Question 1 math - Math for business | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố HCM

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Môn: Math for business

Trường: Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

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Question 1: A firm’s short-run production function is given by
Q=L3e-0.02L
Find the value of L which maximizes the average product of labor.
A/ 100
B/ 200
C/ 50
D/ 150
E/ 250
Question 2: Consider the supply equation
P=7+2Q2
By evaluating the elasticity of supply at the point P = 105, estimate the percentage
increase in supply when price rises by 7%
A/ 3%
B/ 3.75%
C/ 3.25%
D/ 3.5%
E/ 4%
Question 3: A proposed investment costs $130,000 today. The expected revenue
flow is $40,000 at the end of year 1, and $140,000 at the end of year 2. Find the
interval rate of return, correct to one decimal place.
A/ 20.3%
B/ 20.0%
C/ 18.4%
D/ 17.8%
E/ 19.9%
Question 4: A principal of %70,000 is invested at 6% interest for four years. Find
the difference in the future value if the interest compounded quarterly compared to
continuous compounding. Round your answer to two.
A/ $158.45
B/ $614.05
C/ $620.43
D/ $256.65
E/ $469.93
Question 5: Find the value of k so that the equation
x2-10x+2k=8x-k
Has exactly one root.
A/ 1
B/ 3
C/ 27
D/ 9
E/ 81
Question 6: Demand and supply in a market are described by the equations
Qd=66-3P
Qs= -4+2P
How would a per unit sales tax t affect equilibrium price?
A/ Increase of tax25
B/ Decrease of tax25
C/ Increase of tax65
D/ Decrease of tax65
E/ Increase of tax35
Question 7: Simplify
x2x+1+ 2xx2-1
A/ 2x(x + 1)
B/ None of these
C/ 2x(x – 1)
D/ x(x+1)2
E/ x(x-1)2
Question 8: The Ho Chi Minh City People’s Committee has a package to aid low-
income homeowners in urban areas during Covid-19 outbreak. This package
allows certain qualified homeowners to obtain low-interest home improvements
loans. Each loan is processed through a commercial bank. The bank makes home
improvement loans at an annual rate of % compounded monthly. However, the941
Committee subsidizes the bank so that the loan to the homeowner is at the annual
rate of 4% compounded monthly. If the monthly payment at the 4% rate is x VND
(x VND is the homeowner’s monthly payment) and the monthly payment at the
941% rate is y VND (y VND is the monthly payment the bank must receive), then
the government makes up the difference y – x to the bank each month. Form a
practical point of view, the Committee does not want to bother with monthly
payments. Instead, at the beginning of the loan, the government pays the present
value of all such monthly differences, at an annual rate of % compounded941
monthly. If a qualified homeowner takes out a loan for 118,000,000 VND for five
years, determine the Committee’s payment to the bank at the beginning of loan.
A/ 2,173,150
B/ 17,440,680
C/ 2,906,784
D/ 37,812,159.81
E/ 13,921,446.9
Question 9: Given that the cubic function, f(x) = has ax3+ax2+bx+c
stationary point at (2,5), which of the following statements must be true?
A/ b + 2c = 8
B/ b – c = 5
C/ 2b + c = 6
D/ 2b – 3c = 12
E/ b + c = 9
Question 10: A person wishes to save a regular amount at the beginning of each
month in order to buy a car in 18 months’ time. An account offers a return of 4.8%
compounded monthly. Work out the monthly savings if the total amount saved at
the end of 18 months is $18,000. Round your answer to two decimal places.
A/ 966.43
B/ 962.58
C/ 622.01
D/ 651.86
E/ 708.82
Question 11: the table below gives the annual rate of inflation during a five-year
period.
2000 2001 2002 2003 2004
Annual rate of inflation 1.8% 2.1
%
2.9% 2.4% 2.7%
If a nominal house price at the end of 2000 was $10.8 million, find the real house
price adjusted to prices prevailing at the end of the year 2003. Round your answer
to three significant figures
A/ $10.0 million
B/ $11.8 million
C/ $11.6 million
D/ $10.9 million
E/ $9.9 million
Question 11: During 2005 the price of a good increased by 8%. In the sales on
January 1 2006, all items are reduced by 25%. If the sale price of the good is
