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Tài liệu ôn thi itmc + ĐỀ THI ITMC được yopovn sưu tầm và chia sẻ. GỬI TẶNG QUÝ THẦY CÔ, QUÝ PHỤ HUYNH, HỌC SINH.
Hơn 10 năm kinh nghiệm luyện thi Toán Olympic quốc tế của các kỳ thi TIMO, HKIMO, SEAMO, SASMO, ASMO, AMC, IMAS, IKMC, APMOPS, ITMC, IMC…
Là học sinh chuyên toán từ Tiểu học, cựu học sinh Chuyên Toán – Tin, trường THPT Chuyên Lê Hồng Phong, Nam Định;
Đạt giải giải nhì HSG môn Toán quốc gia dành cho khối Tiểu học năm 1996; Cùng với đội ngũ các thầy cô giáo là cựu học sinh Chuyên Toán, đạt giải nhiều giải Toán quốc gia
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Tổng hợp đề thi và đáp án, hướng dẫn giải kỳ thi ITMC khối 2
MỤC LỤC
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Tổng hợp đề thi và đáp án, hướng dẫn giải kỳ thi ITMC khối 2
PHỤ LỤC
| Later | Sau |
| Equal | Bằng |
| Now | Hiện tại |
| Ago | Trước |
| Given that | Biết rằng |
| In total | Tổng số |
| Asumption | Giả sử |
| Insufficient | Thiếu |
| Assume | Giả sử |
| Excessive | Thừa ra |
| Altogether | Tất cả |
| Consecutive | Liên tiếp |
| Increase | Tăng |
| Decrease | Giảm |
| Number sequence | Dãy số |
| Diference | Hiệu |
| Sum | Tổng |
| Pattern | Quy luật |
| Term | Số hạng |
| Calculate | Tính |
| Arithmetic sequence | Dãy số cộng / dãy cách đều |
| Group | Nhóm |
| Term / element / member | Số hạng |
| Value / result | Kết quả |
| Distributive property | Tính chất phân phối |
| Operation | Phép tính |
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Tổng hợp đề thi và đáp án, hướng dẫn giải kỳ thi ITMC khối 2
| Multiplication | Phép nhân |
| How to calculate average? | Cách tính số trung bình |
| Middle | Ở chính giữa |
| Even | Chẵn |
| Odd | Lẻ |
| Last | Cuối cùng |
| How to use average to calculate the sum? | Sử dụng trung bình để tính tổng như thế nào? |
| What is average? | Trung bình là gì? |
| Sequence | Dãy |
| Consecutive numbers | Các số liên tiếp |
| First | Đầu tiên |
| Why do we need average? | Tại sao chúng ta phải tính trung bình? |
| Define | Định nghĩa |
| Symbol | Kí hiệu |
| Operation | Phép toán |
| Units digit | Chữ số hàng đơn vị |
| Tens digit | Chữ số hàng chục |
| Divisibility | Chia hết cho |
| Product | Tích |
| Digit | Chữ số |
| Last digit | Chữ số tận cùng |
| Horizontal line | Đường nằm ngang |
| Vertical line | Đường thẳng đứng |
| Rectangle | Hình chữ nhật |
| Square | Hình vuông |
| How many rectangles? | Có bao nhiêu hình chữ nhật? |
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Tổng hợp đề thi và đáp án, hướng dẫn giải kỳ thi ITMC khối 2
| Side length | Kích thước chiều dài |
| Smaller | Nhỏ hơn |
| Area | Diện tích |
| Perimeter | Chu vi |
| Cut into form by meaning | Cắt thành hình thức theo ý nghĩa |
| Larger | Lớn hơn |
| Cuboid | Hình hộp chữ nhật |
| 3d shape | Hình 3d |
| Cube | Hình lập phương |
| Surface area | Diện tích toàn phần |
| Move right | Đi sang phải |
| Way | Cách đi |
| Route | Đường đi |
| Move up | Đi lên trên |
| Guarantee | Chắc chắn |
| Exist | Tồn tại |
| Choose | Chọn |
| Be sure | Chắc chắn |
| At least | Ít nhất |
