## Tuesday, November 10, 2009

### 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.

## 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 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

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.

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.

## Saturday, September 26, 2009

### 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.

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.

## Friday, September 25, 2009

### 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.

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

## Monday, September 14, 2009

### Common Tangent To A Pair Of Circles

Common tangents are lines or segments that are tangent to more than one circle at the same time.

The possibility of common tangents is closely linked to the mutual position of circles.

If two circles touch inside, the two internal tangents vanish and the two external ones become a single tangent.

If two circles intersect, the common tangent is replaced by a common secant, whence there are only two external tangents.

If two circles touch each other outside, the two internal tangents coincide in a common tangent, thus there are three common tangents.

If two circles are separate, there are four common tangents, two inside and two outside.

The possibility of common tangents is closely linked to the mutual position of circles.

If two circles touch inside, the two internal tangents vanish and the two external ones become a single tangent.

If two circles intersect, the common tangent is replaced by a common secant, whence there are only two external tangents.

If two circles touch each other outside, the two internal tangents coincide in a common tangent, thus there are three common tangents.

If two circles are separate, there are four common tangents, two inside and two outside.

### Tangent Of A Circle.

I started the chapter on circle by introducing the concept of tangent to a circle.

A tangent to a circle has two defining properties

* A tangent touches a circle in exactly one point. This point is called point of tangency.

* The tangent intersects the circle's radius at a 90° angle

Watch Video on Tangent Line

Properties of two tangents to a circle

If two tangents lines are drawn namely AP and BP, they will intersect at a point, P. The properties of the two tangent lines are listed below :

1. CA = CB

2. AP = BP

3. Angle ACP = Angle BCP

4. Angle Angle APC = Angle BPC

5. Angle CAP and angle CBP are both right angles

6. Triangle CAP and BCP are congruent

A tangent to a circle has two defining properties

* A tangent touches a circle in exactly one point. This point is called point of tangency.

* The tangent intersects the circle's radius at a 90° angle

Watch Video on Tangent Line

Properties of two tangents to a circle

If two tangents lines are drawn namely AP and BP, they will intersect at a point, P. The properties of the two tangent lines are listed below :

1. CA = CB

2. AP = BP

3. Angle ACP = Angle BCP

4. Angle Angle APC = Angle BPC

5. Angle CAP and angle CBP are both right angles

6. Triangle CAP and BCP are congruent

## Sunday, September 13, 2009

### Blogging Again

It's been quite a while since my last update. It's not that I'm been so busy, it's just that the drive to write was not there. Writing does not come easily for me, I guess its just not my cup of tea.

School reopened on the 1st of September 2009. I managed to finished off the Earth As A Sphere chapter with my 5KA class before they start their trial exam on the 8th of September. I really hope that my girls will do well in this exam. I'm really amazed at the improvements shown by a number of girls in that class. Good Luck to all of you.

My 4SA class did quite well in the August test. Only 2 students were not able to score an A for the test. I'll have to monitor the two girls more closely. I really need to speed up on my teaching coz I just realized that I only have two weeks after the Hari Raya break before the final exam starts. Last week, I missed the Wednesday class coz I had to go for a meeting in Shah Alam. This week I will again miss the Wednesday class due to another meeting in BTP. Thankfully Datin Lee is around to cover for me. I really feel guilty when I had to miss my class but being the ICT coordinator of my school, I'm frequently called for meetings. I wish someone will take over my job coz I'd rather be teaching than doing all the administrative work.

School reopened on the 1st of September 2009. I managed to finished off the Earth As A Sphere chapter with my 5KA class before they start their trial exam on the 8th of September. I really hope that my girls will do well in this exam. I'm really amazed at the improvements shown by a number of girls in that class. Good Luck to all of you.

My 4SA class did quite well in the August test. Only 2 students were not able to score an A for the test. I'll have to monitor the two girls more closely. I really need to speed up on my teaching coz I just realized that I only have two weeks after the Hari Raya break before the final exam starts. Last week, I missed the Wednesday class coz I had to go for a meeting in Shah Alam. This week I will again miss the Wednesday class due to another meeting in BTP. Thankfully Datin Lee is around to cover for me. I really feel guilty when I had to miss my class but being the ICT coordinator of my school, I'm frequently called for meetings. I wish someone will take over my job coz I'd rather be teaching than doing all the administrative work.

## Wednesday, August 26, 2009

### The Blessed Month

Today is the fifth day of the school holidays, so there's nothing to write about school. I hope all the teachers and students are enjoying their holidays. It is really a much needed rest for all of us. The Form 3 students must be working hard coz the PMR exam is coming soon. The Form 5 students also must use the free time wisely to prepare for the trial and SPM examination.

Today is also the fifth day of the fasting month. Starting Ramadhan during the school holiday is really a blessing. I don't need to rush in the morning to go to work. I'm also able to spend more time with my youngest son. This year is the second year he is fasting. Last year he only missed a day of fasting. I'm really proud of him. Hopefully this year he'll be able to complete the whole month of Ramadhan. This year is also the first year he is going to the mosque for the tarawih prayers. He looks forward to go the mosque every night partly because he likes to pray with his friends and partly because of the food that is served after the prayers.

Today I also did a talk on'teknik menjawab soalan' for SPM Mathematics for the children of the staff of the Public Works Department in Kuala Lumpur. This is my first time giving the talk. Overall, it went quite well. The students were very nice. I hope they'll gain something from my talk. As most students and teachers are aware, one of the most effective way to prepare for the SPM examination is to do the past years exam papers. Each year the format and the type of questions are the same. To be good in Math, students need to do a lot of exercises. There's a whole lot of trials exam papers that can be downloaded from the net.

Today is also the fifth day of the fasting month. Starting Ramadhan during the school holiday is really a blessing. I don't need to rush in the morning to go to work. I'm also able to spend more time with my youngest son. This year is the second year he is fasting. Last year he only missed a day of fasting. I'm really proud of him. Hopefully this year he'll be able to complete the whole month of Ramadhan. This year is also the first year he is going to the mosque for the tarawih prayers. He looks forward to go the mosque every night partly because he likes to pray with his friends and partly because of the food that is served after the prayers.

