This document contains an outline for exercises in number theory, algebra, geometry, and probability. It includes 5 exercises for each topic area with problems involving calculations, proofs, and determining values based on equations. The document appears to be notes for a math curriculum covering fundamental topics in these core areas of mathematics.

1. Outline
English as Medium of Instruction
Novian Nur Fatihah and Maulinda Fitri Septianingrum
Faculty of Teacher Training and Education
University Of Jember
6th June 2013
Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

2. Outline
Outline
1 Number Theory
2 Algebra
3 Geometry
4 Probability
Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

3. Outline
Outline
1 Number Theory
2 Algebra
3 Geometry
4 Probability
Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

4. Outline
Outline
1 Number Theory
2 Algebra
3 Geometry
4 Probability
Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

5. Outline
Outline
1 Number Theory
2 Algebra
3 Geometry
4 Probability
Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

6. Number Theory
Algebra
Geometry
Probability
Number Theory
Exercise
1 If A = 13 − 23 + 33 − 43 + 53 − 63 + · · · + 20053 , determine
the 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 of
a − b!
3 Given a, b, c, d, and e are real numbers. If
a + b + c + d + e = 19 and a2 + b2 + c2 + d2 + e2 = 99.
Determine the maximum value!
4 Calculate the results of the
12 − 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. Number Theory
Algebra
Geometry
Probability
Number Theory
Exercise
1 If A = 13 − 23 + 33 − 43 + 53 − 63 + · · · + 20053 , determine
the 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 of
a − b!
3 Given a, b, c, d, and e are real numbers. If
a + b + c + d + e = 19 and a2 + b2 + c2 + d2 + e2 = 99.
Determine the maximum value!
4 Calculate the results of the
12 − 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. Number Theory
Algebra
Geometry
Probability
Number Theory
Exercise
1 If A = 13 − 23 + 33 − 43 + 53 − 63 + · · · + 20053 , determine
the 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 of
a − b!
3 Given a, b, c, d, and e are real numbers. If
a + b + c + d + e = 19 and a2 + b2 + c2 + d2 + e2 = 99.
Determine the maximum value!
4 Calculate the results of the
12 − 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. Number Theory
Algebra
Geometry
Probability
Number Theory
Exercise
1 If A = 13 − 23 + 33 − 43 + 53 − 63 + · · · + 20053 , determine
the 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 of
a − b!
3 Given a, b, c, d, and e are real numbers. If
a + b + c + d + e = 19 and a2 + b2 + c2 + d2 + e2 = 99.
Determine the maximum value!
4 Calculate the results of the
12 − 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. Number Theory
Algebra
Geometry
Probability
Number Theory
Exercise
1 If A = 13 − 23 + 33 − 43 + 53 − 63 + · · · + 20053 , determine
the 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 of
a − b!
3 Given a, b, c, d, and e are real numbers. If
a + b + c + d + e = 19 and a2 + b2 + c2 + d2 + e2 = 99.
Determine the maximum value!
4 Calculate the results of the
12 − 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. Number Theory
Algebra
Geometry
Probability
Number Theory
Exercise
1 If A = 13 − 23 + 33 − 43 + 53 − 63 + · · · + 20053 , determine
the 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 of
a − b!
3 Given a, b, c, d, and e are real numbers. If
a + b + c + d + e = 19 and a2 + b2 + c2 + d2 + e2 = 99.
Determine the maximum value!
4 Calculate the results of the
12 − 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. Number Theory
Algebra
Geometry
Probability
Algebra
Exercise
1 Determine the value of x, y, z real numbers that satisfy the
equation: 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 value
a2 + b2!
3 Given x, y, z and t are real numbers that are not zero and
satisfies the equation: x + y + z = t · · · (1)
1
x + 1
y + 1
z = 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

13. Number Theory
Algebra
Geometry
Probability
Algebra
Exercise
1 Determine the value of x, y, z real numbers that satisfy the
equation: 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 value
a2 + b2!
3 Given x, y, z and t are real numbers that are not zero and
satisfies the equation: x + y + z = t · · · (1)
1
x + 1
y + 1
z = 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

14. Number Theory
Algebra
Geometry
Probability
Algebra
Exercise
1 Determine the value of x, y, z real numbers that satisfy the
equation: 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 value
a2 + b2!
3 Given x, y, z and t are real numbers that are not zero and
satisfies the equation: x + y + z = t · · · (1)
1
x + 1
y + 1
z = 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

15. Number Theory
Algebra
Geometry
Probability
Algebra
Exercise
1 Determine the value of x, y, z real numbers that satisfy the
equation: 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 value
a2 + b2!
3 Given x, y, z and t are real numbers that are not zero and
satisfies the equation: x + y + z = t · · · (1)
1
x + 1
y + 1
z = 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

16. Number Theory
Algebra
Geometry
Probability
Algebra
Exercise
1 Prove for any positive numbers a, b, c and d apply
a+b+c+d
4
4
√
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

17. Number Theory
Algebra
Geometry
Probability
Algebra
Exercise
1 Prove for any positive numbers a, b, c and d apply
a+b+c+d
4
4
√
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

18. Number Theory
Algebra
Geometry
Probability
Algebra
Exercise
1 Prove for any positive numbers a, b, c and d apply
a+b+c+d
4
4
√
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

