Invitation for Math-lovers in Libels

Join with us !

If you are students of Libels on grade X and XI ( Science or Social subject ) and has more interest in mathematics field for research, join with us.

Make your group ( 3 students for each ) and create your research's proposal, submit to us before the end of november 2010. The proposal based on the general form of the rules in writing proposal. We suggest to choose 3 students with criterias such as : very powerful in math, fluent in english, has a good experience in studying literature.

If your proposal is choosen, then you can start to make a simple research and obtain the solutions for 3 month. You must present all of your work at the forum of mathematics in Libels, in front of the teachers.

Rewards :
1. In the end of the year lesson, we will show all of your work to all members of
Libels family.
2. Your team will be promoted to join with the events of KIR
3. Certificate from SMAN 15 Surabaya

So, what are you waiting for ?? Join with us NOW !!!

CP : Mr. Endrayana
0816 556844
email : endrayanaputut29@gmail.com

Tugas Kelas XI-IA 5,XI-IA 6, XI-IA 7

Submit your work at friday, November, 5th

1. Prove the following identities :
a. ( sin x - sin 2x + sin 3x ) / ( cos x - cos 2x + cos 3x ) = tan 2x
b. cos 3p + sin 3p = ( 1 + 2 sin 2p )( cos p - sin p )
c. 2 tan 2c = ( tan 2c - sin 2c )( cosec^2 c)
d. sin p. cos 2p. sin 3p = 0.25 ( 1 - cos 2p + cos 4p - cos 6p)
e. sin k + sin 2k + sin 3k = 2 sin k cos k ( 2 cos k + 1 )
f. In a triangle PQR, sin 2P + sin 2Q + sin 2R = 4 sinP sinQ sin R
g. In a triangle ABC, sinB sinC sin(B-C) + sinC sinA sin(C-A)
+ sinA sinB sin(A-B) = - sin(B-C) sin(C-A) sin(A-B)

2. Solve the following equations for the angles between 0 to 2 phi radians.
a. cos 5x - cos x = sin 3x
b. sin 2x - sin 4x + sin 6x = 0
c. cos 3x - sin 3x = 2 sinx + cos x

3. Given that sin x = m + n and cos x = m - n.
a. show that m^2 - n^2 = 0.5 sin 2x
b. express m/n in terms of tan x. Hence find the value of tan x if m = 3n.

Do your best, wishes that you can get more advantages from this task.

TUGAS MASA PKL ke-1

TUGAS MATEMATIKA Minggu ke-1
SEKESAL SURABAYA
Kelas XII A,B,C
Instruktur : Endrayana Putut

Kerjakan di kertas folio dan dikumpulkan tanggal 6 November 2010
1. Tentukan turunan dari fungsi berikut :
a. f(x) = x^2 . sin 4x
b. f(x) = ( 2x + 3 ): ( x - 3 )
2. Suatu perusahaan memproduksi obat dengan merk A, memiliki fungsi biaya, yaitu :
B(x) = 4x^2 - 8x + 9 dalam ribuan rupiah. Jika ingin diminimumkan biayanya, maka
berapa banyak obat ( x ) yang harus diproduksi? Tentukan biaya minimum tersebut.
3. Suatu kurva memiliki persamaan y = x^2 - 3x - 4. Tentukan persamaan garis
singgung di titik (1,-6).
4. Tentukan interval dimana fungsi y = x^3 - 3x^2 - 9x + 5 adalah fungsi naik.

Probability

1st Examination
Grade : XI ( SMA 1 Blitar )
Material : Probability

1. There are 4 different English books, 5 different Mathematics books and
3 different Science books on a bookshelf. Find the number of ways in which
a pair of books of different types can be chosen.
2. If 3 British, 3 Indians, 4 Chinese are to be seated in a straight row with 12
seats. how many seating arrangements are possible? If people of the same race
must sit together.
3. In each turn of a game, a player throws a fair die repeatedly until the number
5 is obtained or after he throws it 6 times.
a. Find the probability that the player has exactly 6 throws.
b. Find the probability that the player has more than 3 throws
c. Find the conditional probability that the player has exactly 4 throws in
a turn, given that he has more than 3 throws.

Date of submission : 23 Oct, 2010

coba rumus
x2

1st Examination : Quadratics

1st Examination of Mathematics
Material : Quadratics
Grade : X
School : SMA 1 Blitar

Answer on your paper correctly!

1. Find the range of values of x for which :
(x+2)^2 - 8(x+2) + 15 > 0
2. Given that p and q,are the roots of 2x^2 + 5x - 4 = 0.
Calculate the value of : p^3 + q^3
Hence, construct the new quadratic equation which roots are p/q and q/p.
3. Find the range values of k for which k(x^2 + 2x + 3) - 4x - 2 is always positive
for all real values of x.
4. The curve y = (k - 6)x^2 - 8x + k does not intersect the x-axis and it has
a minimum point. Find the range values of k.

Note : Date of submission : Oct, 22
Do by yourself on a folio size.