Chapter 2 Project

Chapter 5 Project: How to Do Determining the Number of Triangles in the Ambuguous case (SSA): A Contruction Exploration

Exploration 1:

1. First, I drew a line that is over 6 cm and drew a point on that line and labeled it A.
2. Then, I constructed a 120 degree angle.
3. Afterwards, i made a 7 cm arch using a compass. Then the arch touched the 120 degree angle line, so I label it point C. *Note: in my Exploration 1, 1 the 7cm line is suppose to touch point B but it accidently got cut off.
4. I did the same for the other lengths using 5 and 6 cm.

Questions:

1. For 1, I discovered that there was one triangle that could have been made and for 2 and 3, i learned that zero triangles could be made.
3. The rule: BC > AB to make a triangle.



1. First, I drew a 30 degree angle with a protractor.
2. Then, i constructed a perpendicular bisector through point C and measured my height (3.5 cm).
3. Next, i copied a 30 degree angle and drew ray AC and AB.
4. Afterwards, I constructed a perpendicular bisector from AC to ray AB to form a right triangle.
5. I then found a value less than 3.5 cm (2 cm) and drew an arch from point C to see if a triangle could be formed. A triangle couldn't be formed.
6. I repeated steps 3-4 but for the next two triangles, I used a segment equal to the height of my triangle (3.5 cm) and a segment where BC>AC>h (7.3 cm).

Questions-

1. I discovered that i could make zero triangles in 6a, 1 right triangle in 6b, and 2 triangles in 6 c.
2. Rule: Triangles can only be made if its length is equal or greater than its height.




Exploration 3:

1. First, i drew a 30 degree angle with a protractor.
2. Then, I drew a 7 cm and 6 cm segment.
3. Next, I drew a line through the page and made a point and labeled it A.
4. I constructed a 30 degree angle with the line segment of 7 cm.
5. After that, I connected the points and labeled it Line segment AC= 7 cm.
6. Then, I used a 6 cm segment to draw arches on line AB-which should make two archs.
7. I connected these arches to point C, which then formed 2 triangles.
8. Finally, i created a perpendicular bisector through point C and measured the height.

The rule I got was AC>B>h

Questions:

1. SinA is the same as SinC
2. If BC is < or = AB, it can cause a right triangle or obtuse triangle to form.
3. BC = AB makes zero triangles
BC > AB makes one triangle
BC < AB makes zero triangles
BC < h makes zero triangles
BC = h makes one triangle
BC > AC > h makes two triangles
AC > B > makes two triangles

Remedial College Classes Cost Billions

I think that this shows that high school students should take the hardest class available-AP and HP courses. Students should also learn the material well, not just good enough to pass. Some students might think that AP/HP classes will take too much time and effort but it will be worth it in the long run. If students take the steps necessary to succeed not only in high school but also in college then they would also save some money in the future.

California "Cyber-Bully" Bill Takes Effect

I think that cyber-bullying is wrong because i don't understand why some people would spend all their time posting stupid comments online. They may think it is funny but they don't understand how much it will hurt the victim. People are inconsiderate of other people's feelings-they are selfish. They shouldn't post or say things online that they wouldn't say in person. I'm glad this bill is taking place because cyber-bullying can lead to things more serious, like depression.

Chapter 4-Solving Problems with Trigonometry

Chapter 1-Modeling with Functions and Regression Equations

For Chapter 1, it involves applying real world problems to math. The type that we learned were regressions.

For my project, I chose option 3. First, I had to decide on a company and look up its price. I picked the company Apple. Next, I went to http://www.google.com/finance-typed Apple=>clicked historical prices=> weekly=>typed in the month/year I was researching. I did the months/years of March 1996-March 2006 because we needed to look at a ten year trend. Then, I plugged it into my calculator and found my regression line and used it to predict the prices for 2008-2010(See picture above for more details!) Finally, I saw that my correlation coefficient of .69 did not fit my data really well because .69 is not that close to the number 1(best fit for data).

Chapter P-Applying Linear Equations in Two Variables

In Chapter P, we see the usage of linear equations and graphs to solve real life problems. In this case, my project was based on Astronomy. I am suppose to use the linear equation d= r X t (distance= rate X time) to make the calculations with r= 186,000 miles/second. The planet I chose to do was Venus, so for the problem I just searched up the distance from the Moon to Venus, how fast the light travels from Venus to the Sun, and how long it takes for light to travel from the Sun to Venus. Using the information i searched up, I just plugged in the numbers to get my answer.

Chapter P-Graphing Functions

1. The original parent function of this graph was y=|x|

2. Then, I wanted to do a vertical translation 8 units up, which led me to get the equation of y=|x|+8. As you can see, this function was in red and the vertex moved 8 units up on the y-axis.

3. Next, to do a horizontal translation, I decided that I wanted to move the graph 8 units to the right along on x-axis, so the equation became y=|x-8|, the function is shown in blue.

4. After that, I wanted to do a reflection across the x-axis, so my equation was y = -|x|, which was shown in purple. All of my y point from my (x,y) coordinates had become negative.

5. In green, I had done a horizontal translation 2 units to the left, followed by a vertical translation 4 units down(y=|x+2|-4.

6. Finally, for my last black graph, equation I had reflected my original function across the x-axis and then did a vertical translation 10 units down. The equation i ended up with was y= -|x-3|-10.




For Back to School Night, I brought my mom. She laughed at the idea of me teaching her Math, because she had barely been able to get a decent education growing up. As the night proceeded and as she began trying the translations it made a little more sense to her. She got the idea of doing vertical translations and horizontal translations.

About Stephanie

Education -
    •    Preschool: FM Smith
    •    Elementary: Cleveland
    •    Middle School: Edna Brewer
    •    High School: Oakland High

Volunteer Experience -
    •    Volunteer at Asian Library- Children Summer Reading Program

Work Experience -
    •    Highland Hospital Intern

Career Goal-
    •    Pediatrician

Interests-
    •    Enjoying Nature
    •    Listening to music
    •    Writing poetry