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English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Smart Solution
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
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Smart Solution
Smart Solution
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
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Smart Solution
Smart Solution
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
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Smart Solution
Smart Solution
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
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Smart Solution
Smart Solution
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
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Smart Solution
Smart Solution
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
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Smart Solution
Smart Solution
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
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Smart Solution
Smart Solution
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
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Smart Solution
Smart Solution
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
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
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 ?
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
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 ?
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
Algebra
Geometry
Algebra
Probability
Algebra
Number Theory Number Theory Algebra 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
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
Algebra
Geometry
Algebra
Probability
Algebra
Number Theory Number Theory Algebra 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
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
Algebra
Geometry
Algebra
Probability
Algebra
Number Theory Number Theory Algebra Algebra Geometry Algebra Probability Algebra
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...
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
Algebra
Geometry
Algebra
Probability
Algebra
Number Theory Number Theory Algebra Algebra Geometry Algebra Probability Algebra
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...
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
Algebra
Geometry
Algebra
Probability
Algebra
Number Theory Number Theory Algebra Algebra Geometry Algebra Probability Algebra
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...
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
Algebra
Geometry
Algebra
Probability
Algebra
Number Theory Number Theory Algebra Algebra Geometry Algebra Probability Algebra
Answer of Algebra
Answer
1 for a, b ≥ 0, then (√
a +√
b)2=a ∗ b + 2 ∗√
a ∗ b←→√
a +√
b=√
(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
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
Algebra
Geometry
Algebra
Probability
Algebra
Number Theory Number Theory Algebra Algebra Geometry Algebra Probability Algebra
Answer of Algebra
Answer
1 for a, b ≥ 0, then (√
a +√
b)2=a ∗ b + 2 ∗√
a ∗ b←→√
a +√
b=√
(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
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
Algebra
Geometry
Algebra
Probability
Algebra
Number Theory Number Theory Algebra 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
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
Algebra
Geometry
Algebra
Probability
Algebra
Number Theory Number Theory Algebra 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
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
Algebra
Geometry
Algebra
Probability
Algebra
Number Theory Number Theory Algebra 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........
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
Algebra
Geometry
Algebra
Probability
Algebra
Number Theory Number Theory Algebra 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........
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
Algebra
Geometry
Algebra
Probability
Algebra
Number Theory Number Theory Algebra 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........
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
Algebra
Geometry
Algebra
Probability
Algebra
Number Theory Number Theory Algebra 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.
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
Algebra
Geometry
Algebra
Probability
Algebra
Number Theory Number Theory Algebra 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.
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
Algebra
Geometry
Algebra
Probability
Algebra
Number Theory Number Theory Algebra 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........
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
Algebra
Geometry
Algebra
Probability
Algebra
Number Theory Number Theory Algebra 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........
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
Algebra
Geometry
Algebra
Probability
Algebra
Number Theory Number Theory Algebra 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
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction
English asMedium ofInstruction
Ridho Alfarisi(110210101043)
dan AgustinPuspitasari
(110210101061)
Number Theory
Number Theory
Algebra
Algebra
Geometry
Algebra
Probability
Algebra
Number Theory Number Theory Algebra 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
Ridho Alfarisi (110210101043) dan Agustin Puspitasari (110210101061) FKIP
English as Medium of Instruction