Embed Size (px)
Citation preview
Outline
English as Medium of Instruction
Rizky Titie Riddiyani dan Marlia Sari Pangestuti
Fakultas Keguruan dan Ilmu PendidikanUniversitas Jember
24th May 2013
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Outline
Outline
1 Number Theory
2 Algebra
3 Geometry
4 Probability
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Outline
Outline
1 Number Theory
2 Algebra
3 Geometry
4 Probability
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Outline
Outline
1 Number Theory
2 Algebra
3 Geometry
4 Probability
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Outline
Outline
1 Number Theory
2 Algebra
3 Geometry
4 Probability
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Number Theory
Exercise
1 Set last of numbers 777333
2 Show that 55552222 + 22225555 divisible by 7
3 Set the remainder of 31990 if divided 41
4 Specify the number of units 19971991
5 What ’ s the rest of the division of 434343by 10
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Number Theory
Exercise
1 Set last of numbers 777333
2 Show that 55552222 + 22225555 divisible by 7
3 Set the remainder of 31990 if divided 41
4 Specify the number of units 19971991
5 What ’ s the rest of the division of 434343by 10
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Number Theory
Exercise
1 Set last of numbers 777333
2 Show that 55552222 + 22225555 divisible by 7
3 Set the remainder of 31990 if divided 41
4 Specify the number of units 19971991
5 What ’ s the rest of the division of 434343by 10
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Number Theory
Exercise
1 Set last of numbers 777333
2 Show that 55552222 + 22225555 divisible by 7
3 Set the remainder of 31990 if divided 41
4 Specify the number of units 19971991
5 What ’ s the rest of the division of 434343by 10
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Number Theory
Exercise
1 Set last of numbers 777333
2 Show that 55552222 + 22225555 divisible by 7
3 Set the remainder of 31990 if divided 41
4 Specify the number of units 19971991
5 What ’ s the rest of the division of 434343by 10
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Number Theory
Exercise
1 Set last of numbers 777333
2 Show that 55552222 + 22225555 divisible by 7
3 Set the remainder of 31990 if divided 41
4 Specify the number of units 19971991
5 What ’ s the rest of the division of 434343by 10
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Algebra
Exercise
1 Specify the number of roots of the integers from theequation 4x4 − 15x2 + 5x + 6 = 0
2 Known roots of the equation x3 − 2x2 − 3x + 1 = 0 arex1,x2 and x3. Specify the value 1
x1+ 1
x2+ 1
x3
3 Known roots of the equation x3 − 3x2 + 4x + 5 = 0 arex1,x2 and x3. Specify the value x3
1 + x32 + x3
3
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Algebra
Exercise
1 Specify the number of roots of the integers from theequation 4x4 − 15x2 + 5x + 6 = 0
2 Known roots of the equation x3 − 2x2 − 3x + 1 = 0 arex1,x2 and x3. Specify the value 1
x1+ 1
x2+ 1
x3
3 Known roots of the equation x3 − 3x2 + 4x + 5 = 0 arex1,x2 and x3. Specify the value x3
1 + x32 + x3
3
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Algebra
Exercise
1 Specify the number of roots of the integers from theequation 4x4 − 15x2 + 5x + 6 = 0
2 Known roots of the equation x3 − 2x2 − 3x + 1 = 0 arex1,x2 and x3. Specify the value 1
x1+ 1
x2+ 1
x3
3 Known roots of the equation x3 − 3x2 + 4x + 5 = 0 arex1,x2 and x3. Specify the value x3
1 + x32 + x3
3
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Algebra
Exercise
1 Specify the number of roots of the integers from theequation 4x4 − 15x2 + 5x + 6 = 0
2 Known roots of the equation x3 − 2x2 − 3x + 1 = 0 arex1,x2 and x3. Specify the value 1
x1+ 1
x2+ 1
x3
3 Known roots of the equation x3 − 3x2 + 4x + 5 = 0 arex1,x2 and x3. Specify the value x3
1 + x32 + x3
3
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Algebra
Exercise
1 Known roots of the equation x4 − 8x3 + ax2 − bx + c = 0Forming arithmetic progression with different 2. Specify thevalue a, b, dan c
2 If α dan β roots of the equation x2 − ax + b = 0 (a, b real).Make quadratic equations who roots α3
βdan β3
α
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Algebra
Exercise
1 Known roots of the equation x4 − 8x3 + ax2 − bx + c = 0Forming arithmetic progression with different 2. Specify thevalue a, b, dan c
2 If α dan β roots of the equation x2 − ax + b = 0 (a, b real).Make quadratic equations who roots α3
βdan β3
α
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Algebra
Exercise
1 Known roots of the equation x4 − 8x3 + ax2 − bx + c = 0Forming arithmetic progression with different 2. Specify thevalue a, b, dan c
2 If α dan β roots of the equation x2 − ax + b = 0 (a, b real).Make quadratic equations who roots α3
βdan β3
α
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Geometry
Exercise
1 A triangle has base length 3 cm shorter than the height andbreadth of less than 27cm2. If height of triangle t cm so...
2 From a piece of cardboard that breadth of 10dm2 will bemade a blanket cylinder bottom radius 14 cm and height10cm. With π = 22
7 , the rest of cardboard is broad...
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Geometry
Exercise
1 A triangle has base length 3 cm shorter than the height andbreadth of less than 27cm2. If height of triangle t cm so...
2 From a piece of cardboard that breadth of 10dm2 will bemade a blanket cylinder bottom radius 14 cm and height10cm. With π = 22
7 , the rest of cardboard is broad...
