◎Problems 1-10. Six points each. Choose the best answer from (A) – (D) .
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1) Suppose 0.132 ＝
(A) 112
a
, and (a，b)＝1, find a＋b.
b
(B) 113
(C) 1121
(D) 1122
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2) Suppose log34＝log 1 a, find a.
3
(A)
1
4
(B) －
1
4
(C) 2
(D)
1
2
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3) Given that a and b are numbers, and that
4a 3b7
can be written as a finite decimal, what might
180
a＋b be?
(A) 9
(B) 11
(C) 13
(D) 15
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4) Given that a and b are integers where a＜b. If ab－a＋3b＝0, what is the maximum value of b?
(A) 2
(B) 4
(C) 5
(D) 6
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1
5) How many sets of positive integral solutions are there for x＋y＋z＝5?
(A) 6
(B) 7
(C) 10
(D) 15
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6)
6 40
) is written as a decimal 0.……, which number below is the first non-zero number after the
35
decimal point? (log2≒0.3010，log3≒0.4771，log7≒0.8451)
If (
(A) 6
(B) 3
(C) 2
(D) 1
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7) Compute log23．log549．log325．log74.
(A) 8
(B) 5
(C) 4
(D) 3
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2
8) The figure below shows the graph of function for f(x)＝ax ＋bx＋c. Among the four numbers a, b, c,
and a－b＋c, how many of them are negative numbers?
(A) 1
(B) 2
(C) 3
(D) 4
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2
9) Given that a＜1000, and (a，30)＝1, how many such a's are there that satisfy the conditions above?
(A) 266
(B) 278
(C) 299
(D) 366
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10) The bacteria are grown in a lab. Suppose on each day, the number of bacteria will be a times the
number of bacteria on the previous day. According to the growth rate, 2 days later, the number of
6
7
bacteria is 2×10 ; and 5 days later, the number of bacteria is 5.4×10 . If n days after the
8
experiment starts, the number of bacteria is 4.86×10 , find n.
(A) 9
(B) 8
(C) 7
(D) 6
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◎Problems 11-15. Eight points each. Choose the best answer from (A) – (D) .
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a
 a2 a 3 a 4
＝ ＝ ＝L＝ 60 ＝ 2

11) Suppose  a1 a2 a 3
, find a6.
a59
60
 a1 ＋ a2 ＋ a 3 ＋L＋ a 60 ＝ 2 －1

(A) 64
(B) 32
(C) 30
(D) 24
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4
3
2
12) Suppose a, b, and c are real numbers. Given that the remainder is 3 when x ＋ax ＋bx ＋c is
2
divided by x＋1, and the remainder is 2x＋1 when it is divided by x ＋1, find a－b＋c.
(A) －2
(B) 0
(C) 2
(D) 3
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3
13)
If f(x)＝ax＋b, 1 ≤ f(1) ≤ 3, and 1 ≤ f(2) ≤ 2, what is the maximum value of f(3)?
(A) 3
(B) 5
(C) 7
(D) 8
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14) Which of the two graphs of functions are not symmetric to line y＝x?
(B) y ＝ 2－x 、 y ＝－ log 2 x
1
(D) y ＝ ( ) x 、 y ＝ log 1 x
3
3
(A) y ＝ 2 x 、 y ＝ log 2 x
(C) y ＝ 2 x 、 y ＝－ 2 x
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100
15) What is the remainder when x
(A) 100x－99
2
＋1 is divided by (x－1) ?
(B) 100x－98
(C) 10x－8
4
(D) 2