Tài liệu ôn thi toán AMO lớp 8, 9 năm 2019 | Kỳ thi toán AMO 2019

In the first break time, each girl bought a cheese cake, each boy bought a coke (both the price of a cheese cake and a coke are integers). In the second break time, each girl bought a co[r]

TRAINING COURSE FOR AMO 2019

PREPARE FOR AMO 2019 - GRADE 8-9

Exercise 1 The below diagram shows an equilateral triangle and a square of side length 2 joined

along an edge What is the area of the shaded triangle?

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Exercise 2 In 4P QR, U is a point on P R, S is a point on P Q, T is a point on QR with U S k RQ

and U T k P Q The area of 4P SU is 120 cm2 and the area of 4T U R is 270 cm2 What is the area

Exercise 9 The blood groups of 200 people is distributed as follows: 50 have type A blood, 65

have B blood type, 70 have O blood type and 15 have type AB blood If a person from this group

is selected at random, what is the probability that this person has O blood type?

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Exercise 10 A box contains 5 chips, numbered 1, 2, 3, 4, and 5 Chips are drawn randomly one at

a time without replacement until the sum of the values drawn exceeds 4 What is the probabilitythat the number of draws is 3?

Exercise 11 A number m is randomly selected from the set {11, 13, 15, 17, 19}, and a number n is

randomly selected from {1999, 2000, 2001, , 2018} What is the probability that the unit digit of

mn is 1?

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TRAINING COURSE FOR AMO 2019

PREPARE FOR AMO 2019 - GRADE 8-9

Y Z

1 6 7 5

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Exercise 5 In the diagram, OM N P is a square, O is a centre of a circle and OM is a radius Point

Lis on the circle such that LK is perpendicular to M N and K is a midpoint of segment M N Findthe measure of angle [OLN

N P

K L

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Exercise 6 Ms Forest likes to let her students choose who their partners will be; however, no

pair of students may work together more than seven class periods in a row Adam and Baxter havestudied together seven class periods in a row Carter and Dennis have worked together three classperiods in a row Carter does not want to work with Adam Who should be assigned to work withBaxter? In your answer sheet, write 001 for Adam, 002 for Baxter, 003 for Carter, 004 for Dennis

Exercise 7 The high school math department needs to appoint a new chairperson, which will

be based on seniority Ms West has less seniority than Mr Temple, but more than Ms Brody Mr.Rhodes has more seniority than Ms West, but less than Mr Temple Mr Temple doesn’t want thejob Who will be the new math department chairperson? In your answer sheet, write 001 for Ms.West, 002 for Mr Temple, 003 for Ms Brody, 004 for Mr Rhodes

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Exercise 8 As they prepare for the state championships, one gymnast must be moved from the

Level 2 team to the Level 1 team The coaches will move the gymnast who has won the biggest prizeand who has the most experience In the last competition, Roberta win a bronze medal and hascompeted seven times before Jamie has won a silver medal and has competed fewer times thanRoberta Beth has won a higher medal than Jamie and has competed more times than Roberta.Michele has won a bronze medal, and it is her third time competing Who will be moved to theLevel 1 team? In your answer sheet, write 001 for Roberta, 002 for Jamie, 003 for Beth, 004 forMichele

Exercise 9 The school that Stefan went to was selling tickets to a choral performance On the first

day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38 Theschool took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets Find thetotal price of a senior citizen ticket and a child ticket

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Exercise 10 Some students want to order shirts with their school logo One company charges

$9.65per shirt plus a setup fee of $43 Another company charges $8.40 per shirt plus a $58 fee Forwhat number of shirts would the cost be the same?

Exercise 11 Monica and Jacob decided to shoot arrows at a simple target with a large outer ring

and a smaller bull’s-eye Monica went first and landed 3 arrows in the outer ring and 5 arrows inthe bull’s-eye, for a total of 440 points Jacob went second and got 1 arrow in the outer ring and

4 arrows in the bull’s-eye, earning a total of 317 points How many points was the outer ring isworth?

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TRAINING COURSE FOR AMO 2019

PREPARE FOR AMO 2019 - GRADE 8-9

Exercise 1 In a group of people, the ratio of women to men is 12 : 8 The average age of women

is 22 and that of men is 32 What is the average age of people in this group?

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Exercise 3 The function f has the properties that f (1) = 6 and f (2x + 1) = 3f (x) for every

integer x What is the value of f (31) ?

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Exercise 6 A woman is baking some cakes for her children She counts the number of baked

cakes and thinks, "If each child receive 5 cakes, then I have to bake 3 more cakes; but if each childreceive 4 cakes, then there will be 3 remaining cakes for me." So, how many children does thiswoman have?

Exercise 7 Given a polynomial P (x) of degree 4 with leading coefficient 1 such that P (1) = 3,

P (3) = 11, P (5) = 27 Find the value of 12 × (P (−2) + 7P (6))

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Exercise 8 An egg is thrown from a platform 100m in the air From the time t in seconds when

thrown until it hits the ground below, the egg’s height from the ground in metres follows theformula h = −5t2+ 30t + 100 Assume that air resistance is negligible Find the difference betweenthe maximum height and the minimum height of the egg in the first 5 seconds

Exercise 9 A class has 30 students, most of them are boys One night, all of them went to the

cinema In the first break time, each girl bought a cheese cake, each boy bought a coke (both theprice of a cheese cake and a coke are integers) In the second break time, each girl bought a coke,each boy bought a cheese cake They realized that in the second break, they paid 2 dollars lessthan in the first break How many boys does the class have?

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for all values of x Determine the value of |2f (2) g (−2) |.

Exercise 11 Lately, my wrist watch is running 56 minutes more slowly after 24 hours, and my alarmclock is running 112 minutes more slowly after 24 hours At the midday of Monday, I adjust my wristwatch and clock A week later, I ask my mother what time it is Mom said, "I don’t know, but thedifference in time between your watch and your clock is 4 minutes and 15 seconds." So, what time

is it when I ask my mother about time?

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