Outline

English as Medium of Instruction

Novian Nur Fatihah and Maulinda Fitri Septianingrum

Faculty of Teacher Training and EducationUniversity Of Jember

6th June 2013

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Outline

Outline

1 Number Theory

2 Algebra

3 Geometry

4 Probability

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Outline

Outline

1 Number Theory

2 Algebra

3 Geometry

4 Probability

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Outline

Outline

1 Number Theory

2 Algebra

3 Geometry

4 Probability

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Outline

Outline

1 Number Theory

2 Algebra

3 Geometry

4 Probability

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Number Theory

Exercise

1 If A = 13 − 23 + 33 − 43 + 53 − 63 + · · ·+ 20053 , determinethe value of A !

2 Given a = 12

1 + 22

3 + 32

5 + · · ·+ 10022

2003 and

b = 12

3 + 22

5 + 32

7 + · · ·+ 10022

2005 Show the nearest integer ofa− b!

3 Given a, b, c, d , and e are real numbers. Ifa + b + c + d + e = 19 and a2 + b2 + c2 + d2 + e2 = 99.Determine the maximum value!

4 Calculate the results of the12 − 22 + 32 − 42 + 52 − 62 + ... + 20092 − 20102 + 20112 !

5 Prove for any real numbers a, b apply a2 + b2 ≥ 2ab !Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Number Theory

Exercise

1 If A = 13 − 23 + 33 − 43 + 53 − 63 + · · ·+ 20053 , determinethe value of A !

2 Given a = 12

1 + 22

3 + 32

5 + · · ·+ 10022

2003 and

b = 12

3 + 22

5 + 32

7 + · · ·+ 10022

2005 Show the nearest integer ofa− b!

3 Given a, b, c, d , and e are real numbers. Ifa + b + c + d + e = 19 and a2 + b2 + c2 + d2 + e2 = 99.Determine the maximum value!

4 Calculate the results of the12 − 22 + 32 − 42 + 52 − 62 + ... + 20092 − 20102 + 20112 !

5 Prove for any real numbers a, b apply a2 + b2 ≥ 2ab !Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Number Theory

Exercise

1 If A = 13 − 23 + 33 − 43 + 53 − 63 + · · ·+ 20053 , determinethe value of A !

2 Given a = 12

1 + 22

3 + 32

5 + · · ·+ 10022

2003 and

b = 12

3 + 22

5 + 32

7 + · · ·+ 10022

2005 Show the nearest integer ofa− b!

3 Given a, b, c, d , and e are real numbers. Ifa + b + c + d + e = 19 and a2 + b2 + c2 + d2 + e2 = 99.Determine the maximum value!

4 Calculate the results of the12 − 22 + 32 − 42 + 52 − 62 + ... + 20092 − 20102 + 20112 !

5 Prove for any real numbers a, b apply a2 + b2 ≥ 2ab !Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Number Theory

Exercise

1 If A = 13 − 23 + 33 − 43 + 53 − 63 + · · ·+ 20053 , determinethe value of A !

2 Given a = 12

1 + 22

3 + 32

5 + · · ·+ 10022

2003 and

b = 12

3 + 22

5 + 32

7 + · · ·+ 10022

2005 Show the nearest integer ofa− b!

3 Given a, b, c, d , and e are real numbers. Ifa + b + c + d + e = 19 and a2 + b2 + c2 + d2 + e2 = 99.Determine the maximum value!

4 Calculate the results of the12 − 22 + 32 − 42 + 52 − 62 + ... + 20092 − 20102 + 20112 !

5 Prove for any real numbers a, b apply a2 + b2 ≥ 2ab !Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Number Theory

Exercise

1 If A = 13 − 23 + 33 − 43 + 53 − 63 + · · ·+ 20053 , determinethe value of A !

2 Given a = 12

1 + 22

3 + 32

5 + · · ·+ 10022

2003 and

b = 12

3 + 22

5 + 32

7 + · · ·+ 10022

2005 Show the nearest integer ofa− b!

3 Given a, b, c, d , and e are real numbers. Ifa + b + c + d + e = 19 and a2 + b2 + c2 + d2 + e2 = 99.Determine the maximum value!

4 Calculate the results of the12 − 22 + 32 − 42 + 52 − 62 + ... + 20092 − 20102 + 20112 !

5 Prove for any real numbers a, b apply a2 + b2 ≥ 2ab !Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Number Theory

Exercise

1 If A = 13 − 23 + 33 − 43 + 53 − 63 + · · ·+ 20053 , determinethe value of A !

2 Given a = 12

1 + 22

3 + 32

5 + · · ·+ 10022

2003 and

b = 12

3 + 22

5 + 32

7 + · · ·+ 10022

2005 Show the nearest integer ofa− b!

3 Given a, b, c, d , and e are real numbers. Ifa + b + c + d + e = 19 and a2 + b2 + c2 + d2 + e2 = 99.Determine the maximum value!

