TIMO Final 2019 卷P3f [PDF]

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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：120 分鐘 Time allowed:

120

minutes

試題 Question 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

2

3

2

4

9

3

6

19

4

8

33

5

10

？

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。 3 、 5 、 9 、 17 、 33 、 65 、 __ 、….

3.

The age of Samuel 7 years later is equal to the age of Joseph 3 years later. Given that Joseph is 25 years old now, how old is Samuel now? 森姆 7 年後的年齡與約瑟夫 3 年後的年齡相等。已知約瑟夫今年 25 歲，那麼森姆今年多少歲？ 森姆 7 年后的年龄与约瑟夫 3 年后的年龄相等。已知约瑟夫今年 25 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，求在橫線的數字。 按以下规律，求在横线的数字。 2 、 7 、 13 、 20 、 28 、 37 、 __ 、….

5.

In Class 3A, all students queue up to form a rectangle. Amy stands on the most left row. On her right hand side, there are 5 students. There are 2 students in front of and 3 students behind Amy respectively. How many student(s) is / are in Class 3A? 在 3A 班，所有學生排隊排成一個矩形，艾美站在最左邊的一行，她的右手方有 5 名學生，前面有 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. 2 名學生，後面有 4 名學生。問 3A 班有多少名學生？ 在 3A 班，所有学生排队排成一个矩形，艾美站在最左边的一行，她的右手方有 5 名学生，前面有 2 名学生，后面有 4 名学生。问 3A 班有多少名学生？

6.

6th April 2019 is Saturday. Which day of the week is 27th December this year? 今日 2019 年 4 月 6 日是星期六，今年 12 月 27 日是星期幾？ 今日 2019 年 4 月 6 日是星期六，今年 12 月 27 日是星期几？

Arithmetic 算術 算术

7.

Find the value of 465  534  798  202  466  535 . 求 465  534  798  202  466  535 的值。 求 465  534  798  202  466  535 的值。

8.

Find the value of 29  52  25  29  29  23 . 求 29  52  25  29  29  23 的值。 求 29  52  25  29  29  23 的值。

9.

Find the value of 1111111 . 求 1111111 的值。 求 1111111 的值。

10. Find the value of 1  3  5  7  9 1113  ...  39  41. 求 1  3  5  7  9 1113  ...  39  41的值。 求 1  3  5  7  9 1113  ...  39  41的值。 11. Find the value of 375  48  8  25 . 求 375  48  8  25 的值。 求 375  48  8  25 的值。 12. Find the value of 960  32  960  4  960 12 . 求 960  32  960  4  960 12 的值。 求 960  32  960  4  960 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 (15  5) . 定義運算 a  b  (a  b)  (a  b) ，求 (15  5) 的值。 定义运算 a  b  (a  b)  (a  b) ，求 (15  5) 的值。 14. Define the operation symbol: 定義運算如下： 1 5  1 2  3  4  5 38  3 4  5  6  7 8

Find the value of (5  10)  (4  9) .

59  5 6 7 89

求 (5  10)  (4  9) 的值。 15. The numbers below follow the arithmetic sequence, what is the 21st number? 根據以下的等差數列，問第 21 個數是甚麼？ 根据以下的等差数列，问第 21 个数是甚么？ 22、31、40、49、58、… 16. 6 students have 39 balloons in total and each of them has a different number of balloons. At least how many balloon(s) does the student with the most balloons have? 6 個小孩一共有 39 個氣球。已知當中沒有任何小孩有相同數量的氣球，問擁有最多氣球的小孩最 少有多少個氣球？ 6 个小孩一共有 39 个气球。已知当中没有任何小孩有相同数量的气球，问拥有最多气球的小孩最 少有多少个气球？ 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.

17. Find the smallest 3-digit odd number without repeated digits. 求最小三位數位沒有重複的奇數。 求最小三位数字没有重复的奇数。 18. The sum of A and B is 406. A is 28 times of B. Find the value of A. A、B 兩數之和是 406，A 是 B 的 28 倍，求 A 的值。 A、B 两数之和是 406，A 是 B 的 28 倍，求 A 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 prism has 406 vertices, how many face(s) does this prism have? 有一個柱體有 406 個頂點，問這個柱體有多少個面？ 有一个柱体有 406 个顶点，问这个柱体有多少个面？ 21. A rectangle has a perimeter of 40cm. If the length and width of the rectangle are both integers in cm, 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.

what is the least possible area among that rectangle? 一個矩形的周界是 40 厘米，而該矩形的長和闊的長度都是整數厘米；那麼在這些條件可組成的矩 形之中，面積的最小值是多少平方厘米？ 一个矩形的周界是 40 厘米，而该矩形的长和阔的长度都是整数厘米；那么在这些条件可组成的矩 形之中，面积的最小值是多少平方厘米？ 22. At least how many square(s) can be seen if viewing the figure below from the font? 如果從正面視下圖的立體，最少可以看見多少個正方形？ 如果从正面视下图的立体，最少可以看见多少个正方形？

Question 22 第 22 題 第 22 題

23. How many rectangle(s) with “*” is / are there in the figure below? 請問下圖有多少個含有「*」的矩形？ 请问下图有多少个含有「*」的矩形？

*

Question 23 第 23 題 第 23 题

24. How many triangle(s) can be formed below? 請問下圖可組成多少個三角形？ 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. 请问下图可组成多少个三角形？

Question 24 第 24 題 第 24 题

Combinatorics 組合數學 组合数学 25. Choose 6 digits, without repetition, from 8, 5, 4, 9, 6 and 7 to form two 3-digit even numbers and add them up. What is the maximum value of the sum? 從 8、5、4、9、6、7 中選 6 個不可重複的數位組成 2 個三位偶數，然後加起來，求和的最大值。 从 8、5、4、9、6、7 中选 6 个不可重复的数字组成 2 个三位偶数，然后加起来，求和的最大值。 26. Choose 3 digits, without repetition, from 2, 5, 8, 7, 6 to form 3-digit numbers. How many even number(s) is / are there? 從 2、5、8、7、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偶數？（偶數即是 雙數） 从 2、5、8、7、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偶数？（偶数即是 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. 双数） 27. A group of 13 students are taking photos 2 students at a time. Each student has to take photo with each of their schoolmate. How many picture(s) at least are there to be taken? 一個小組有 13 位同學，每位同學都要和其餘每一位同學合照一張，而且每張合照只有兩位同學。 問一共要照多少張照片？ 一个小组有 13 位同学，每位同学都要和其余每一位同学合照一张，而且每张合照只有两位同学。 问一共要照多少张照片？ 28. Numbers are drawn from the 58 integers 1 to 58. At least how many numbers are drawn at random to ensure that there are two numbers whose sum is 23? 在 1 至 58 這 58 個整數中最少任意選出多少個，才必定有兩個數之和是 23？ 在 1 至 58 这 58 个整数中最少任意选出多少个，才必定有两个数之和是 23？ 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 287th terms, how many even number(s) is / are there? 求下列數列中，首 287 項中有多少個偶數？（偶數即是雙數） 求下列数列中，首 287 项中有多少个偶数？（偶数即是双数） 1, 1, 2, 3, 5, 8, 13, 21, …

~ 全卷完 ~ ~ 全卷完 ~ 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.

~ 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.