Week18/19 — Precalculus11

Top 5 in Pre-calculus11 that I have learned

  1. I leanred how to cooperate with other students in the class, I really enjoyed working as a group and a team together trying so hard to solve a problem, it has helped us to get to know each other better at the end of  the semester.  Asking others questions or teaching others how to do a problem can reinforce my knowledge deeper in my mind.
  2. New knowlege. Precalculus11 this year is quite different from math 10 but it is fairly similar to it, math 11 has a great part that is based on math 10’s basics. For example, in math 10, we mostly learned pythagoras in trigonometry, however, in math11, it is implemented more stuff like sin law and cosine law.
  3. All the resources on Ms. Burton’s blog are really  useful and helpful. I found it interesting to use, it helped me to study, to review and stuff.
  4. Precalculus11 gave me self-recognition that can help me with choosing the grade12 courses and so many things. As having precalculus11, I found that I can handle problems on my own but just needed a little bit more time, so if I can’t figure out, I’d ask questions. I became more confident throughout the semester, it was one of the reason that I’m choosing Precalculus12 and Calculus12, i wanted to give myself challenge.
  5. Review from the ” Past test” folder. In the folder, it has all my past test, so that I can look on where I got wrong in my past test to prevent from making the same mistake again.

Week 17 — Precalculus11

This week we learned about trigonometry. Firstly, we reviewed what we learned from grade10 . Then we started up with new stuff that we’ve never learned before. More terms showed up like reference angle.

This is what I found very interesting, it is certain for the proportion so that it is easier for us to remeber. What’s more,  it can be really convenient during the test if we remember this to quickly find out the unknow side.

Man with hat

The Way He Looks

In Town High, students are rushing to the class, embracing the joy of the first day in school, Bill is one of them. People are all sharing their excitement from last vacation with friends except for Bill in the corner as if nobody can see him ever existed. People’s conversations filled the entire classroom, the roof is nearly lifted up by the joys and cheers among them, they have too much to talk and share except for the invisible Bill silently in the corner of the room, staring at people and didn’t know what to do, waiting for the teacher to come to the class and lecture and yet, the teacher has not came. Bill looked out side of the window, his eyes were getting blurred somehow, then he turned his head back and closed his eyes. The bell rang, the teacher Ms. Z came in and started taking attendance, Bill’s name was somewhere in the middle of the list, about 30 second after, the teacher finished taking attendance, she missed one, Bill who sat at the end of the class, Ms. Z hasn’t realized that . Bill raised his hands “ You didn’t say my name”, Ms. Z finally noticed that there’s a boy in the back row “ Oops sorry, what’s your name?” “Bill” everybody looked at Bill the same moment then turned their heads back the front. The class has ended, Bill was wandering in the hallway, he heard people talking about him right in front of him as if he weren’t there and didn’t exist in their eyes. Bill heard them all, he got pissed, upset , frustrated and all that kind of complex of feeling, emotions. At lunch time, he met his friend Robin who is his only friend in school that he knew for a long time. Robin encouraged him to be himself and helped him to get rid of the negative thoughts and feelings and eased his mind. Days after, Bill gathered his courage to engage in many events and all sort of presentations in front of class and school. He proved him self and changed the incorrect critical perspective that people have toward him .He was no longer invisible, people started talking and hanging out with him.

Week16– Precalculus11

This week we are still learning adding, subtraction, multiplying and dividing rational expressions, the calculation with the denominators. In addition, we learned about applications of rational expressions which is to solve practical problems with expressions.

Here’s an question that I need to use an equation to solve. It is asking for the amount of bleach that should be added into 47L water. I firstly assumed that the amount of bleach that we are adding is X. Then I thought about the relationships between water and added bleach and the final 6% of bleach in water. I came up with the equation as listed. Then I solve it and I got 3 L of adding bleach.

Week15–Precalculus11

This week we kept on learning simplifying ,multiplying , dividing fractions and non-permissible values. I need to be more careful and pay more attention when I solve this kind of questions because they get too complex to solve sometimes.

This question is about finding non-permissibe value for each expression, the key is that the denominator of the fraction expressions cannot be zero which gives me a clue of finding the non-permissible value. For the first one t cannot be 0 because 2 is a value and I just need to make sure t isn’t 0. Then x+2 for the second one can’t be 0 hence x cannot be -2. Last, I finish the square first then I determine x cannot be 3 and -1.

Wave Phenomena: wave interference

Constructive interference:

IMG_0359

When a crest from one side (source) meets a crest from another side( source) , the energies combine to produce a higher crest,  the amplitude of the resulting is equal to the sum of the individual amplitudes.

IMG_0363

When trough meets trough , same thing occurs.

Destructive interference:

IMG_0364

When a crest and trough meet , the energies cancel each other.