Today I also did a talk on'teknik menjawab soalan' for SPM Mathematics for the children of the staff of the Public Works Department in Kuala Lumpur. This is my first time giving the talk. Overall, it went quite well. The students were very nice. I hope they'll gain something from my talk. As most students and teachers are aware, one of the most effective way to prepare for the SPM examination is to do the past years exam papers. Each year the format and the type of questions are the same. To be good in Math, students need to do a lot of exercises. There's a whole lot of trials exam papers that can be downloaded from the net.

## Thursday, August 20, 2009

### Ramadhan's Coming

The fasting month of Ramadhan is fast approaching. It was confirmed today that the fasting month will start this Saturday. I love the month of Ramadhan. Everything seems so relaxed and peaceful during this month. I don't have to rush like the regular days. I don't have to think about what to eat for breakfast and lunch. I also seem to eat less in this month and thus feel much healthier. Fasting is good for our health. We are able to enjoy the food we have coz we were deprived of it for the whole day. We humans like to take things for granted. We never appreciate the things that we have. Everyone will also make a point to make it home on time to break fast together. Thus the fasting month is also good in strengthening the family ties.

Tomorrow is also the last day of school before the school holidays. The school will be closed for holiday for 1 week from 22 - 31 August. The form 4 classes just finished the August test on Tuesday, so I gave them a day off from lessons on Wednesday. I had to carry on with my lessons with my 5SA class coz the trial exam will start on the 4th of August and I still have a few topics on Earth As A Sphere to cover.

So on Monday, I taught the girls how to find the distance between 2 point on the meridian. These are the steps:

1. Find the difference in angle between the two points.

2. Use the formula Distance = difference in angle x 60 to obtain the distance.

The unit for distance on the sphere is nautical miles (nm). The same steps can be used if you want to find the distance between two points on the equator.

Problem 1 : Find the distance between the following points :

A (85°N , 105°E) and B (27°N, 105°E)

Solution :

Note that points A and B are on the same longitude or the same meridian.

Step 1 : Find the difference in angle between the 2 points. Since the 2 points are in the same hemisphere, substract the latitude of both points to obtain the difference in angle between 2 latitudes.

Difference in angle is (85 - 27) = 58°.

Step 2 : Use the formula Distance = 58 x 60 = 3360 nm.

Problem 2 : Find the distance between the following points

A (30°S , 50°W) and B (15°N , 50°W)

Step 1 : Find the difference in angle. Since the 2 points are in a different hemisphere, we have to add the angles of the two latitudes to obtain the difference between the 2 points.

Thus the difference in angle is (30° + 15°) = 45°

Step 2 : Distance = 45 x 60 = 2700 nm.

The same steps can be use to find the distance between 2 points on the equator.

Example : Find the distance between A (0° , 14°E) and B (0° , 15°W)

1. Difference in angle (14 + 15) = 29 - Different side of the meridian

2. Distance = 29 x 60 = 1740 nm

Tomorrow is also the last day of school before the school holidays. The school will be closed for holiday for 1 week from 22 - 31 August. The form 4 classes just finished the August test on Tuesday, so I gave them a day off from lessons on Wednesday. I had to carry on with my lessons with my 5SA class coz the trial exam will start on the 4th of August and I still have a few topics on Earth As A Sphere to cover.

So on Monday, I taught the girls how to find the distance between 2 point on the meridian. These are the steps:

1. Find the difference in angle between the two points.

2. Use the formula Distance = difference in angle x 60 to obtain the distance.

The unit for distance on the sphere is nautical miles (nm). The same steps can be used if you want to find the distance between two points on the equator.

Problem 1 : Find the distance between the following points :

A (85°N , 105°E) and B (27°N, 105°E)

Solution :

Note that points A and B are on the same longitude or the same meridian.

Step 1 : Find the difference in angle between the 2 points. Since the 2 points are in the same hemisphere, substract the latitude of both points to obtain the difference in angle between 2 latitudes.

Difference in angle is (85 - 27) = 58°.

Step 2 : Use the formula Distance = 58 x 60 = 3360 nm.

Problem 2 : Find the distance between the following points

A (30°S , 50°W) and B (15°N , 50°W)

Step 1 : Find the difference in angle. Since the 2 points are in a different hemisphere, we have to add the angles of the two latitudes to obtain the difference between the 2 points.

Thus the difference in angle is (30° + 15°) = 45°

Step 2 : Distance = 45 x 60 = 2700 nm.

The same steps can be use to find the distance between 2 points on the equator.

Example : Find the distance between A (0° , 14°E) and B (0° , 15°W)

1. Difference in angle (14 + 15) = 29 - Different side of the meridian

2. Distance = 29 x 60 = 1740 nm

## Saturday, August 15, 2009

### Schooling On A Saturday

Today is a school day. It is suppose to be a replacement day for the extended holiday the school will be taking for the Deepavali celebration in October. Schooling on a Saturday is not a good idea as proven by the poor attendance of students today. There's only 4 girls present in 5KA and only a handful in my 4SA class today. Merit marks were given to all students who were present today.

My 4SA class was taken over by the physics teacher. The students needs more help in Physics than in Math. As for my 5KA class, I continued with the Earth As A Sphere chapter. Lesson was a breeze today compared with the regular days where I have to handle 23 boisterous girls who doesn't know the meaning of quiet. Its sure is a challenge teaching these girls but I enjoy every minute of it. Today we tried some problems on determining the location of places on the earth's surface.

Any location on Earth is described by two numbers--its latitude and its longitude. If a pilot or a ship's captain wants to specify position on a map, these are the "coordinates" they would use. Actually, these are two angles, measured in degrees, "minutes of arc" and "seconds of arc." These are denoted by the symbols ( °, ', " ) e.g. 35° 43' 9" means an angle of 35 degrees, 43 minutes and 9 seconds (do not confuse this with the notation (', ") for feet and inches!). A degree contains 60 minutes of arc and a minute contains 60 seconds of arc--and you may omit the words "of arc" where the context makes it absolutely clear that these are not units of time.

