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### ppt Smart Solution With latex

1. 1. OutlineEnglish as Medium of InstructionNovian Nur Fatihah and Maulinda Fitri SeptianingrumFaculty of Teacher Training and EducationUniversity Of Jember6th June 2013Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction
2. 2. OutlineOutline1 Number Theory2 Algebra3 Geometry4 ProbabilityNovian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction
3. 3. OutlineOutline1 Number Theory2 Algebra3 Geometry4 ProbabilityNovian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction
4. 4. OutlineOutline1 Number Theory2 Algebra3 Geometry4 ProbabilityNovian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction
5. 5. OutlineOutline1 Number Theory2 Algebra3 Geometry4 ProbabilityNovian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction
6. 6. Number TheoryAlgebraGeometryProbabilityNumber TheoryExercise1 If A = 13 − 23 + 33 − 43 + 53 − 63 + · · · + 20053 , determinethe value of A !2 Given a = 121 + 223 + 325 + · · · + 100222003 andb = 123 + 225 + 327 + · · · + 100222005 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
7. 7. Number TheoryAlgebraGeometryProbabilityNumber TheoryExercise1 If A = 13 − 23 + 33 − 43 + 53 − 63 + · · · + 20053 , determinethe value of A !2 Given a = 121 + 223 + 325 + · · · + 100222003 andb = 123 + 225 + 327 + · · · + 100222005 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
8. 8. Number TheoryAlgebraGeometryProbabilityNumber TheoryExercise1 If A = 13 − 23 + 33 − 43 + 53 − 63 + · · · + 20053 , determinethe value of A !2 Given a = 121 + 223 + 325 + · · · + 100222003 andb = 123 + 225 + 327 + · · · + 100222005 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
9. 9. Number TheoryAlgebraGeometryProbabilityNumber TheoryExercise1 If A = 13 − 23 + 33 − 43 + 53 − 63 + · · · + 20053 , determinethe value of A !2 Given a = 121 + 223 + 325 + · · · + 100222003 andb = 123 + 225 + 327 + · · · + 100222005 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
10. 10. Number TheoryAlgebraGeometryProbabilityNumber TheoryExercise1 If A = 13 − 23 + 33 − 43 + 53 − 63 + · · · + 20053 , determinethe value of A !2 Given a = 121 + 223 + 325 + · · · + 100222003 andb = 123 + 225 + 327 + · · · + 100222005 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
11. 11. Number TheoryAlgebraGeometryProbabilityNumber TheoryExercise1 If A = 13 − 23 + 33 − 43 + 53 − 63 + · · · + 20053 , determinethe value of A !2 Given a = 121 + 223 + 325 + · · · + 100222003 andb = 123 + 225 + 327 + · · · + 100222005 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
12. 12. Number TheoryAlgebraGeometryProbabilityAlgebraExercise1 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 + 1y + 1z = 1t · · · (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
13. 13. Number TheoryAlgebraGeometryProbabilityAlgebraExercise1 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 + 1y + 1z = 1t · · · (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
14. 14. Number TheoryAlgebraGeometryProbabilityAlgebraExercise1 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 + 1y + 1z = 1t · · · (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
15. 15. Number TheoryAlgebraGeometryProbabilityAlgebraExercise1 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 + 1y + 1z = 1t · · · (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
16. 16. Number TheoryAlgebraGeometryProbabilityAlgebraExercise1 Prove for any positive numbers a, b, c and d applya+b+c+d44√abcd !2 If α dan β roots of the equation x2 − ax + b = 0 (a, breal).Make quadratic equations who roots α3β dan β3αNovian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction
17. 17. Number TheoryAlgebraGeometryProbabilityAlgebraExercise1 Prove for any positive numbers a, b, c and d applya+b+c+d44√abcd !2 If α dan β roots of the equation x2 − ax + b = 0 (a, breal).Make quadratic equations who roots α3β dan β3αNovian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction
18. 18. Number TheoryAlgebraGeometryProbabilityAlgebraExercise1 Prove for any positive numbers a, b, c and d applya+b+c+d44√abcd !2 If α dan β roots of the equation x2 − ax + b = 0 (a, breal).Make quadratic equations who roots α3β dan β3αNovian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction
19. 19. Number TheoryAlgebraGeometryProbabilityGeometryExercise1 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 360oaround 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
20. 20. Number TheoryAlgebraGeometryProbabilityGeometryExercise1 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 360oaround 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
21. 21. Number TheoryAlgebraGeometryProbabilityGeometryExercise1 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 360oaround 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
22. 22. Number TheoryAlgebraGeometryProbabilityGeometryExercise1 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 360oaround 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
23. 23. Number TheoryAlgebraGeometryProbabilityGeometryExercise1 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 360oaround 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
24. 24. Number TheoryAlgebraGeometryProbabilityGeometryExercise1 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 360oaround 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
25. 25. Number TheoryAlgebraGeometryProbabilityProbabilityExercise1 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
26. 26. Number TheoryAlgebraGeometryProbabilityProbabilityExercise1 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
27. 27. Number TheoryAlgebraGeometryProbabilityProbabilityExercise1 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
28. 28. Number TheoryAlgebraGeometryProbabilityProbabilityExercise1 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
29. 29. Number TheoryAlgebraGeometryProbabilityProbabilityExercise1 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
30. 30. Number TheoryAlgebraGeometryProbabilityProbabilityExercise1 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
31. 31. Number TheoryAlgebraGeometryProbabilityProbabilityExercise1 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