TIMO Mock 2019 卷P3f [PDF]

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奧冠 教育 中心 OLYMPIAD CHAMPION EDUCATION CENTRE 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: [email protected]

THAILAND

泰國國際數學競賽總決賽 2019 INTERNATIONAL MATHEMATICAL OLYMPIAD FINAL 2019

小學三年級 Primary 3 時限:90 分鐘 Time allowed:

90

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. 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. 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. 填空題(第 1 至 30 題)(每題 5 分,答錯及空題不扣分) 填空题(第 1 至 30 题)(每题 5 分,答错及空题不扣分) Open-Ended Questions (1st ~30th) (5 points for correct answer, no penalty point for wrong answer) Logical Thinking 邏輯思維 逻辑思维 1.

What is the value of the number to represent “?” in the following table? 求在下表中?代表的值。 求在下表中?代表的值。

2.

1

1

2

2

3

7

3

5

16

4

7

29

5

9



According to the pattern shown below, what is the 103rd symbol counting from the left? 按以下規律,由左數起,由第 1 個至第 103 個符號共有多少個圓形? 按以下规律,由左数起,由第 1 个至第 103 个符号共有多少个圆形?

○ △ □ ○ ○ △ □ ○ ○ △ □ ○… 3.

The age of Samuel 7 years later is equal to the age of Joseph 3 years ago. Given that Joseph is 22 years old now, how old is Samuel now? 森姆 7 年後的年齡與約瑟夫 3 年前的年齡相等。已知約瑟夫今年 22 歲,那麼森姆今年多少歲? 森姆 7 年后的年龄与约瑟夫 3 年前的年龄相等。已知约瑟夫今年 22 岁,那么森姆今年多少岁?

4.

According to the pattern shown below, what is the number in the blank? 按以下規律,求在橫線上的數字。 按以下规律,求在横在线的数字。 1 、 4 、 16 、 25 、 36 、 49、 __ 、….

5.

According to the pattern shown below, what is the number in the blank? 按以下規律,求在橫線上的數字。 按以下规律,求在横在线的数字。 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. 1 、 3 、 7 、 15 、 31 、 63 、 __ 、…. 6.

Today is 5th April, Friday. Which day of the week is 11th June? 今天是 4 月 5 日星期五,6 月 11 日是星期幾? 今天是 4 月 5 日星期五,6 月 11 日是星期几? Arithmetic 算術 算术

7.

Find the value of 2  4  6  8 10 12 14 16 18  20  22 . 求 2  4  6  8 10 12 14 16 18  20  22 的值。 求 2  4  6  8 10 12 14 16 18  20  22 的值。

8.

Find the value of 27 12 15  27  27  23 . 求 27 12 15  27  27  23 的值。 求 27 12 15  27  27  23 的值。

9.

Find the value of 111111 . 求 111111 的值。 求 111111 的值。

10. Find the value of 1  3  5  ...  23  25  23  ...  5  3 1 . 求 1  3  5  ...  23  25  23  ...  5  3 1 的值。 求 1  3  5  ...  23  25  23  ...  5  3 1 的值。 11. Find the value of 625  32 16 125 . 求 625  32 16 125 的值。 求 625  32 16 125 的值。 12. Find the value of 96  4  96  8  96 12 . 求 96  4  96  8  96 12 的值。 求 96  4  96  8  96 12 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.

