Tổng hợp Đề thi và Đáp án, Hướng dẫn giải Kỳ thi ITMC Khối 5 các năm

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Tổng hợp Đề thi và Đáp án, Hướng dẫn giải Kỳ thi ITMC Khối 5 các năm
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Luyện thi Toán Olympic quốc tế
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 TỔNG HỢP
 ĐỀ THI VÀ ĐÁP ÁN, HƯỚNG DẪN GIẢI
 KỲ THI ITMC
 khốiKhối
 55
 cáccác nămnăm
 Tải ứng dụng mobile
 Biên tập: Ðào Hưng Hotline:
 ToanCodeMathVN @CodeMathVN 0346 475 489 Tổng hợp đề thi và đáp án kỳ thi ITMC khối 5 
 MỤC LỤC 
ĐỀ SỐ 01: ..............................................................................................................8 
ĐỀ SỐ 02 .............................................................................................................. 15 
ĐỀ SỐ 03 .............................................................................................................. 22 
ĐỀ SỐ 04 .............................................................................................................. 26 
ĐÁP ÁN ĐỀ SỐ 01 .............................................................................................. 31 
 3 Tổng hợp đề thi và đáp án kỳ thi ITMC khối 5 
 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 Sử dụng trung bình để tính tổng như thế 
 sum? 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? 
 5 Tổng hợp đề thi và đáp án kỳ thi ITMC khối 5 
 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 
 7 Tổng hợp đề thi và đáp án kỳ thi ITMC khối 5 
Q7. A factor of n is a positive integer which is a divisor of n. For example, 
 There are 6 factors of 12 which are 1, 2, 3, 4, 6, 12. 
 There are 2 factors of 3 which are 1, 3. 
 There is only 1 factor of 1. 
Which one of the following numbers has the least number of factors? 
 A. 24 B. 30 C. 37 D. 40 E. 42 
Q8. Let a be the smallest 2-digit number which is divided by 7 with a remainder of 
2 and let b be the largest 2-digit number which is divided by 7 with a remainder of 2. 
Find the value of a + b. 
 A. 109 B. 102 C. 116 D. 110 E. 112 
Q9. Which one of the following numbers has smallest remainder when it is divided 
by 7? 
 A. 2018 B. 2561 C. 4036 D. 5122 E. 543 
Q10. International trade is the exchange of goods and services between countries. 
Total trade equals exports plus imports. A country has a balance of trade surplus 
when it exports more than it imports and has a balance of trade deficit when it 
imports more than it exports. 
Suppose that in this year Thailand has the value of exports 3.99 trillion baht and the 
value of imports 3.45 trillion baht. Which one of the following statements is true ? 
A. In this year, Thailand has a balance of trade deficit of value 5.4 trillion baht. 
B. In this year, Thailand has a balance of trade deficit of value 0.54 trillion baht. 
C. In this year, Thailand has a balance of trade surplus of value 5.4 trillion baht. 
D. In this year, Thailand has a balance of trade surplus of value 0.54 trillion baht. 
E. In this year, Thailand has a balance of trade deficit of value 0.054 trillion baht. 
Q11. In a year, if the 5th August is Sunday, which one of the followings is Monday? 
 A. the 5th July B. the 5th September 
 C. the 5th October D. the 5th November 
 E. the 5th December 
Q12. How many natural numbers from 100 to 999 are there of which the sum of the 
digits in units place and tensplace is equal to 9? 
 A. 81 B. 90 C. 100 D. 180 E. 450 
 9 Tổng hợp đề thi và đáp án kỳ thi ITMC khối 5 
Q18. A pizza of radius 8 inches is divided into 3 equal pieces. 
A pizza of radius 10 inches is divided into 4 equal pieces 
A pizza of radius 12 inches is divided into 6 equal pieces. 
A pizza of radius 14 inches is divided into 8 equal pieces. 
All pizzas have the same thickness. David wants to select a piece of pizza whose 
quantity is greatest. What radius of pizza is selected by David? 
 A. 8 inches B. 10 inches 
 C. 12 inches D. 14 inches 
 E. Any piece of pizza could be selected since they have the same quantity 
Q19. A box contains cards of number 1 to 10 (one card one number). If a card is 
taken away from the box, the cards left in the box could be divided into two piles 
each of which the product of numbers on the cards are equal. What number is on the 
card taken away from the box? 
 A. 7 B. 6 C. 5 D. 3 E. 2 
Q20. Consider the following sequence of letters. 
 PRENEEXAMPRENEEXAMPRENEEXAM . . . 
What is the 100th letter in the sequence? 
 A. P B. R C. E D. N E. X 
 Q21. Count numbers from innermost circle to 
 outermost circle in the following figure. Let x be the 
 10th number in sector A and y be the 20th number in 
 sector D. Find x + y. 
 A. 135 B. 138 C. 140 
 D. 143 E. 145 
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 played 
together only one match. Each match the winner got 3 points, no point for the loser. 
If a match ended in a tie, each team got 1 point. After the first round ended, the first 
two teams with highest points in each groups would enter to the second round. 
 11 Tổng hợp đề thi và đáp án kỳ thi ITMC khối 5 
Q26. ABCD is a square. Construct rectangle ABEF by giving the points E and F on 
BC and AD respectively. Construct square AGHF by giving the points G and H on 
AB and EF respectively. The perimeters of the square AGHF and the rectangle 
ABEF are 25 and 61 respectively. What is the perimeter of the square ABCD? 
Q27. Let d1, d2, d3, . . . , d15 be an increasing sequence of 15 different numbers, each 
of which is a factor of 2500. Determine d12. 
Q28. In writing numbers from 1 to 20 as follows: 
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 
it is found that digit “1” is written 12 times. For example, there are 2 times of writing 
“1” in 11. Find the number of times that the digit “5” is written in writing numbers 
from 1 to 231. 
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 marble but not exceed 5 
 marbles into the squares. The players must put marbles started from the most 
 left square continuously. The last player who puts 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. 
 If there is a row of 50 squares in the game, how many 
 marbles should the player in Turn 1 put insquares in 
 order to guarantee a win? 
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. 
 13 

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