st
$688.50, find the original price at the beginning of 2005.
A/ $558
B/ $925
C/ $935
D/ $2,395
E/ $850
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Question 1: A firm’s short-run production function is given by Q=L3e-0.02L
Find the value of L which maximizes the average product of labor. A/ 100 B/ 200 C/ 50 D/ 150 E/ 250
Question 2: Consider the supply equation P=7+2Q2
By evaluating the elasticity of supply at the point P = 105, estimate the percentage
increase in supply when price rises by 7% A/ 3% B/ 3.75% C/ 3.25% D/ 3.5% E/ 4%
Question 3: A proposed investment costs $130,000 today. The expected revenue
flow is $40,000 at the end of year 1, and $140,000 at the end of year 2. Find the
interval rate of return, correct to one decimal place. A/ 20.3% B/ 20.0% C/ 18.4% D/ 17.8% E/ 19.9%
Question 4: A principal of %70,000 is invested at 6% interest for four years. Find
the difference in the future value if the interest compounded quarterly compared to
continuous compounding. Round your answer to two. A/ $158.45 B/ $614.05 C/ $620.43 D/ $256.65 E/ $469.93
Question 5: Find the value of k so that the equation x2-10x+2k=8x-k Has exactly one root. A/ 1 B/ 3 C/ 27 D/ 9 E/ 81
Question 6: Demand and supply in a market are described by the equations Qd=66-3P Qs= -4+2P
How would a per unit sales tax t affect equilibrium price? A/ Increase 25 of tax B/ Decrease 25 of tax C/ Increase 65 of tax D/ Decrease 65 of tax E/ Increase 35 of tax Question 7: Simplify x2x+1+ 2xx2-1 A/ 2x(x + 1) B/ None of these C/ 2x(x – 1) D/ x(x+1)2 E/ x(x-1)2
Question 8: The Ho Chi Minh City People’s Committee has a package to aid low-
income homeowners in urban areas during Covid-19 outbreak. This package
allows certain qualified homeowners to obtain low-interest home improvements
loans. Each loan is processed through a commercial bank. The bank makes home
improvement loans at an annual rate of 941% compounded monthly. However, the
Committee subsidizes the bank so that the loan to the homeowner is at the annual
rate of 4% compounded monthly. If the monthly payment at the 4% rate is x VND
(x VND is the homeowner’s monthly payment) and the monthly payment at the
941% rate is y VND (y VND is the monthly payment the bank must receive), then
the government makes up the difference y – x to the bank each month. Form a
practical point of view, the Committee does not want to bother with monthly
payments. Instead, at the beginning of the loan, the government pays the present
value of all such monthly differences, at an annual rate of 941% compounded
monthly. If a qualified homeowner takes out a loan for 118,000,000 VND for five
years, determine the Committee’s payment to the bank at the beginning of loan. A/ 2,173,150 B/ 17,440,680 C/ 2,906,784 D/ 37,812,159.81 E/ 13,921,446.9
Question 9: Given that the cubic function, f(x) = x3+ax2+bx+c has a
stationary point at (2,5), which of the following statements must be true? A/ b + 2c = 8 B/ b – c = 5 C/ 2b + c = 6 D/ 2b – 3c = 12 E/ b + c = 9
Question 10: A person wishes to save a regular amount at the beginning of each
month in order to buy a car in 18 months’ time. An account offers a return of 4.8%
compounded monthly. Work out the monthly savings if the total amount saved at
the end of 18 months is $18,000. Round your answer to two decimal places. A/ 966.43 B/ 962.58 C/ 622.01 D/ 651.86 E/ 708.82
Question 11: the table below gives the annual rate of inflation during a five-year period. 2000 2001 2002 2003 2004
Annual rate of inflation 1.8% 2.1 2.9% 2.4% 2.7% %
If a nominal house price at the end of 2000 was $10.8 million, find the real house
price adjusted to prices prevailing at the end of the year 2003. Round your answer to three significant figures A/ $10.0 million B/ $11.8 million C/ $11.6 million D/ $10.9 million E/ $9.9 million
Question 11: During 2005 the price of a good increased by 8%. In the sales on
January 1st 2006, all items are reduced by 25%. If the sale price of the good is
$688.50, find the original price at the beginning of 2005. A/ $558 B/ $925 C/ $935 D/ $2,395 E/ $850