Friday, October 23, 2009
Final Exam's Over
This Thursday will be the Open Day for my 4SA class. Overall, most of them did very well in the final exam. As I mention earlier, Maths is not a problem for my 4SA girls. Amanda even scored 100. I was expecting Aini to do the same but because of one careless mistake, she only scored 99. Sometimes I do wonder, did I have a hand in their success or they're just plain smart. I would say teaching the 4SA class is a pleasure. Not only they're smart, they're very pleasant and hardworking too. I've no problem getting them to do or pass up their assignments. I'm sure they will do well in Form 5. I wished them all the best. Maybe I'll see some of them again in Form 5 next year.
Friday, October 9, 2009
Angles of Elevation and Depression
This is the last topic I taught before the final exam. This is a very simple topic that can be taught in one sitting. It involved trigonometry which the students are exposed to in lower forms.
The angle of elevation of an object as seen by an observer is the angle between the horizontal and the line from the object to the observer's eye (the line of sight).
If the object is below the level of the observer, then the angle between the horizontal and the observer's line of sight is called the angle of depression
Word Problems: Angles of Elevation and Depression
In order to solve problems involving angles of elevation and depression, it is necessary to
* use basic right triangle trigonometry
* solve equations which involve one fractional term is also important to know.
* find an angle given a right triangle ratio of sides.
* the fact that corresponding angles formed by parallel lines have the same measure.
A typical problem of angles of elevation and depression involves organizing information regarding distances and angles within a right triangle. In some cases, you will be asked to determine the measurement of an angle; in others, the problem might be to find an unknown distance.
Suppose a tree 50 feet in height casts a shadow of length 60 feet. What is the angle of elevation from the end of the shadow to the top of the tree with respect to the ground?
First we should make a diagram to organize our information. Look for these diagrams to involve a right triangle. In this case, the tree makes a angle 90ยบ with the ground. A diagram of this right triangle is shown below.
In the diagram, known distances are labeled. These are the 50 and 60 foot legs of the right triangle corresponding to the height of the tree and the length of the shadow.
The variable q is chosen to represent the unknown measurement, the object of the question.
To relate the known distances and the variable, an equation is written. In this case the equation involves the lengths of the sides which are opposite and adjacent to the angle q. Using the ratio of opposite to adjacent sides, we have
We use inverse tangent of
or
which is the angle of elevation.
Watch Video on Word Problems on Angle of Elevation & Depression
The angle of elevation of an object as seen by an observer is the angle between the horizontal and the line from the object to the observer's eye (the line of sight).
If the object is below the level of the observer, then the angle between the horizontal and the observer's line of sight is called the angle of depression
Word Problems: Angles of Elevation and Depression
In order to solve problems involving angles of elevation and depression, it is necessary to
* use basic right triangle trigonometry
* solve equations which involve one fractional term is also important to know.
* find an angle given a right triangle ratio of sides.
* the fact that corresponding angles formed by parallel lines have the same measure.
A typical problem of angles of elevation and depression involves organizing information regarding distances and angles within a right triangle. In some cases, you will be asked to determine the measurement of an angle; in others, the problem might be to find an unknown distance.
Suppose a tree 50 feet in height casts a shadow of length 60 feet. What is the angle of elevation from the end of the shadow to the top of the tree with respect to the ground?
First we should make a diagram to organize our information. Look for these diagrams to involve a right triangle. In this case, the tree makes a angle 90ยบ with the ground. A diagram of this right triangle is shown below.
In the diagram, known distances are labeled. These are the 50 and 60 foot legs of the right triangle corresponding to the height of the tree and the length of the shadow.
The variable q is chosen to represent the unknown measurement, the object of the question.
To relate the known distances and the variable, an equation is written. In this case the equation involves the lengths of the sides which are opposite and adjacent to the angle q. Using the ratio of opposite to adjacent sides, we have
We use inverse tangent of
or
which is the angle of elevation.
Watch Video on Word Problems on Angle of Elevation & Depression
Final Exam
I can't believe it! It's already nearing the end of the year.Personally, it has been a good year for me. I'm very thankful for all the things God has bestowed on me. My view on life have gradually changed over the years. The worldly gains are not as important to me as it used to be. Being a teacher is something that I really treasure. Hopefully in the 18 years of teaching, I was able to touch some of my student's life.
This week is the study leave for the Form 5 but some of my 5KA girls were called back for extra classes. On Wednesday, they had a six hours session on mathematics with Pn Chan, En Cheah and Pn Yeap. I really hope these extra sessions will help them. They must realize that nobody is able to help them if they are not willing to help themselves. To Amirah Azhar and Nani, I'm really proud of both of you. You've shown that you can really do it if you work hard for it. To Syuhadah, Farhain and Sara, you can always come in for extra sessions with me after school. To Azreen and Azzin, you still have time to make improvement. It's better late than never.
The final exam for the Form 4 started on the 7th of October. I still have one more chapter to go, but I decided to finish it after the final exam coz this chapter won't be tested in the exam. I'm not worried about my 4SA girls coz I know they can do well in Mathematics.
This week is the study leave for the Form 5 but some of my 5KA girls were called back for extra classes. On Wednesday, they had a six hours session on mathematics with Pn Chan, En Cheah and Pn Yeap. I really hope these extra sessions will help them. They must realize that nobody is able to help them if they are not willing to help themselves. To Amirah Azhar and Nani, I'm really proud of both of you. You've shown that you can really do it if you work hard for it. To Syuhadah, Farhain and Sara, you can always come in for extra sessions with me after school. To Azreen and Azzin, you still have time to make improvement. It's better late than never.
The final exam for the Form 4 started on the 7th of October. I still have one more chapter to go, but I decided to finish it after the final exam coz this chapter won't be tested in the exam. I'm not worried about my 4SA girls coz I know they can do well in Mathematics.
Thursday, October 1, 2009
Hari Raya Holidays
Last week, from 19 to 27 of September, school was off for the Hari Raya Aidil Fitri holidays. Hopefully everybody enjoyed their raya holidays.
This week school starts again. All students will have to buck up coz all the major exams are just around the corner. The form 5 are finishing their trial exam tomorrow. I've checked through some of my students mathematics paper 2 answer scripts. They didn't do as well as I expected them to. Every time I marked my student's paper, the same question will pop up. What did I do wrong? The students were not able to answer the same type of questions that were discussed in class. Sometimes the only conclusion that I can make is not all people are able to do math.
This week school starts again. All students will have to buck up coz all the major exams are just around the corner. The form 5 are finishing their trial exam tomorrow. I've checked through some of my students mathematics paper 2 answer scripts. They didn't do as well as I expected them to. Every time I marked my student's paper, the same question will pop up. What did I do wrong? The students were not able to answer the same type of questions that were discussed in class. Sometimes the only conclusion that I can make is not all people are able to do math.
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