| Draw | Chọn |
| At random | Ngẫu nhiên |
| Minimum | Ít nhất |
| Make sure | Chắc chắn |
| Randomly | Ngẫu nhiên |
| Assure | Chắc chắn |
| Ensure | Chắc chắn |
| With repetition | Được ghép lặp lại |
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Tổng hợp đề thi và đáp án, hướng dẫn giải kỳ thi ITMC khối 2
| Without repetition | Không được phép lặp lại |
| Front face | Mặt trước |
| Bottom face | Mặt dưới |
| Right side face | Mặt bên phải |
| Left side face | Mặt bên trái |
| Top face | Mặt trên |
| Back face | Mặt sau |
| Face | Mặt |
| How many ways are there? | Có bao nhiêu cách đi |
| Go up | Đi lên |
| Step | Bậc |
| Inverse | Ngược từ |
| Backwards from the end | Suy ngược từ cuối |
| Back-to-end inference | Suy ngược từ cuối |
| Originally | Ban đầu |
| Constant | Hằng số |
| Geometric sequence | Dãy cấp số nhân |
| Plus | Cộng |
| Minus | Trừ |
| Quotient | Thương |
| Minimum | Nhỏ nhất |
| Smallest | Nhỏ nhất |
| Maximum | Lớn nhất |
| Greatest | Lớn nhất |
| Area | Diện tích |
| Positive integer | Số nguyên dương |
| Perimeter | Chu vi |
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Tổng hợp đề thi và đáp án, hướng dẫn giải kỳ thi ITMC khối 2
ĐỀ SỐ 01:
2018 Preliminary National Examinations (Pre-NE)
Part I For question 1 – 12, each correct answer is worth 4 points, 1 point for a blank answer, and 0 point for each incorrect answer. Q1. The sum of 654 + 789 is equal to the sum of
A. 860 + 483 B. 582 + 851 C. 747 + 686 D. 618 + 815 E. 568 + 875 Q2. In the adjoining circle, how many more even numbers than odd numbers?
A. 2 B. 3 C. 4 D. 5 E. 6 Q3. The total of numbers of pens and pencils on a table is 128. The number of pens is 69. What is the difference between the number of pencils and pens on the table?
A. 10 B. 12 C. 20 D. 49 E. 59 Q4. Given that ABCD is a rectangle. Let E and F be points on ABand CD respectively to obtain the square AEFD. FE = 5 and EB = 4. What is the perimeter of ABCD?
A. 24 B. 26 C. 28 D. 30 E. 32 Q5. Which one of the following pair of lengths whose sum is equal to 1 meter 45 centimeters?
A. 90 centimeters and 45 centimeters B. 86 centimeters and 59 centimeters C. 78 centimeters and 77 centimeters D. 63 centimeters and 72 centimeters E. 53 centimeters and 82 centimeters
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Tổng hợp đề thi và đáp án, hướng dẫn giải kỳ thi ITMC khối 2
Q6. Which one of the followings is true for the adjoining figure?
A. equal sides
B. ellipse.
C. symmetry of shape
D. 7 sides
E. hexagon
Q7. Suppose that the 5th August is Sunday. In the same year, what date is the first Sunday of September?
A. 1st B. 2nd C. 3rd D. 4th E. 6th Q8. Tom said “my class will finish in 30 minutes later”. If Tom finished his class at 15:30, at what time would Tom say?
A. 15:05 B. 15:00 C. 14:35 D. 14:30 E. 14:25
Q9. Chusri has 670 dollars that are a 500 dollars bank note, a 100 dollars bank note, a 50 dollars bank note, and a 20 dollars bank note. Chusri buys a carton of milk of price 13 dollars by a bank note. Which one of the followings is not the possible change Chusri should get back?
