Chapter 8.1 Vocabuary Presentation

http://prezi.com/qfdlaayb-ydj/young-vocab/#

Trigonometric Identities Review

Today, we review the previous chapter which is trigonometric Identities. Theres has 46 identities we have to memorize. 

      

   

    

                     

 

    



   

Count by three song

Here is a interesting video about a song. Hope you guys can enjoy it.

Here’s a song for you and me,

Shows us how to count by 3,
Hop two numbers at a time,
Check it on the number line…

3-6-9-12-15-18,
21-24-27,
Brings us to 30…
3-6-9-12-15-18,
21-24-27,
Brings us to 30…

Hop a number,
Skip a number,
Hop and skip those numbers now,
3 then 6…
Skip  4 and 5…
Hop a number,
Skip a number,
Hop and skip those numbers now
6 then 9,
Skip 7, 8 …

3-6-9-12-15-18,
21-24-27,
Brings us to 30…
3-6-9-12-15-18,
21-24-27,
Brings us to 30…
 
What are things we count by three?
Let us think and let us see…
What are things we count by three?
Let us think and let us see…

A tricycle, that’s got 3 wheels,
3 blind mice eat cheese for meals,
A tricycle, that’s got 3 wheels,
3 blind mice eat cheese for meals,

Things in 3 just can’t be beat,
A yards the length of 3 feet…
Things in 3 just can’t be beat,
A yard’s the length of 3 feet…

Triangles made of 3 sides each,
Count by three is what we’ll teach!
Triangles made of 3 sides each,
Count by three is what we’ll teach!

3-6-9-12-15-18,
21-24-27,
Brings us to 30…
3-6-9-12-15-18,
21-24-27,
Brings us to 30…

Leonardo of Pisa

 Leonardo of Pisa, also known as Fibonacci, was a brilliant Italian mathematician who is known  by several different names: Leonard Pisano Bigollo, Leonard Pisano, and Leonardo Bonacci. He is well known because of his sequences that a lot of students will learn nowadays, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, … a number sequence that is generated by adding the previous two terms to create the current term, known as the Fibonacci number. 

Linear Programming

This section is focused on the word problem base on our daily life. The question always ask for the maximun amount or the minimum amount, and by solving that type of problem, we should always use the following steps:
1 Carefully read the problem, and write the constraints or inequalities
2 Graph the inequalities, and shade the region corresponding to the stsyem 
3 Find the vertices of the region
4Write the function to find the maximum or the minimum (z=ax+by)
5 Put the vertices into the function to find the answer

Number Pattern of 6174

Today I am going to introduce 6174. It is a number well known to many. Some say it  It is, however, a very interesting number. Indeed, the number 6174 is also known as the Kaprekar constant. It is named after the Indian mathematician Dattaraya Ramchandra Kaprekar who studied the mystery behind 6174.Well, first, if you arrange the digits such that you have the highest number (7641) and also the lowest number (1467), and then determine the difference between the two, you arrive at 6174 (7641 – 1467 = 6174). 

Here is am example. If you try 3177! 

 3177 -> 7731, 1377

7731 – 1377 = 6354And again:
6354 -> 6543, 3456
6543 – 3456 = 3087Continuing:
3087 -> 8730, 0378
8730 – 378 = 8352
Continuing
8352 -> 8532, 2358
8532 – 2358 = 6174

System of Inequatilies

Today, we learned how to solve the system of inequalities and graph the solution of inequality. To sketch the graph of an inequality, begin by sketching the graph of the corresponding equation (which is replace the inequality sign with the equal sign). The graph of the equation will normally seperate the plane into two or more regions. In each such region, one of the following must be true.

1 All points in the region are solutions of the inequality

2 No point in the region is a solution of the inequality

Note: During the graph, we use a dashed line for < or >，and a solid line for ≤ or ≥.

Example： x+y≤5

                  x≥2

                  y≥0

                             

Replace the inequality sign with the equal sign, and sketch the graph of the resulting equation with solid line since all inequality are ≤ or ≥. Then test one point in each of the regions formed by graph to find their solution, and the shadow in red will be the final solution.

Partial Fractions

In this section, we learned how to write the partical fractions decomposition for the rational expression. There have four types of problems, which are distinct linear factors, repeated linear factors, distince linear and quadratic factors; repeated quadratic factors.

Distinct Linear Factors

Repeated linear factors

Distinct Linear and Quadratic Factors

The way to calculate the date

January has 31 days. Since February has 28 days, it means that every date in February will be three days later than the same date in January. Following the total number of days in every month, here is a list. 

January 0

February 3

March 3

April 6

May 1

June 4

July 6

August 2

September 5

October 0

November 3

December 5

To find the exact day of the week, here are the following steps. For example 1986.2.19

Step 1. Find the number on the list, February is 3

Step 2. Take the date of the month, 19

Step 3. Take the last two digits of the year, 86

Step 4. Find the number of leap years, take the last two digits of the year and divide it by 4. 86/4=21

Step 5. Add the four numbers together. 3+19+86+21=129

Step 6. Number divided by 7, remainder is 3. (Wednesday)

Systems of linear equations in two variable

The method of elimination is the other way to solve the equation, and I think it is faster and easier way to solve the equations. During the elimination, there are few steps we should follow:

1 Obtain same coefficient for one variable in both equations

2 Add/subtract equations to get rid of one variable 

3 Substitute the answer to solve for the other variable

4 Check the answer in both original equations

          

Also, we learned the graphical interpreation of solutions, and there have thhree kinds answers:

1 Exactly one solution                             Two lines intersect at one point

2 Infinitely many solutions                        Two lines are identical

3 No solution                                          Two lines are parallel

Solving systems of equations by substitution

The substitution is one of the way to sovle the equation. During the substitution, there are several rules,which are:

1 Express one of equation in terms of the variable in the other equation

2 Obtain an equation in one variable equation by combining the two equations

3 Solve the new equation

4 Substitute the solution in step3, to find the other variable

5 Check by substituting answers into the originial equations