4 Calculate the results of the12 − 22 + 32 − 42 + 52 − 62 + ... + 20092 − 20102 + 20112 !

5 Prove for any real numbers a, b apply a2 + b2 ≥ 2ab !Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Algebra

Exercise

1 Determine the value of x , y , z real numbers that satisfy theequation: x2 + 2yz = x · · · (1) y2 + 2zx = y · · · (2)z2 + 2xy = z · · · (3)

2 Given aandb are real numbers that are satisfy :i .a3 − 3ab2 = 44 ii .b3 − 3a2b = 8 . Determine the valuea2 + b2!

3 Given x , y , z and t are real numbers that are not zero andsatisfies the equation: x + y + z = t · · · (1)1x + 1

y + 1z = 1

t · · · (2) x3 + y3 + z3 = 10003 · · · (3) .Determine the value of x + y + z + t !

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Algebra

Exercise

1 Determine the value of x , y , z real numbers that satisfy theequation: x2 + 2yz = x · · · (1) y2 + 2zx = y · · · (2)z2 + 2xy = z · · · (3)

2 Given aandb are real numbers that are satisfy :i .a3 − 3ab2 = 44 ii .b3 − 3a2b = 8 . Determine the valuea2 + b2!

3 Given x , y , z and t are real numbers that are not zero andsatisfies the equation: x + y + z = t · · · (1)1x + 1

y + 1z = 1

t · · · (2) x3 + y3 + z3 = 10003 · · · (3) .Determine the value of x + y + z + t !

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Algebra

Exercise

1 Determine the value of x , y , z real numbers that satisfy theequation: x2 + 2yz = x · · · (1) y2 + 2zx = y · · · (2)z2 + 2xy = z · · · (3)

2 Given aandb are real numbers that are satisfy :i .a3 − 3ab2 = 44 ii .b3 − 3a2b = 8 . Determine the valuea2 + b2!

3 Given x , y , z and t are real numbers that are not zero andsatisfies the equation: x + y + z = t · · · (1)1x + 1

y + 1z = 1

t · · · (2) x3 + y3 + z3 = 10003 · · · (3) .Determine the value of x + y + z + t !

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Algebra

Exercise

1 Determine the value of x , y , z real numbers that satisfy theequation: x2 + 2yz = x · · · (1) y2 + 2zx = y · · · (2)z2 + 2xy = z · · · (3)

2 Given aandb are real numbers that are satisfy :i .a3 − 3ab2 = 44 ii .b3 − 3a2b = 8 . Determine the valuea2 + b2!

3 Given x , y , z and t are real numbers that are not zero andsatisfies the equation: x + y + z = t · · · (1)1x + 1

y + 1z = 1

t · · · (2) x3 + y3 + z3 = 10003 · · · (3) .Determine the value of x + y + z + t !

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Algebra

Exercise

1 Prove for any positive numbers a, b, c and d applya+b+c+d

44√

abcd !

2 If α dan β roots of the equation x2 − ax + b = 0 (a, breal).Make quadratic equations who roots α3

β dan β3

α

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Algebra

Exercise

1 Prove for any positive numbers a, b, c and d applya+b+c+d

44√

abcd !

2 If α dan β roots of the equation x2 − ax + b = 0 (a, breal).Make quadratic equations who roots α3

β dan β3

α

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Algebra

Exercise

1 Prove for any positive numbers a, b, c and d applya+b+c+d

44√

abcd !

2 If α dan β roots of the equation x2 − ax + b = 0 (a, breal).Make quadratic equations who roots α3

β dan β3

α

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Geometry

Exercise

1 The area bounded by the curve y = x2 − 4x + 3 andy = 3− x are ...

2 The area bounded by the curve y = x2 + 3x + 4 andy = 1− x are ...

3 Turn the volume of the object that occurs when the areabounded by the curve y = x2 and y = 4x − 3 rotated 360o

around the X axis is ...

4 A triangle has base length 3 cm shorter than the height andbreadth of less than 27cm2. If height of triangle t cm so...

5 Given a triangle ABC with sides AB, BC and CArespectively is 5 cm, 6 cm and 4 cm. What is sin2(< BAC)

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Geometry

Exercise

1 The area bounded by the curve y = x2 − 4x + 3 andy = 3− x are ...

2 The area bounded by the curve y = x2 + 3x + 4 andy = 1− x are ...

3 Turn the volume of the object that occurs when the areabounded by the curve y = x2 and y = 4x − 3 rotated 360o

around the X axis is ...

4 A triangle has base length 3 cm shorter than the height andbreadth of less than 27cm2. If height of triangle t cm so...

5 Given a triangle ABC with sides AB, BC and CArespectively is 5 cm, 6 cm and 4 cm. What is sin2(< BAC)

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Geometry

Exercise

1 The area bounded by the curve y = x2 − 4x + 3 andy = 3− x are ...

2 The area bounded by the curve y = x2 + 3x + 4 andy = 1− x are ...

3 Turn the volume of the object that occurs when the areabounded by the curve y = x2 and y = 4x − 3 rotated 360o

around the X axis is ...

4 A triangle has base length 3 cm shorter than the height andbreadth of less than 27cm2. If height of triangle t cm so...

