Đề thi Chung kết quốc tế HKIMO 2021 Khối 6

 奧 冠 教 育 中 心
 O L Y M P I A D C H A M P I O N E D U C A T I O N C E N T R E
 Room 309-310, 8 Jordan Road, Yau Ma Tei, Kowloon, Hong Kong SAR, CHINA
 Tel (852) 3153 2028 / 9310 1240 Fax (852) 3153 2074
 Website: www.olympiadchampion.com Email: olympiadchampion@gmail.com
 香港國際數學競賽總決賽
 HONG KONG INTERNATIONAL
 MATHEMATICAL OLYMPIAD
 FINAL ROUND
 小學六年級 Primary 6
 時限：120 分鐘
 Time allowed: 120 minutes
 模擬試題
 Mock Paper
考生須知：
Instructions to Contestants:
1. 本卷包括 試題 乙份，試題紙不可取走。
 Each contestant should have ONE Question-Answer Book which CANNOT be taken away.
2. 本卷共 5 個範疇，每範疇有 6 題，共 30 題，每題 5 分，總分 150 分，答錯不扣分。
 There are 5 exam areas and 6 questions in each exam area. There are a total of 30 questions in this
 Question-Answer Book. Each carries 5 marks. Total score is 150 marks. No points are deducted for
 incorrect answers.
3. 請將答案寫在 答題紙 上。
 All answers should be written on ANSWER SHEET.
4. 比賽期間，不得使用計算工具。
 NO calculators can be used during the contest.
5. 本卷中所有圖形不一定依比例繪成。
 All figures in the paper are not necessarily drawn to scale.
6. 比賽完畢時，本試題會被收回。
 This Question-Answer Book will be collected at the end of the contest.
 本試題不可取走。
 THIS Question-Answer Book 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-Answer Book without approval of the examiner.
 Otherwise, contestant may be DISQUALIFIED.
 請以最簡形式填寫答案，若計算結果是分數，請確保為真分數或帶分數，或將計算結果寫成小數。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. 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.
 Arithmetic
 算術
7. Find the value of 2.018 51 2.018 11 2.018 12 2.018 26 .
 求 2.018 51 2.018 11 2.018 12 2.018 26 的值。
 1 1 1 1 1
8. Find the value of ... .
 3 5 5 7 21 23 23 25 25 27
 1 1 1 1 1
 求 ... 的值。
 3 5 5 7 21 23 23 25 25 27
9. Find the value of 1 2 2 3 3 4 ... 37 38 38 39 39 40 .
 求1 2 2 3 3 4 ... 37 38 38 39 39 40 的值。
10. Find the value of 4 7 10 ... 94 97 100 .
 求 4 7 10 ... 94 97 100 的值。
11. Find the value of 4 16 64 ... 1024 4096 16384.
 求 4 16 64 ... 1024 4096 16384 的值。
12. Find the value of 111,111,111 111,111,111 .
 求111,111,111 111,111,111 的值。
 Number Theory
 數論
13. Find the number of factors for 513.
 問 513 有多少個因數？
14. How many simplified fraction(s) with denominator 71 is / are there?
 分母為 71 的最簡真分數有多少個？
15. The sum of positive numbers A and B is 600. A is 4 times of B. Find the value of B.
 兩個正整數 A、B 之和是 600，A 是 B 的 4 倍。求 B 的值。
16. How many 4-digit number(s) that can be divisible by 3 and of units digit 5 is / are there?
 有多少個四位數能被 3 整除且個位值是 5？
17. The sum of 7 consecutive numbers is 119. Find the middle number.
 某 7 個連續數之和是 119，求中間的數字。
18. There are 3 prime numbers. Their product is 130. Find the value of the largest number among these 3
 numbers.
 現有三個質數，它們的乘積是 130，求這三個數中最大數的值。
 請以最簡形式填寫答案，若計算結果是分數，請確保為真分數或帶分數，或將計算結果寫成小數。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. 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.
 Combinatorics
 組合數學
25. If Andy goes from point B to point A, each step can only move down or move left. How many way(s) is /
 are there?
 如果安迪從 B 點走到 A 點，每步只能向下或向左走，共有多少種走法？
 B
 A
 Question 25
 第 25 題
26. It is given that the total weight of 4 apples and 3 melons is 1700g and the total weight of 3 apples and 4
 melons is 1800g. What is the total weight of 1 apple and 1 melon?
 已知 4 個蘋果與 3 個蜜瓜共重 1700 克，而 3 個蘋果與 4 個蜜瓜共重 1800 克；那麼 1 個蘋果與 1
 個蜜瓜共重多少克？
27. There are 44 students in Grade 6. 19 and 23 students like playing basketball and volleyball respectively. 3
 students don’t like both ball games. Find the number of students who like both ball games.
 六年級有 44 人，其中 19 人喜歡打籃球，23 人喜歡打排球，3 人兩項都不喜歡，那麼兩項球類喜
 歡的人有多少個？
28. When do the hour hand and the minute hand form a right-angle between 4pm and 5pm for the earliest
 case?
 在下午 4 時至 5 時之間，時針和分針何時最快形成直角？
29. Andy has 28 $5 and $10 coins altogether. He has $185 in total. How many $5 coin(s) does he have?
 安迪有 5 元和 10 元硬幣共 28 個，合共 185 元。問安迪有多少個 5 元硬幣？
30. There are 10 boys and 4 girls in a class. Choose 3 boys and 2 girls to form a study group. How many
 way(s) is / are there in total?
 某班有 10 個男生和 4 個女生，從中選取 3 名男生及 2 名女生組成讀書小組，問一共有多少方法？
 ~ 全卷完 ~
 ~ End of Paper ~
 請以最簡形式填寫答案，若計算結果是分數，請確保為真分數或帶分數，或將計算結果寫成小數。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. Marks will NOT be given for incorrect unit.