HELLO 2010

It's already the end of the first month of 2010. How fast time seems to fly. It's been quite a while since my last update. Actually my original plan was just to let this blog die its natural death but today I accidently mention it to my 5KB class (i didn't plan it actually). Looks like it will be given another life line.

Well, what has happened in the last one month in school. Lots, actually. Firstly I'm very proud to say that my school was selected as one of the 20 schools nationwide that was awarded the status of High Performance School. The success is the culmination of all the hard work done by the students, teachers, school administrators , non-academic staff and not forgetting the parents. An organization can only achieve success if every one played their role to their best of abilities. Now, we have to work doubly hard to ensure that the trust put on us is fulfilled. It's scary actually..

This year I'm only given to teach Form 5 classes, namely 5SA and 5KB. I got to meet most of my 4SA girls again. In a way, I'm glad. Hopefully the feeling is mutual but I did mention to them that they have to bear with me for another year. This year is the first time I'm teaching the 5KB girls. It has been exciting coz there's lots of interesting characters in this class. So far so good (i think). I realized that i need to monitor some students more closely. Sometimes this is difficult given the 1 hour slot given to me each day for 3 days a week to be with them.

I've also started my training sessions with the teachers. You see, as an IT Coordinator, I'm suppose to train the teacher in using ICT. So far i've done 2 sessions with about 60 teachers on 'Online School' i.e showing teachers ways of giving online assignments to students using the school portal. Hopefully the teachers and students can really gain some benefit from this. I have one more session to go next Monday.

I've also given 2 talks on "Smart School" to parents during the orientation day and students right after the morning assembly. The response has been encouraging. Now the school portal seems to be more alive with new members.

Next on my agenda will be the SPS (Sistem Pengurusan Sekolah). The system is now ready with the school time table successfully uploaded with the help of En Saiful, the facilitator from Rebound Asia. There's been a lot of discussions on the SPS but from my personal point of view, I'm quite confident with this system compared to the earlier systems that were introduced to the Smart Schools. Me with a few of my fellow IT Coordinators have been reviewing the system for the whole of last year to ensure that it will be able to fulfill the school's need. Hopefully by March, we'll be able to use the system fully especially for teachers to do their lesson plans online.

Wow!!! This must be the longest post i've done so far. Got to go. It's time for the Maghrib prayer.

Mantap Minda Programme

The 'Mantap Minda Programme' for the Form 5 started 2 weeks ago and tomorrow will be the last day. I'm glad to see that some of the girls are taking this programme seriously. Today I managed to give some tips in answering the transformations question in Paper 2. I know quite a number of the students find this topic a bit difficult. Thank you for two girls in the front row for making my day. I didn't even got their name (they're not my students). They really showed their appreciation after I explained how to tackle this question easily. It's easy to make teachers happy. A show of appreciation is all that it takes. I wished all the Form 5 girls all the best for the SPM Examinations especially 'my 5KA girls'. May God Bless You Always.

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.

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 90º 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.

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.

Reference Angle

Reference angles are used to determine the values of the trigonometric functions in the second, third and fourth quadrants, in particular, for the "nice" angles. The reference angle for an angle θ is the smallest angle φ from the (positive or negative) x-axis to the terminal ray of the angle θ.

2nd Quadrant

For an angle θ in the second quadrant the reference angle φ is the remaining angle needed to complete a straight angle, that is, π radians or 180°. Thus θ + φ = π or θ + φ = 180°, and so

φ = π - θ or φ = 180° - θ.





3rd Quadrant

For an angle θ in the third quadrant the reference angle φ is the angle that must be subtracted from θ to leave a straight angle, that is, π radians or 180°. Thus θ - φ = π or θ - φ = 180°, and so

φ = θ - π or φ = θ - 180°





4th Quadrant

For an angle θ in the fourth quadrant the reference angle φ is the remaining angle needed to complete a full circle angle, that is, 2π radians or 360°. Thus θ + φ = 2π or θ + φ = 360°, and so

φ = 2π - θ or φ = 360° - θ.

Signs of sine, cosine and tangent, by Quadrant

The definition of the trigonometric functions cosine and sine in terms the coordinates of points lying on the unit circle tell us the signs of the trigonometric functions in each of the four quadrants, based on the signs of the x and y coordinates in each quadrant.




First Quadrant
For an angle in the first quadrant the point P has positive x and y coordinates. Therefore: In Quadrant I, cos(θ) > 0, sin(θ) > 0 and tan(θ) > 0 (All positive).

2nd Quadrant
For an angle in the second quadrant the point P has negative x coordinate and positive y coordinate. Therefore: In Quadrant II, cos(θ) < 0, sin(θ) > 0 and tan(θ) < 0 (Sine positive).

3rd Quadrant
For an angle in the third quadrant the point P has negative x and y coordinates. Therefore: In Quadrant III, cos(θ) < 0, sin(θ) < 0 and tan(θ) > 0 (Tangent positive).

4th Quadrant
For an angle in the fourth quadrant the point P has positive x coordinate and negative y coordinate. Therefore: In Quadrant IV, cos(θ) > 0, sin(θ) < 0 and tan(θ) < 0 (Cosine positive).

The quadrants in which cosine, sine and tangent are positive are often remembered using a favorite mnemonic.
One example: All Students Take Calculus.

Unit Circle

So... what is a Unit Circle?

A unit circle is a circle with a radius of one (a unit radius). In trigonometry, the unit circle is centered at the origin.

For the point (x,y) in Quadrant I, the lengths x and y become the legs of a right triangle whose hypotenuse is 1.

In the diagram above, we're measuring the angle θ between the x-axis of the Cartesian plane and a line that extends from the origin. Now, here's the really interesting thing; the sine of the angle is equal to the y-coordinate of the point on the unit circle where the line crosses, and the cosine of the angle is equal to the x-coordinate. This is true for any line extending from the origin.

Why is this? Well, the line segment from the origin to the point where it crosses the unit circle forms the hypotenuse of a right-angled triangle. Because the radius of the circle is 1, the length of the hypotenuse is likewise 1. SOHCAHTOA's rules then boil down to:

Sin θ = Opposite

Cos θ = Adjacent

Tan θ = Opposite/Adjacent

In other words:

Sin θ = y

Cos θ = x

Tan θ = y/x

Properties Of Common Tangents