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
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

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

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

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

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

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

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

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

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

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

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 3
(1)
(2)
(3)
If 120 is divided into 3 parts which are proportional to 1, 1/2, 1/6, what is
the middle part?
If b3 = .25, what is the value of b3 ?
Two drivers leave city A at the same time for city B which is 450 miles
away. The first driver travels a

MC 8
(1)
At a new job, Bobs starting monthly salary is $1000, and he gets a $20 raise
each succeeding month. In total, how much does Bob earn in his first year at this job?
(2)
When the digits 2 through 9 are placed in the squares below, one digit per
squ

MC 5
(1)
Alexs uncle paid Alex $5 a week for doing a few minor chores. However, if
Alex failed to do all the chores in any week, he did not get paid for that week and he had
to give his uncle $7.50 for that week. During the first 52 weeks, Alex failed to

MC 2
(1)
Leila is preparing boxed lunches for a group of 150 people. The lunches are
the same except for the sandwiches. The four sandwich options are ham, turkey, roast beef
or vegetarian. From past experience, she knows she will need 30% turkey, 31 as m

MC 4
(1)
Jasmine had 3 paperclips on Monday, then she had 6 on Tuesday, and her
number of paperclips proceeded to double on each subsequent day. On what day of the
week did she first have more than 100 paperclips?
(2)
Wally buys a baseball card for $5.00,

MC 7
(1)
Two hundred fifty eighth-graders took a test. Eighty percent of them
passed. One-fifth of those who did not pass received a score below 60. One-half of those
below 60 scored below 50. How many students scored below 50?
(2)
Let p(x) = 2x 1, where

MC 6
(1)
Of the five points (3, 10), (6, 20), (12, 35), (18, 40) and (20, 50), what is
the sum of the x-coordinates of the points that lie in the region above the line y = 2x + 7
in the coordinate plane?
(2)
On a recent math test, the mean score for Mr. B