亞洲 國際 數學 奧林 匹克 聯合 會
ASIA INTERNATIONAL MATHEMATICAL OLYMPIAD UNION
2022 亞洲國際數學奧林匹克公開賽初賽
2022 Asia International Mathematical Olympiad Open Trial
小二組 Grade 2
時限：90 分鐘
Time allowed:
90
試題
Question Paper
本試題不可取走。
THIS QUESTION PAPER CANNOT BE TAKEN AWAY.
未得監考官同意，切勿翻閱試題，否則參賽者將有可能被取消資格。
DO NOT turn over this Question Paper without approval of the examiner.
Otherwise, contestant may be DISQUALIFIED.
minutes
請將答案寫在 答題紙 上。
All answers should be written on the ANSWER SHEET.
Section A – each question carries 4 marks
甲部：每題 4 分
1)
76  81  24  19  50  ?
A) 140
2)
D) 250
E) 340
B) 400
C) 290
D) 390
E) 490
C) 5
D) 192
E) 2
6  5  5  4  4  3  3  2  2 1  ?
A) 18
4)
C) 240
345  280  145  480  ?
A) 300
3)
B) 150
B) 0
小貝有 20 本書，而小克比小貝多 10 本書。那麽小克要給小貝多少本書，他們才會
擁有同樣多的書？
小贝有 20 本书，而小克比小贝多 10 本书。那么小克要给小贝多少本书，他们才会
拥有同样多的书？
Beck has 20 books. Chris has 10 more books than Beck. How many books does Chris
have to give Beck, so that they will have the same number of books?
A) 10
5)
B) 5
C) 20
D) 15
E) 30
每盒月餅有 5 個月餅，小艾買了 10 盒，共有多少個月餅？
每盒月饼有 5 个月饼，小艾买了 10 盒，共有多少个月饼？
There are 5 mooncakes in each box. Aiden bought 10 boxes. How many mooncakes are
there?
A) 10
B) 20
C) 30
D) 40
E) 50
請以最簡形式填寫答案。若計算結果是分數，請化至最簡，並確保為真分數或帶分數，或將計算結果寫成小數。
答案可以根式表示，唯該根式必須是最簡形式。除特別註明外，毋需填寫單位。錯誤單位將不給予任何分數。
Write down the answer in the simplest form. If the calculation result is a fraction, please write down the answer as a proper or mixed fraction,
decimal figure is also accepted. You may use square root to represent the answer which is in the simplest form.
Unless otherwise stated, no need to write down any unit. Marks will NOT be given for incorrect unit.
請將答案寫在 答題紙 上。
All answers should be written on the ANSWER SHEET.
6)
小童電影票一張 5 元，成人電影票一張 8 元。媽媽帶著兩個兒子去看電影，給了一
張 20 元的紙幣，問應該找回多少元？
小童电影票一张 5 元，成人电影票一张 8 元。妈妈带着两个儿子去看电影，给了一
张 20 元的纸币，问应该找回多少元？
A child theater ticket is 5 dollars, and an adult theater ticket is 8 dollars. A mother took
her two sons to the theater and gave a 20-dollar notes. How much change would mom get
back in dollars?
A) 1
B) 2
C) 3
D) 4
E) 5
(C) 2020 Asia International Mathematical Olympiad Union (AIMO Union) http://aimo.world/
All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means,
electronic mechanical, photocopying, recording or otherwise, without the prior permission of Asia International Mathematical Olympiad Union.
請將答案寫在 答題紙 上。
All answers should be written on the ANSWER SHEET.
7)
小迪把 10 根繩子結在一起成爲一根繩子，那麽他合共需要打多少個結？
小迪把 10 根绳子结在一起成为一根绳子，那么他合共需要打多少个结？
Dylan wants to tie 10 ropes together to form one rope. How many knots does he need to
tie?