A. 487 dollars B. 87 dollars C. 37 dollars D. 17 dollars E. 7 dollars
Q10. Students in a grade 2 class choose one of their favorite fruits from 4 kinds of fruits namely orange, banana, apple, and mango as shown in the following table.
Let represent 3 students.
If there are 36 students in the grade 2 class, how many students choose mango? A. 3 B. 6 C. 9 D. 12 E. 15
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Tổng hợp đề thi và đáp án, hướng dẫn giải kỳ thi ITMC khối 2
Q11. The number of students each grade in a primary school are shown in the following table. How many students are in grade 2 of this school?
A. 135 B. 136 C. 137 D. 138 E. 139
Q12. Mary draws a marble from a bag. The bag contains 5 orange marbles, 2 yellow marbles, 1 red marble, 8 blue marbles, and 3 green marbles. What color of marbles has the most possible chance to be drawn?
A. orange B. yellow C. red
D. green E. blue
Part II For question 13 – 24, each correct answer is worth 6 points, 1.5 points for a blank answer, and 0 point for each incorrect answer. Q13. What number is to make the symbolic statement 35 < 26 + < 40 true?
A. 7 B. 9 C. 12 D. 14 E. 16 Q14. Find the sum of all two digit numbers which has 3 as the sum of the digits. A. 30 B. 52 C. 42 D. 33 E. 63 Q15. Given that A = 12, B = 24 and C = 34. Which one of the followings is true? A. C – B = A B. A + B = C – 1 C. C – A = B D. A + B + C = 67 E. A + C = B + 22
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Tổng hợp đề thi và đáp án, hướng dẫn giải kỳ thi ITMC khối 2
Q16. In the given figure, how many quadrilaterals are
in the circle?
A. 3 B. 4 C. 5
D. 6 E. 7
Q17. Given that a bucket of rice weighs 15 kilograms and 1 sack weighs 100 kilograms. How many more kilograms of 2 sacks than 4 buckets?
A. 120 kilograms B. 130 kilograms C. 140 kilograms D. 220 kilograms E. 240 kilograms
Q18. A pizza of radius 8 inches is divided into 3 equal pieces.
A. 48 B. 44 C. 40 D. 32 E. 20
Q19. Students start to take a test at 10.45 A.M.. If they are given 1 hour 30 minutes to finish the test, at what time should students finish the test?
A. 10.45 B. 11.15 C. 11.45 D. 11.55 E. 12.15 Q20. How many numbers are there from 10 to 99 having digit 2? A. 20 B. 18 C. 17 D. 16 E. 19 Q21. If the sum of 5 consecutive numbers is 55, what is the greatest number among the 5 numbers?
A. 10 B. 11 C. 12 D. 13 E. 14 The following information is needed to answer question 22 to 24. At the 2018 FIFA world cup tournaments, the 32 teams were drawn into 8 groups A, B, C, D, E, F, G, and H of 4 teams. In the first round any two teams play together only one match. Each match the winner gets 3 points, no point for the loser. If a match ended in a tie, each team gets 1 point. After the first round ended, the first two teams with highest points in each groups will enter to the second round.
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Tổng hợp đề thi và đáp án, hướng dẫn giải kỳ thi ITMC khối 2
Q22. In the first round, the match results of group A consisting of nation teams of Saudi Arabia, Egypt, Russia, and Uruguay are as follows:
Russia VS Saudi Arabia Russia won 5 – 0 Egypt VS Uruguay Egypt lost 0 – 1 Russia VS Egypt Russia won 3 – 1 Uruguay VS Saudi Arabia Uruguay won 1 – 0 Saudi Arabia VS Egypt Saudi Arabia won 2 – 1 Uruguay VS Russia Uruguay won 3 – 0 After the first round ended, what is the total points of group A?
A. 18 B. 17 C. 16 D. 15 E. 14 Q23. In the first round of the 2018 FIFA world cup tournaments, how many matches are in each group?
