core competency reflection precalc 12

The functions and transformations unit had a large impact on my critical and creative thinking and communication skills.  Math is all about critical thinking.  In every unit critical thinking is a key component to success and a well understanding.  This first unit of precalc 12 has taught me more about critical thinking at a grade 12 level compared to precalc 11, it’s a big change.  Being able to communicate with other classmates has also taught me a lot about my communication skills within the classroom.

My creative thinking has been tested a lot this semester.  Jumping from precalc 11 to precalc 12 I had to find new ways to study since the curriculum is very different.  I created new study habits and strategies in order to help me with my understanding of the concepts.  Since I had precalc 11 in the first semester of last year, it has forced me to really think about the past units in order to use that information to help me with this unit.

Constructive and destructive wave

constructive wave :

A constructive wave id when two crests from opposite directions converge and the end result wave is the sum of the two crests.

destructive wave :

A destructive wave is when a crest and a troph from opposite directions converge.  the end result wave usually cancels out (no wave) or they act against each other.


How do noise-cancelling headphones use wave interference to eliminate unwanted sound?

A : The music going into the ear acts as a constructive wave.  Another wave is created through the headphones that acts as the troph with the same amplitude, and the background noise acts as the crest that creates a destructive wave that cancels out any noise.

Types of waves

Pulse wave: A pulse wave is a non-repeating wave; single disturbance.

Pulse wave

Periodic : Periodic waves are waves that repeat at regular intervals.  they require regularly repeating disturbances in order to be considered a periodic wave.

Periodic wave

Longitudinal:  A longitudinal wave is when several turns of the spring are compressed and released.  The disturbance is in the same direction as the direction of travel.  This wave occurs lengthwise.

Longitudinal wave

Transverse: This wave occurs sideways.  The spring is pulled sideways at a 90 degree angle (right angle) then released.  The wave will travel across instead of lengthwise.

Transverse wave