Đề vòng chung kết Quốc gia kỳ thi Olympic toán học Quốc tế TIMO 2020-2021 Khối 6 (Kèm đáp án)

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Đề vòng chung kết Quốc gia kỳ thi Olympic toán học Quốc tế TIMO 2020-2021 Khối 6 (Kèm đáp án)
 THAILAND INTERNATIONAL 
 MATHEMATICAL OLYMPIAD 
 FINAL ROUND 2020 – 2021 
 Secondary 1 
 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. 
 1 
 All answers should be written on the ANSWER SHEET. 
 Number Theory 
13. Find the number of all positive factor(s) of 2021. 
 4
14. It is known that x is rational and x 5 . Find the maximum value of x. 
 4
 5 
 4
 5 
15. It is known that the remainders of a 4-digit number x divided by 4, 5, 7 and 
 9 are 3, 4, 6 and 8 respectively. What is such largest 4-digit number x ? 
16. It is known that n! n n 1 n 2 1. Find the number of “0” at 
 the end of 641!. 
17. Now is Wednesday. Find the day of the week after 412021 days. 
18. Find the greatest common divisor of 882 and 378. 
 Geometry 
19. S(,) x y is a point on HK such that HS: SK 5:3 . If H 9,10 and 
 K 1,2 , find xy . 
20. It is given that the area of a rectangle is 2021. The width and length are 
 integers. Find the smallest value of the perimeter. 
21. In the figure, ACD and BCE are straight lines and AB// DE . It is given that 
 AB 6, BC 8, AC 4 and DE 15. Find the length of CE . 
22. The polar coordinates of the points A, B and C are 7,70 , 8,160 and 
 18,340 respectively. Find the area of ABC . 
 3 

File đính kèm:

  • pdfde_vong_chung_ket_quoc_gia_ky_thi_olympic_toan_hoc_quoc_te_t.pdf
  • pdfTIMO Final 202021_Ans_ALL.pdf