A. 6 B. 8 C. 10 D. 12 E. 16
Q24. After the first round of the 2018 FIFA world cup tournaments ended, what is the possible maximum total points of 4 teams?
A. 16 B. 17 C. 18 D. 19 E. 20 PART III For questions 25 – 29, each correct answer is worth 7 points and 0 point for each incorrect or blank answer.
In the case that an answer is not integral, students have to put the most nearest integral answer. Students have to answer the last five digits in the case that the answer from calculating is more than 5 digits. Q25. In the given figure, the equilateral octagon
ABCDEFGH consists of the equilateral triangle ABH, the
square BCGH, and the equilateral pentagon CDEFG. The
perimeter of the equilateral octagon ABCDEFGH equals
112 units. What is the area of the square BCGH equal to?
(Area of a square = length of side × length of side)
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Tổng hợp đề thi và đáp án, hướng dẫn giải kỳ thi ITMC khối 2
Q26. What is the value of 2 × 18 + 25 – 61?
Q27. Let TMCrepresent a 3 digit positive number where different letters represent different digits. If TMC× T = 2560, what is the value of TMC+ T? Q28. Jane took 3 hours to walk in a street on the way back home yesterday. How many minutes did Jane walk in the street?
Q29. A game of putting marbles in a row of 10 small squares, there are two players. The rule of the game are the following:
(i) The players alternate turns.
(ii) Each player, when it is their turn, put at least one marbles but not exceed 5 marbles into the squares. The players must put marbles started from the most left square continuously.
The last player who put marble (s) is the loser.
For example :
A and B are players and player A begins the game.
Turn 1 : Player A puts 2 marbles.
Turn 2 : Player B puts 3 marbles.
Turn 3 : Player A puts 2 marbles.
Turn 4 : Player B puts 2 marbles.
Turn 5 : Only one square is left. Player must put
a marble. The loser is player A.
A winning strategy for this game is that player who puts marbles at first is always the winner.
If there is a row of 20 squares in the game, how many marbles should the player in Turn 1 put in squares in order to guarantee a win?
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Tổng hợp đề thi và đáp án, hướng dẫn giải kỳ thi ITMC khối 2
Bonus Question (Student may or may not give the answer) A correct answer is worth 20 points. An incorrect answer is lost 7 points and 0 point for blank answer.
In the case that an answer is not integral, students have to put the most nearest integral answer. Students have to answer the last five digits in the case that the answer from calculating is more than 5 digits. Q30. Mark and John play a game of guessing a row of 4 digits each of which can be any one of 0 to 9 and without repeating. Mark writes 4 digits on a piece of paper and John guesses the 4 digits. Each time John guesses the 4 digits, Mark will tell the number of right digits and right positions in the row of the 4 digits being guessed. For example, Mark writes a row of 4 digits as 2561 and John guesses as 2018. That is “John guesses 2 right digits (2 and 1) and 1 right position (2 is in the first position)”. Suppose that John guesses 5 times a row of 4 digits written by Mark and Mark tells the number of right digits and right positions as in the following table.
What is the row of 4 digits written by Mark?
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Tổng hợp đề thi và đáp án, hướng dẫn giải kỳ thi ITMC khối 2
ĐỀ SỐ 02
1. Find the perimeter of a rectangle which has the width of 3 cm and the length is 2 times as many as than the width.
A. 12 cm B. 6 cm C. 9 cm D. 18 cm E. 24 cm 2. There are 12 books on a shelf and five children in a room. How many books will be left on the shelf if each child takes one book?
A. 12 B. 7 C. 4 D. 2 E. 0 3. In the picture, each shape stands for a different number. Which number should be written in place of the question mark?
A. 10 B. 12 C. 14 D. 16 E. 18 4. George has 2 cats of the same weight. What is the weight of one cat if George weighs 28 kilograms and the weight of him and two cats is 36 kg?
