Showing posts with label Mathematics. Show all posts

Saturday, October 31, 2009

Friday, October 30, 2009

Additional Mathematics Trial Paper SPM 2009

Negeri Sembilan ( P1+P2+ Marking Scheme)

Negeri Kelantan ( P1 + P2+ Marking Scheme )

Negeri Sarawak Zon A (P1+P2+Marking scheme)

Negeri Terangganu ( P1+P2+Marking Scheme)

Negeri Pahang (P1+P2 + Marking Scheme)

Negeri Kedah ( P1+P2+Marking Scheme)

Negeri Selangor ( P1+P2+Marking Scheme)

Negeri Johor ( P1+ P2 + Marking Scheme)

Negeri Melaka ( P1+P2 + Marking Scheme)

Negeri Sabah ( P1 + P2+Marking Scheme)

Source:www.mathsmozac.blogspot.

Thursday, October 29, 2009

Differentiation of the Function y=ax, Differentiation of the Sum and Difference of Algebraic Functions

In general,

If $\, y = ax^n$ then $\frac{{dy}}{{dx}} = ax^{n - 1} or \frac{{\rm d}}{{{\rm dx}}}(ax^n ) = anx^{n - 1}$ where a is a constant and n is an integer and rational number.

In particular,

If $n = 1, y = a x$ , then $\frac{{dy}}{{dx}} = a$

If $n = 0, y = a$ , then $\frac{{dy}}{{dx}} = 0$

Example

Find the $\frac{{dy}}{{dx}}$ when $y=4\sqrt x + 3x^4 - \frac{{5}}{{x^3}}$

Solution

$y=4\sqrt x + 3x^4 - \frac{{5}}{{x^3}}$

$=4x^\frac{{1}}{{2}} + 3x^4 - 5x^{-3}$

$\frac{{dy}}{{dx}}= \frac {{1}}{{2}}(4x^{-\frac{{1}}{{2}}})+4(3x^3)-(-3)(5x^{-4})$

$= \frac {{2}}{{\sqrt x}} + 12x^3 + \frac {{15}}{{x^4}}$

Saturday, September 12, 2009

Soalan Gempur Sejarah SPM 2009 - JPN Kelantan

Sila download Koleksi Soalan Gempur Sejarah SPM 2009 yang dikeluarkan oleh Unit Kurikulum, Jabatan Pelajaran Kelantan:

Kertas 1 – Set 1 serta Jawapannya
Kertas 1 – Set 2 serta Jawapannya
Kertas 1 – Set 3 serta Jawapannya
Kertas 1 – Set 4 serta Jawapannya
Kertas 1 – Set 5 serta Jawapannya

Kertas 2 – Set 1 serta Skema Jawapannya
Kertas 2 – Set 2 serta Skema Jawapannya
Kertas 2 – Set 3 serta Skema Jawapannya
Kertas 2 – Set 4 serta Skema Jawapannya
Kertas 2 – Set 5 serta Skema Jawapannya

Selamat menjawab!

source: http://panitiasejarahsmkkamil.blogspot.com

Kertas Soalan Percubaan Matematik PMR l SPM 2009

Saturday, June 27, 2009

Algebra - Fun with Calendars

May 08

S	M	T	W	TH	F	S
				1	2	3
4	5	6	7	8	9	10
11	12	13	14	15	16	17
18	19	20	21	22	23	24
25	26	27	28	29	30	31

A fun mathematical puzzle to play with your friends.
(Or teachers, with your class.)

18	19
25	26

Take any calendar. Tell your friend to choose 4 days that form a square like the four to the right. 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).

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.

Summary: So how does the puzzle work again? Your friend adds any 4 numbers that form a square on the calendar and tells you the sum. You divide by four and then subtract 4. That gives you the first number. You add 1, 7, and 8 to get the other numbers.

And algebra makes it all possible.

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Thursday, June 18, 2009

Success Mathematics SPM (Oxfort fajar)

Mathematics

	Success Mathematics PMR (Passport to Success Form 1)

	Success Mathematics PMR (Passport to Success Form 2)

	Success Mathematics PMR (Passport to Success Form 3)

	Success Mathematics SPM (Passport to Success Form 1 - 3)

	Success Mathematics SPM (Passport to Success Form 4 - Chapter 1)

	Success Mathematics SPM (Passport to Success Form 4 - Chapter 2)

	Success Mathematics SPM (Passport to Success Form 4 - Chapter 3)

	Success Mathematics SPM (Passport to Success Form 4 - Chapter 4)

	Success Mathematics SPM (Passport to Success Form 4 - Chapter 5)

	Success Mathematics SPM (Passport to Success Form 4 - Chapter 6)

	Success Mathematics SPM (Passport to Success Form 4 - Chapter 8)

	Success Mathematics SPM (Passport to Success Form 4 - Chapter 9)

	Success Mathematics SPM (Passport to Success Form 4 - Chapter 10)

	Success Mathematics SPM (Passport to Success Form 4 - Chapter 11)

	Success Mathematics SPM (Passport to Success Form 5 - Chapter 1)

	Success Mathematics SPM (Passport to Success Form 5 - Chapter 2)

	Success Mathematics SPM (Passport to Success Form 5 - Chapter 3)

	Success Mathematics SPM (Passport to Success Form 5 - Chapter 5)

	Success Mathematics SPM (Passport to Success Form 5 - Chapter 6)

	Success Mathematics SPM (Passport to Success Form 5 - Chapter 7)

	Success Mathematics SPM (Passport to Success Form 5 - Chapter 8)

	Success Mathematics SPM (Passport to Success Form 5 - Chapter 10)

	Success Mathematics SPM (Zoom In Form 4 - Chapter 1)

	Success Mathematics SPM (Zoom In Form 4 - Chapter 2)

	Success Mathematics SPM (Zoom In Form 4 - Chapter 3)

	Success Mathematics SPM (Zoom In Form 4 - Chapter 4)

	Success Mathematics SPM (Zoom In Form 4 - Chapter 5)

	Success Mathematics SPM (Zoom In Form 4 - Chapter 6)

	Success Mathematics SPM (Zoom In Form 4 - Chapter 7)

	Success Mathematics SPM (Zoom In Form 4 - Chapter 8)

	Success Mathematics SPM (Zoom In Form 4 - Chapter 9)

	Success Mathematics SPM (Zoom In Form 4 - Chapter 10)

	Success Mathematics SPM (Zoom In Form 4 - Chapter 11)

	Success Mathematics SPM (Zoom In Form 5 - Chapter 1)

	Success Mathematics SPM (Zoom In Form 5 - Chapter 2)

	Success Mathematics SPM (Zoom In Form 5 - Chapter 3)

	Success Mathematics SPM (Zoom In Form 5 - Chapter 4)

	Success Mathematics SPM (Zoom In Form 5 - Chapter 5)

	Success Mathematics SPM (Zoom In Form 5 - Chapter 6)

	Success Mathematics SPM (Zoom In Form 5 - Chapter 7)

	Success Mathematics SPM (Zoom In Form 5 - Chapter 8)

	Success Mathematics SPM (Zoom In Form 5 - Chapter 9)

	Success Mathematics SPM (Zoom In Form 5 - Chapter 10)

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