials)
-perform operations on rational expressions (limited to monomials & binomials)
-solve problems involving rational expressions (limited to monomials & binomials)

Unit III:  Exponential & Logarithmic Functions 25%
-solve problems involving exponential equations and functions
-demonstrate an understanding of logarithms and laws of logarithms
-solve problems involving logarithmic functions

Unit IV:  Polynomial & Sinusoidal Functions 25%
-represent data and solve problems involving polynomial functions (of degree < or = 3)
-represent data and solve problem using sinusoidal functions

Unit V:  Set Theory 10%
                -analyze puzzles and games involving numerical and logical reasoning
                -solve problems involving the application of set theory

                                    Year's Work:                                     Final Mark:   
                                    Quizzes/Projects:  10%                       Year’s Work:  50%                
 Exams:                 90%                       Final Exam:     50%
                                                                 100%                                              100%

Saturday, February 5, 2011

Radian Measure

Radian measure is defined as a ratio of arc length to the radius of a a similar way as "pi" is the ratio of circumference to diameter of a given circle.  The ratio of circumference to radius of a given circle is therefore "2pi".

Radian measure is like a new language and it is often easier to relate radians to the equivalent number of degrees.  ie.  one rotation = 2pi =360 degrees; therefore, 1pi = 180 degrees.  We can easily determine all angles in radian measure by referencing 1pi = 180 degrees.  For example, pi/2 = 90 degrees, pi/3 = 60 degrees, pi/6  =30 degrees and so on.  Just know that radian measure is always the ratio of arc length to radius; therefore the numerator is your arc length while the radius determines your  denominator.

Radian measure is actually much easier to use when measuring angles on a large scale.  For example, if I want to map out the "foot-print" of the house I would like to build on my farm, the use of arc length and radius makes the work very quick and easy.  The garage of my house will be perpendicular to the road; to obtain an angle of 90 degrees to the road I pound a stake into the ground and tie a rope to it.  I then walk parallel to the road........let's say 20 paces; this is my radius.  To create an angle of 90 degrees, my arc length must be 10pi or approximately 31.4 paces; this ratio meets the requirements for 90 degrees (10pi/20 =pi/2).  I hold the rope taught against my hip and try to walk directly away from the road............the rope pulls me in an arc until I reach 31.4 paces (estimate).  I pound another stake in the ground at this point; the line of sight (L1) between the two stakes is perpendicular to the road. 

I would also like a 60 degree angle created at this point from which to continue my house; this angle replicates the angle at which a nearby creek flows (the creek movement resembles a sine curve but its equilibrium is running at an angle of 60 degrees to the line of sight (L1) just created.  To create this 60 degree angle, the rope is tied to the second stake that was used.  This time, I will walk 30 paces further along my  line (L1) just drawn; this is my radius for the next arc.  When I've reached my 30 pace radius, I again hold the rope taught against my hip and attempt to walk pependicular to L1.  The rope will swing me in an arc..........this arc must be 10pi (31.4) paces once again.  This ratio (10pi/30 = pi/3) creates an angle of 60 degrees with respect to L1.  A third stake is pounded in the ground at this point and I have my basic layout established.........reference my diagram in the link below:

Diagram of Radian Measure
Radian Measure Illustrated

Click on the following link for additional information on radian measure: