Entrance exam to technical curriculums: logical thinking questions (part 2):
ANSWER EACH QUESTION ON THE SEPARATE RESULT SHEET IN THE CORRECT PLACE
correct answer +1 p, wrong answer -1 p, empty 0 p
1. What is the reading of the following spring balance? a

Solutions to quadratic functions
43.
2
R( x)
x
C( x)
10x
2x
12
b)
a)
Recall that the break even
quantity
is a point for which R(x)=C(x).
40
30
R( x)
C( x)
2
x
20
10x = 2 x
2
6
The minimum break even point is x=2.
10
0
2
4
6
8
NOTE: The business is profita

Solutions for exercises on page 583 25.
S( x)
a)
1000
b)
x
800 e
800 e
1000
c)
d)
1000
0
200
x
800 e
= 500 solve x
ln( 8 )
0.47years
ln( 5 )
No, see the graph below.
The limit is 1000. This is clear
from the graph on the right.
3
1 10
800
1000 800 e
x
600

Algebra and Geometry
System of equations
Example 1. The Gonzalez Company makes ROM chips and RAM chips for
computers. Both require time on two assembly lines. Each unit of ROM chips
requires 1 hr on line A and 2 hr on line B. Each unit of RAM requires 3 h

Trigonometry
In a right triangle we have:
sin
cos
b
c
tan
c
a
c
a
b
b
a
Also remember the Pythagorean theorem:
2
a
2
b
2
c
The following formulas work in ANY triangle:
Law of sines:
Here
b
a
sin
sin
is the angle opposite to a, and
Law of cosines:
2
c
Here

Algebra and Geometry Vector algebra exercises
1. Determine the horizontal and vertical components of the force vector:
a) (3.6 kN, 1.8 kN)
b) (9.1 kN, -3.0 kN)
2. Determine the resultant force. (114 N, direction angle 21 degrees)
3. Determine the tension

Algebra and Geometry Vector algebra
Physical quantities can be divided into two categories: scalars and vectors.
Scalar quantities have only magnitude: mass, time, energy etc. Vectors
have both magnitude and direction: velocity, acceleration, force etc. S

Glo-Bus Quiz 2 Formulas:
ROE = Profit / Average Equity of current year and past year (in my hometown,
RoE is just profit/equity)
EPS = Earnings/ Common Shares
Free Cash Flow = Net income + depreciation dividends
Times Interest Earned = Operating Profit of

Japan has evolved over the last half century to become one of the worlds most technologically
advanced economies. And Japan offers lots of investment and market opportunities to
international organizations. However, due to its uniqueness in culture or mar

The Equal Pay Act of 1963 (EPA), which is part of the Fair Labor Standards Act
of 1938, is administered and enforced by the Equal Employment Opportunity
Commission (EEOC), prohibits sex-based wage discrimination between men and
women in the same establish

What was the root cause of the housing crisis?
With the economic growth of the U.S., the housing price also increased
dramatically before the housing crisis. People started to borrow the money from
the bank to bought the houses which they couldnt afford a

1. Do pharmaceutical companies have a responsibility to distribute drugs for free or at low
cost in developing countries? What are the main arguments for and against such an
approach? What are the advantages and disadvantages of giving drugs for free vers

What is the root cause of Brexit?
The first point is about immigration. Many citizens believe that Brexit can reduce the number of
immigrants and refugees coming to Europe. However, as mentioned in the video, for the
majority of the leaver voters, the con

Good:
Vision to invite millions to reduce their environment impact and carbon footprint
with eco-chic lifestyle products.
Stylish kit
To measure and share its environmental and economic performance, BlueAvocado
publishes an annual sustainability report, f

Equal Pay Act of 1963 (EPA)
History of EPA
World War II, large number of American women took jobs.
In 1942, the National War Labor Board encouraged industry leaders to make adjustments.
In 1950, Rep. Katharine St. George, equal pay for equal work.
In 1963

Solutions to exercises on page 95.
7.
AB is 2x2
BA is 2x2
10.
AB is 4x6
BA is not defined
11.
AB is not defined
BA is 3x2
13. "To find the product matrix AB, the number of columns of A must be the same as the
number of rows of B."
14.
"The product matrix

Solutions for problems on page 16:
60.
a) We want to find the sales line
y = mx
b
Given
5
1.5 10
27000 = m 2
b
63000 = m 5
b
5
Find( m b )
1 10
12000x 3000
12000
4
5 10
3000
Answer:
y = 12000x
3000
0
2
4
6
8
10
x
b)
100000 = 12000x
3000 solve x
97
12
8.08

Entrance exam to technical curriculums 05.06.2000
Entrance exam to technical curriculums: calculation tasks (part 3):
ANSWER EACH QUESTION IN THE SEPARATE RESULT SHEET IN THE CORRECT PLACE
1. One corner of a triangle has a 60 angle and the length of the t

Entrance examination June 2001 1/4
1.
a) A figure has been omitted inside
the adjoining frame. On your answer
sheet, render the numeral of the
figure which logically fills the
empty space (one of the figures 1 to
9).
1
In problems b and c, a different rul

B page 1(7)
Instructions
7.6.2002
ENTRANCE EXAMINATION FOR THE TECHNICAL CURRICULUM
Mathematics, logical deduction and physics/chemistry
For problems that include calculations the result of the calculation must be written in the
space provided on the answ

B page 1(6)
PROBLEMS
7.6.2004
ENTRANCE EXAM FOR ENGINEERING CURRICULUM
The duration of the examination is 2 h 15 min.
Mathematics, logical deduction and physics/chemistry
For each problem, write the answer in the space provided on the answer sheet, and in

PROBLEMS
6.6.2005
ENTRANCE EXAM FOR ENGINEERING CURRICULUM
The duration of the examination is 2 h 15 min.
Mathematics, logical deduction and physics/chemistry
There are nine problems to solve, each worth 3 points. For each problem, write the
answer in the

B Page 1 (4)
PROBLEMS
5.6.2006
ENRANCE EXAM FOR ENGINEERING CURRICULUM
INSTRUCTIONS
The duration of the examination is 2 h 45 min
Part 1 (Reading comprehension test)
There are 10 statements to be marked false or true. The maximum score is 5
points.
Part 2

Algebra and Geometry Annuities
Example 1. Suppose we deposit $1500 to a single account at the end of each
year for 3 years. How much money do we have after 3 years, if the interest
rate is 5, 0 %?
Solution. The amount of money after 1 year is simply
1500.

Algebra and Geometry Compound interest
Example 1. Suppose 1000 is deposited for 6 years in an account paying
5.0 % interest per year compounded annually. How much money is in the
account after 6 years?
Remark. The term compounded annually means that the i

Algebra and Geometry Exponential
functions and the logarithm
Denition. Let C and a be any numbers so that a > 0 and C = 0. Then
the function
f (x) = C ax
is called an exponential function. Here the number a is called the base for the
exponential function.

Algebra and Geometry
Finance mathematics problems
1. $10000 is deposited to an account paying 6 % annual interest rate
compounded annually. How much money is in the account after
a) 1 year b) 8 years?
2. $6500 is deposited to an account paying 12 % annual

Koreans often arrange oneonone business meetings. Nevertheless, this one
Koreanbusinesspersonwillhavetosellyourproposaltohisorherentirecompany.
Itisimportantthatyouestablishastrongrelationshipwithyourcontactperson.
Whiletheyoungergenerationisopentoglobali