Đề thi AMC8 năm 2018

he MAA Committee on the American Mathematics Competitions reserves the right to disqualify scores from a school if it determines that the required security procedures were not followed.

he publication, reproduction or communication of the problems or solutions of this exam during the period when students are eligible to participate seriously jeopardizes the integrity of the results. Dissemination via phone, email, or digital media of any type during this period is a violation of the competition rules.

© 2018 Mathematical Association of America

INSTRUCTIONS

1. DO NOT OPEN THIS BOOKLET UNTIL YOUR COMPETITION MANAGER TELLS YOU.

2. his is a 25-question multiple-choice exam. For each question, only one answer choice is correct. 3. Mark your answer to each problem on the answer sheet with a #2 pencil. Check the blackened circles for accuracy and erase errors and stray marks completely. Only answers that are properly marked on the answer form will be scored. 4. here is no penalty for guessing. Your score is the number of correct answers. 5. Only scratch paper, graph paper, rulers, protractors, and erasers are allowed as aids. Calculators are NOT allowed. No problems on the exam require the use of a calculator. 6. Figures are not necessarily drawn to scale. 7. Before beginning the exam, your competition manager will ask you to record your name and other information on the answer sheet. 8. You will have 40 minutes to complete the exam once your competition manager tells you to begin. 9. When you inish the exam, sign your name in the space provided at the bottom of the answer sheet.

MAA American Mathematics Competitions

34th Annual AMC 8

American Mathematics Competition 8 Tuesday, November 13, 2018

AMC 8

MAA Partner Organizations

We acknowledge the generosity of the following organizations in supporting the MAA AMC and Invitational Competitions:

Patron’s Circle Akamai Foundation

Innovator’s Circle he D. E. Shaw Group Two Sigma

Winner’s Circle MathWorks Tudor Investment Corporation

Achiever’s Circle Art of Problem Solving Jane Street Capital

Sustainer’s Circle American Mathematical Society Ansatz Capital Army Educational Outreach Program

Collaborator’s Circle American Statistical Association Casualty Actuarial Society Conference Board of the Mathematical Sciences Mu Alpha heta Society for Industrial and Applied Mathematics

2 MAA AMC 8

1. An amusement park has a collection of scale models, with ratio 1:20, of build- ings and other sights from around the country. The height of the United States Capitol is 289 feet. What is the height in feet of its replica at this park, rounded to the nearest whole number?

(A) 14 (B) 15 (C) 16 (D) 18 (E) 20

2. What is the value of the product

1 C 1

1

1 C 1

2

1 C 1

3

1 C 1

4

1 C 1

5

1 C 1

6

‹

(A) 7

6 (B) 4

3 (C) 7

2 (D) 7 (E) 8

3. Students Arn, Bob, Cyd, Dan, Eve, and Fon are arranged in that order in a circle. They start counting: Arn first, then Bob, and so forth. When the number contains a 7 as a digit (such as 47) or is a multiple of 7 that person leaves the circle and the counting continues. Who is the last one present in the circle?

(A) Arn (B) Bob (C) Cyd (D) Dan (E) Eve

4. The twelve-sided figure shown has been drawn on 1 cm 1 cm graph paper. What is the area of the figure in cm2?

(A) 12 (B) 12:5 (C) 13 (D) 13:5 (E) 14