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ĐỀ THI SEAMO - CẤP ĐỘ C (KHỐI 5 + 6) NĂM 2018

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ĐỀ THI SEAMO - CẤP ĐỘ C (KHỐI 5 + 6) NĂM 2018
ĐỀ THI SEAMO - CẤP ĐỘ C (KHỐI 5 + 6) NĂM 2018
ĐỀ THI SEAMO - CẤP ĐỘ C (KHỐI 5 + 6) NĂM 2018
ĐỀ THI SEAMO - CẤP ĐỘ C (KHỐI 5 + 6) NĂM 2018
ĐỀ THI SEAMO - CẤP ĐỘ C (KHỐI 5 + 6) NĂM 2018

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ĐỀ THI SEAMO - CẤP ĐỘ C (KHỐI 5 + 6) NĂM 2018

  1. 1. SEAMO 2018 Paper C © TCIMO 1 1. Find the ones digit in 1" + 2% + 3'( + 4'* + 5,' +6,' + 7,% + 8," (A) 5 (B) 6 (C) 7 (D) 8 (E) 9 3. Evaluate 1 1 × 2 × 3 + 1 2 × 3 × 4 + 1 3 × 4 × 5 + ⋯ + 1 99 × 100 × 101 (A) 5049 20200 (B) 10099 20200 (C) 1 2 (D) 10099 10100 (E) None of the above2. The figure is made of 13 squares, each of side length 2 cm. It is known that line AB divides the figure into 2 regions of equal areas. Find the length of AX, in cm. (A) 4 1 8 (B) 4 1 4 (C) 4 1 2 (D) 4 3 4 (E) None of the above 4. How many shortest paths are there from point A to point B passing through P and Q? (A) 48 (B) 54 (C) 60 (D) 66 (E) 72 QUESTIONS 1 TO 10 ARE WORTH 3 MARKS EACH
  2. 2. SEAMO 2018 Paper C © TCIMO2 5. The product of the numerator and denominator of a proper fraction is 420. How many such possible proper fractions are there? (A) 7 (B) 8 (C) 9 (D) 10 (E) None of the above 7. After a certain amount of water is added to a bottle of sodium chloride, its salt content becomes 15%. The same amount of water is added the 2nd time and the salt content becomes 12%. What is the salt content, in %, after the same amount of water is added a 3rd time? (A) 6 (B) 7 (C) 8 (D) 9 (E) None of above 6. Find the remainder in 565656567777777777777 56777 × 1 9 (A) 4 (B) 5 (C) 6 (D) 7 (E) 8
  3. 3. SEAMO 2018 Paper C © TCIMO 3 8. There are 3, 6 and 10 vertices in Figures 1, 2 and 3, respectively. Find the number of vertices in Fig 20. (A) 155 (B) 198 (C) 231 (D) 243 (E) None of the above 10. The formula to convert temperature in Celsius to Fahrenheit is 89:;99 <= >9?@<AB × 9 5 + 32 At what temperature will Fahrenheit be 60 more than Celsius? (A) 34℃ (B) 35℃ (C) 36℃ (D) 37℃ (E) None of the above 9. Miss Nutcharat is driving from Bangkok to Chiang Mai. If she drives at a constant speed of 100 km/h, she will be 30 minutes late. If she drives at 120 km/h, she will be 35 minutes early. What is the distance between Bangkok and Chiang Mai? (A) 620 km (B) 640 km (C) 650 km (D) 720 km (E) None of the above 11. A big truck has a capacity of 8 tonnes and consumes 15ℓ of diesel per trip. A small truck has a capacity of 2 tonnes and consumes 4ℓ of diesel per trip. What is the minimum amount of diesel needed to transport 100 tonnes of goods? (A) 165ℓ (B) 172ℓ (C) 180ℓ (D) 188ℓ (E) None of the above QUESTIONS 11 TO 20 ARE WORTH 4 MARKS EACH
  4. 4. SEAMO 2018 Paper C © TCIMO4 12. In the year 2010, Anand’s age is 4 times the sum of the ages of his two sons. In 2018, Anand’s age is twice the sum of the ages of his two sons. In which year is Anand born? (A) 1962 (B) 1963 (C) 1964 (D) 1966 (E) None of the above 14. In ∆FG> , >8 = 3G8 and 8I = FI . Given that the area of ∆FG> is 14 cm2 , find the total area, in @J, , of the shaded regions. (A) 5 (B) 6 (C) 7 (D) 8 (E) None of the above 13. Three scholars Sam, Rex and Ted, study English, Math, Science, Dance, Music and