MATHCOUNTS
2000 National Competition
Countdown Round
In the Village League, the team to
win two of three softball games
becomes the champion. If the
probability of Team Alpha
beating Team Beta is 60% for
every game, what is the
Answer:
44
125
Circles A an
Forward Presence
FP = MP
Forward presence is military presence
Zakheim et al 96 former Deputy Undersecretary of Defense for Planning and Resources (Dov,
Political and Economic Implications of Global Naval Presence, 9/30,
http:/handle.dtic.mil/100.2/ADA319
50 AMC Lectures
Chapter 8 Divisibility
Example 1. Show that for any positive integer n, n(n 1)(2n 1) is always divisible by 6.
Example 2. (AMC) If n is any whole number, n2(n2 1) is always divisible by:
(A) 12
(B) 24
(C) any multiple of 12
(D) 12 n
(E) 12
50 AMC Lectures
Chapter 1 Algebraic Manipulation
PROBLEMS
Problem 1: Find m 2
1
1
if m 4 .
2
m
m
Problem 2: Find a 3
1
1
if a 3 .
3
a
a
(A) 0 (B)
5 3
3
(C) 1
Problem 3: Find m6
(D) 5 3
(E)
3.
1
1
if m 4 .
6
m
m
Problem 4: Find a quadratic equation that
50 AMC Lectures
Chapter 21 Similar Triangles
BASIC KNOWLEDGE
Similar triangles are triangles whose corresponding angles are congruent and whose
corresponding sides are in proportion to each other. Similar triangles have the same shape
but are not necessar
2016
State Competition
Team Round
Problems 110
School
Chapter
Team
Members
, Captain
DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO
DO SO.
This section of the competition consists of 10 problems which the teamhas
20 minutes to complete. Team members may work to
2017 State Competition Solutions
Are you wondering how we could have possibly thought that a Mathlete would be able
to answer a particular Sprint Round problem without a calculator?
Are you wondering how we could have possibly thought that a Mathlete woul
0
1
2
3
4
2017
State Competition
Target Round
Problems 1 & 2
5
6
7
8
Name
9
School
Chapter
DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO.
This section of the competition consists of eight problems, which will be presented in
pairs. Work on one pair of pr
National Society of Professional Engineers
MATHCOUNTS.
2003
I National Competition I
Target Round
Problems 1 and 2
Name
School 12
State
DO NOT BEGIN UNTIL YOU ARE
INSTRUCTED TO DO SO.
This round consists of eight problems, which will be presen
0
1
2
3
2017
State Competition
Sprint Round
Problems 130
4
5
6
7
HONOR PLEDGE
I pledge to uphold the highest principles of honesty and integrity as a Mathlete. I will neither give nor
accept unauthorized assistance of any kind. I will not copy anothers wo
2017
State Competition
Answer Key
The appropriate units (or their abbreviations) are provided in
the answer blanks.
Note to coordinators: Answers to the Tiebreaker Round
problems appear in the Tiebreaker Round Booklet.
National Sponsors
Raytheon Company
N
2017
State Competition
Countdown Round
Problems 180
This booklet contains problems to be used
in the Countdown Round.
National Sponsors
Raytheon Company
Northrop Grumman Foundation
U.S. Department of Defense
National Society of Professional Engineers
CNA
0
1
2
3
2017
State Competition
Team Round
Problems 110
4
5
6
7
School
8
Chapter
9
Team
Members
, Captain
DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO
DO SO.
This section of the competition consists of 10 problems which the teamhas
20 minutes to complete. Team
50 AMC Lectures
Chapter 10 Area And Area Method
BASIC KNOWLEDGE
1. FORMULAS
1. S
1
1
1
aha = bhb = chc
2
2
2
(1)
2. Let ha b sin C, hb c sin A, and hc a sin B. Equation (1) becomes:
S
1
1
1
bc sin A = ac sinB = ab sinC
2
2
2
(2)
3. S s(s a)(s b)(s c)
s=
MATHCOUNTS
2006
Chapter Competition
Answer Key
The appropriate units (or their abbreviations) are
provided in the answer blanks.
Note to coordinators: Answers to the Tiebreaker Round
problems appear in the Tiebreaker Round Booklet.
Founding Sponsors
Natio
2016 State Competition Solutions
Are you wondering how we could have possibly thought that a Mathlete would be able
to answer a particular Sprint Round problem without a calculator?
Are you wondering how we could have possibly thought that a Mathlete woul
The MATHEMATICAL ASSOCIATION of AMERICA
American Mathematics Competitions
9th Annual American Mathematics Contest 10
AMC 10
Contest A
Solutions Pamphlet
Tuesday, February 12, 2008
This Pamphlet gives at least one solution for each problem on this years co
Mathcounts Chapter Competition 2001
2001 CHAPTER COMPETITION
SPRINT ROUND QUESTIONS
2.
3.
4.
Th
5.
40 hours of work @ $30 per hour =
40 $30 = $1200 Answer
The probability that it will not rain
tomorrow = 1 - the probability that it will
rain tomorrow. The
1999 Mathcounts National Sprint Round Solutions
5
.
12
A 3-digit number is divisible by 3 if the sum of its digits is divisible by 3.
The first digit cannot be 0, so we have the following four groups of 3 such that the three
different numbers sum to a mul
MC 11
(1)
A restaurant raised its price for a hamburger 20% to $1.50. What did the
hamburger cost before?
(2)
Sara buys 20 dinosaurs and 30 alligators from a pet store. She then sells
each dinosaur for $21.50 and each alligator for $36.70. If Sara sells a
MC 12
(1)
Twenty 11 17 sheets were printed on both sides so that when the
sheets were stacked and folded down the center, an 8 12 11 booklet with the pages
numbered 1-80 would be formed. When stacked and folded, however, the sheets containing
pages 12 and
2016
State Competition
Answer Key
The appropriate units (or their abbreviations) are provided in
the answer blanks.
Note to coordinators: Answers to the Tiebreaker Round
problems appear in the Tiebreaker Round Booklet.
National Sponsors
Raytheon Company
N
MATHCOUNTS
2004
Chapter Competition
Sprint Round
Problems 130
Name
School
DO NOT BEGIN UNTIL YOU ARE
INSTRUCTED TO DO SO.
This round of the competition consists of 30 problems. You will
have 40 minutes to complete the problems. You are not
allowed to use
MATHCOUNTS.
2001
n
Chapter Competition I
Sprint Round
Problems l-30
Name
School
DO NOT BEGIN UNTIL YOU ARE
INSTRUCTED TO DO SO.
This round of the competition consists of 30 problems.
You will have 40 minutes to complete the problems. You
are not allowed t
2016 Chapter Competition Solutions
Are you wondering how we could have possibly thought that a Mathlete would be able
to answer a particular Sprint Round problem without a calculator?
Are you wondering how we could have possibly thought that a Mathlete wo
2015 Chapter Competition Solutions
Are you wondering how we could have possibly thought that a Mathlete would be able to
answer a particular Sprint Round problem without a calculator?
Are you wondering how we could have possibly thought that a Mathlete wo
1. Raquel has collected $3.80 in nickels and dimes. She has
exactly 48 nickels. How many dimes does she have?
1. _
2. One of the following four-digit numbers is not divisible by 4:
3544, 3554, 3564, 3572, 3576. What is the product of the
units digit and t
2005
Chapter Competition
Sprint Round
Problems 130
Name
School
DO NOT BEGIN UNTIL YOU ARE
INSTRUCTED TO DO SO.
This round of the competition consists of 30 problems.
You will have 40 minutes to complete the problems. You
are not allowed to use calculators
1
1. Tami had 1800 baseball cards. She sold 2 of them and then
4
gave away 5 of her remaining ones. How many cards does
Tami have left?
1. _
2. During the 20th century, eighteen different men held the office
of President of the United States. Eleven of th