Smart solution for 4

English asMedium ofInstruction

Ridho Alfarisi(110210101043)

dan AgustinPuspitasari

(110210101061)

Smart Solution

English as Medium of Instruction

Ridho Alfarisi dan Agustin Puspitasari

Pendidikan MatematikaPendidikan MIPA

Fakultas Keguruan dan Ilmu PendidikanUniversitas Jember

22nd May 2013

Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP

(110210101061)

Smart Solution

1 Number Theory

2 Answer of Number Theory

3 Algebra

4 Answer of Algebra

5 Geometry

6 Answer of Geometry

7 Probability

8 Answer of Probability

(110210101061)

Smart Solution

1 Number Theory

3 Algebra

4 Answer of Algebra

5 Geometry

7 Probability

(110210101061)

Smart Solution

1 Number Theory

3 Algebra

4 Answer of Algebra

5 Geometry

7 Probability

(110210101061)

Smart Solution

1 Number Theory

3 Algebra

4 Answer of Algebra

5 Geometry

7 Probability

(110210101061)

Smart Solution

1 Number Theory

3 Algebra

4 Answer of Algebra

5 Geometry

7 Probability

(110210101061)

Smart Solution

1 Number Theory

3 Algebra

4 Answer of Algebra

5 Geometry

7 Probability

(110210101061)

Smart Solution

1 Number Theory

3 Algebra

4 Answer of Algebra

5 Geometry

7 Probability

(110210101061)

Smart Solution

1 Number Theory

3 Algebra

4 Answer of Algebra

5 Geometry

7 Probability

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

Number Theory Number Theory Algebra Algebra Geometry Algebra Probability Algebra

Number Theory

Exercise1 How many digit of multiplication 22002*52003 ?

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

Number Theory

Exercise1 How many digit of multiplication 22002*52003 ?

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

Answer of Number Theory

Answer1 22002 ∗ 52003 = 22002 ∗ 52002 ∗ 5 = (2 ∗ 5)2002 ∗ 5 =

(10)2002 ∗ 5 so all digits is 2003

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

Answer of Number Theory

Answer1 22002 ∗ 52003 = 22002 ∗ 52002 ∗ 5 = (2 ∗ 5)2002 ∗ 5 =

(10)2002 ∗ 5 so all digits is 2003

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

Exercise1 Lets a and b is natural number with a > b. if√

(94 + 2 ∗√

(2013)) =√

(a) +√

(b), then value ofa− b is.....

2 Let’s p and q is prims number. if its known equationx2014 − p ∗ x2013 + q = 0 haveing root integersnumber, then value of p + q is...

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

(94 + 2 ∗√

(2013)) =√

(a) +√

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

(94 + 2 ∗√

(2013)) =√

(a) +√

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

Answer of Algebra

Answer

1 for a, b ≥ 0, then (√

a +√

b)2=a ∗ b + 2 ∗√

a ∗ b←→√

a +√

(a + b) + 2 ∗√

a ∗ b.We back

that√

94 + 2 ∗√

2013=(61 + 33) + 2 ∗√

61 ∗ 33,therefore

√94 + 2 ∗

√2013=

√61 +

√33 so we get

the value a = 61, b = 33, then a− b=61− 33=28

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

Answer of Algebra

Answer

1 for a, b ≥ 0, then (√

a +√

b)2=a ∗ b + 2 ∗√

a ∗ b←→√

a +√

(a + b) + 2 ∗√

a ∗ b.We back

that√

94 + 2 ∗√

2013=(61 + 33) + 2 ∗√

61 ∗ 33,therefore

√94 + 2 ∗

√2013=

√61 +

√33 so we get

the value a = 61, b = 33, then a− b=61− 33=28

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

Answer of Algebra

Answer1 Let’s one of root integers of equation

x2014 − p ∗ x2013 + q = 0 is t, then we gett2014 − p ∗ t2013 + q = 0⇐⇒ q = t2013(p − t).Following that −1 and 0 isn’t root of equationx2014 − p ∗ x2013 + q = 0. So with remember that q isprims number, then we get t = 1 therefore q = p − 1⇐⇒ p − q = 1. This information of above canconcluded that one of p,q is even and because evenprims number only 2, then we get q = 2 and p = 3.So p + q = 5