To determine the latitude of a location, imagine that the Earth is a transparent sphere (actually the shape is slightly oval; because of the Earth's rotation, its equator bulges out a little). Through the transparent Earth (drawing) we can see its equatorial plane, and its middle the point is O, the center of the Earth.

To specify the latitude of some point P on the surface, draw the radius OP to that point. Then the elevation angle of that point above the equator is its latitude λ--northern latitude if north of the equator, southern (or negative) latitude if south of it. In the diagram below, the latitude of P is 30°N.

Longitude is distance east or west of a base line called greenwich meridian or prime meridian. The longitude of any given place is its distance, measured in degrees of arc, from this base line.

My 4SA class was taken over by the physics teacher. The students needs more help in Physics than in Math. As for my 5KA class, I continued with the Earth As A Sphere chapter. Lesson was a breeze today compared with the regular days where I have to handle 23 boisterous girls who doesn't know the meaning of quiet. Its sure is a challenge teaching these girls but I enjoy every minute of it. Today we tried some problems on determining the location of places on the earth's surface.

Any location on Earth is described by two numbers--its latitude and its longitude. If a pilot or a ship's captain wants to specify position on a map, these are the "coordinates" they would use. Actually, these are two angles, measured in degrees, "minutes of arc" and "seconds of arc." These are denoted by the symbols ( °, ', " ) e.g. 35° 43' 9" means an angle of 35 degrees, 43 minutes and 9 seconds (do not confuse this with the notation (', ") for feet and inches!). A degree contains 60 minutes of arc and a minute contains 60 seconds of arc--and you may omit the words "of arc" where the context makes it absolutely clear that these are not units of time.

To determine the latitude of a location, imagine that the Earth is a transparent sphere (actually the shape is slightly oval; because of the Earth's rotation, its equator bulges out a little). Through the transparent Earth (drawing) we can see its equatorial plane, and its middle the point is O, the center of the Earth.

To specify the latitude of some point P on the surface, draw the radius OP to that point. Then the elevation angle of that point above the equator is its latitude λ--northern latitude if north of the equator, southern (or negative) latitude if south of it. In the diagram below, the latitude of P is 30°N.

Longitude is distance east or west of a base line called greenwich meridian or prime meridian. The longitude of any given place is its distance, measured in degrees of arc, from this base line.

## Thursday, August 13, 2009

### Longitude and Latitude

Started the Earth As A Sphere topic by explaining the concept of longitude and latitude.

Lines of latitude run East & West or horizontal but measure distance North & South of the Equator—vertically. The equator is labeled as zero degrees latitude. The greatest amount of latitude is 90 degrees at the North or South poles. We can then label our equator as 0 and our North and South poles as 90. These lines of latitude are parallel to the equator and are even referred to as “parallels” or “parallels of latitude.”

Moving to lines of longitude, they run perpendicular to lines of latitude. That is, longitude lines run North and South but measure East and West of zero degrees longitude which is a line called the Prime Meridian. This arbitrary north/south line was marked by the British in the 17th century and runs through a town just outside of London called Greenwich.

Starting at the Prime Meridian, we measure the earth east or west with these north/south-running lines called “meridians.” We can measure halfway around the world till these meridians meet at 180 degrees. This meridian line at 180 east or west is called the International Date Line. So unlike latitude, where the greatest or maximum latitude is 90 at either the north or south poles, the greatest amount of longitude is 180—halfway around the world from the prime meridian. One other important way these longitude lines differ from parallel latitude lines is that lines of longitude are not parallel, and in fact converge at both the North and South poles.

You can read more on longitude and latitude below :

What Is Longitude and Latitude?

Lines of latitude run East & West or horizontal but measure distance North & South of the Equator—vertically. The equator is labeled as zero degrees latitude. The greatest amount of latitude is 90 degrees at the North or South poles. We can then label our equator as 0 and our North and South poles as 90. These lines of latitude are parallel to the equator and are even referred to as “parallels” or “parallels of latitude.”

Moving to lines of longitude, they run perpendicular to lines of latitude. That is, longitude lines run North and South but measure East and West of zero degrees longitude which is a line called the Prime Meridian. This arbitrary north/south line was marked by the British in the 17th century and runs through a town just outside of London called Greenwich.

Starting at the Prime Meridian, we measure the earth east or west with these north/south-running lines called “meridians.” We can measure halfway around the world till these meridians meet at 180 degrees. This meridian line at 180 east or west is called the International Date Line. So unlike latitude, where the greatest or maximum latitude is 90 at either the north or south poles, the greatest amount of longitude is 180—halfway around the world from the prime meridian. One other important way these longitude lines differ from parallel latitude lines is that lines of longitude are not parallel, and in fact converge at both the North and South poles.

You can read more on longitude and latitude below :

What Is Longitude and Latitude?

## Tuesday, August 11, 2009

### Back To School

We're back in school today after a 1 week break. Had a short assembly in the gallery. Pn Loh reminded the students on the Influenza A (H1N1)again. It seems to be getting worse as the death toll from Influenza A (H1N1) rose to 38 today. Some of the students and teachers were wearing masks. You can read more about using face mask here.

The August test is postponed to next week. That's good news for the Form 1, 2 and 4 students, they'll have more time to prepare for the test.

I still have one more chapter to cover for my form 5 class. It's the Earth As a Sphere chapter. A lot of students find this chapter quite difficult. Luckily students can choose not to answer the question on this topic for the SPM. Most probably my 5KA students will also give this topic a miss. So I won't be spending too much time on it. Hopefully by the mid term holidays, I'm able to complete the syllabus. I'm very happy with the progress shown by some of the girls in this class. It shows that nothing is impossible if you put your heart and mind to it.

The August test is postponed to next week. That's good news for the Form 1, 2 and 4 students, they'll have more time to prepare for the test.

I still have one more chapter to cover for my form 5 class. It's the Earth As a Sphere chapter. A lot of students find this chapter quite difficult. Luckily students can choose not to answer the question on this topic for the SPM. Most probably my 5KA students will also give this topic a miss. So I won't be spending too much time on it. Hopefully by the mid term holidays, I'm able to complete the syllabus. I'm very happy with the progress shown by some of the girls in this class. It shows that nothing is impossible if you put your heart and mind to it.