19. Number Theory
Algebra
Geometry
Probability
Geometry
Exercise
1 The area bounded by the curve y = x2 − 4x + 3 and
y = 3 − x are ...
2 The area bounded by the curve y = x2 + 3x + 4 and
y = 1 − x are ...
3 Turn the volume of the object that occurs when the area
bounded 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 and
breadth of less than 27cm2. If height of triangle t cm so...
5 Given a triangle ABC with sides AB, BC and CA
respectively 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. Number Theory
Algebra
Geometry
Probability
Geometry
Exercise
1 The area bounded by the curve y = x2 − 4x + 3 and
y = 3 − x are ...
2 The area bounded by the curve y = x2 + 3x + 4 and
y = 1 − x are ...
3 Turn the volume of the object that occurs when the area
bounded 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 and
breadth of less than 27cm2. If height of triangle t cm so...
5 Given a triangle ABC with sides AB, BC and CA
respectively 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. Number Theory
Algebra
Geometry
Probability
Geometry
Exercise
1 The area bounded by the curve y = x2 − 4x + 3 and
y = 3 − x are ...
2 The area bounded by the curve y = x2 + 3x + 4 and
y = 1 − x are ...
3 Turn the volume of the object that occurs when the area
bounded 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 and
breadth of less than 27cm2. If height of triangle t cm so...
5 Given a triangle ABC with sides AB, BC and CA
respectively 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. Number Theory
Algebra
Geometry
Probability
Geometry
Exercise
1 The area bounded by the curve y = x2 − 4x + 3 and
y = 3 − x are ...
2 The area bounded by the curve y = x2 + 3x + 4 and
y = 1 − x are ...
3 Turn the volume of the object that occurs when the area
bounded 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 and
breadth of less than 27cm2. If height of triangle t cm so...
5 Given a triangle ABC with sides AB, BC and CA
respectively 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. Number Theory
Algebra
Geometry
Probability
Geometry
Exercise
1 The area bounded by the curve y = x2 − 4x + 3 and
y = 3 − x are ...
2 The area bounded by the curve y = x2 + 3x + 4 and
y = 1 − x are ...
3 Turn the volume of the object that occurs when the area
bounded 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 and
breadth of less than 27cm2. If height of triangle t cm so...
5 Given a triangle ABC with sides AB, BC and CA
respectively 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. Number Theory
Algebra
Geometry
Probability
Geometry
Exercise
1 The area bounded by the curve y = x2 − 4x + 3 and
y = 3 − x are ...
2 The area bounded by the curve y = x2 + 3x + 4 and
y = 1 − x are ...
3 Turn the volume of the object that occurs when the area
bounded 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 and
breadth of less than 27cm2. If height of triangle t cm so...
5 Given a triangle ABC with sides AB, BC and CA
respectively 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. Number Theory
Algebra
Geometry
Probability
Probability
Exercise
1 Suppose there are 5 cards where each card is given a
different number is 2, 3, 4, 5, 6. The cards are then lined up
from left to right so that the randomly shaped line. What is
the probability that the number of cards lined up from left to
right and placed on the i − th place will be greater or equal
to i for each i with 1 ≤ i ≤ 5?
2 N circle drawn on a flat surface so that there are six point
where 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. Number Theory
Algebra
Geometry
Probability
Probability
Exercise
1 Suppose there are 5 cards where each card is given a
different number is 2, 3, 4, 5, 6. The cards are then lined up
from left to right so that the randomly shaped line. What is
the probability that the number of cards lined up from left to
right and placed on the i − th place will be greater or equal
to i for each i with 1 ≤ i ≤ 5?
2 N circle drawn on a flat surface so that there are six point
where 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. Number Theory
Algebra
Geometry
Probability
Probability
Exercise
1 Suppose there are 5 cards where each card is given a
different number is 2, 3, 4, 5, 6. The cards are then lined up
from left to right so that the randomly shaped line. What is
the probability that the number of cards lined up from left to
right and placed on the i − th place will be greater or equal
to i for each i with 1 ≤ i ≤ 5?
2 N circle drawn on a flat surface so that there are six point
where 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. Number Theory
Algebra
Geometry
Probability
Probability
Exercise
1 Given four dice equilibrium and different, each of which is
octagonal irregularly edged 1, 2, 3, ..., 8. Four dice collide
(thrown) together one time. Probability of occurrence of
two 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 Last
reviewed, then the number of possible arrangements is ...
3 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...
Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

29. Number Theory
Algebra
Geometry
Probability
Probability
Exercise
1 Given four dice equilibrium and different, each of which is
octagonal irregularly edged 1, 2, 3, ..., 8. Four dice collide
(thrown) together one time. Probability of occurrence of
two 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 Last
reviewed, then the number of possible arrangements is ...
3 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...
Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

30. Number Theory
Algebra
Geometry
Probability
Probability
Exercise
1 Given four dice equilibrium and different, each of which is
octagonal irregularly edged 1, 2, 3, ..., 8. Four dice collide
(thrown) together one time. Probability of occurrence of
two 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 Last
reviewed, then the number of possible arrangements is ...
3 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...
Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction

31. Number Theory
Algebra
Geometry
Probability
Probability
Exercise
1 Given four dice equilibrium and different, each of which is
octagonal irregularly edged 1, 2, 3, ..., 8. Four dice collide
(thrown) together one time. Probability of occurrence of
two 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 Last
reviewed, then the number of possible arrangements is ...
3 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...
Novian Nur Fatihah and Maulinda Fitri Septianingrum English as Medium of Instruction