Expanding the walls of our classroom. This is an interactive learning ecology for students and parents in my Pre-Cal Math 40S class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.
This unit was difficult for me. There were formulas that you could use, but you don't need them you just have to think, VERY hard. Logic was part of it and honestly I'm not the brightest apple when it comes to logic. I constantly get the pick and choose formulas mixed up. I know I could have done better during quizzes and I should have done the homework because it's just like the trigonometric identities where you get good at it when you do lots of it. That sentence sounds funny! Overall, it was difficult and I'm just happy we're done with it. Hope everyone does well! See you all tomorrow.
First thing we started off with was a quiz that was on counting. The first question dealt with 3 positions with ten people and how they are arranged. we came up with 10*9*8 because there are ten people that can have one position, after that nine people can be assigned the second position since one is already assigned. And 8 because there are 8 people that can be in the third position. The second question was about how many words can be generated with the word CALCULUS. Since there are 8 letters it should be 8! However, there are two L's, two U's, and two C's which are all non-distinguishable objects because we can't tell the difference between the doubles. So, it is 8!/ 2!2!2!. 2! are the U's, L's, and C's since we can't tell them apart. Question 3 the answer is (7-1)! which is equivalent to 720. That's because since 7 people are sitting in a circle and one person could be the point so 6 others sit around. Question 4 the answer is 4!2!2!2!2! because there are four couples that could be arranged and two people in the four couples and they too can be rearranged. The answer for question five is 1152 because if the men and women alternate then it would look like this
4 would go first because there are 4 men and 4 in the second because there are 4 women. 3 would go into the third because of 3 men left and 3 for women and so on. The next line is the same but a woman first. They both equal 576. To get the answer you add 576 + 576= 1152. The sixth deals with simplifying expressions. We did a bit of the new unit.
AFTERNOON CLASS:
We did a bit more work on the Binomial Theorem. We noticed patterns all over the place. We learned how to find whatever term we want. If we were not given the X^n than we could find out what term it is. We could find the term using a system of equation! If you want to see more of what happened in class click here for more details! Homework for the weekend was Exercise 34, do all. I apologize for the late scribe. For tomorrow, the next scriber is...........................................................................
Trigonometric Identities, what a hard unit to grasp. At first I didn't understand a thing. That was because I was absent on the day we started working on it. I wasn't present in class because of an extra-curricular thing happening. I didn't do most of the homework excericeises, but I wanted to catch up so I started doing them on a weekend. Honestly, I'm not confident about anything. I just get by when doing problems such as proving one side to the other. The identities are hard to rememeber, so I'm really happy that we're getting a sheet that shows all the identities. Well, I hope that everyone studies hard tonight. Good Luck!
Today, we started off class by talking about the calender we have on the blog and what the squared dates mean. Mr. Kuropatwa told us that one of the students had come up to him and talked to him about the math project. The project where each student must generate 4 different equations about what they had learned in the time period. He pointed out that each individual is responsible for choosing a due date for our project. That is why we see different dates marked. If you want to use tools that help you present you work differently like making a movie out of it or doing a slide show, then you should definitely check out studentblogwikitools. The rubric will be made by us. The rubric will be made on Google docs.
He also talked to us about how everyone isn't at the same level and how experts are. Experts don't do problems at their level, they go beyond and push themselves. They never feel like an expert and is constantly not satisfied with where they are. They do problems that they're not comfortable with, but they push themselves.
1)This is the first equation that we worked on in class. The first slide shows the equation that was given and we had to prove that the right side of the equation was equal to the left side of the equation.
2)Although we see and equal sign does not mean that the right side of the equation is equal to the left side of the equation. So, we treat the equal sign as though it were a question mark because we don't know if they are equal and we can't assume that they are equal.
3)Ladies and gentlemen, introducing the "Great Wall of China" in math. We use the "wall" because the things on the right side of the sign cannot cross to the left side and vice-versa.
4)As you can see in the fourth slide. The equation on the left hand side can be simplified into 1/ tan²ß + tan²ß/tan²ß.
5)You could also simplify that equation further into cos²ß/sin²ß. That is because tan²ß/tan²ß is equivalent to 1. 1/ tan²ß is equal to 1/ sin²ß/cos²ß, a complex fraction. What you do then is multiply 1/1 by the reciprocal of sin²ß/cos²ß, which is cos²ß/sin²ß.
6)You might have noticed that cos²ß/sin²ß is equivalent to cot²ß. So, you end up with cot²ß + 1.
7)You might have noticed that cot²ß + 1 is equal to csc²ß because it is one of the trigonometric identities that come up a lot.
8)Q.E.D is an acronym, three words in Latin. It's in Latin and is translated to "what was meant to be demonstrated or shown." It's like proven what you wanted to show. Unfortunately, I don't remember exactly what the words are in Latin.
FACT: sometimes in university what may be shown instead of an equal sign is a sign that looks like an equal sign but with another line on top of it. It doesn't mean that this side of the equal REALLY REALLY means that it is equal to the other but it's the same as a question mark where you have to prove that it is equal.
Here are the slides on what we worked on today. Some stuff in the slide is a review from Friday when we first started working on trigonometric identities. There are a couple of new questions on it. We didn't get to go over all of them in class today, but your free to try them. Remember that homework tonight is exercise 15 and I hope this scribe helped. The next scribe for tomorrow is............................................................................... ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. .................................................................................
TRANSFORMATIONS, what a unit. It was really hard to grasp at first, still kind of is because of all the word problems. What I found the least difficult was solving for things like f(x) when given the graph and equation, so finding the original equations are good for me. I have to remember, stretches before translations! Sometimes I have this weird habit of stretching the graph vertically a unit too high or low. I know how to find the inverse of a function algebraically and graphing it is no problem. What stumps me is that 'witches curve'. I still have problems with finding the period and sometimes when I'm doing one of those word problems, I don't know where to start. Drawing the graph is the beginning, but generating the equation is hard when you're not sure what the period is. I really don't feel confident doing the word problems that have to do with the months of the year. It confuses me because sometimes the dates start on weird dates, a date that may be during the middle of the month. I'm not sure where to start drawing my graph. Well, I hope everyone studies really hard and practices, good luck. See you all tomorrow fellow classmates!
Circular Functions, our first unit in 40s. There was a lot to remember and Mr. K was right, we really do dance in grade 12 mathematics. There was the clock dance. There was also a mnemonic to remember the coordinates for a circle, which was 1, 2, 3. The math dictionary comes in handy when I'm stuck on a problem. This unit wasn't easy. I had a lot of difficulty grasping it. I still have trouble, but i find that i have more trouble with things dealing with the period, graphing the equation without the aid of a calculator, and generating an equation from the graph. I often get mixed up with what to graph first and how the equation would work with the graph that was given. If I accidentally missed something on the graph, its completely wrong and if i add something that wasn't supposed to be there in the equation, that also makes everything else completely wrong. I am very comfortable with converting radians to degrees or degrees to radians. I like to deal with circular function problems that are similar to algebra. I am comfortable with finding the area of a sector or finding a missing arc length. I hope everyone studies hard for the test that's on this Wednesday. Good luck!