## Wednesday, August 5, 2009

### School's Out

School is off for a whole week due to the increasing number of students and teachers getting sick. Hopefully its just the regular flu and not caused by the Influenza A (H1N1) virus. Teachers and students are instructed to quarantined themselves at home for the whole week. I hope everyone will follow the instruction given by the authorities. Anyway, the August test was postponed to the last week before the school holidays. Use the time wisely to prepare for the test and the BIG exams that are coming soon. I'm putting up some mathematical jokes I found to lighten up the atmosphere :

1. Math problems? Call 1-800-[(10x)(13i)^2]-[sin(xy)/2.362x].

2. If I had only one day left to live, I would live it in my statistics class: it would seem so much longer

3. It is proven that the celebration of birthdays is healthy. Statistics show that those people who celebrate the most birthdays become the oldest.

4. Q : Why was the maths book unhappy A : It had too many problems

5. Teacher: "Who can tell me what 7 times 6 is?"

Student: "It's 42!"

Teacher: "Very good! - And who can tell me what 6 times 7 is?"

Same student: "It's 24!

6. Q: How does a mathematician induce good behavior in her children?

A: `I've told you n times, I've told you n+1 times.

7. Student Howler 1: An average is a thing that hens lay their eggs on - for example, "My hens lay four eggs a week on average."

8. A professor, when asked how many problems there would be on the final, turned to the student and replied, "I think you will have lots of problems on the final."

9. What keeps a square from moving? Square roots, of course.

10. Teacher : If you had one dollar and you asked your father for another, how

many dollars would you have?

Student : One dollar.

Teacher : You don't know your arithmetic.

Student : You don't know my father !

Happy Face Math

1. Math problems? Call 1-800-[(10x)(13i)^2]-[sin(xy)/2.362x].

2. If I had only one day left to live, I would live it in my statistics class: it would seem so much longer

3. It is proven that the celebration of birthdays is healthy. Statistics show that those people who celebrate the most birthdays become the oldest.

4. Q : Why was the maths book unhappy A : It had too many problems

5. Teacher: "Who can tell me what 7 times 6 is?"

Student: "It's 42!"

Teacher: "Very good! - And who can tell me what 6 times 7 is?"

Same student: "It's 24!

6. Q: How does a mathematician induce good behavior in her children?

A: `I've told you n times, I've told you n+1 times.

7. Student Howler 1: An average is a thing that hens lay their eggs on - for example, "My hens lay four eggs a week on average."

8. A professor, when asked how many problems there would be on the final, turned to the student and replied, "I think you will have lots of problems on the final."

9. What keeps a square from moving? Square roots, of course.

10. Teacher : If you had one dollar and you asked your father for another, how

many dollars would you have?

Student : One dollar.

Teacher : You don't know your arithmetic.

Student : You don't know my father !

Happy Face Math

## Friday, July 31, 2009

### Missing Students

I planned to do a revision on statistics with my 4SA girls today but majority of them are MIA. Only 6 girls were in class today (I was told there should be 9). The rest are either in the hall (prefect's installation) or are absent. I thought I saw Su Yi in school today. She's not a prefect, so I wonder how come she's not in class during the math period. How about the other 2 girls. I guess they have some explaining to do comes Monday Math class. So instead of doing the revision, I asked the girls present to upload their online assignments. There are still some girls who has not uploaded their assignment. 4SA girls, take note - the online assignments will be included as part of the formative marks for the August test. As for the test, students will be tested on Chapters 1-7. I've uploaded some revision questions on my site links for you all to revise. (All questions were taken from Koleksi Soalan SMS Muzaffar Shah)

### Plan & Elevation

Today, I discussed questions on Plan & Elevation with my 5KA girls. Questions on this topic usually requires student to draw the plan (view from above), the front or the side elevation of a 3-dimensional object. The diagrams must be drawn using the actual measurements given. Every year this topic came out in the SPM Mathematics Paper 2. Students are advised to be well verse with this topic coz it carries 12 marks and are quite easy as it does not require any calculations to be done. Example of the questions on this topic are shown below:

The first part of the question usually requires student to draw the plan (view from above) of a solid object. Example :

Then the second part of the question usually requires students to draw the elevation of the combined solid (with another solid added or parts of the original solid removed) as viewed from the direction given.

These questions require students to imagine how the solids looks like when viewed from above or from the directions given.

See the answers here

The first part of the question usually requires student to draw the plan (view from above) of a solid object. Example :

Then the second part of the question usually requires students to draw the elevation of the combined solid (with another solid added or parts of the original solid removed) as viewed from the direction given.

These questions require students to imagine how the solids looks like when viewed from above or from the directions given.

See the answers here

## Thursday, July 30, 2009

### SPS Again

Yesterday and today I'm at the Bahagian Teknologi Pendidikan (Educational Technology Division) in Bukit Kiara Kuala Lumpur reviewing more modules of the smart school school system (SPS). We still have a lot to go thru. I intentionally did not leave any work for my 4SA students coz I think they need the time to do revision on the more difficult subject like Additional Mathematics, Physics and Chemistry. Math or formerly known as modern math is the easiest of the science subjects. In a boarding school environment, all students will score A1 for the SPM examination. So that's why I'm not so worried about a class like 4SA. They'll be able to ace this subject with just a little help from me.

## Monday, July 27, 2009

### End of Statistics Chapter

Today, I managed to finish the chapter on statistics for my 4SA class. We learned how to interpret and how to obtain information from an ogive. The following terms are usually associated with an ogive :

1. first quartile (The first quartile is the 25th percentile. It is that point

below which lie ¼ of the data)

2. median (The median is the point below which lie half the data. It is the 50th

percentile.

3. third quartile (The third quartile is the 75th percentile point. It is that

point below which lie 75% of the data)

4. interquartile range (The interquartile range is the difference between the first

and third quartiles.