Number Theory 數論 数论 13. Define the operation symbol a  b  a  b  a  b , find the value of (12  4) . 定義運算 a  b  a  b  a  b ,求 (12  4) 的值。 定义运算 a  b  a  b  a  b ,求 (12  4) 的值。 14. The sum of A and B is 2019. The difference between A and B is 405. Given A is larger than B, find the value of A. A、B 兩數之和是 2019,A、B 兩數之差是 405。已知 A 比 B 大,求 A 的值。 A、B 两数之和是 2019,A、B 两数之差是 405。已知 A 比 B 大,求 A 的值。 15. The numbers below follow the arithmetic sequence, what is the 20th number? 根據以下的等差數列,問第 20 個數是甚麼? 根据以下的等差数列,问第 20 个数是甚么? 21、34、47、60、73、… 16. 5 students have 50 balloons in total and each of them has a different number of balloons and at least 1 balloon. At most how many balloon(s) does the student with the most balloons have? 5 個小孩一共有 50 個氣球。已知當中沒有任何小孩有相同數量的氣球,而每人至少有 1 個,問擁 有最多氣球的小孩最多擁有多少個氣球? 5 个小孩一共有 50 个气球。已知当中没有任何小孩有相同数量的气球,而每人至少有 1 个,问拥 有最多气球的小孩最多拥有多少个气球? 17. What is the largest 3-digit number that can be divisible by 8 and 12? 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. 求最大的三位數能同時被 8 及 12 整除。 求最大的三位数能同时被 8 及 12 整除。 18. The sum of A and B is 405. A is 80 times of B. Find the value of B. A、B 兩數之和是 405,A 是 B 的 80 倍,求 B 的值。 A、B 两数之和是 405,A 是 B 的 80 倍,求 B 的值。

Geometry 幾何 几何 19. How many square(s) is / are there in the figure below? 請問下圖有多少個正方形? 请问下图有多少个正方形?

Question 19 第 19 題 第 19 题 20. A pyramid has 405 vertices, how many edge(s) does this pyramid have? 有一個錐體有 405 個頂點,問這個錐體有多少條棱? 有一个锥体有 405 个顶点,问这个锥体有多少条棱? 21. The perimeter of a rectangle is 84. Find the maximum value of the area of this rectangle. 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. 矩形的周界是 84,求矩形面積的最大值。 矩形的周界是 84,求矩形面积的最大值。 22. At least how many square(s) can be seen if viewing the figure below from side? 如果從側面視下圖的立體,最少可以看見多少個正方形? 如果从侧面视下图的立体,最少可以看见多少个正方形?

Question 22 第 22 題 第 22 題 23. There are 6 points on a plane. How many quadrilateral(s) can you draw? 在平面上有 6 點,可以畫出多少個四邊形? 在平面上有 6 点,可以画出多少个四边形?

24. How many line segment(s) is / are there in the figure below? 請問下圖有多少條線段? 请问下图有多少条线段?

Question 24 第 24 題 第 24 题

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 组合数学 25. Peter has 4 $5 coins and 6 $10 coins. How many $20 notes can he exchange? 彼得有 4 枚 5 元、6 枚 10 元硬幣,他可換多少個 20 元紙幣? 彼得有 4 枚 5 元、6 枚 10 元硬币,他可换多少个 20 元纸币? 26. Choose 3 digits, without repetition, from 2, 3, 4, 5, 6 to form 3-digit numbers. How many odd number(s) is / are there? 從 2、3、4、5、6 中選 3 個不可重複的數位組成三位數。請問當中有多少個是奇數?(奇數即是 單數) 从 2、3、4、5、6 中选 3 个不可重复的数字组成三位數。请问当中有多少个是奇数?(奇数即是 单数) 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.

27. Separate 108 candies into six equal groups, how many candy(ies) is / are there in each group? 把 108 粒糖果分成六等份,每份有多少粒糖果? 把 108 粒糖果分成六等份,每份有多少粒糖果? 28. What is the largest 5-digit odd number by using 3, 1, 0, 6 and 9? (Each number can only be used once) 利用 3、1、0、6 和 9 組合成最大的五位奇數是多少?(每個數字只能用一次)(奇數即是單數) 利用 3、1、0、6 和 9 组合成最大的五位奇数是多少?(每个数字只能用一次)(奇数即是单数) 29. If Andy goes from point A to point B, each step can only move up or move right. How many way(s) is / are there? 如果安迪從 A 點走到 B 點,每步只能向上或向右走,共有多少種走法? 如果安迪从 A 点走到 B 点,每步只能向上或向右走,共有多少种走法? B

A Question 29 第 29 題 第 29 题 30. According to the following sequence for first 297th terms, how many odd number(s) is / are there? 求下列數列中,首 297 項中有多少個奇數?(奇數即是單數) 求下列数列中,首 297 项中有多少个奇数?(奇数即是单数) 1, 2, 3, 6, 11, 20, 37, 68, …

~ 全卷完 ~ ~ 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.