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

Answer of Algebra

Answer1 Let’s one of root integers of equation

x2014 − p ∗ x2013 + q = 0 is t, then we gett2014 − p ∗ t2013 + q = 0⇐⇒ q = t2013(p − t).Following that −1 and 0 isn’t root of equationx2014 − p ∗ x2013 + q = 0. So with remember that q isprims number, then we get t = 1 therefore q = p − 1⇐⇒ p − q = 1. This information of above canconcluded that one of p,q is even and because evenprims number only 2, then we get q = 2 and p = 3.So p + q = 5

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

Geometry

Exercise1 Lets P is interior point in the triangle ABC, so value

of < PAB = 10◦,< PBA = 20◦,< PCA = 30◦,< PAC = 40◦, value of< ABC = .......

2 Given a triangle ABC with this area 10. Point D,E,dan F respectively lies on the edge AB, BC, dan CAwith AD =2, DB=3. If a triangle ABE and a rectangleDBFE has same the area, then it’s the area is........

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

Geometry

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

Geometry

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

Answer of Geometry

Answer1 Following a sketch at below: Because the area

∆ABE=�DBFE cause the area ∆ADE=∆DEF. Weknow that DE is partnership edge among ∆ADE and∆DEF, so distance point A to the edge DE equal todistance point F to the edge DE. in other words AFparallel DE so CE

EB = ADDB = 2

3 . Therefore, the area ∆

ABE = 35 ∗ 10 = 6.

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

Answer of Geometry

Answer1 Following a sketch at below: Because the area

∆ABE=�DBFE cause the area ∆ADE=∆DEF. Weknow that DE is partnership edge among ∆ADE and∆DEF, so distance point A to the edge DE equal todistance point F to the edge DE. in other words AFparallel DE so CE

EB = ADDB = 2

3 . Therefore, the area ∆

ABE = 35 ∗ 10 = 6.

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

Probability

Exercise1 A dice at toss six times. How many trick for get total

dies 28 correctly one dice arises digit 6 is........

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

Probability

Exercise1 A dice at toss six times. How many trick for get total

dies 28 correctly one dice arises digit 6 is........

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

Answer of Probability

Answer1 Tanpa mengurangi keumuman misalkan tos pertama

muncul angka 6. maka pada tos ke dua sampai toske enam hanya boleh muncul angka 1, 2, 3, 4, 5 danjumlanya 22. kemungkinan hal seperti ini hanya ada3 kasus yaitu : yang pertama (2, 5, 5, 5, 5) ada 5 caradari 5!

4! , yang kedua (3, 4, 5, 5, 5) ada 20 cara dari 5!3! ,

yang ketiga (4, 4, 4, 5, 5) ada 10 cara dari 5!2!∗3! .

sehingga total ada 35 cara jika pada tos pertamamuncul angka 6. Karena keenam tos memilikipeluang yang sama untuk muncul angka 6 berartitotal keseluruhan cara yang mungkin yaitu6 ∗ 35 = 210 cara

(110210101061)

Number Theory

Algebra

Geometry

Algebra

Probability

Algebra

Answer of Probability

Answer1 Tanpa mengurangi keumuman misalkan tos pertama

muncul angka 6. maka pada tos ke dua sampai toske enam hanya boleh muncul angka 1, 2, 3, 4, 5 danjumlanya 22. kemungkinan hal seperti ini hanya ada3 kasus yaitu : yang pertama (2, 5, 5, 5, 5) ada 5 caradari 5!

4! , yang kedua (3, 4, 5, 5, 5) ada 20 cara dari 5!3! ,

yang ketiga (4, 4, 4, 5, 5) ada 10 cara dari 5!2!∗3! .

sehingga total ada 35 cara jika pada tos pertamamuncul angka 6. Karena keenam tos memilikipeluang yang sama untuk muncul angka 6 berartitotal keseluruhan cara yang mungkin yaitu6 ∗ 35 = 210 cara

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