The following diagram shows how the values of the item above can be obtained from an ogive

After finishing up the chapter, we had a short quiz on statistics. The quiz questions can be downloaded here

1. first quartile (The first quartile is the 25th percentile. It is that point

below which lie ¼ of the data)

2. median (The median is the point below which lie half the data. It is the 50th

percentile.

3. third quartile (The third quartile is the 75th percentile point. It is that

point below which lie 75% of the data)

4. interquartile range (The interquartile range is the difference between the first

and third quartiles.

The following diagram shows how the values of the item above can be obtained from an ogive

After finishing up the chapter, we had a short quiz on statistics. The quiz questions can be downloaded here

## Friday, July 24, 2009

### Student's Presentation

I had a presentation session with my 4SA girls today. The presentations covers the topic of Statistics (histogram & frequency polygons). 5 groups presented their findings on the survey that they did on their classmates. It's up to the students to determine the topic of their survey. The only criteria I gave them was it has to be an interesting topic. Overall all the groups were able to achieve the objective of this activity that is to collect, tabulate, draw graphs, analyze and make conclusions on the data collected. I'm quite impressed with the outcome of this activity. Sri Aman girls never fails to deliver.

Students are suppose to upload their presentation to the sriaman online school website at http://smkpsriaman.net/onlineschool.

Students are suppose to upload their presentation to the sriaman online school website at http://smkpsriaman.net/onlineschool.

### Back In School Again

Finally I'm back in school again after spending 3 days in BTP, Bukit Kiara Kuala Lumpur scrutinizing the new Sistem Pengurusan Sekolah (SPS). We're not able to finish reviewing the SPS within the 3 days given, so we might be called again next week for another 3 days. There goes my classes again. This time I'm not so worried coz Datin Yap will be able to cover my classes when I'm away.

Today, I started Plan and Elevation with my 5KA girls. I decided to skip the Earth as a Sphere chapter coz its quite a difficult chapter. I'll keep it to the end. We learn how to draw plans (view from above), side and front elevation (side and front view) of a 3-dimensional object. Most of the girls are getting a grip on this chapter coz they are able to come out with the correct plan, side and front elevation of the 3-dimensional objects given. I'm happy to see that Safanaz is also able to come up with the correct drawings. Next math period I will discuss actual SPM questions on this topic.

Today, I started Plan and Elevation with my 5KA girls. I decided to skip the Earth as a Sphere chapter coz its quite a difficult chapter. I'll keep it to the end. We learn how to draw plans (view from above), side and front elevation (side and front view) of a 3-dimensional object. Most of the girls are getting a grip on this chapter coz they are able to come out with the correct plan, side and front elevation of the 3-dimensional objects given. I'm happy to see that Safanaz is also able to come up with the correct drawings. Next math period I will discuss actual SPM questions on this topic.

## Monday, July 20, 2009

### Busy, Busy Busy.....

The last couple of weeks has been crazy for me. After coming back from the 4 days course in Shah Alam, I had to attend another meeting again in Shah Alam on Monday last week (missed my 4SA class but I managed to do something with my 5SA coz I arrived in school just in time for the class at 12.00 noon). Then on Wednesday, inspectorates from the PPD (District Education Dept) and PKG (Teacher's Activity Centre) came to look at the smart school program in Sri Aman (there goes my classes again). On Friday the school had the Co-curriculum and Prize Giving Day. So I didn't get to enter class the whole of last week.

This week I'll be away again from Tuesday till Thursday. Thankfully Datin Yap will be here to cover for me.

Today I revised again the topic of histogram and frequency polygons with my 4SA girls. The assignment below was given to them :

1. Work in groups of 5.

2. Collect interesting data from the members of the 4SA class.

3. Tabulate the data in a frequency table.

4. Construct a histogram or a frequency polygon based on the data using Micosoft Excel (integrating ICT in teaching & learning). The histogram or frequency polygon must at least have 5 class intervals.

5. Analysed the data collected. Example : Calculate the mean and determine the modal class.

6. Present the finding to the class on Friday (25 July) using powerpoint.

7. The group that is able to present the best report will get merit marks.

For those who doesn't know how to create histogram with Excel, you can watch the movie below showing steps of creating frequency table and histogram using the Excel

program

Histogram Movie

or you can refer to a step by step guide here. Good Luck.

This week I'll be away again from Tuesday till Thursday. Thankfully Datin Yap will be here to cover for me.

Today I revised again the topic of histogram and frequency polygons with my 4SA girls. The assignment below was given to them :

1. Work in groups of 5.

2. Collect interesting data from the members of the 4SA class.

3. Tabulate the data in a frequency table.

4. Construct a histogram or a frequency polygon based on the data using Micosoft Excel (integrating ICT in teaching & learning). The histogram or frequency polygon must at least have 5 class intervals.

5. Analysed the data collected. Example : Calculate the mean and determine the modal class.

6. Present the finding to the class on Friday (25 July) using powerpoint.

7. The group that is able to present the best report will get merit marks.

For those who doesn't know how to create histogram with Excel, you can watch the movie below showing steps of creating frequency table and histogram using the Excel

program

Histogram Movie

or you can refer to a step by step guide here. Good Luck.

## Friday, July 10, 2009

### Updates

Finally I'm able to update my blog again after quite a while. I was very busy doing all the administrative work that I had so little time to spend on my teaching and learning activities. I managed to finish off the mathematical reasoning topic for my 4 SA and Area Under The Graph for my 5KA before I was sent for another course for 4 days in Bahagian Teknologi Pendidikan Negeri Selangor in Shah Alam.

The last topic for Mathematical Reasoning involves making conclusion by induction and deduction (Inductive and Deductive Reasoning)

Inductive and deductive reasoning are two methods of logic used to arrive at a conclusion based on information assumed to be true.Deductive reasoning arrives at a specific conclusion based on generalizations. Inductive reasoning takes events and makes generalizations

Looks like I have to continue another time. Suddenly I feel so tired and sleepy. It must be because of the hearty meal I had for dinner earlier.

The last topic for Mathematical Reasoning involves making conclusion by induction and deduction (Inductive and Deductive Reasoning)

Inductive and deductive reasoning are two methods of logic used to arrive at a conclusion based on information assumed to be true.Deductive reasoning arrives at a specific conclusion based on generalizations. Inductive reasoning takes events and makes generalizations

Looks like I have to continue another time. Suddenly I feel so tired and sleepy. It must be because of the hearty meal I had for dinner earlier.

