Đề vòng chung kết Quốc gia kỳ thi Olympic toán học Quốc tế TIMO 2020-2021 Khối 7 (Kèm đáp án)

 THAILAND INTERNATIONAL 
 MATHEMATICAL OLYMPIAD 
 FINAL ROUND 2020 – 2021 
 Secondary 2 
 Time allowed: 120 minutes 
 Question Paper 
 Instructions to Contestants: 
1. Each contestant should have ONE Question-Answer Book which CANNOT be 
 taken away. 
2. There are 5 exam areas and 6 questions in each exam area. There are a total of 30 
 questions in this Question-Answer Book. Each question carries 5 marks. Total 
 score is 150 marks. No points are deducted for incorrect answers. 
3. All answers should be written on ANSWER SHEET. 
4. NO calculators can be used during the contest. 
5. All figures in the paper are not necessarily drawn to scale. 
6. 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. 
7. This Question-Answer Book will be collected at the end of the contest. 
 DO NOT turn over this Question-Answer Book without approval of the examiner. 
 Otherwise, contestant may be DISQUALIFIED. 
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 All answers should be written on the ANSWER SHEET. 
 Number Theory 
13. If the difference of two positive integers is 2021, and their highest common factor is d. 
 Find the largest possible value of d. 
14. It is known that x is rational, x 0 and x 28 3 28 3 . Find the value of x. 
15. Find the sum of all positive factors of 2021. 
 1
16. Find the numbers of “6” of the expression 17 102404 10 1202 1 . 
 3
17. Now is Wednesday. Which day of the week will it be after 551207 days? 
18. Find the numbers of simplified fractions with denominator 2021. 
 Geometry 
19. Find the area enclosed by the x-axis, y-axis and the straight line 8yx 5 40. 
20. The polar coordinates of the points A, B and C are 14,40 , 26,130 and 7,310 
 respectively. Find the area of ABC . 
21. Find the angles’ difference of the minute hand of a clock after 1700 minutes. 
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22. In the figure, AB 17 , DB 15 and CD 28 . If AB BC and AC BD , find 
 8
 AB: BC . 
 A 
 D 
 B C 
 Question 22 
23. Given a triangle XYZ with two lines XY XZ , YX 7 and XZ 4 , find the value of 
 1
 . 
 cosXYZ sin  XYZ 2
24. A solid cuboid is formed by merging 819 cubes with side length 1cm. Find the minimum 
 value of the total surface area of the cuboid. 
 3