This document contains an outline for a course on mathematics that includes sections on number theory, algebra, geometry, and probability. Each section includes sample exercises related to that topic. For example, the number theory section includes exercises involving properties of numbers, divisibility, and remainders. The overall document provides an outline and examples of problems for a mathematics course covering various fundamental topics in the field.

1. Outline
English as Medium of Instruction
Rizky Titie Riddiyani dan Marlia Sari Pangestuti
Fakultas Keguruan dan Ilmu Pendidikan
Universitas Jember
9th June 2013
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

2. Outline
Outline
1 Number Theory
2 Algebra
3 Geometry
4 Probability
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

3. Outline
Outline
1 Number Theory
2 Algebra
3 Geometry
4 Probability
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

4. Outline
Outline
1 Number Theory
2 Algebra
3 Geometry
4 Probability
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

5. Outline
Outline
1 Number Theory
2 Algebra
3 Geometry
4 Probability
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

6. Number Theory
Algebra
Geometry
Probability
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 434343
by 10
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

7. Number Theory
Algebra
Geometry
Probability
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 434343
by 10
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

8. Number Theory
Algebra
Geometry
Probability
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 434343
by 10
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

9. Number Theory
Algebra
Geometry
Probability
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 434343
by 10
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

10. Number Theory
Algebra
Geometry
Probability
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 434343
by 10
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

11. Number Theory
Algebra
Geometry
Probability
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 434343
by 10
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

12. Number Theory
Algebra
Geometry
Probability
Algebra
Exercise
1 Specify the number of roots of the integers from the
equation 4x4 − 15x2 + 5x + 6 = 0
2 Known roots of the equation x3 − 2x2 − 3x + 1 = 0 are
x1,x2 and x3. Specify the value 1
x1
+ 1
x2
+ 1
x3
3 Known roots of the equation x3 − 3x2 + 4x + 5 = 0 are
x1,x2 and x3. Specify the value x3
1 + x3
2 + x3
3
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

13. Number Theory
Algebra
Geometry
Probability
Algebra
Exercise
1 Specify the number of roots of the integers from the
equation 4x4 − 15x2 + 5x + 6 = 0
2 Known roots of the equation x3 − 2x2 − 3x + 1 = 0 are
x1,x2 and x3. Specify the value 1
x1
+ 1
x2
+ 1
x3
3 Known roots of the equation x3 − 3x2 + 4x + 5 = 0 are
x1,x2 and x3. Specify the value x3
1 + x3
2 + x3
3
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

14. Number Theory
Algebra
Geometry
Probability
Algebra
Exercise
1 Specify the number of roots of the integers from the
equation 4x4 − 15x2 + 5x + 6 = 0
2 Known roots of the equation x3 − 2x2 − 3x + 1 = 0 are
x1,x2 and x3. Specify the value 1
x1
+ 1
x2
+ 1
x3
3 Known roots of the equation x3 − 3x2 + 4x + 5 = 0 are
x1,x2 and x3. Specify the value x3
1 + x3
2 + x3
3
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

15. Number Theory
Algebra
Geometry
Probability
Algebra
Exercise
1 Specify the number of roots of the integers from the
equation 4x4 − 15x2 + 5x + 6 = 0
2 Known roots of the equation x3 − 2x2 − 3x + 1 = 0 are
x1,x2 and x3. Specify the value 1
x1
+ 1
x2
+ 1
x3
3 Known roots of the equation x3 − 3x2 + 4x + 5 = 0 are
x1,x2 and x3. Specify the value x3
1 + x3
2 + x3
3
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

16. Number Theory
Algebra
Geometry
Probability
Algebra
Exercise
1 Known roots of the equation x4 − 8x3 + ax2 − bx + c = 0
Forming arithmetic progression with different 2. Specify the
value 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
β dan β3
α
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

17. Number Theory
Algebra
Geometry
Probability
Algebra
Exercise
1 Known roots of the equation x4 − 8x3 + ax2 − bx + c = 0
Forming arithmetic progression with different 2. Specify the
value 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
β dan β3
α
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

18. Number Theory
Algebra
Geometry
Probability
Algebra
Exercise
1 Known roots of the equation x4 − 8x3 + ax2 − bx + c = 0
Forming arithmetic progression with different 2. Specify the
value 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
β dan β3
α
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

19. Number Theory
Algebra
Geometry
Probability
Geometry
Exercise
1 A triangle has base length 3 cm shorter than the height and
breadth of less than 27cm2. If height of triangle t cm so...
2 From a piece of cardboard that breadth of 10dm2 will be
made a blanket cylinder bottom radius 14 cm and height
10cm. With π = 22
7 , the rest of cardboard is broad...
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

20. Number Theory
Algebra
Geometry
Probability
Geometry
Exercise
1 A triangle has base length 3 cm shorter than the height and
breadth of less than 27cm2. If height of triangle t cm so...
2 From a piece of cardboard that breadth of 10dm2 will be
made a blanket cylinder bottom radius 14 cm and height
10cm. With π = 22
7 , the rest of cardboard is broad...
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

21. Number Theory
Algebra
Geometry
Probability
Geometry
Exercise
1 A triangle has base length 3 cm shorter than the height and
breadth of less than 27cm2. If height of triangle t cm so...
2 From a piece of cardboard that breadth of 10dm2 will be
made a blanket cylinder bottom radius 14 cm and height
10cm. With π = 22
7 , the rest of cardboard is broad...
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