Art. • The Science and Math students are neighbors. • The youngest among them is Rex. • Sam exercises with the Dance, Music and Math students. • The Dance student is older than the English student. • Rex plays chess with the Music and English students. • Each student studies two subjects Which two subjects does Ted study? (A) Science and Art (B) Math and English (C) Math and Science (D) Dance and Music (E) None of the above 15. Twenty-four 4-digit numbers can be formed using the digits 3, 4, 6 and 8, without repeat. Find the average of these 4-digit numbers. (A) 5250 (B) 5625.5 (C) 5832.75 (D) 5830 (E) None of the above
  5. 5. SEAMO 2018 Paper C © TCIMO 5 16. How many numbers at maximum can be selected from: 1, 2, 3, … , 49, 50 such that the sum of any two numbers cannot be divided by 7? (A) 19 (B) 20 (C) 21 (D) 22 (E) 23 18. Akani has two 20¢ and three $1 coins in his pocket. He picks out the coins at random, one after another, without replacement. What is the probability that the total value of the two coins is $1.20? (A) 1 4 (B) 2 5 (C) 4 7 (D) 3 5 (E) None of the above 17. There are ten cards numbered: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 Each time a card is drawn, the number is recorded, then put back into the deck and shuffled. After repeating the process 4 times, the product of all the recorded numbers is M. Which of the following numbers cannot be M? 136, 198, 455, 1925, 2018 (A) 455 and 2018 (B) 136 and 455 (C) 136 and 198 (D) 1925 and 2018 (E) None of the above 19. The figure shows two circles and a square of side 12 cm. Find the total area of the shaded regions. (A) 14N @J, (B) 16N @J, (C) 18N @J, (D) 20N @J, (E) None of the above
  6. 6. SEAMO 2018 Paper C © TCIMO6 20. Madam Evie drives from Bandung to Surabaya at a constant speed V km/h. If she increases her speed by 20%, she will arrive 2 hours ahead of schedule. If she travels the first 100 km at V km/h, the increases her speed by 25%, she will still arrive 2 hours ahead of schedule. Find the distance, in km, between Bandung and Surabaya. (A) 480 (B) 520 (C) 560 (D) 600 (E) None of the above 23. Find the difference between the area of the three squares and the area of the four triangles in the figure below. 24. A queue is building up at a constant rate at the museum before its opening at 10:30 AM. If 3 entrances are opened, the queue clears at 10:39 AM. If 5 entrances are opened, the queue clears at 10:35 AM. What time did the 1st visitor start queuing?21. A new operation is defined as: J ⨁ = = J × (J + 1) × (J + 2) × … × (J + = − 1) Given that (J ⨁ 3) ⨁ 2 = 3660 , find the value of m. 25. A number from 1 to 9 is filled into each circle below, such that the sum of 4 numbers on any face is the same and cannot divide 45. Which number cannot be used? 22. Evaluate (2, + 4, + ⋯ + 100, ) − (1, + 3, + ⋯ + 99,) 1 + 2 + 3 + ⋯ + 9 + 10 + 9 + ⋯ + 3 + 2 + 1 End of Paper QUESTIONS 21 TO 25 ARE WORTH 6 MARKS EACH
  7. 7. © SEAMO 2018 Paper C 1 SEAMO 2018 Paper C – Answers Multiple-Choice Questions Questions 1 to 10 carry 3 marks each. Q1 Q2 Q3 Q4 Q5 B C A E B Q6 Q7 Q8 Q9 Q10 A E C C B Questions 11 to 20 carry 4 marks each. Q11 Q12 Q13 Q14 Q15 D A D B C Q16 Q17 Q18 Q19 Q20 E A D C D Free-Response Questions Questions 21 to 25 carry 6 marks each. 21 22 23 24 25 3 50.5 122 $%& 9:45 AM 7

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