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4th International Talent Mathematics Contest 2022 (4th ITMC 2022)

Question paper Grade 2 (English Version)

Instructions

The question paper consists of 3 parts: 29 questions in total and 1 bonus question. Part 1: Questions no. 1 – 12, each correct answer is worth 4 points, 1 point for each blank answer, and 0 point for each incorrect answer. Part 2: Questions no. 13 – 24, each correct answer is worth 6 points, 1.5 points for each blank answer, and 0 point for each incorrect answer. Part 3: Questions no. 25 – 29, each correct answer is worth 7 points, and 0 point for each incorrect or blank answer. Bonus Question (Student may or may not give the answer) A correct answer is worth 20 points. An incorrect answer is deducted 7 points and 0 point for blank answer.

Information:

• Time limit 90 minutes. • Use only pencil 2B to fill the circles. • Any calculators and electronic devices are not allowed. • Diagrams shown may not be drawn to scale. • At the end of the contest, your answer sheet must be returned. • Violation will be disqualified.

4th International Talent Mathematics Contest 2022 Part 1 Questions no. 1 – 12.

• 4 points for each correct answer. • 1 points for each blank answer. • 0 point for each incorrect answer. 1. Which of the following values is the smallest? A. 2 + 0 + 2 + 2 B. 2 × 0 + 2 + 2 D. 2 + 0 + 2 × 2 E. 2 × 0 × 2 × 2

C. 2 + 0 × 2 + 2

2. Which of the following is equal to 15 + 16 − 17 − 18 + 19 ? A. (2 × 8) − 1 B. (3 × 4) + 2 C. 21 − 8 E. 3 + 3 + 3 + 3 D. (11 + 12) − (4 + 5)

3. Given that T + M = 123. If M equals 45, then what is the difference between T and M? A. 29 B. 33 C. 57 D. 59 E. 78

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4th International Talent Mathematics Contest 2022 4. A boy weighs 28 kilograms and 700 grams. If the weight of the boy is equal to T × 100 grams, what is the value of T? A. 287 B. 2870 C. 7820 D. 782 E. 28700

5. A capacity of a tank is 5 liters. It contains 2 liters 800 milliliters of water. After that, pour 1 liter and 700 milliliters of water into the tank. Now, what is the amount of water that must be poured into the tank to make an exact full tank? A. 1 liter 500 milliliters B. 1 liter 200 milliliter C. 500 milliliters D. 300 milliliters E. 200 milliliters

6. A rope with length 23 meters 71 centimeters is cut into four ropes. The length of the 1st rope is 1 meter 45 centimeters. The length of the 2nd rope is 3 meters 78 centimeters. The length of the 3rd rope is 2 meters 56 centimeters. What is the length of the 4th rope? A. 12 meters 82 centimeters B. 13 meters 82 centimeters C. 14 meters D. 15 meters 92 centimeters E. 14 meters 92 centimeters

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4th International Talent Mathematics Contest 2022 7. A man has money n baht. If he can give all of his money equally to three children, which one of the following cannot be the value of n?

(Note that baht is the currency of Thailand.)

A. 162 D. 316

B. 201 E. 351

8. The date 23 February 2022 is Wednesday. What day of the week is the date 25 March 2022? A. Friday B. Thursday D. Tuesday E. Monday

C. 225

C. Wednesday

9. Consider the following sequence pattern T, M, C, 1, 0, T, M, C, 1, 0, T, . . . Which one of the following is the 42nd letter in the above sequence? A. T B. M C. C D. 1 E. 0

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4th International Talent Mathematics Contest 2022 10. Consider the expression (I × T) + (M × C) where different letters represent different digits from 2, 5, 6, 4. How many different values can be obtained? A. 1 B. 2 C. 3 D. 4 E. 6

11. There are five cards in a box. Each card is labeled one number from 1, 3, 5, 7, 9 without repetition. If two cards are picked up from this box, then which one of the following events cannot be occurred? A. The sum of two cards equals 10. B. The sum of two cards equals 14. C. The sum of two cards is an even number. D. The difference between of two cards equals 6. E. The difference between of two cards equals 9.

12. A Mathematics test has 50 questions. Each correct answer gets 3 points. Each incorrect answer or no answer deducts 1 point. If Malee answers 36 questions correctly, how many points will she get? A. 118 B. 104 C. 108 D. 94 E. 88

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4th International Talent Mathematics Contest 2022 Part 2 Questions no. 13 – 24. • 6 points for each correct answer. • 1.5 points for each blank answer. • 0 point for each incorrect answer.

13. Let A, B, C , D and E be positive integers such that 1000 = 965 + A , 965 = 925 + B , 925 = 880 + C , = 775 + E . 880 = 830 + D and 830 Find the value of A + B + C + D + E . B. 235 C. 225 A. 245 D. 215

E. 205

14. A boy has some pencils at first. He gives 6 pencils to his friend and he lost 2 pencils, after that his mother bought new 5 pencils for him. Now, he has 17 pencils in total. What is the number of pencils of the boy at first? A. 15 B. 16 C. 18 D. 20 E. 22

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4th International Talent Mathematics Contest 2022 15. Given that 3 ♥ 2 = ( 3 + 2) − ( 3 − 2) = 4 , 5 ♥ 3 = (5 + 3) − (5 − 3) = 6 . Find the value of 65 ♥ 22. A. 34 B. 36 D. 42 E. 44

16. Given that the area of a square

C. 38

is 4 cm2.