A. 1 kg B. 2 kg C. 4 kg D. 3 kg E. 5 kg 5. There are 3 children in a family. Kitty is 2 cm taller than Betty, Dannie is 3 cm shorter than Kitty. Who is the tallest and who is the shortest?
A. Annie is the tallest and Dannie is the shortest
B. Betty is the tallest and Dannie is the shortest
C. Kitty is the tallest and Dannie is the shortest
D. Kitty is the shortest and Dannie is the tallest
E. Kitty is the shortest and Annie is the tallest
6. A goose weighs 10 kilograms. The goose is 6 kilograms heavier than a duck. The chicken is 2 kilogram lighter than a duck. How many kilograms does the goose weigh more than the chicken?
A. 6 B. 7 C. 8 D. 9 E. 10 7. What is the sum of the smallest and the biggest 2-digit number? A. 89 B. 10 C. 90 D. 99 E. 109 8. It takes half an hour for Jenny to go half of the way from school to home. How long does it take Jenny to go to school from home?
A. 15 mins B. Half an hour C. 1 hour D. 2 hours E. 40 mins
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Tổng hợp đề thi và đáp án, hướng dẫn giải kỳ thi ITMC khối 2
9. Mother ordered 4 pizzas and sliced each of them into 8 pieces for Vera’s birthday. There were 15 children at the party including Vera. How many slices are left over if mother gives two slices to each child?
A. 5 B. 4 C. 3 D. 2 E. 1 10. There were 10 flags on a straight track of a race. The first one was at the start, the last one at the end. The distance between each flag was 8 m. How long was the track?
A. 24m B. 48m C. 80m D. 72m E. 88m 11. During 3 days Joy, the cat was catching mice. Each day, Joy caught 2 mice more than the previous day. On the third day, Joy caught twice as many mice as on the first day. In total, how many mice did Joy catch during the three days?
A. 12 B. 6 C. 18 D. 20 E. 24 12. We left for a summer camp yesterday at 4:32 PM and got to our destination today at 6:11 AM. For how long did we travel?
A. 13 hours 39 minutes B. 14 hours 39 minutes C. 14 hours 21 minutes D. 13 hours 21 minutes E. 2 hours 21 minutes
13. Find the next term of the following sequence: 3, 5, 8, 13, 21, … A. 23 B. 27 C. 34 D. 35 E. 12 14. A shop sells sweets where every 3 sweet wrappers can be exchanged for one more sweet. Ali has enough money to buy only 7 sweets. What is the biggest number of sweets that he can get from the shop?
A. 7 B. 8 C. 9 D. 10 E. 11 15. Given number 408. How many units will the new number be less than the original number if we take away 2 units from the digit in the hundreds place?
A. 100 B. 200 C. 300 D. 400 E. 500 16. How many triangles can be found in the diagram
below?
A. 4 B. 5 C. 6
D. 7 E. 8
17. David takes 40 seconds to climb from the first floor to the third floor. How many seconds does he take to climb from the third floor to the sixth floor? A. 30s B. 35s C. 40s D. 60s E. 50s 18. Find y, given that: 36 + 65 = y + 22
A. 79 B. 65 C. 80 D. 37 E. None of them
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Tổng hợp đề thi và đáp án, hướng dẫn giải kỳ thi ITMC khối 2
19. A random month has the first Sunday which is on the second day of that month. What is the date of the third Sunday of that month?
A. 16th B. 9th C. 2nd D. 1st E. 5th 20. 989 individual candies are packed into packages which each contains 4 candies. In order to complete the last package, how many more candies are needed?
A. 2 B. 3 C. 4 D.5 E.6 21. Find a number given that if subtract that number by 95 we will get the difference which is equals to 39 minus 22.
