G.S. (HKMO Classified Questions by topics) Created by Mr.

Francis Hung Last updated: 2017-05-02

1991 HI2 2001 FI3.3
某科學家發現某樣本中細菌的數量每小時增加一倍。於下午四時，他發現 若 sin 30 + sin2 30 +  + sin7 30 = 1 – cosR 45，求 R 的值。
細菌的數量為 3.2  108，若於同日正午該樣本中細菌的數量為 N  107，求 N。 If sin 30 + sin2 30 +  + sin7 30 = 1 – cosR 45, find the value of R.
A scientist found that the population of a bacteria culture doubled every hour. At
2002 FI2.2
4:00 pm, he found that the number of bacteria was 3.2108. If the number of
bacteria in that culture at noon on the same day was N107, find N. 99 99 99 2 99 3
已知 99Q = (1 + + + +)，求 Q 的值。
1994 HI1 100 100 100 2 100 3
1 1 1 99 99 99 2 99 3
設 log3 p  1      至無窮項，求 p。 Given that 99Q = (1 + + + +), find the value of Q.
2 4 8 100 100 100 2 100 3
1 1 1 2005 FG2.4
Suppose log3 p  1      to an infinite number of terms. Find p.
2 4 8 1 2 3 4 10
設 d        10 ，求 d 的值。
1997 FG1.3 2 4 8 16 2
3 c
 1 3 c
 1 1 2 3 4 10
若 1 + 3 + 32 +  +38 = ，求 c。If 1 + 3 + 32 +  +38 = , find c. Let d        10 , find the value of d.
2 2 2 4 8 16 2
1998 HI2 2006 HG3
已知 8、a、b 形成一等差級數，且 a、b、36 形成一等比級數。若 a 和 b 皆為正數， 3
求 a、b 的和。 已知 0  θ  90 及 1  sin θ  sin 2
θ    。若 y  tan θ ，求 y 的值。
2
Given that 8, a, b form an A.P. and a, b, 36 form a G.P. If a and b are both positive 3
numbers, find the sum of a and b. Given that 0 <  < 90 and 1 + sin  + sin2  + ..... = . If y = tan , find the
1998 FG4.3 2
value of y.
圖形 S0，S1，S2，用以下方法構成：把綫段[0, 1]的中間三分之一取去，
2007 FG2.1
得到 S0，把 S0 的兩條組成綫段，每段的中間三分之一取去，得到 S1，把
若 R = 12 + 222 + 323 +  + 10210，求 R 的值。
S1 的四條組成綫段，每段的中間三分之一取去，得到 S2，S3、S4 等用類
If R = 12 + 222 + 323 +  + 10210, find the value of R.
似方法獲得。求在構成 S5 的過程中取去的綫段的總長度 c(答案以分數表示)。 2009 FI1.3
A sequence of figures S0, S1, S2,  are constructed as follows. S0 is obtained by
removing the middle third of [0,1] interval; S1 by removing the middle third of each of 設 F = 1 + 2 + 22 + 23 +  + 2120 及 T =
log1  F 
，求 T 的值。
the two intervals in S0; S2 by removing the middle third of each of the four intervals in log 2
S1; S3, S4,  are obtained similarly. Find the total length c of the intervals removed in log1  F 
the construction of S5 (Give your answer in fraction). Let F = 1 + 2 + 22 + 23 +  + 2120 and T = , find the value of T.
|———————( )———————| S0 log 2
1 2 2010 FG2.1
0 1 若 p = 2 – 22 – 23 – 24 –  – 29 – 210 + 211，求 p 的值。
3 3
|——( )——( )——( )——| S1 If p = 2 – 22 – 23 – 24 –  – 29 – 210 + 211, find the value of p.
1 2 1 2 7 8
0 1
9 9 3 3 9 9
|–( )–( )–( ) –( )–( )–( )–( )–| S2

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G.S. (HKMO Classified Questions by topics) Created by Mr. Francis Hung Last updated: 2017-05-02
2012 HI5
1 1 1
已知 log4 N = 1      ，求 N 的值。
3 9 27
1 1 1
Given that log4 N = 1      , find the value of N.
3 9 27
2015 FI1.4
若 n 為正整數及 f (n) = 2n + 2n–1 + 2n–2 +  + 22 + 21 + 1，求 = f ()的最值。
If n is a positive integer and f (n) = 2n + 2n–1 + 2n–2 +  + 22 + 21 + 1,
determine the value of  = f (10).
2017 FI3.4
若 f(x) = 20 + 21 + 22 +  + 2x–2 + 2x–1，求 d = f(10) 的值。
If f(x) = 20 + 21 + 22 +  + 2x–2 + 2x–1, determine the value of d = f(10).

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G.S. (HKMO Classified Questions by topics) Created by Mr. Francis Hung Last updated: 2017-05-02
Answers
1998 FG4.3
1991 HI2 1994 HI1 1997 FG1.4 1998 HI2 665
2 9 9 40
729
2005 FG2.4 2006 HG3
2001 FI3.3 2002 FI2.2 509 2007 FG2.1
2
14 1 18434
256 4
2009 FI1.3 2010 FG2.1 2012 HI5 2015 FI1.4 2017 FI3.4
11 6 8 2047 1023

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