Find the total area, in cm2, of the geometric figure below. A. 28 D. 18

B. 24 E. 14

C. 20

17. How many of rectangles are there in the figure? A. 7 B. 9 C. 12 D. 13 E. 16

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4th International Talent Mathematics Contest 2022 18. Let ABCD be a rectangle with the length of CD being 25 centimeters. If BC is 16 centimeters shorter than CD, then what are the perimeters of a rectangle ABCD?

A. 64 D. 76

B. 68 E. 84

C. 74

19. A two-digits number that less than 30 has the following properties (1) The remainder is 2 when the number is divided by 4. (2) The remainder is 1 when the number is divided by 5. Find the product of all digits of the two-digits number. A. 12 B. 6 C. 4 D. 15 E. 18

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4th International Talent Mathematics Contest 2022 20. Ceva is an orange merchant. Today he has 2565 oranges. He takes all the oranges into baskets for sale. Each basket will contain 24 oranges, except for the last basket that must be contained less than 24 oranges. Find the number of baskets that Ceva needs to use. A. 105 B. 106 C. 107 D. 108

E. 109

21. Consider the following pattern

T

TTT

Figure 1 Figure 2

TTTTT

TTTTTTT

Figure 3

Figure 4

How many of letter T are there in figure 25? A. 37 B. 47 D. 53 E. 57

...

C. 49

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4th International Talent Mathematics Contest 2022 22. There are 4 buildings I, T, M, C at the top of each building has bridges connected between buildings as shown in the figure. Now, a girl stays at the top of building I. How many ways are there that she walks with the bridge to visit all building exactly once? A. 5 B. 6 C. 7 T I D. 8 E. 9

M

C

23. There are a group of children each of them like only one of the colors from five colors as yellow, pink, green, orange, and blue. There is a total of 2 children who like yellow and pink. There is a total of 5 children who like pink and green. There is a total of 6 children who like green and orange. There is a total of 5 children who like orange and blue. Consider the following statements (1) There are a total of 11 children in this group. (2) The number of children who like green is greatest. (3) The number of children who like orange is less than the number of children who like blue. Which one of the following is true? A. Only statements (1) and (2) are correct. B. Only statements (1) and (3) are correct. C. Only statements (2) and (3) are correct. D. All of three statements are correct. E. The number of correct statements is less than 2.

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4th International Talent Mathematics Contest 2022 24. Euler plays a game of darts with six darts. On the target shown each circle has a different score. He will get the points that specified in each circle if a dart into the target and will not get score when a dart out of the target If Euler gets 37 scores, then what is the least number of darts that he has to throw into the target. 1 A. 1 B. 2 C. 3 D. 4

E. 5

2 4 8 16

32

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4th International Talent Mathematics Contest 2022 Part 3 Questions no. 25 – 29.

• 7 points for each correct answer. • 0 point for each blank or incorrect answer. In the case that an answer is not integral, students have to put the nearest integral answer. Students have to answer the last five digits in the case that the answer from calculating is more than 5 digits. 25. Let X be the product of all positive integers from 1 to 8. and Y the sum of all positive integers from 1 to 8. Find the value of X ÷ Y.

26. A positive integer is written 2022 in repeating to be 100 digits as 20222022202220222022 ... 20222022 .  100 digits

Find the sum of the first 33 digits from the left of the number.

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4th International Talent Mathematics Contest 2022 true.

27. Let T, M, C be the nonzero digits that make the following addition

T M C T M

T + M + C C

Find the three-digits number TMC .

28. The given figure 2 is obtained by turning figure 1 for 180o. If figure 2 is put on the top figure 1 such that they are completely overlapped, find the number of 1 × 1 which is not shaded squares that are overlapped.

figure 1

figure 2

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4th International Talent Mathematics Contest 2022 29. Given that I , T , M , C are four distinct positive integers in ascending order.

If the sum of all four integers is 90, find the largest possible value of M.

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4th International Talent Mathematics Contest 2022 Bonus Questions no. 30. (Student may or may not give the answer) • 20 points for the correct answer. • 0 point for the blank answer. • -7 points for the incorrect answer.

In the case that an answer is not integral, students have to put the nearest integral answer. Students have to answer the last five digits in the case that the answer from calculating is more than 5 digits. 30. There are 30 boxes, each containing a different number of coins from 1 to 30 coins. An operation is that we must select at least one box and take the same number of coins from every selected box. For example, the first of the operation students may select the boxes containing 10 to 30 coins and remove 10 coins from each of the 21 selected boxes. Find the smallest number of operations that we have to do so that every coin is taken out of every box. This will make all boxes to be empty.

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