TIMO Mock 2019 卷P2f [PDF]

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

小學二年級 Primary 2 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.

Given Amy has 2 sisters and 3 brothers, how many child(ren) does Amy’s mother have? 已知艾美有 2 名姊妹及 3 名兄弟，問艾美的母親有多少名孩子？ 已知艾美有 2 名姊妹及 3 名兄弟，问艾美的母亲有多少名孩子？

2.

According to the pattern shown below, what is the English alphabet in the space provided? 按以下規律，求在橫線上的英文字母。 按以下规律，求在横在线的英文字母。 B 、 E 、 H 、 K 、 __ 、….

3.

5 years ago, Amy was 14 years old. How old will Amy be 4 years later? 五年前艾美是 14 歲，請問 4 年後她多少歲？ 五年前艾美是 14 岁，请问 4 年后她多少岁？

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。 2 、 9 、 16 、 23 、 27 、 34、 __ 、….

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。 3 、 3 、 6 、 9 、 15 、 24、 __ 、….

6.

Today is 5th April, Friday. Which day of the week is 26th May? 今天是 4 月 5 日星期五，5 月 26 日是星期幾？ 今天是 4 月 5 日星期五，5 月 26 日是星期几？

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 算术 7.

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

8.

Find the value of 1513 15 3 15 6 . 求 1513 15 3 15 6 的值。 求 1513 15 3 15 6 的值。

9.

Find the value of 1  3  5  7  9 11 13 15 17 . 求 1  3  5  7  9 11 13 15 17 的值。 求 1  3  5  7  9 11 13 15 17 的值。

10. What is the number that should be filled in the blank if the equation below is correct? 在以下算式填上甚麼數字會使算式正確？ 在以下算式填上甚么数字会使算式正确？ 113  _____  904 11. Find the value of 20  4  20  5  20 1. 求 20  4  20  5  20 1的值。 求 20  4  20  5  20 1的值。 12. Find the value of 1  2  3  ...  7  8  7  ...  3  2 1 . 求 1  2  3  ...  7  8  7  ...  3  2 1 的值。 求 1  2  3  ...  7  8  7  ...  3  2 1 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. Amy has 137 apples and John has 37 apples. How many apple(s) does Amy have to give John to make them have the same number of apples? 艾美有 137 個蘋果，約翰有 37 個蘋果。要使兩人有相同數量的蘋果，艾美要給約翰多少個蘋果？ 艾美有 137 个苹果，约翰有 37 个苹果。要使两人有相同数量的苹果，艾美要给约翰多少个苹果？ 14. 4 students have 40 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? 4 個小孩一共有 40 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？ 4 个小孩一共有 40 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？ 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、31、41、51、61、… 16. How many 3-digit number(s) that have the unit digit 0 is / are there? 有多少個三位數的個位數是 0？ 有多少个三位数的个位数是 0？ 17. What is the largest 2-digit number that can be divisible by 8 and 12? 求最大的兩位數能同時被 8 及 12 整除。 求最大的两位数能同时被 8 及 12 整除。 18. Find the largest 3-digit even number. 求最大三位偶數的值。 求最大三位偶数的值。

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.

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 9 faces, how many vertice(s) does this prism have? 有一個柱體有 9 個面，問這個柱體有多少個頂點？ 有一个柱体有 9 个面，问这个柱体有多少个顶点？ 21. A pyramid has 18 vertices, how many face(s) does this pyramid have? 有一個錐體有 18 個頂點，問這個錐體有多少個面？ 有一个锥体有 18 个顶点，问这个锥体有多少个面？ 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 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.

23. 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 23 第 23 題 第 23 题 24. According to the pattern shown below, what is the figure in the space provided? 按以下規律，橫線上的圖案應該是甚麼？ 按以下规律，横在线的图案应该是甚么？

○ □ □ △ △ ○ ○ □ □ △ △ ○ ○ □ _ △ △… 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. Separate 54 candies into six equal groups, how many candy(ies) is / are there in each group? 把 54 粒糖果分成六等份，每份有多少粒糖果？ 把 54 粒糖果分成六等份，每份有多少粒糖果？ 26. Choose 2 digits, without repetition, from 1, 4, 6, 8, 9 to form 2-digit numbers. How many even number(s) is / are there? 從 1、4、6、8、9 中選 2 個不可重複的數位組成兩位數。請問當中有多少個是偶數？（偶數即是 雙數） 从 1、4、6、8、9 中选 2 个不可重复的数字组成两位數。请问当中有多少个是偶数？（偶数即是 双数） 27. According to the pattern shown below, what is the 50th symbol counting from the left? 按以下規律，由左數起，由第 1 個至第 50 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 50 个符号共有多少个圆形？

○ △ □ ○ ○ △ □ ○ ○ △ □ ○… 28. What is the smallest 5-digit number by using 3, 1, 0, 5 and 8? (Each number can only be used once) 利用 3、1、0、5 和 8 組合成最小的五位數是多少？（每個數字只能用一次） 利用 3、1、0、5 和 8 组合成最小的五位数是多少？（每个数字只能用一次） 29. According to the following sequence for first 190th terms, how many odd number(s) is / are there? 求下列數列中，首 190 項中有多少個奇數？（奇數即是單數） 求下列数列中，首 190 项中有多少个奇数？（奇数即是单数） 1, 2, 3, 6, 11, 20, 37, 68, … 30. Peter has 5 $2 coins and 6 $5 coins. How many $10 coins can he exchange? 彼得有 5 枚 2 元、6 枚 5 元硬幣，他可換多少個 10 元硬幣？ 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. 彼得有 5 枚 2 元、6 枚 5 元硬币，他可换多少个 10 元硬币？

~ 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.