5 Given a triangle ABC with sides AB, BC and CArespectively is 5 cm, 6 cm and 4 cm. What is sin2(< BAC)

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Geometry

Exercise

1 The area bounded by the curve y = x2 − 4x + 3 andy = 3− x are ...

2 The area bounded by the curve y = x2 + 3x + 4 andy = 1− x are ...

3 Turn the volume of the object that occurs when the areabounded by the curve y = x2 and y = 4x − 3 rotated 360o

around the X axis is ...

4 A triangle has base length 3 cm shorter than the height andbreadth of less than 27cm2. If height of triangle t cm so...

5 Given a triangle ABC with sides AB, BC and CArespectively is 5 cm, 6 cm and 4 cm. What is sin2(< BAC)

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Geometry

Exercise

1 The area bounded by the curve y = x2 − 4x + 3 andy = 3− x are ...

2 The area bounded by the curve y = x2 + 3x + 4 andy = 1− x are ...

3 Turn the volume of the object that occurs when the areabounded by the curve y = x2 and y = 4x − 3 rotated 360o

around the X axis is ...

4 A triangle has base length 3 cm shorter than the height andbreadth of less than 27cm2. If height of triangle t cm so...

5 Given a triangle ABC with sides AB, BC and CArespectively is 5 cm, 6 cm and 4 cm. What is sin2(< BAC)

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Geometry

Exercise

1 The area bounded by the curve y = x2 − 4x + 3 andy = 3− x are ...

2 The area bounded by the curve y = x2 + 3x + 4 andy = 1− x are ...

3 Turn the volume of the object that occurs when the areabounded by the curve y = x2 and y = 4x − 3 rotated 360o

around the X axis is ...

4 A triangle has base length 3 cm shorter than the height andbreadth of less than 27cm2. If height of triangle t cm so...

5 Given a triangle ABC with sides AB, BC and CArespectively is 5 cm, 6 cm and 4 cm. What is sin2(< BAC)

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Probability

Exercise

1 Suppose there are 5 cards where each card is given adifferent number is 2, 3, 4, 5, 6. The cards are then lined upfrom left to right so that the randomly shaped line. What isthe probability that the number of cards lined up from left toright and placed on the i − th place will be greater or equalto i for each i with 1 ≤ i ≤ 5?

2 N circle drawn on a flat surface so that there are six pointwhere the six points are contained in at least three circles.What is the smallest N that satisfies these conditions?

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Probability

Exercise

1 Suppose there are 5 cards where each card is given adifferent number is 2, 3, 4, 5, 6. The cards are then lined upfrom left to right so that the randomly shaped line. What isthe probability that the number of cards lined up from left toright and placed on the i − th place will be greater or equalto i for each i with 1 ≤ i ≤ 5?

2 N circle drawn on a flat surface so that there are six pointwhere the six points are contained in at least three circles.What is the smallest N that satisfies these conditions?

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Probability

Exercise

1 Suppose there are 5 cards where each card is given adifferent number is 2, 3, 4, 5, 6. The cards are then lined upfrom left to right so that the randomly shaped line. What isthe probability that the number of cards lined up from left toright and placed on the i − th place will be greater or equalto i for each i with 1 ≤ i ≤ 5?

2 N circle drawn on a flat surface so that there are six pointwhere the six points are contained in at least three circles.What is the smallest N that satisfies these conditions?

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Probability

Exercise

1 Given four dice equilibrium and different, each of which isoctagonal irregularly edged 1, 2, 3, ..., 8. Four dice collide(thrown) together one time. Probability of occurrence oftwo dice with the same eye for emerging are...

2 Five students A, B, C, D, E are in one group in a relay race.If A is not able to run the first and D could not run Lastreviewed, then the number of possible arrangements is ...

3 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...

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Probability

Exercise

1 Given four dice equilibrium and different, each of which isoctagonal irregularly edged 1, 2, 3, ..., 8. Four dice collide(thrown) together one time. Probability of occurrence oftwo dice with the same eye for emerging are...

2 Five students A, B, C, D, E are in one group in a relay race.If A is not able to run the first and D could not run Lastreviewed, then the number of possible arrangements is ...

3 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...

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Probability

Exercise

1 Given four dice equilibrium and different, each of which isoctagonal irregularly edged 1, 2, 3, ..., 8. Four dice collide(thrown) together one time. Probability of occurrence oftwo dice with the same eye for emerging are...

2 Five students A, B, C, D, E are in one group in a relay race.If A is not able to run the first and D could not run Lastreviewed, then the number of possible arrangements is ...

3 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...

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

Number TheoryAlgebra

GeometryProbability

Probability

Exercise

1 Given four dice equilibrium and different, each of which isoctagonal irregularly edged 1, 2, 3, ..., 8. Four dice collide(thrown) together one time. Probability of occurrence oftwo dice with the same eye for emerging are...

2 Five students A, B, C, D, E are in one group in a relay race.If A is not able to run the first and D could not run Lastreviewed, then the number of possible arrangements is ...

3 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...

Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction