Đề thi AMC8 năm 2017

The 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.

The 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.

© 2017 Mathematical Association of America

INSTRUCTIONS

1. DO NOT OPEN THIS BOOKLET UNTIL YOUR COMPETITION MANAGER

TELLS YOU.

2. This is a 25 question multiple choice test. 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 properly marked on the answer form will be scored. 4. There 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 test require the use of a calculator. 6. Figures are not necessarily drawn to scale. 7. Before beginning the test, 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 test once your competition manager tells

you to begin. 9. When you finish the exam, sign your name in the space provided at the bottom of the

answer sheet.

MAA American Mathematics Competitions

33rd Annual AMC 8

American Mathematics Competition 8 Tuesday, November 14, 2017

AMC 8

The MAA American Mathematics Competitions are supported by:

Patron’s Circle

Akamai Foundation

Innovator’s Circle

The D. E. Shaw Group Susquehanna International Group

Tudor Investment Corporation

Two Sigma

Winner’s Circle

MathWorks

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 Theta Society for Industrial and Applied Mathematics

MAA AMC 8 2

1. Which of the following values is largest?

(A) 2 C 0 C 1 C 7 (B) 2 0 C 1 C 7 (C) 2 C 0 1 C 7

(D) 2 C 0 C 1 7 (E) 2 0 1 7

2. Alicia, Brenda, and Colby were the candidates in a recent election for student president. The pie chart below shows how the votes were distributed among the three candidates. If Brenda received 36 votes, then how many votes were cast all together?

(A) 70 (B) 84 (C) 100 (D) 106 (E) 120

3. What is the value of the expression

r

16 q

8 p

4 ?

(A) 4 (B) 4 p

2 (C) 8 (D) 8 p

2 (E) 16

4. When 0:000315 is multiplied by 7;928;564 the product is closest to which of the following?

(A) 210 (B) 240 (C) 2;100 (D) 2;400 (E) 24;000

5. What is the value of the expression 1 2 3 4 5 6 7 8 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8?

(A) 1020 (B) 1120 (C) 1220 (D) 2240 (E) 3360