## Wednesday, June 24, 2009

### Speed-Time Graph

Continued with the topic of distance-time graph with my 5KA girls today. We discussed a couple of questions on the topic. Most of the students were able to solve the problems given (I wish they can do the same in the next test). Then I managed to introduce the speed-time graph.

Speed-Time Graph

We can represent the movement of objects using a graph, usually plotting time on the x-axis (horizontal) and the speed on the y-axis (vertical).

Consider a train accelerating from a station along a straight and level track to a maximum speed and slowing down to a stop at the next station. The easiest way to show this is with a speed time graph.

Acceleration is the gradient of the speed-time graph.

From the graph,

* between O and A, the train is accelerating;

* between A and B, the train travels at a constant speed;

* between B and C, the train slows down. Slowing down can also be called

negative acceleration, or deceleration. It is given a minus sign.

Distance is the area under the speed-time graph. To work out the total distance, we would add the areas of:

* triangle OAX;

* rectangle ABXY;

* triangle BCY.

Speed-Time Graph

We can represent the movement of objects using a graph, usually plotting time on the x-axis (horizontal) and the speed on the y-axis (vertical).

Consider a train accelerating from a station along a straight and level track to a maximum speed and slowing down to a stop at the next station. The easiest way to show this is with a speed time graph.

Acceleration is the gradient of the speed-time graph.

From the graph,

* between O and A, the train is accelerating;

* between A and B, the train travels at a constant speed;

* between B and C, the train slows down. Slowing down can also be called

negative acceleration, or deceleration. It is given a minus sign.

Distance is the area under the speed-time graph. To work out the total distance, we would add the areas of:

* triangle OAX;

* rectangle ABXY;

* triangle BCY.

### Mathematical Reasoning

Started Chapter 4 - Mathematical Reasoning for my 4SA today. In the first part, students were introduced with the concepts of statement, quantifiers, negation and compound statements. The powerpoint presentation below was used in today's class.

Mathematical Reasoning

View more OpenOffice presentations from marzmd.

## Saturday, June 20, 2009

### Distance-Time Graph

My course on the school management system in Ipoh was cut short by one day coz some of the participants were called for a meeting on Friday in Kuala Lumpur. It has been a fruitful 3 days here in Ipoh learning about the new system which will be installed in the school server next week. Anyway, I'm glad to be able to continue my lesson with 5 KA on Friday coz i really need to cover a lot more chapters before the trial exam. Managed to start the topic on distance-time graph.

Introduction

Information about movement can be presented in a number of ways. Data for the total distance moved at different times during movement can be recorded in a table. Alternatively, the same information can be presented in a graph. Plotting distance against time can tell you a lot about a journey.

If something is not moving, a horizontal line is drawn on a distance-time graph (dt-graph).

Time is increasing to the right, but its distance does not change. It is stationary

If something is moving at a steady speed, it means we expect the same increase in distance in a given time:

Time is increasing to the right, and distance is increasing steadily with time. It moves at a steady speed.

Slope and the Speed

When you look at a slope of a line on a distance-time graph you may notice how slopes can be different. The slope of the line determines the speed; the higher the slope the greater the speed, but if the slope is low then the speed is low.

As you can see in the first chart, the slope is very high, this means that the car must be traveling at a great speed. In the second graph, the slope is relatively low, which means that the car is driving at a very low speed

You can learn more on distance-time graph here

Introduction

Information about movement can be presented in a number of ways. Data for the total distance moved at different times during movement can be recorded in a table. Alternatively, the same information can be presented in a graph. Plotting distance against time can tell you a lot about a journey.

If something is not moving, a horizontal line is drawn on a distance-time graph (dt-graph).

Time is increasing to the right, but its distance does not change. It is stationary

If something is moving at a steady speed, it means we expect the same increase in distance in a given time:

Time is increasing to the right, and distance is increasing steadily with time. It moves at a steady speed.

Slope and the Speed

When you look at a slope of a line on a distance-time graph you may notice how slopes can be different. The slope of the line determines the speed; the higher the slope the greater the speed, but if the slope is low then the speed is low.

As you can see in the first chart, the slope is very high, this means that the car must be traveling at a great speed. In the second graph, the slope is relatively low, which means that the car is driving at a very low speed

You can learn more on distance-time graph here

### More on Probability

The Form Four syllabus on probability require students to calculate the probability of a specific or single event occurring. The equations below provide the formula for calculating simple probability. The first one is written out, while the second is in symbol form

Properties of Probability

Property 1

Property 2

Property 3

Click here to do challenge exercises on probability.

## Wednesday, June 17, 2009

### Probability

Hi, I'm back after a two week school break. Only managed to teach probability for my 4 SA class on Monday coz I've to be in Ipoh for the rest of the week for a course on the new Smart School Management System. The Probability topic for Form 4 is a very short and simple topic

The study of probability helps us figure out the likelihood of something happening. For instance, when you roll a pair of dice, you might ask how likely you are to roll a seven. In math, we call the "something happening" an "event.

Definitions :

The sample space is a set consisting of all the possible outcomes of an event (like drawing a marble from a jar, or picking a card from a deck). The number of different ways you can choose something from the sample space is the total number of possible outcomes.

Because each probability is a fraction of the sample space, the sum of the probabilities of all the possible outcomes equals one.

An experiment is a situation involving chance or probability that leads to results called outcomes.

An outcome is the result of a single trial of an experiment.

An event is one or more outcomes of an experiment.

Probability is the measure of how likely an event is.

The study of probability helps us figure out the likelihood of something happening. For instance, when you roll a pair of dice, you might ask how likely you are to roll a seven. In math, we call the "something happening" an "event.

Definitions :

The sample space is a set consisting of all the possible outcomes of an event (like drawing a marble from a jar, or picking a card from a deck). The number of different ways you can choose something from the sample space is the total number of possible outcomes.

Because each probability is a fraction of the sample space, the sum of the probabilities of all the possible outcomes equals one.

