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國立嘉義大學 102 學年度基礎學科學力競賽試題卷:
科目: 經濟數學
1. Each unit of a certain commodity costs p = 47x + 12 cents when x units of
the commodity are produced. If all units are sold at this price, express the
revenue derived from the sales as a function of x.
A)46x + 12 cents
C) 48x + 12 cents
D) x(47x + 12) cents
B) 47 x 2  12 cents
題型:選擇題(共 25 題)
0 is
A)
配分:100%
y = 5x + 1
B)
y = 5x – 1
f ( x) 
f (t ) 
x 1
x3
A)all real numbers x except x = 1, x = –1, and x = –3
B)all real numbers x
C)all real numbers x except x = –3
D)all real numbers x except x = 1 and x = 4
f ( x) 
2
8. What is the rate of change of
9
19
A) 4
B) 4
C) 16
x 2  3x  2
lim
x 1
x2  1
B) 6
C)
3
2
A)
D)
3
1
4
10. Find f ( x)
A) f ( x)  
C) 2
D)
–2
B) f ( x)  
5. List all values of x for which f (x) is not continuous.
2x  1
f ( x)  2
x x .

A)
1
2
D) 0.0006
7t  5
t  2 with respect to t when t = 2?
17
D) 4
selling 4 per day.
C) R (4)  4.52;
they'll sell about 5 refrigerators if they run 4 ads per day.
D) R (4)  203.36; they'll sell about 203 refrigerators if they run 4 ads per day.
4. Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is
+ or – .
x4
y = 10x + 1
ad when they're running 4 ads.
B) R (4)  203.36; the cost of refrigerators will be rising by $203.36 if they're
A) Does not exist
x 2
x4
1

4
B)
D)
9. An appliance store manager estimates that for x television ads run per day,
R( x)  0.01x3  x 2  3x  200 refrigerators will be sold per month. Find
R (4) and interpret what it tells us about sales.
A) R (4)  4.52;
sales will be increasing at about 5 refrigerators per month per
3. Find the indicated limit if it exists.
lim
y = 10x – 1
x
5
2x  1
decrease approximately by as x
7. How much will the function
decreases from 3 to 2.7?
A) 0.006
B) 0.06
C) 0.6
2. Determine the domain of the given function.
C)
B) –1
C)
None
f ( x) 
if
15
16 x
3
3x
15
8 x3 3x


72
x5
72
x5
1
3x

3
 7
x2
C)
D)
f ( x)  
5
3

72
x5
72 x 3x
3
3
f ( x)   3
 3
8 x 3x x
11. The cost of producing x units of a certain commodity is C ( x)  3x2  5 x  5 dollars.
If the price is p(x) = (41 – x) dollars per unit, determine the level of production that
maximizes profit.
A) x = 3
B) x = 1
C) x = 5
D) x = 2
D) 0 and –1
2
5
6. An equation for the tangent line to the curve y  (7 x  x  1) at the point where x =
1
3
2
12. Find the absolute minimum of the function f ( x)  x  3x on the interval 1  x  5.
A) 5
–4
B)
–1
C)
D) 0
f   x   xe36 x ;
2
3
2
13. Determine where the graph of f ( x)  x  6 x  8x  4
A) For x > 2
For x < –2
B)
C) For x > –2
is concave down.
D) For x < 2
14. Determine the critical points of the given function and classify each critical point as
a relative maximum, a relative minimum, or neither.
f ( x)  3 x 4  8 x 3  6 x 2  3
A)
B)
(0, 2) neither; (1, 3) relative minimum
(0, 2) relative minimum; (1, 3) relative maximum
C)
D)
(0, 3) relative minimum; (1, 4) neither
(0, 2) relative minimum; (1, 4) neither
15. Locate all inflection points of f ( x)  x 4  6 x3  24 x 2  26 .
A) (1, 9) and (–4, –486)
B)
(1, 9)
C)
None
D) (0, 26)
16. Solve for x: a 7 x 1  b
 ln b 
 1

 ln a 
C)
1  ln b 
x  1  1 

7  ln a 
B)
x
D)
ln b
7 ln a
2/9
dx
C
2
1
y   e36  x
2
3 1 36 x2
 e
2 2
2
1
y  1  e36 x
2
D)
A) u = x3
B)
u
x3
2x
C)
u  2x
D)
u  ln x3
21. Water flows into a tank at the rate of 2t  5 ft3/min. If the tank is empty when t = 0, how much water does
it contain 6 minutes later? Express the answer to two decimal places.
A) 0.63 ft3
B) 19.64 ft3
C) 32.08 ft3
D) 24.74 ft3
x 1
 32 + 5 x
B)
2
2
5
C) 0,
2
5
D) 0, –
2
5
23. How quickly will $700 grow to $2,000 if interest is 8% compounded quarterly? Round your answer to two
decimal places, if necessary.
A) in 13.00 years
B) in 13.15 years
C) in 13.20 years
D) in 13.25 years
3
24. Find the derivative of ln  ln x 4   .


3
x ln x
B)
12
x ln x
C)
12
x  ln x
D)
12
ln(ln x)
.
11/9
9 x

  9
11  9

y
C)
ln x3
 2 x dx
A)
C)
81  x

  9
11  9

D)
x2
 9x  C
18
11/9
B)
1 1 36 x 2
 e
2 2
20. Specify the substitution you would choose to evaluate the integrals.
A) 0
11/9
C
y
1
 
9
per minute. How far does the object travel from the end of minute 2 to the end of minute
3?
A) 37 meters
B) 78 meters
C) 157 meters
D) 77 meters
x

A)   9 
9

B)
1  ln b 
1 

7  ln a 
2
17. An object is moving so that its velocity after t minutes is v(t )  1  8t  9t meters
x

  9  9 
18. Evaluate
A)
(–6, 1)
22. Find all real numbers x that satisfy the given equation.
7
A)
19. The slope f (x) at each point (x, y) on a curve y = f (x) is given, along with a
particular point (a, b) on the curve. Use this information to find f (x).
C
25. The graph of x 3e 3 has
A) a relative maximum at x = 0
B) a relative minimum at x = 0
C)
D)
a point of inflection at x = 0
nothing significant at x = 0
國立嘉義大學 102 學年度基礎學科學力競賽試題卷:
科目: 經濟數學
題型:選擇題(共 25 題)
配分:100%
18. C
1.
D
19. C
2.
C
20. D
3.
A
21. B
4.
B
22. D
5.
D
23. D
6.
B
24.
7.
A
25. C
8.
C
9.
A
10. B
11.
C
12. B
13. D
14. C
15. A
16. B
17. B
3
A