A. 70 B. 112 C. 39 D.95 E. None 22. What is 2018 + 2 x 0 x 1 x 4 equal to?
A. 2016 B. 2018 C. 2021 D.2022 E. None 23. Eight pop bottles can be traded in for a pencil. What is the maximum number of pencils that can be obtained from 34 pop bottles?
A. 1 B. 2 C. 3 D. 4 E. 5 24. What is the minimum number of straight cuts required to divide a cylindrical cake into eight identical pieces?
A. 1 B. 2 C. 3 D. 4 E. 5 25. Two classes 2A and 2B are going on a field trip. To divide the number of students of these two classes into two equal groups, teacher needs to exchange 6 female students from 2A to 2B, and 4 male students of from 2B to 2A. Then each group has 32 students. Find out the number of students in each class in the beginning. 26. At present, Mai is 7 years old, Hoa is 10 years old, Hong is 9 years old. What is the sum of ages of these 3 girls when the age of Mai equals to Hong’s age at the moment?
27. Today is Monday, May 4th. In 10 days, it will be Minh’s birthday. On which date is Minh’s birthday and on which day of the week?
28. Find the difference between the biggest 2-digit even number and the smallest 2- digit odd number?
29. How many 2–digit numbers could be formed from 1, 2, 3, 4 and 7. 30. Given 6 digits 0, 1, 2, 3, 4, 5. What is the smallest difference we can get from 3- digit distinctive numbers formed by the given digits
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Tổng hợp đề thi và đáp án, hướng dẫn giải kỳ thi ITMC khối 2
ĐỀ SỐ 03
1. Double me is 16. Who am I?
A. 4 B. 8 C. 12 D. 16 E. 20 2. What operation signs must replace the and so that the mathematical sentence 10 + 1 + 5 = 1 3 5 is correct?
A. + for and × for B. × for and – for C. + for and ÷ for D. × for and ÷ for E. × for and + for
3. How many odd numbers from 1 to 100?
A. 49 B. 50 C. 51 D. 52 E. 53 4. What is the difference between the largest three-digit number and the smallest three- digit number can you make with a set of digit cards: 7, 4, 9, 1?
A. 997 B. 827 C. 769 D. 625 E. 523 5. What is the value of the giraffe in the picture below?
A. 9 B. 11 C. 6 D. 10 E. 12 6. Tim had 17 sweets but he ate six. May had 15 sweets and she ate four. How many sweets do they have now?
A. 32 B. 22 C. 42 D. 18 E. 12 7. Bob ran the race in 60 seconds. Ben ran the race in 74 seconds. Vishni ran the race in 53 seconds. Lin ran the race in 70 seconds. Who is the slowest? A. Bob B. Ben C. Vishni D. Lin E. Mike
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Tổng hợp đề thi và đáp án, hướng dẫn giải kỳ thi ITMC khối 2
8. A snail tried to climb up a vertical wall. At the first time, it tried to climb 60 centimeters upward, but it unfortunately slid 44 centimeters downward. At the second time, it climbed 28 centimeters upward, and slid 35 centimeters downward, and then it rested. How many centimeters apart are the current position and the initial position of the snail?
A. 10 B. 7 C. 11 D. 8 E. 9 9. Which sum is an even number?
A. 62+ 36+ 42 + 18 B. 7+82+ 34 + 10 C. 12 + 31 + 47 + 23 D. 33 + 31 + 15 + 38 E. 20 + 47 + 31 +5
10. Nas’s plane flew half a meter. Aziz’s plane flew 1 and a half meters. Khalid’s plane flew 2 meters. Tom’s plane flew 2 and a half meters. Beck’s plane flew one fourth meter. Whose plane flew the furthest in total?
A. Nas’s B. Aziz’s C. Khalid’s D. Tom’s E. Beck’s 11. Find the value of question mark “?”
A. 25 B. 27 C. 29 D. 32 E. 35 12. The hippo wants to get to the river. Known that, each block is one step. How many steps East does he have to walk in all?
A. 1 B.2 C. 3 D. 4 E. 5
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