22. Number Theory
Algebra
Geometry
Probability
Geometry
Exercise
1 Given a triangle ABC with sides AB, BC and CA
respectively is 5 cm, 6 cm and 4 cm. What is sin2(< BAC)
2 A boy stood in a place A in the banks of rivers straight. He
observed two trees B right across the river. Tree B right
across tree A. The distance tree B and C are 8
√
6 meter
and Large angular BAC = 30o. the width of the river is...
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

23. Number Theory
Algebra
Geometry
Probability
Geometry
Exercise
1 Given a triangle ABC with sides AB, BC and CA
respectively is 5 cm, 6 cm and 4 cm. What is sin2(< BAC)
2 A boy stood in a place A in the banks of rivers straight. He
observed two trees B right across the river. Tree B right
across tree A. The distance tree B and C are 8
√
6 meter
and Large angular BAC = 30o. the width of the river is...
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

24. Number Theory
Algebra
Geometry
Probability
Geometry
Exercise
1 Given a triangle ABC with sides AB, BC and CA
respectively is 5 cm, 6 cm and 4 cm. What is sin2(< BAC)
2 A boy stood in a place A in the banks of rivers straight. He
observed two trees B right across the river. Tree B right
across tree A. The distance tree B and C are 8
√
6 meter
and Large angular BAC = 30o. the width of the river is...
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

25. Number Theory
Algebra
Geometry
Probability
Geometry
Exercise
1 Trapezoid ABCD, DC AB. is parallel DC. T intersection
extension of AD dan BC. The long TA is ...
Look at the picture!
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

26. Number Theory
Algebra
Geometry
Probability
Geometry
Exercise
1 Trapezoid ABCD, DC AB. is parallel DC. T intersection
extension of AD dan BC. The long TA is ...
Look at the picture!
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

27. Number Theory
Algebra
Geometry
Probability
Probability
Exercise
1 The quarter-final champions 2010 followed 8 team
A,B,C,D,E,F,G dan H. Every team has a chance 1/2 to go
to the next round. A chance occurrence A meet G in the
final and in the end A champion is ...
2 For example, the first appearance of dice numbers A and
dice both bring up numbers B then the possibilities that will
be obtained if the A and B is the numbers on the dice are
mutually contradictory is ...
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

28. Number Theory
Algebra
Geometry
Probability
Probability
Exercise
1 The quarter-final champions 2010 followed 8 team
A,B,C,D,E,F,G dan H. Every team has a chance 1/2 to go
to the next round. A chance occurrence A meet G in the
final and in the end A champion is ...
2 For example, the first appearance of dice numbers A and
dice both bring up numbers B then the possibilities that will
be obtained if the A and B is the numbers on the dice are
mutually contradictory is ...
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

29. Number Theory
Algebra
Geometry
Probability
Probability
Exercise
1 The quarter-final champions 2010 followed 8 team
A,B,C,D,E,F,G dan H. Every team has a chance 1/2 to go
to the next round. A chance occurrence A meet G in the
final and in the end A champion is ...
2 For example, the first appearance of dice numbers A and
dice both bring up numbers B then the possibilities that will
be obtained if the A and B is the numbers on the dice are
mutually contradictory is ...
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

30. Number Theory
Algebra
Geometry
Probability
Probability
Exercise
1 In a pouch there are 2 white balls and six balls red. Taken
one ball at random and ball took its color is noted. After
which the ball is returned to the pockets and later retrieved
again one ball at random. Opportunity took two balls of
different colors is...
2 How many the phone number consists of 7 figures can be
made with 4 digit originally was 0812, the remaining three
digits must be different and not a number 0, 3 or 5, and the
last digit is not a number 9
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

31. Number Theory
Algebra
Geometry
Probability
Probability
Exercise
1 In a pouch there are 2 white balls and six balls red. Taken
one ball at random and ball took its color is noted. After
which the ball is returned to the pockets and later retrieved
again one ball at random. Opportunity took two balls of
different colors is...
2 How many the phone number consists of 7 figures can be
made with 4 digit originally was 0812, the remaining three
digits must be different and not a number 0, 3 or 5, and the
last digit is not a number 9
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

32. Number Theory
Algebra
Geometry
Probability
Probability
Exercise
1 In a pouch there are 2 white balls and six balls red. Taken
one ball at random and ball took its color is noted. After
which the ball is returned to the pockets and later retrieved
again one ball at random. Opportunity took two balls of
different colors is...
2 How many the phone number consists of 7 figures can be
made with 4 digit originally was 0812, the remaining three
digits must be different and not a number 0, 3 or 5, and the
last digit is not a number 9
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

33. Number Theory
Algebra
Geometry
Probability
Probability
Exercise
1 Many telephone connection to number 108, between hours
23.00 until 24.00 for 1 month is Poisson distribution with
average 5 connections every day, based on this, determine
the odds that one day on the hour when there are 5
connection!
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction

34. Number Theory
Algebra
Geometry
Probability
Probability
Exercise
1 Many telephone connection to number 108, between hours
23.00 until 24.00 for 1 month is Poisson distribution with
average 5 connections every day, based on this, determine
the odds that one day on the hour when there are 5
connection!
Rizky Titie Riddiyani dan Marlia Sari Pangestuti English as Medium of Instruction