Semester 2 Review

Hi Ms. V,

Overall, in Semester 2, things were pretty interesting. We started off with less lessons than the first semester. We had Raymond read us Storytime for the first time, and it was hilarious. However, on the math end, towards the end of the semester, we started to do previews into calculus. Things like parametric equations and limits. Overall, second semester was pretty fun and interesting. Since this is the last blog we will do probably, I will take this time to say thank you for the wonderful years I've had in your class. I thoroughly enjoyed learning from you, even if webassign was a thing (just kidding). We ended with trigonometry, which we had previously somewhat covered. However, now we should be mastered in it.

Thanks for a great two years,

Kaili Chiu

Trig Review Week

Hello,

Today I will talk about trigonometry. Trigonometry can be a simple or hard topic to learn, depending on if one is comfortable with the identities and many other oddities in the subject. Some terms to for sure be familiar with are sine, cosine, tangent, cosecant, secant, and cotangent. These terms describe parts of a triangle. Sine is equivalent to the opposite side divided by the hypotenuse and so on and so forth. Trigonometry as we learned during this week uses certain identities to solve and verify trigonometric statements. In verifying, we are given an equation in which the left and right side are equivalent, although they have different variations, and we must manipulate only one side to make them both appear the same. In solving, we solve with the aid of identities and find answers in terms of angles of pi. Sometimes we are asked for a range or a general equation. The general equation just means that we must add a 2npi or npi depending on whether it is sine, cosines, or tangent.

That's all for today,
Kaili Chiu

Repeating Decimals

Hi,

Repeating Decimals are very interesting. We can express them as fractions, and also decimals with a line above the repeated numbers. Prior to this we could not define them mathematically as a fraction. With the formula a1/1-r we can. This is a very easy formula to use, and for things like 0.33333.... we just take (3/10)/1-(1/10) So then we can get 1/3. Overall, this is a very easy and helpful lesson. Hopefully it will show up more on the final because that would be enjoyable.

Thanks,
Kaili Chiu

Parametric Equations

Hello,

This week we learned about parametric equations. This is the first part of our calculus integration, and is a very simple topic. Parametric functions set parameters, and tell us the direction, start and end points. In solving, we are given two values, x and y. These are generally either given in trigonometric functions such as: sin(x), cos(x), tan(x), etc... There are other variations and transformations of these basic functions. When solving parametric equations, we do so by eliminating the parameter. By solving for t, we can substitute into the y= equation and eliminate the parameter. To graph them, we make a chart and plug in values in the range for "t". We can graph the xy points created by the table, and successfully graph the Parametric function.

Thanks,
Kaili Chiu

Partial fractions

Hi,

Today I will be talking about Partial Fractions. Partial fractions are the individual parts that create a fraction. In an example problem, we are asked to first identify whether the degree of the top is greater than the denominator. If it is greater, then we must use long division and take the partial fraction of the remainder. IF it is lesser than the denominator, we can skip this step and go to step 2. Step 2 is factoring the denominator. Once factored (if possible), we can add constants to the numerators of the factored parts. By solving for the constants, we can solve the Partial Fractions. Opposite to the saying "easier said than done", Partial Fractions are much easier to work out than I am explaining.

Kaili Chiu
 

Tower of Hanoi Puzzle

The tower of Hanoi was a very interesting way to learn about mathematical induction. By solving the ancient puzzle, we were able to understand recursive formulas and practice our finding the general formulas. According to the legend, a bunch of Brahmin priests found a temple with three posts surrounded by 64 gold disks. The prophecy explained that when the puzzle would be completed, the world would end. There are a certain set of rules, only one disk can be moved at a time, they have to be in decreasing order from top to bottom, and you can only take the top disk from the pile when moving. Whilst trying to solve the puzzle, I noticed a certain pattern. In order to get the rings to the last pole, I had to put the first ring on the middle rung and then larger one on the last. This would allow me to place them in increasing size order. The number of moves can be determined by the formula (2^n)-1. This formula will work for any number of disks, and with this formula we can calculate that the priests would have to be doing the puzzle for 585 billion years. At least now we know that the world is safe!

Graphing Systems of Inequalities

Hi,

Systems of Inequalities is very interesting, because it is a review topic. Generally we've finished a lot of the systems of inequalities, but now we are touching over it again. When graphing systems of inequalities, graph it without the inequality and fill in the inequality. It's generally pretty easy to do. However we must remember to observe the rule: when dividing by a negative, we must flip the inequality sign. Sometimes it is easy to make careless errors, but most of the errors will be made in the algebra. The solution will be located in the shaded part.

Thanks,
Kaili Chiu