TIMO Heat 2020 Mock P3 [PDF]

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泰國國際數學競賽初賽 2020 THAILAND INTERNATIONAL MATHEMATICAL OLYMPIAD HEAT ROUND 2020

小學三年級 Primary 3

時限：90 分鐘

Time allowed:

考生須知： Instructions to Contestants:

90

minutes

模擬試題 Mock Paper

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.

John, Amy and Peter are good friends. One of them is a merchant. One of them is a student. One of them is a soldier. In addition, they know the following situations: Amy is older than Soldier. Peter’s age is larger than soldier’s. Student’s age is smaller than Amy’s. John’s age is different from that of student’s. Who is the merchant? 約翰、艾美、彼得三個人是好朋友，他們中間其中一人是商人，一人是學生，一人是士兵。此外 他們還知道以下條件：艾美年齡比士兵大；彼得的年齡比士兵的大；學生的年齡比艾美小；約翰 的年齡和學生的年齡不一樣。請問誰是商人？

2.

According to the pattern shown below, counting from the left how many circles are there from the 1st to the 103th one? 按以下規律，由左至右數第 1 個至第 103 個符號當中共有多少個圓形？

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

Amy bought a pair of beautiful shoes. Her classmates never saw this pair of shoes before. So they start guessing. Peter said that “Your shoes are not red.” John said that “Your shoes are either blue or black.” Andy said that “Your shoes must be black.” Within the point of view of these 3 people, only one of them is wrong. What colour are Amy’s shoes? 艾美買了一雙漂亮的鞋子，她的同學都沒有見過這雙鞋了，於是大家就猜，彼得說：「你買的鞋 不會是紅色的。」約翰說：「你買的鞋子不是藍色的就是黑色的。」安迪說：「你買的鞋子一定 是黑色的。」這三個人的看法只有一種是錯誤的。請問艾美的鞋子到底是什麼顏色的？

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. 4.

John wrote a 3-digit number on a piece of paper and asked Peter to guess it. Peter asked: “Is the number 123?” John replied: “One of the digits is correct, the position of that digit is also correct.” Peter asked again: “Is the number 178?” John replied: “Two digits are correct, but the positions of those digits are both wrong.” Peter asked again: “Is the number 782?” John said: “All three digits are correct, but the digits are all in the wrong places.” 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 123？」 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 178？」 約翰回覆：「這裏有兩個數位是正確的，但該兩個數位的位置都是錯誤的。」 彼得再問：「這個數是否 782？」 約翰回覆：「這裏有三個數位是正確的，但所有數位的位置都是錯誤的。」 求約翰寫出來的數字。

5.

According to the pattern shown below, how many circles are there in the 20th group? 按以下規律，問第 20 組有多少個圓？

1st Group 第1組

2nd Group 3rd Group 第2組 第3組 Question 5 第5題

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 366  978  166  22  895  126  526  595 . 求 366  978  166  22  895  126  526  595 的值。

7.

Find the value of 11111 11111 . 求 11111 11111 的值。

8.

Find the value of 3  6  9  12  15  ...  27  30 . 求 3  6  9  12  15  ...  27  30 的值。

9.

Find the value of 1  2  3  4  5  6  7  8  9  ...  50  51 . 求 1  2  3  4  5  6  7  8  9  ...  50  51 的值。

10. Find the value of 2018  121  1018  121 . 求 2018  121  1018  121 的值。 Number Theory 數論 11. The numbers below follows the arithmetic sequence, what is the 19th number? 根據以下的等差數列，問第 19 個數是甚麼？ 26、33、40、47、54、… 12. Define the operation symbol a  b  a  b  2  a  3 , find the value of (12  16)  20 . 定義運算 a  b  a  b  2  a  3 ，求 (12  16)  20 的值。 13. The sum of A and B is 144. The difference between A and B is 36. Given A is larger than B, find the value of B. A、B 兩數之和是 144，A、B 兩數之差是 36。已知 A 比 B 大，求 B 的值。 14. The sum of A and B is 84. A is 6 times of B. Find the value of A. A、B 兩數之和是 84，A 是 B 的 6 倍。求 A 的值。 15. What is the smallest 3-digit number that can be divisible by 4 and 6? 求最小的三位數能同時被 4 及 6 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. The figure is formed by 3 squares with perimeters 24cm, 44cm and 24cm respectively. Find the area of the following figure. 下圖由三個周界分別是 24 厘米、44 厘米及 24 厘米的正方形組成。求下圖的面積。

Question 16 第 16 題 17. How many cubes are there in the figure below? 請問下圖有多少個正方體？

Question 17 第 17 題 18. In the figure below, all the small triangles are equilateral triangles. If the perimeter of a small triangle is 15cm, what is the perimeter of the figure below? 附圖中所有小三角形皆為等邊三角形。如果小三角形的周界是 15 厘米，求下圖的周界。

Question 18 第 18 題 19. A prism has 150 edges, how many faces does it have? 有一個柱體有 150 條棱，問這個立體有多少個面？ 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 rectangles are there in the figure below? 下圖中有多少個矩形？

Question 20 第 20 題 Combinatorics 組合數學 21. A flight of stairs has 6 steps. David can go up for 1 step or 2 steps at a time. How many ways are there for David to go up the stairs? 一道有 6 級的樓梯，大衛每一步可以上 1 或 2 級，問大衛走上這道樓梯共有多少種方法？ 22. Choose 3 numbers, without repetition, from 1, 4, 5, 7, 9 to form a three-digit number. How many even numbers are there? 從 1、4、5、7、9 中選 3 個不可重複的數字組成三位數，可以組成多少個偶數？ 23. There are 1-dollar, 2-dollar, 5-dollar and 10-dollar coins and 1 for each type. How many different amount can be formed? 現有 1 元、2 元、5 元及 10 元硬幣各 1 枚，可以組合出多少種不同的金額？ 24. What is the smallest 5-digit even number by using 3, 0, 2, 8 and 9? (Each number can be used once) 利用 3、0、2、8 和 9 組合成最小的五位偶數是多少？（每個數字只能用一次） 25. Choose 2 numbers, without repetition, from 0, 3, 5, 6, 9 to form a two-digit number. How many numbers with a digit “9” are there? 從 0、3、5、6、9 中選 2 個不可重複的數字組成兩位數，可以組成多少個包括數位「9」的數？ ~ 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.