2nd Semester Summary

This semester at first was very difficult for me. I didn't d to well on my tests and quizzes and the material was very challenging to understand. As the semester went on, I began to understand the material better and my tests scores went up gradually. This summer, I will be looking at note colleges across the U.S. and go to see my relatives in Boston. I probably will also go to the beach a lot and spend some quality time with my friends and family just relaxing. I am also going to be doing a lot of SAT prep this summer and be doing more and more MATH yahhhhhhh!!!! But I can't wait until finals are over and I can take a break from studying. 

Trig review week

This week I relearned how to do partial fraction decompositions, SOH-COA-TOA, parametric equations, double angles and half angles. For parametric equations I learned the steps again, for example graphing and eliminating the parameter when solving for the rectangular equation. Also, doing a t,x,y chart and plotting x and y coordinate pairs to form a graph. I also learned verifying and solving trig equations and that when verifying we make one side look like the other side. And for solving trig equations we set x equal to a certain radian measure and look where that radian measure is on the unit circle and those radian measures are the solutions to the problems. Lastly, I relearned the binomial theorem and how Pascals Triangle relates to the Binomial Theroem and helps solve the questions more easily. 

Repeating decimals

A repeating or recurring decimal is a way of representing rational numbers in base 10 arithmetic. The decimal representation of a number is said to be repeating if it becomes periodic (repeating its values at regular intervals) and the infinetely - repeated portion is not zero. The infinitely-repeated digit sequence is called the repeated or reptend. If the repetend is a zero, this decimal representation is called a terminating decimal rather than a repeating decimal, since the zeros can be omitted and the decimal terminates before these zeros. Steps for solving: write as a geometric series, and lastly find the sum. The sum formula is s=a1/1-r. 

Parametric equations

In mathematics, parametric equations of a curve express the coordinates of the points of the curve as functions of a variable, called a parameter. For example, x=cos ty=sin t. These are parametric equations for the unit circle, where t is the parameter. Each value of t defines a point (x, y)= (f(t), g(t)) that we can plot. The collection of points that we get by letting t be all possible values is the graph of the parametric equations and is called the parametric curve. Steps to solve parametric equations include sketching the graph and eliminating the parameter. For graphing you want to write a t,x,y chart and solve for the x, y pairs to graph. For eliminating the parameter, you want to either use the trig identities or use elimination or substitution to solve for the rectangular equation. 

 

Systems of equations

A system of equations is a set of two or more equations that you deal with at one time. When solving the system, you must consider all of the equations involved and find a solution that satisfies all of the equations. When you graph a system, the point of interesection is the solution. A linear system of equations will only have one solution, and that is the point of intersection. Although, as always, there are times when you will find no solution or an infinte number of solutions. When a linear system has no solution, then the lines are parallel. If a linear system has an infinite amount of solutions, then the lines are the same. 

Partial Fraction Decomposition

For partial fraction decomposition, your either going to be solving it as a linear or quadratic problem. The steps include first multiply by the LCD. Second group terms by powers of x. Lastly, equate coefficients and solve the system of equations. If the degree of the numerator is bigger than the degree of the denominator then we will be using long division. And when it's a quadratic problem, we write Bx+C as the numerator. 

Probability of an Event

In probability theory, an event is a set of outcomes of an experiment, to which a probability is assigned. A single outcome may be an element of many different events, and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. In words, this means that the probability of an event must be a number between 0 and 1(inclusive). Also, probability of an impossible event is always zero. On the other hand, the probability of an impossible event is always zero.