TIMO 2017 Heat Round P4-1 [PDF]

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泰國國際數學競賽 2017 THAILAND INTERNATIONAL MATHEMATICAL OLYMPIAD 2017

小學四年級 Primary 4 時限：90 分鐘 Time allowed:

90

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 5 題，共 25 題，每題 4 分，總分 100 分，答錯不扣分。 There are 5 exam areas and 5 questions in each exam area. There are a total of 25 questions in this Question-Answer Book. Each carries 4 marks. Total score is 100 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. 填空題（第 1 至 25 題）（每題 4 分，答錯及空題不扣分） Open-Ended Questions (1st ~25th) (4 points for correct answer, no penalty point for wrong answer) Logical Thinking 邏輯思維 1.

What is the value of the number to represent “?” in the following sequence? 求在以下數列中？代表數字的值。 1, 1, 2, 4, 7, 13, 24, ？ , 81, 149, …

2.

According to the pattern shown below, how many circle(s) is / are there from the 1st to the 200th symbol counting from the left? 按以下規律，由左數起第 1 至第 200 個符號中共有多少個圓形？

○ △ □ ○ ○ △ △ □ □ ○ ○ ○ △ △ △ □ □ □… 3.

A stationery store had a batch of ball pens. One half but 2 few pens were sold on the first day. One half of the remaining part but 3 few pens were sold on the second day. Finally 11 ball pens are left. How many ball pen(s) did the stationery store have originally? 文具店有一批原子筆，第一天賣掉了總數的一半少 2 支，第二天則賣掉剩下的一半少 3 支，最後剩下 11 支。那麼文具店原有多少支原子筆？

4.

John wrote a 3-digit number on a piece of paper and asked Peter to guess it. Peter asked: “Is the number 723?” John replied: “One of the digits is correct. The position of that digit is also correct.” Peter asked again: “Is the number 745?” John replied: “One of the digits is correct. The position of that digit is wrong.” Peter asked again: “Is the number 842?” John said: “One of the digits is correct. The position of that digit is also correct.” Given all the digits in that 3-digit number are all different, what is the number written by John? 約翰寫一個 3 位數在一張紙上，吩咐彼得來猜猜它。 彼得問：「這個數是否 723？」 約翰回覆：「這裏有一個數位是正確的，而且該數位的位置也是正確的。」 彼得再問：「這個數是否 745？」 約翰回覆：「這裏有一個數位是正確的，但是那個數位的位置是錯誤的。」 彼得再問：「這個數是否 842？」 約翰回覆：「這裏有一個數位是正確的，而且該數位的位置也是正確的。」 已知這個三位數的三個數位都不一樣，求約翰寫出來的數字。

5.

There are a total of 40 tigers and cranes in a zoo. The animals have a total of 104 legs. How many tiger(s) is / are there? 動物園裡有老虎和鶴共 40 隻，共有 104 條腿。那麼老虎有多少隻？

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 6.

Find the value of 2052 19  2052  3  2052  9 . 求 2052 19  2052  3  2052  9 的值。

7.

Find the value of 13131313  8080808  4  11111111 5 . 求 13131313  8080808  4  11111111 5 的值。

8.

Find the value of 1  2  3  ...  49  50  49  ...  3  2  1 . 求 1  2  3  ...  49  50  49  ...  3  2  1 的值。

9.

Find the value of 10 10  9  9  8  8  7  7  6  6  5  5  4  4  3  3  2  2  11 . 求 10 10  9  9  8  8  7  7  6  6  5  5  4  4  3  3  2  2  11 的值。

10. Find the value of 12345654321 12321 . 求 12345654321 12321 的值。

Number Theory 數論 11. If 9-digit number 20171221A is divisible by 9, find the value of A. 若 9 位數 20171221A 可被 9 整除，求 A 的值。

12. Find the unit digit of A if A  5  5  5  ...  5  6  6  6  ...  6 . 2017 ' s

2017 ' s

若 A  5  5  5  ...  5  6  6  6  ...  6 ，求 A 的個位數的值。 2017 ' s

2017 ' s

13. Define the operation symbol a  b  b  b  a  a , find the value of (121  131) . 定義運算 a  b  b  b  a  a ，求 (121  131) 的值。

14. The product of positive numbers A and B is 392. A is larger than B by 1 time. Find the value of A. 兩個正整數 A、B 的積是 392，A 比 B 大 1 倍。求 A 的值。

15. What is the greatest 3-digit number that can be divisible by 3 and 5? 求最大的三位數能同時被 3 及 5 整除。

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 16. How many square(s) is / are there in the figure below? 請問下圖有多少個長方形？

Question 16 第 16 題

17. Find the perimeter of the figure shown below in cm. 求下圖的周界﹝以厘米表示答案﹞。 4 cm

5 cm 3cm 4 cm

7 cm

Question 17 第 17 題

18. Find the area of the figure shown below in cm2. 求下圖的面積﹝以平方厘米表示答案﹞。 3 cm 8 cm

4 cm 3 cm 2 cm

2 cm

Question 18 第 18 題

19. A big square is formed by 36 small squares with side length 5 cm. What is the perimeter of the big square in cm? 利用 36 個邊長 5 厘米的小正方形砌成一個大正方形，大正方形的周界是多少厘米？

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. 20. How many right-angled triangle(s) is / are there in the figure below? 下圖中有多少個直角三角形？

Question 20 第 20 題

Combinatorics 組合數學 21. A flight of stairs has 7 steps. David can go up for 1 step or 2 steps each time. How many way(s) is / are there for David to go up the stairs? 一道有 7 級的樓梯，大衛每一步可以上 1 級或 2 級，問大衛走上這道樓梯共有多少種方法？ 22. Two boys Bobby, Benny and two girls Grace, Gloria are to be seated in a row according to the rule that a boy will not sit next to another boy and a girl will not sit next to another girl. Find the number of the combination(s) satisfying the above condition. 兩名男孩波比、賓利和兩名女孩麗思、歌莉亞就坐一排座位，並滿足「男孩不會坐在另一名男孩旁邊 及女孩不會坐在另一名女孩旁邊」的條件。求滿足上述條件的排列數目。 23. Choose 2 digits, without repetition, from 1, 2, 4, 6, 7 to form 2-digit numbers. How many number(s) can be divisible by 3? 從 1、2、4、6、7 中選 2 個不可重複的數位組成兩位數。請問當中有多少個數能被 3 整除？ 24. How many 2-digit number(s) is / are there such that the number contains digit “6” and no digits are repeated? 有多少個包含數位 6 且沒有重複數位的兩位數？ 25. If Andy goes from point A to point B, each step can only move up or move right. How many way(s) is / there?

are

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？ B

A Question 25 第 25 題 ~ 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.