A) 6
8)
B) 7
C) 8
D) 9
E) 10
小艾從上午 x 時 y 分開始做功課，做完功課時是下午 2 時 32 分。已知小艾一共用了
156 分鐘做功課，求 x  y 的值。
小艾从上午 x 时 y 分开始做功课，做完功课时是下午 2 时 32 分。已知小艾一共用了
156 分钟做功课，求 x  y 的值。
Amy used a total of 156 minutes to finish her homework. If she began at x : y a.m. and
finished at 2:32 p.m. Find the value of x  y .
A) 156
B) 1156
C) 67
D) 38
E) 34
~ End of section A ~
~ 甲部完 ~
請以最簡形式填寫答案。若計算結果是分數，請化至最簡，並確保為真分數或帶分數，或將計算結果寫成小數。
答案可以根式表示，唯該根式必須是最簡形式。除特別註明外，毋需填寫單位。錯誤單位將不給予任何分數。
Write down the answer in the simplest form. If the calculation result is a fraction, please write down the answer as a proper or mixed fraction,
decimal figure is also accepted. You may use square root to represent the answer which is in the simplest form.
Unless otherwise stated, no need to write down any unit. Marks will NOT be given for incorrect unit.
請將答案寫在 答題紙 上。
All answers should be written on the ANSWER SHEET.
Section B – each question carries 5 marks
乙部：每題 5 分
9)
123  213  312  132  231  321  ?
A) 0
10)
B) 10
C) 100
D) 1000
E) 666
C) 134730
D) 1042570
E) 1
C) 16
D) 1
E) 12
134652  78  9  0  ?
A) 0
B) 135354
11) 12  4  4  3  6  16  4  ?
A) 0
B) 13
12) 在以下算式謎中，兩個空格要填上兩個不同的數字，求這兩個數字的和。
在以下算式谜中，两个空格要填上两个不同的数字，求这两个数字的和。
In the following cryptarithm, the two boxes are to be filled by two different digits, what is
the sum of those two digits?
5
–
4 = 1 4
A) 9
B) 10
C) 11
D) 12
E) 13
13) 兩數之和為 65，若該兩數之差為 11，求該兩個數中較小的一個。
两数之和为 65，若该两数之差为 11，求该两个数中较小的一个。
The sum of two numbers is 65 and the difference is 11, find the smaller one of the two
numbers.
A) 27
B) 26
C) 29
D) 28
E) 25
14) 把 14 分解成兩個正整數的和，有多少種方法？（相同的數但不同次序視為同一種方
法）
把 14 分解成两个正整数的和，有多少种方法？ （相同的数但不同次序视为同一种
方法）
How many ways are there to rewrite 14 into a sum of two positive integers? (Same
numbers but different orders are considered the same way)
A) 5
B) 6
C) 7
D) 8
E) 9
(C) 2020 Asia International Mathematical Olympiad Union (AIMO Union) http://aimo.world/
All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means,
electronic mechanical, photocopying, recording or otherwise, without the prior permission of Asia International Mathematical Olympiad Union.
請將答案寫在 答題紙 上。
All answers should be written on the ANSWER SHEET.
15) 已知圖 15 不是一筆畫，最少要加上多少條線才能令該圖變成一筆畫？
已知图 15 不是一笔画，最少要加上多少条线才能令该图变成一笔画？
Figure 15 cannot be drawn in one stroke without drawing a line twice. At least how many
lines must be added so that the figure can be drawn in one stroke without drawing a line
twice?
圖 15 图 15 Figure 15
A) 1
B) 2
C) 3
D) 4
E) 5
16) 圖 16.1 中的正方形的面積為 1 平方厘米，問圖 16.2 的面積是多少平方厘米？
图 16.1 中的正方形的面积为 1 平方厘米，问图 16.2 的面积是多少平方厘米？
The area of the square in Figure 16.1 is 1 square centimetre, what is the area of Figure
16.2 in square centimetre?
