Algebra ?

Assalamualaikum wbt my form 2 students.

Teacher : Students, what was the most difficult maths topic in form one?
Student 1 : Algebra,teacher!
Student 2 : Surely algebra!

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Oh my student!

Algebra isnt that bad my dear.hehe. Let see how awesome algebra can be. Let's do an activity!
Take any calendar. Tell your friend to choose 4 days that form a square like the four i highlighted in BLUE . Your friend should tell you only the sum of the four days, and you can tell her what the four days are.

How does the puzzle work? You know how people always want to see a use for algebra? Well this puzzle uses algebra. Here's what I mean.

Let's pretend that the 4 numbers that the person chose were the highlighted ones here - 18, 19, 25, and 26. She adds up the four numbers and tells you only that the sum is 88.

You make a couple of calculations and tell her the numbers. What calculations? Lets figure that out with algebra. Let's call the first number n. Then you know that the next number would be n + 1 and the next number would be n + 7 and the next number would be n + 8. We had our friend add up the four numbers, so let's add our four numbers:

n + n + 1 + n + 7 + n + 8

And since our friend got 88 when she added them, let's make our sum equal 88:

n + n + 1 + n + 7 + n + 8 = 88

Simplify our equation by adding like terms:

4n + 16 = 88

How would you solve this equation? Subtract 16 from both sides?

4n = 72

Divide both sides by 4?

n = 18

Subtract 16 and divide by 4. That's exactly how you solve the puzzle. When your friend tells you the sum, you subtract 16 then divide by 4. This gives you the first number n. (Then add 1 and 7 and 8 for the other numbers).

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Alternate and easier method: Subtracting 16 mentally isn't so easy. Go back to that equation:

4n + 16 = 88

I think I see a better way. Factor 4 from the left side of the equation:

4(n + 4) = 88

Now, I could divide both sides by 4:

(n + 4) = 22

Subtract 4 from both sides.

n = 18

That's a lot easier to do mentally. Divide by four and then subtract 4.

Okay? You might find it a little bit difficult..but trust me,it's only at the beginning.You might be suprised what algebra can do in your daily life.

Do your best!

Gradient and Area Under Graph

Assalamualaikum wbt dear Form 5 students,

Next week will be your standardize 1 exam! make sure you be prepared before you enter the hall.
I would like to share some notes and exercise on Gradient and Area Under Graph that may help you in your standardize.

Notes!

Math(F5) Gradient And Area Under A Graph

Gradient & area under a graph

Exercises!

Gradient and Area under Graph

Happy study~!

Assalamualaikum wbt my dear form 5 students,

As you were being told by me before your school holiday, your homework for this holiday is to make a mind map on topic Angle of Elevation and Depression.

Here are some notes on the topics that might help your for reference. :)

Angle of Elevation and Depression

In the diagram below, AB is the horizontal line. q is the angle of elevation from the observer at A to the object at C .

The angle of depression is the angle between a horizontal line from the observer and the line of sight to an object that is below the horizontal line.

In the diagram below, PQ is the horizontal line. q is the angle of depression from the observer at P to the object at R .

Example:

In the diagram below, AB and CD are two vertical poles on horizontal ground. Draw in the angle of elevation of D from B and the angle of depression of C from B

Solution:

Example:

Two poles on horizontal ground are 60 m apart. The shorter pole is 3 m high. The angle of depression of the top of the shorter pole from the top of the longer pole is 20˚. Sketch a diagram to represent the situation.

Solution:

Step 1 : Draw two vertical lines to represent the shorter pole and the longer pole.

Step 2 : Draw a line from the top of the longer pole to the top of the shorter pole. (This is the line of sight).

Step 3 : Draw a horizontal line to the top of the pole and mark in the angle of depression.

Example:

A man who is 2 m tall stands on horizontal ground 30 m from a tree. The angle of elevation of the top of the tree from his eyes is 28˚. Estimate the height of the tree.

Solution :

Let the height of the tree be h. Sketch a diagram to represent the situation.

tan 28˚ =

h – 2 = 30 tan 28˚

h = (30 ´ 0.5317) + 2 ← tan 28˚ = 0.5317

= 17.951

The height of the tree is approximately 17.95 m