An experiment is a situation involving chance or probability that leads to results called outcomes.

An outcome is the result of a single trial of an experiment.

An event is one or more outcomes of an experiment.

Probability is the measure of how likely an event is.

## Saturday, May 23, 2009

### Direct, Inverse and Joint Variation

Had to cover this topic during the exam week coz it will also be included in the midyear exam. Thankfully there was a break in the Form 5 exam schedule. Discuss the problems from PATS 5 with my girls. This is another topic that is very easy and can be covered in 1 or 2 periods only. The girls were able to solve the problems given. Its a happy moment for me to see the happy faces of my students when they're are able solve a problem. As I mention earlier, the 5 KA girls are my 'special' girls. I've seen a lot of changes in them. You see I've been teaching them since Form 4. This year they are more eager and serious to learn except one or two students. I really have to work more closely with this 'one' particular girl. It's quite difficult to give full attention to her coz I have one whole class depending on me (as oppose to my 4 SA class as majority of them are able to do maths with just a little bit of help). The extra class I have with a few of the 5KA students seem to be helping them cope with math. Maybe I have to schedule personal tuition for this girl after school. I'm always willing to help out coz I'm usually available after school (except when I have to go for courses or meetings).

I'm putting up this video on direct, inverse and joint variations for your revision

Writing Up Direct, Inverse and Joint Variation Formula

Direct and Inverse Variation Video

Joint Variation Video

I'm putting up this video on direct, inverse and joint variations for your revision

Writing Up Direct, Inverse and Joint Variation Formula

Direct and Inverse Variation Video

Joint Variation Video

## Tuesday, May 19, 2009

### Exams

It's been quite sometimes since my last entry. You see my girls are having their mid year exams now so there is no teaching going on. I really hope they will do well in their exams. The Form 4 have finished their Math paper but Form 5 still have Maths 1 on Thursday. My 5 KA girls didn't do so well in paper 2. I hope they can do better in Paper 1. Well at least the girls and I know the topic that they are weak in. Hopefully we can brushed up on these topics before the real SPM exam in November. I have high hopes on them coz I know they can do a lot better if they put more effort into it. The're so much that a teacher can do, the rest is up to the individual students. Success comes only to those who work hard, that's the law of nature.

## Saturday, May 9, 2009

### Interactive White Board (IWB)

I've just learned how to use the IWB last Tuesday (very interesting and useful for teaching math). Tested the IWB with my 4 SA girls on Friday. I can be more relax for this class coz I've finished the syllabus for the mid year exam. Thank you Poh Liang for calibrating the board for me. Got Mesia, Sukania and Yuet Ting to use the IWB for solving some problems on sets. It took some time to get used to writing on the board. The good thing is we don't have to rub the board, we just have to flip to a new page and all the workings that were done can be saved directly to my laptop. Furthermore whatever we wrote on the board can be captured and turned into a movie (i'll post the movie we captured on that day here)

The questions I use was from the modules on sets (questions 4, 6 and 7) available on the extra worksheet link. Answers are also provided there.

The questions I use was from the modules on sets (questions 4, 6 and 7) available on the extra worksheet link. Answers are also provided there.

### Extra Lessons

Had an extra session with my 5 KA girls on Thursday at Hazira's place. Surprised to see Hidayah (my ex-5SE 2008 student) there. It turned out that hidayah is hazira's elder sister. Glad to know that she'll be joining KDU to take a hotel management course there. Wish her the all the best in her studies. Five students were there at the session namely fatin, nina, siti, farhain and hazira. Glad to see that they're very serious for this upcoming mid year exam. We manage to cover 4 topics - sets, graph function, number bases and matrices and yes, they were able to solve all the problems given correctly. See...,math is not so bad after all. Used the PATS worksheets prepared by Pn Noraizah (thank you for that). I'll post the worksheets and answers asap. Manage to work closely with Farhain this time. I think she needs the extra coaching coz she's been missing quite a number of classes due to her Police Cadet activities. Hopefuly we'll get to continue our sessions again. I know the students can do much better if they put in more efforts in their studies. The best present for any teacher is to see that that their students are successful.

## Wednesday, May 6, 2009

### Revision Again

Did more revision for my Form 4SA girls. Some students still need to do more exercises (Students can download more questions from the extra worksheet site link). Some are tired of doing the same things over and over again. I gave time for them to do their stuff during half of the math lesson (feel a bit guilty coz I'm suppose to use the time fully). Got to think of what to do for Friday class.

Thank you to the teacher from SMS Muzaffar Shah for all the modules. That's the beauty of internet. You are able to share and use the vast resources that are available on the net.

Thank you to the teacher from SMS Muzaffar Shah for all the modules. That's the beauty of internet. You are able to share and use the vast resources that are available on the net.

### Solving Simultaneous Equations using Matrices

Did this topic in my 5KA class today. Had to rush thru a little bit coz this topic will be included in the mid year exam which will start next Monday.Very happy to see most of them are able to solve the problems given. I was told by my students that Datin Lee taught them this topic when I was away. Thank you Datin for making my job easier. Gave them some homework from the textbook. Hope they will complete it by the next class coz I really need to rush to cover the topic for the midyear exam. I consider the 5KA girls my special girls and I really hope they can do well in their exam. These are the things that were done in class today

Simultaneous equations can also be solved using matrices

Example:

Using matrices, calculate the values of x and y for the following simultaneous equations:

2x – 2y – 3 = 0

8 y = 7x + 2

Solution:

Step 1: Write the equations in the form ax + by = c

2x – 2y – 3 = 0 ⇒ 2x – 2y = 3

8y = 7x + 2 ⇒ 7x – 8y = –2

Step 2: Write the equations in matrix form.

Step 3: Find the inverse of the 2 × 2 matrix.

Determinant = (2 × –8) – (–2 × 7) = – 2

Step 4: Multiply both sides of the matrix equations with the inverse

So, x = 14 and y = 12.5

You can download extra questions on matrices from the site links

Simultaneous equations can also be solved using matrices

Example:

Using matrices, calculate the values of x and y for the following simultaneous equations:

2x – 2y – 3 = 0

8 y = 7x + 2

Solution:

Step 1: Write the equations in the form ax + by = c

2x – 2y – 3 = 0 ⇒ 2x – 2y = 3

8y = 7x + 2 ⇒ 7x – 8y = –2

Step 2: Write the equations in matrix form.

Step 3: Find the inverse of the 2 × 2 matrix.

Determinant = (2 × –8) – (–2 × 7) = – 2

Step 4: Multiply both sides of the matrix equations with the inverse

So, x = 14 and y = 12.5

You can download extra questions on matrices from the site links

### Sekolah Bestari (Smart School)

Was away for two days last week for Seminar Sedekad Sekolah Bestari(Smart School) in Sekolah Alam Shah Putrajaya. Didn't realised that i've been involved with the Smart School for almost a decade already. Did the Smart School had any effect on me? Definately the answer is yes. I don't think I'll be in this position now if it's not for the Smart School. I was exposed to so many things on ICT that I wouldn't have if I'm not in the Smart School. Did see some interesting presentation from students from selected Smart Schools around the country. The Victoria Institution (VI) Band was fantastic. No wonder they are able to go internationally. The Sekolah Alam Shah Wind Orchestra was also impressive as all the other presentations by the other students like the research done by the Tunku Kurshiah College Girls, robotic and F1 by the Alam Shah boys and the use of I-Kit in teaching & learning by 2 teachers from SMK (P) Temenggong Ibrahim, Johor. I really think that students nowdays are a lucky lot to experience all these while still in school. I didn't had that oppurtinity when I was in school (that was ages ago). So students, make the best of your years in school, there's so many things to look forward to.

Posted here are some photos on the VI Band (courtesy of BTP)

Posted here are some photos on the VI Band (courtesy of BTP)

## Wednesday, April 29, 2009

## Monday, April 27, 2009

### Revision Questions

I did revision on standard form and quadratic expressions and equations for my 4 SA class. Used the PATS 1 and PATS 2 worksheets. Only about 1/2 of the class are able to finish the worksheets within the 1 hour period. Students need to time themselves in answering the questions coz they only have 2 1/2 hours to answer the exam paper. I'm quite comfident students in this class will do well in the mid year exam. I'm putting up the PATS 1, PATS 2 question paper and the answers (PATS 1, PATS 2)here.

### Identity and Inverse Matrix

Taught Identity and Inverse Matrix for my 5 KA class today. Glad to see most of them are able to find the inverse of a 2 x 2 matrix. Sadly there are some girls who are not interested at all in learning. It's not easy being a teacher, having to deal with all sorts of students. There are those who are very bright and self motivated. I don't have to worry about them. Then there's those who are slower but willing to learn. I enjoy being able to help them. Then there are those who's not interested at all, that's where my headache is. How to make them interested in learning???? Any ideas?? Sometimes I do wonder what they think about when they're in school. The sad thing is I know that they're capable of better things but they're are not willing to try. Enough of my ramblings, I'm suppose to write on the lesson that I did today :

Identity Matrix (I)

A square matrix in which all the main diagonal elements are 1’s and all the remaining elements are 0’s is called an Identity Matrix.

# Identity Matrix is denoted with the letter “In×n”, where n×n represents the order of the matrix.

# One of the important properties of identity matrix is: A×In×n = A, where A is any square matrix of order n×n.

Example

2 x 2 Identity Matrix

3 x 3 Identity matrix

n x n Identity matrix

Inverse Matrix

For a square matrix A, the inverse is written A-1. When A is multiplied by A-1 the result is the identity matrix, I.

AA-1 = A-1A = I

Example: For matrix A = ,

its inverse is

since AA-1 =

and A-1A =

Please do all the assignment given so that we can discuss the answers next week.

Identity Matrix (I)

A square matrix in which all the main diagonal elements are 1’s and all the remaining elements are 0’s is called an Identity Matrix.

# Identity Matrix is denoted with the letter “In×n”, where n×n represents the order of the matrix.

# One of the important properties of identity matrix is: A×In×n = A, where A is any square matrix of order n×n.

Example

2 x 2 Identity Matrix

3 x 3 Identity matrix

n x n Identity matrix

Inverse Matrix

For a square matrix A, the inverse is written A-1. When A is multiplied by A-1 the result is the identity matrix, I.

AA-1 = A-1A = I

Example: For matrix A = ,

its inverse is

since AA-1 =

and A-1A =

Please do all the assignment given so that we can discuss the answers next week.

## Friday, April 24, 2009

### Chocolate Solves Anything

Need to pass that math test? Better stock up on chocolate. According to a recent study-

Mental arithmetic became easier after volunteers had been given large amounts of compounds found in chocolate, called flavanols, in a hot cocoa drink.

They were also less likely to feel tired or mentally drained, the findings, presented at the British Psychological Society annual conference in Brighton show.....Read more

## Thursday, April 23, 2009

### Revision

Exam is right around the corner. It's time to do revision on the topics that my students have learned so far. Topics that will be included in the exams are

1. Standard Form

2. Quadratic Expressions and Equation

3. Sets

4. The Straight Line

and some Form 3 topics. I will have to check with Mrs Chan on what those topics will be.

There's some good sites students can check on :

Quadratic Equation.

Below is some excerpt from one of the site

Example

Calculate the solutions of the quadratic equation below by factoring

quadratic equation: y = x² + 4x + 4

Solutions

You can read more at the Math Warehouse site

The Straight Line.

These links provide useful information about straight lines.

Interactive Mathematics

Maths Library

Thinkquest

1. Standard Form

2. Quadratic Expressions and Equation

3. Sets

4. The Straight Line

and some Form 3 topics. I will have to check with Mrs Chan on what those topics will be.

There's some good sites students can check on :

Quadratic Equation.

Below is some excerpt from one of the site

Example

Calculate the solutions of the quadratic equation below by factoring

quadratic equation: y = x² + 4x + 4

Solutions

You can read more at the Math Warehouse site

The Straight Line.

These links provide useful information about straight lines.

Interactive Mathematics

Maths Library

Thinkquest

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