When your teacher gives the signal, begin working on the problems.
I I nt n te er rn na at t io i on n al a l M Ma at t he h em ma at ti ic cs s A A ss s se es ss sm me en n ts t s f fo or r S Sc ch ho oo ol ls s
2018JUNIORDIVISIONFIRSTROUND PAPER Time allowed:75 minutes
Record your answers on the reverse side of the Answer Sheet (not on the question paper) by FULLY filling in the circles which correspond to your choices.. Your Answer Sheet will be read[r]
When your teacher gives the signal, begin working on the problems.
I I nt n te er rn na at t io i on n al a l M Ma at t he h em ma at ti i cs c s A A ss s se es ss sm me en n ts t s f fo or r S Sc ch ho oo ol ls s
2017 JUNIORDIVISIONFIRSTROUND PAPER Time allowed:75 minutes
Record your answers on the reverse side of the Answer Sheet (not on the question paper) by FULLY filling in the circles which correspond to your choices.. Your Answer Sheet will be read[r]
(A)20 (B)31 (C)42 (D)53 (E)64
19. In an election between four candidates, they are supported respectively by 11, 12, 13 and 14 of the first 50 voters. Six more votes are to be cast, each for one of the four candidates. In how many ways can the candidate currently with 13 supporters become the uncontested winner?
Do not open the contest booklet until you are told to do so.
Be sure that your name and code are written on the space provided above.
Round 2 of IMAS is composed of three parts; the total score is 100 marks.
Questions 1 to 5 are given as a multiple-choice test. Each question has five possible options marked as A, B, C, D and E. Only one of these options is correct.
If 2 and 8 are both to the right of 4, the sequence partially looks like 4ab2c8, where 1 must be a.
If 4 is the first from the left, then the sequence looks like 41b2c8de, 3 and 6 must be at b, d, two choices for them and two choices for remaining 5 and 7;
22. How many ways can we divide 6 students into 3 groups so that each group has exactly 2 students?
23. In the figure below, ABCD, EFGH and AJKL are squares. The area of AJKL is 2018 cm 2 . If rectangles EFCI and JBFK both have an area of 1360 cm 2 , then what is the area, in cm 2 , of CGHI?
Questions 21-25, 6 marks each
21. Mike constructs a sequence in the following way: the first two terms are 1 and 2.
Starting from the third term, each term is the smallest possible integer that is not relatively prime to the previous term and has not yet appeared in any of the previous terms. Find the 20 th term of this sequence.
z Do not open the contest booklet until you are told to do so.
z Be sure that your name and code are written on the space provided above.
z Round 2 of IMAS is composed of three parts; the total score is 100 marks.
z Questions 1 to 5 are given as a multiple-choice test. Each question has five possible options marked as A, B, C, D and E. Only one of these options is correct.
Do not open the contest booklet until you are told to do so.
Be sure that your name and code are written on the space provided above.
Round 2 of IMAS is composed of three parts; the total score is 100 marks.
Questions 1 to 5 are given as a multiple-choice test. Each question has five possible options marked as A, B, C, D and E. Only one of these options is correct.
Do not open the contest booklet until you are told to do so.
Be sure that your name and code are written on the space provided above.
Round 2 of IMAS is composed of three parts; the total score is 100 marks.
Questions 1 to 5 are given as a multiple-choice test. Each question has five possible options marked as A, B, C, D and E. Only one of these options is correct.
z Do not open the contest booklet until you are told to do so.
z Be sure that your name and code are written on the space provided above.
z Round 2 of IMAS is composed of three parts; the total score is 100 marks.
z Questions 1 to 5 are given as a multiple-choice test. Each question has five possible options marked as A, B, C, D and E. Only one of these options is correct.
3 2 5 2
2016 − 2016 = 2016 (2016 × − = 1) 2015 2016 2017 × × = × × × × × × 2 3 5 7 13 31 2017 , so the prime factors of the positive integer which satisfy the conditions should be 11, 17, 19, …, 29, 37, …, 2011, 2027, …. Since the positive integer has 12 positive divisors, it is of the form p 11 , p q 5 , p q 3 2 or p qr 2 , where p, q and r are different prime numbers. It is obviously that the first three forms are all greater than 10 5 and the smallest value of the last one is 11 2 × × = 17 19 39083 10 < 5 .
(A)12 (B)18 (C)24 (D)30 (E)36
【Solution 1】
From the given information, one student will participate in two events and each of other two students participate on exactly one event. Let the student (the one will participate in 2 events) choose the events that he wants to register, then there are 4 ways of registering the two events, follow by the first student with one event has 3 ways to register his event, the second student with one event has also 3 ways to choose his event. Thus, the total number is 3 4 3 × × = 36 ways of participating.
From the given information, it shows the sum of the three numbers in the second row is equal to twice the sum of the three numbers in the first row, it follows that the difference of the sum of three numbers in the second row and the sum of three numbers in the first row equal the sum of three numbers in the first row, that is; the difference of these two rows is 19 + 20-5-6 = 28, then we have ☆ = 28-5-6 = 17. Thus, we select option (D).
Subtracting this from the total surface area of the individual cubes, we have
14 6 42 42 . Answer: (C)
19. In an election between four candidates, they are supported respectively by 11, 12, 13 and 14 of the first 50 voters. Six more votes are to be cast, each for one of the four candidates. In how many ways can the candidate currently with 13 supporters become the uncontested winner?
Record your answers on the reverse side of the Answer Sheet (not on the question paper) by FULLY filling in the circles which correspond to your choices.. Your Answer Sheet will be read[r]
Record your answers on the reverse side of the Answer Sheet (not on the question paper) by FULLY filling in the circles which correspond to your choices.. Your Answer Sheet will be read[r]
14. There are two routes starting in a bus stop. A bus departs for the first route every 8 minutes and departs the second route every 10 minutes. At 6:00 in the morning, two buses depart for the two routes at the same time. Among the choices below, when will the buses depart for the two routes simultaneously?