A) 1
圖 16.1
圖 16.2
图 16.1
Figure 16.1
图 16.2
Figure 16.2
B) 2
C) 3
D) 4
E) 5
~ End of section B ~
~ 乙部完 ~
請以最簡形式填寫答案。若計算結果是分數，請化至最簡，並確保為真分數或帶分數，或將計算結果寫成小數。
答案可以根式表示，唯該根式必須是最簡形式。除特別註明外，毋需填寫單位。錯誤單位將不給予任何分數。
Write down the answer in the simplest form. If the calculation result is a fraction, please write down the answer as a proper or mixed fraction,
decimal figure is also accepted. You may use square root to represent the answer which is in the simplest form.
Unless otherwise stated, no need to write down any unit. Marks will NOT be given for incorrect unit.
請將答案寫在 答題紙 上。
All answers should be written on the ANSWER SHEET.
Section C – each question carries 7 marks
丙部：每題 7 分
17) 216  4  ?
A) 50
B) 44
C) 52
D) 54
E) 48
18) 有一個二人遊戲，規則如下︰「有 22 枝火柴，兩人輪流去拿，若每人每次只許拿 1
至 3 枝火柴，不許不拿，誰拿最後一枝誰勝。」若小貝先拿，爲了確保勝出，她應
該先拿多少枝火柴？
有一个二人游戏，规则如下︰「有 22 枝火柴，两人轮流去拿，若每人每次只许拿 1
至 3 枝火柴，不许不拿，谁拿最后一枝谁胜。」若小贝先拿，为了确保胜出，她应
该先拿多少枝火柴？
There is a two-player game. Here are the rules, ‘There are 22 matches. Two people take
matches out one after another. In each turn, each player must take 1 to 3 matches out, and
cannot choose not to take any matches out. The one who takes the last match out wins the
game.’ If Bella takes matches out first, how many matches should she take in the first
turn so that she can make sure she will win the game?
A) 0
B) 1
C) 2
D) 3
E) 4
19) 小艾和媽媽去 AIMO 樂園玩，AIMO 樂園裏有 5 位公主。小艾決定要和每個公主拍
一張合照，並且替每兩位公主們拍一張合照。小艾會得到多少張照片？
小艾和妈妈去 AIMO 乐园玩，AIMO 乐园里有 5 位公主。小艾决定要和每个公主拍
一张合照，并且替每两位公主们拍一张合照。小艾会得到多少张照片？
Amy goes to the AIMO land with her mother. There are 5 princesses in AIMO land. Amy
decides to take a photo with each princess. She will take a photo for each pair of
princesses also. How many photos will Amy get?
A) 10
B) 12
C) 15
D) 17
E) 20
(C) 2020 Asia International Mathematical Olympiad Union (AIMO Union) http://aimo.world/
All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means,
electronic mechanical, photocopying, recording or otherwise, without the prior permission of Asia International Mathematical Olympiad Union.
請將答案寫在 答題紙 上。
All answers should be written on the ANSWER SHEET.
20) 小艾到超級市場買東西，他一共要付 42 元，他有 5 個十元硬幣、4 個五元硬幣、3
個二元硬幣和 2 個一元硬幣，請問一共有多少種付錢的組合？
小艾到超级市场买东西，他一共要付 42 元，他有 5 个十元硬币、4 个五元硬币、3
个二元硬币和 2 个一元硬币，请问一共有多少种付钱的组合？
Aiden went grocery shopping and had to pay exactly 42 dollars in total. He had 5
ten-dollar coins, 4 five-dollar coins, 3 two-dollar coins, and 2 one-dollar coins. How
many ways were there for him to pay?
A) 8
B) 9
C) 10
D) 11
E) 12
~ End of Paper ~
~ 全卷完 ~
請以最簡形式填寫答案。若計算結果是分數，請化至最簡，並確保為真分數或帶分數，或將計算結果寫成小數。
答案可以根式表示，唯該根式必須是最簡形式。除特別註明外，毋需填寫單位。錯誤單位將不給予任何分數。
Write down the answer in the simplest form. If the calculation result is a fraction, please write down the answer as a proper or mixed fraction,
decimal figure is also accepted. You may use square root to represent the answer which is in the simplest form.
Unless otherwise stated, no need to write down any unit. Marks will NOT be given for incorrect unit.