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Geometry
Exercise
1 A triangle has base length 3 cm shorter than the height andbreadth of less than 27cm2. If height of triangle t cm so...
2 From a piece of cardboard that breadth of 10dm2 will bemade a blanket cylinder bottom radius 14 cm and height10cm. With π = 22
7 , the rest of cardboard is broad...
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Geometry
Exercise
1 A boy stood in a place A in the banks of rivers straight. Heobserved two trees B right across the river. Tree B rightacross tree A. The distance tree B and C are 8
√6 meter
and Large angular BAC = 30o. the width of the river is...
2 Trapezoid ABCD, DC ‖ AB. is parallel DC. T intersectionextension of AD dan BC. The long TA is, ...
3 Given a triangle ABC with sides AB, BC and CArespectively is 5 cm, 6 cm and 4 cm. What is sin2(< BAC)
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Geometry
Exercise
1 A boy stood in a place A in the banks of rivers straight. Heobserved two trees B right across the river. Tree B rightacross tree A. The distance tree B and C are 8
√6 meter
and Large angular BAC = 30o. the width of the river is...
2 Trapezoid ABCD, DC ‖ AB. is parallel DC. T intersectionextension of AD dan BC. The long TA is, ...
3 Given a triangle ABC with sides AB, BC and CArespectively is 5 cm, 6 cm and 4 cm. What is sin2(< BAC)
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Geometry
Exercise
1 A boy stood in a place A in the banks of rivers straight. Heobserved two trees B right across the river. Tree B rightacross tree A. The distance tree B and C are 8
√6 meter
and Large angular BAC = 30o. the width of the river is...
2 Trapezoid ABCD, DC ‖ AB. is parallel DC. T intersectionextension of AD dan BC. The long TA is, ...
3 Given a triangle ABC with sides AB, BC and CArespectively is 5 cm, 6 cm and 4 cm. What is sin2(< BAC)
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Geometry
Exercise
1 A boy stood in a place A in the banks of rivers straight. Heobserved two trees B right across the river. Tree B rightacross tree A. The distance tree B and C are 8
√6 meter
and Large angular BAC = 30o. the width of the river is...
2 Trapezoid ABCD, DC ‖ AB. is parallel DC. T intersectionextension of AD dan BC. The long TA is, ...
3 Given a triangle ABC with sides AB, BC and CArespectively is 5 cm, 6 cm and 4 cm. What is sin2(< BAC)
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Probability
Exercise
1 The quarter-final champions 2010 followed 8 teamA,B,C,D,E,F,G dan H. Every team has a chance 1/2 to goto the next round. A chance occurrence A meet G in thefinal and in the end A champion is ...
2 For example, the first appearance of dice numbers A anddice both bring up numbers B then the possibilities that willbe obtained if the A and B is the numbers on the dice aremutually contradictory is ...
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Probability
Exercise
1 The quarter-final champions 2010 followed 8 teamA,B,C,D,E,F,G dan H. Every team has a chance 1/2 to goto the next round. A chance occurrence A meet G in thefinal and in the end A champion is ...
2 For example, the first appearance of dice numbers A anddice both bring up numbers B then the possibilities that willbe obtained if the A and B is the numbers on the dice aremutually contradictory is ...
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Probability
Exercise
1 The quarter-final champions 2010 followed 8 teamA,B,C,D,E,F,G dan H. Every team has a chance 1/2 to goto the next round. A chance occurrence A meet G in thefinal and in the end A champion is ...
2 For example, the first appearance of dice numbers A anddice both bring up numbers B then the possibilities that willbe obtained if the A and B is the numbers on the dice aremutually contradictory is ...
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Probability
Exercise
1 In a pouch there are 2 white balls and six balls red. Takenone ball at random and ball took its color is noted. Afterwhich the ball is returned to the pockets and later retrievedagain one ball at random. Opportunity took two balls ofdifferent colors is...
2 How many the phone number consists of 7 figures can bemade with 4 digit originally was 0812, the remaining threedigits must be different and not a number 0, 3 or 5, and thelast digit is not a number 9
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Probability
Exercise
1 In a pouch there are 2 white balls and six balls red. Takenone ball at random and ball took its color is noted. Afterwhich the ball is returned to the pockets and later retrievedagain one ball at random. Opportunity took two balls ofdifferent colors is...
2 How many the phone number consists of 7 figures can bemade with 4 digit originally was 0812, the remaining threedigits must be different and not a number 0, 3 or 5, and thelast digit is not a number 9
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Probability
Exercise
1 In a pouch there are 2 white balls and six balls red. Takenone ball at random and ball took its color is noted. Afterwhich the ball is returned to the pockets and later retrievedagain one ball at random. Opportunity took two balls ofdifferent colors is...
2 How many the phone number consists of 7 figures can bemade with 4 digit originally was 0812, the remaining threedigits must be different and not a number 0, 3 or 5, and thelast digit is not a number 9
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Probability
Exercise
1 Many telephone connection to number 108, between hours23.00 until 24.00 for 1 month is Poisson distribution withaverage 5 connections every day, based on this, determinethe odds that one day on the hour when there are 5connection!
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
Number TheoryAlgebra
GeometryProbability
Probability
Exercise
1 Many telephone connection to number 108, between hours23.00 until 24.00 for 1 month is Poisson distribution withaverage 5 connections every day, based on this, determinethe odds that one day on the hour when there are 5connection!
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction
