당신은 주제를 찾고 있습니까 “**mathcounts 2004 chapter sprint round solutions – 2020 MathCounts Chapter Sprint Round Live Solve (PERFECT SCORE!)**“? 다음 카테고리의 웹사이트 https://ppa.charoenmotorcycles.com 에서 귀하의 모든 질문에 답변해 드립니다: https://ppa.charoenmotorcycles.com/blog/. 바로 아래에서 답을 찾을 수 있습니다. 작성자 On The Spot STEM 이(가) 작성한 기사에는 조회수 1,808회 및 좋아요 50개 개의 좋아요가 있습니다.

## mathcounts 2004 chapter sprint round solutions 주제에 대한 동영상 보기

여기에서 이 주제에 대한 비디오를 시청하십시오. 주의 깊게 살펴보고 읽고 있는 내용에 대한 피드백을 제공하세요!

## d여기에서 2020 MathCounts Chapter Sprint Round Live Solve (PERFECT SCORE!) – mathcounts 2004 chapter sprint round solutions 주제에 대한 세부정보를 참조하세요

In this video, On The Spot STEM live-solves the 2020 MathCounts Chapter Sprint Round. The problems can be found here https://www.mathcounts.org/programs/competition-series/past-competitions.

The score was a perfect 30/30 in 3/4 of the allotted time!

Be sure to like and subscribe if you enjoyed!

## mathcounts 2004 chapter sprint round solutions 주제에 대한 자세한 내용은 여기를 참조하세요.

### MATHCOUNTS – MATH WITH MS. LIN

MATHCOUNTS is the premiere U.S. competition and enrichment program that motivates and rewards mdle school students for math achievement.

Source: mathteamnyc.weebly.com

Date Published: 7/5/2021

View: 1600

### Chapter ~ 2004 Solutions » MathCounts – Course Hero

The following pages prove solutions to the Sprint, Target and Team Rounds of the2004 MATHCOUNTS®Chapter Competition.Though these solutions prove creativeand …

Source: www.coursehero.com

Date Published: 1/29/2022

View: 7424

### MATHCOUNTS – s3. · PDF file2004 Chapter Competition …

2004 Chapter Competition Answer Key MATHCOUNTSÒ ‘2003 MATHCOUNTS Foundation, 1420 King Street, Alexandria, VA 22314 Optional units are indicated in …

Source: dokumen.tips

Date Published: 12/19/2021

View: 8503

### PAST COMPETITIONS | MATHCOUNTS Foundation

Last year’s school, chapter and state competitions are always available for … resources or books to access additional MATHCOUNTS competition problems.

Source: www.mathcounts.org

Date Published: 1/6/2021

View: 6496

### Mathcounts 2004 Chapter Sprint Round Solutions

Mathcounts 2004 Chapter Sprint Round Solutions | Example Problems And Tips For The Mathcounts Sprint Round 상위 54개 베스트 답변.

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Date Published: 2/3/2021

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### 2005 Chapter Solutions – StudyLib

2005 MATHCOUNTS CHAPTER SPRINT ROUND 4. Shooting hoops for 30 minutes 1. We are given the following chart: Bangkok Bangkok Cape Town Honolulu London Cape Town …

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Date Published: 5/30/2021

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### MathCounts – Art of Problem Solving

MATHCOUNTS is a large national mathematics competition and mathematics coaching program that has … Sprint: 1-1.5 (School/Chapter), 2-2.5 (State/National)

Source: artofproblemsolving.com

Date Published: 4/4/2021

View: 2152

### mathcounts state PDF,Doc ,Images – PDFprof.com

[PDF] 2020 State Competition Team Round Problems 1?10 · 2004 Sprint – MATHCOUNTS 2004 Chapter Competition Sprint Round · 1990 – 2000 MATHCOUNTS State Problems …Source: www.pdfprof.com

Date Published: 12/7/2022

View: 9590

### Past Tests – repl.it

State Competition. Sprint Round Target Round Team Round Competition Answers Competition Solutions. The 2020 MathCounts National Competition was cancelled. 2019.

Source: easy-as-314-final.savi05.repl.co

Date Published: 9/14/2022

View: 7304

## 주제와 관련된 이미지 mathcounts 2004 chapter sprint round solutions

주제와 관련된 더 많은 사진을 참조하십시오 **2020 MathCounts Chapter Sprint Round Live Solve (PERFECT SCORE!)**. 댓글에서 더 많은 관련 이미지를 보거나 필요한 경우 더 많은 관련 기사를 볼 수 있습니다.

## 주제에 대한 기사 평가 mathcounts 2004 chapter sprint round solutions

- Author: On The Spot STEM
- Views: 조회수 1,808회
- Likes: 좋아요 50개
- Date Published: 2020. 4. 14.
- Video Url link: https://www.youtube.com/watch?v=IXSVX5Mgxks

### What is a good score on MATHCOUNTS sprint round?

Coaches and students should view an individual written competition score of **23 (out of a possible 46)** as highly commendable.

### How hard is MATHCOUNTS?

This round is very fast-paced and requires speed and accuracy as well. The earlier problems are usually the easiest problems in the competition, and the later problems can be **as hard as some of the Team Round questions**. No calculators are allowed during this round.

### How do I get better at MATHCOUNTS?

**General Tips for MathCounts preparation**

- Prepare with your friends. …
- The earlier you start your preparation, the better it is. …
- Try to work for 30-45 minutes 3-4 times a week during school time. …
- Do not time yourself the first time you solve a paper. …
- Apart from topic knowledge, improve your problem-solving skills.

### How long is the sprint round in MATHCOUNTS?

Sprint Round

Focuses on speed and accuracy. Students have **40 minutes** to complete 30 math problems without a calculator.

### What do you get if you win MATHCOUNTS?

Prizes & Selection of Winners

The winning team will receive: **Recognition on the MATHCOUNTS website and social media channels**. First Place Medals (1 each for the 4 team members and Team Advisor, presented to the team at the MATHCOUNTS National Competition) $1,000 college scholarship (1 each for the 4 team members)

### How do you qualify for the Mathcount nationals?

**Only U.S. students in grades 6-8** are eligible to participate in MATHCOUNTS competitions. MATHCOUNTS defines a U.S. student as any student who either (1) attends a school located in a U.S. state or territory or (2) attends an overseas school that is affiliated with the U.S. Departments of Defense or State.

### Who won MATHCOUNTS 2022?

**Allan Yuan** is the National Champion! Allan Yuan, a 13-year-old eighth grader from Hoover, Alabama, won the Countdown Round by answering this question in 6 seconds: “From a group of 9 students, three separate teams are to be formed—one consisting of 2 students, and one consisting of 4 students.

### Can 5th graders take MATHCOUNTS?

**Students enrolled in grades 6-8 are eligible to participate in the MATHCOUNTS Competition Series**. Students taking middle school mathematics classes who are not full‑time students in grades 6-8 are not eligible.

### Why is MATHCOUNTS important?

MATHCOUNTS **builds the critical thinking and problem-solving skills necessary for success**. In an independent study, 87% of MATHCOUNTS students said their confidence in their STEM abilities improved after participating in the Competition Series.

### What is a good score on AMC 8?

On the AMC-8, out of the 25 questions on the test:

The average score was **10 right**. Honor Roll (top 5%) was 18 right. Distinguished Honor Roll (top 1%) was 21 right.

### Can you use calculator on MATHCOUNTS?

Calculators are not permitted in the Sprint and Countdown Rounds, but they are permitted in the Target, Team and Tiebreaker (if needed) Rounds. When calculators are permitted, students may use any calculator (including programmable and graphing calculators) that does not contain a QWERTY (typewriter-like) keypad.

### How does MATHCOUNTS team round work?

The target round is **a written exam consisting of 8 problems presented in four pairs of two.** **Students have 6 minutes to work on each pair of problems.** **Contestants work individually.** **Calculators are allowed.**

### Who won MATHCOUNTS 2021?

NJSPE is proud to announce that this year’s first-place finisher in the National MATHCOUNTS competition is New Jersey’s own **Marvin Mao**. Marvin is an eighth grader from Davidson Academy from our Bergen Hudson Chapter! He will receive a $10,000 scholarship.

### How do I prepare for Chapter MATHCOUNTS?

**Practice previous year competitions**.

Study one level up. For example, in order to do well in school level you should be practicing all the chapter level competitions; for chapter level you should practice state level competitions; for state levels practice national level competitions; and so on.

## s3. · PDF file2004 Chapter Competition Answer Key MATHCOUNTS Ò ‘2003 MATHCOUNTS Foundation, 1420 King Street, Alexandria, VA 22314 Optional units

2004Chapter Competition

Answer Key

MATHCOUNTS

2003 MATHCOUNTS Foundation, 1420 King Street, Alexandria, VA 22314

Optional units are indicated in parentheses. Standardabbreviations have been used for units of measure.Complete words or symbols are also acceptable.Square units or cube units may also be expressed asunits2 or units3.

Note to coordinators: Answers to the TiebreakerRound problems appear in the Tiebreaker RoundBooklet.

Founding Sponsors National SponsorsCNA Foundation The Dow Chemical Company Foundation

National Society of Professional Engineers General Motors FoundationNational Council of Teachers of Mathematics Lockheed Martin

National Aeronautics and Space AdministrationNEC Foundation of AmericaTexas Instruments Incorporated3M Foundation

## MATHCOUNTS Foundation

You can purchase online resources or books to access additional MATHCOUNTS competition problems. Click the buttons at the left to learn more.

We sell resources to help cover the cost of the free materials and programs we provide, so purchasing MATHCOUNTS materials helps support the work we do!

## Mathcounts 2004 Chapter Sprint Round Solutions | Example Problems And Tips For The Mathcounts Sprint Round 상위 54개 베스트 답변

당신은 주제를 찾고 있습니까 “mathcounts 2004 chapter sprint round solutions – Example Problems and Tips for the MATHCOUNTS Sprint Round“? 다음 카테고리의 웹사이트 https://ppa.covadoc.vn 에서 귀하의 모든 질문에 답변해 드립니다: https://ppa.covadoc.vn/blog/. 바로 아래에서 답을 찾을 수 있습니다. 작성자 Auxin Academy 이(가) 작성한 기사에는 조회수 457회 및 좋아요 12개 개의 좋아요가 있습니다.

mathcounts 2004 chapter sprint round solutions 주제에 대한 동영상 보기

여기에서 이 주제에 대한 비디오를 시청하십시오. 주의 깊게 살펴보고 읽고 있는 내용에 대한 피드백을 제공하세요!

d여기에서 Example Problems and Tips for the MATHCOUNTS Sprint Round – mathcounts 2004 chapter sprint round solutions 주제에 대한 세부정보를 참조하세요

In this video, we go over the basics of how the MATHCOUNTS competition works, and some example problems from the Sprint Round of the competition. The math problems shown in the video are owned by MATHCOUNTS, and can be found at the bottom of the page linked below: https://www.mathcounts.org/press-room

mathcounts 2004 chapter sprint round solutions 주제에 대한 자세한 내용은 여기를 참조하세요.

MATHCOUNTS – MATH WITH MS. LIN

MATHCOUNTS is the premiere U.S. competition and enrichment program that motivates and rewards mdle school students for math achievement.

+ 여기에 보기

Source: mathteamnyc.weebly.com

Date Published: 4/1/2021

View: 693

Chapter ~ 2004 Solutions » MathCounts – Course Hero

2004 CHAPTER COMPETITIONSPRINT ROUND QUESTIONS1.Each of the 3 math es has 24 students.Each student is in only one of the mathes.Therefore, there are 3 …

+ 여기에 표시

Source: www.coursehero.com

Date Published: 10/27/2022

View: 8422

MATHCOUNTS – s3. · PDF file2004 Chapter Competition …

2004 Chapter Competition Answer Key MATHCOUNTSÒ ‘2003 MATHCOUNTS Foundation, 1420 King Street, Alexandria, VA 22314 Optional units are indicated in …

+ 여기에 보기

Source: dokumen.tips

Date Published: 7/22/2022

View: 8160

PAST COMPETITIONS | MATHCOUNTS Foundation

Last year’s school, chapter and state competitions are always available for free on … Purchase past years’ MATHCOUNTS competitions, …

+ 여기에 자세히 보기

Source: www.mathcounts.org

Date Published: 8/30/2022

View: 2895

2005 Chapter Solutions – StudyLib

Ans. 2005 MATHCOUNTS CHAPTER SPRINT ROUND 4. … The answer is still the same.) 11,535. … CD is perpendicular to AB and AC is the radius of the circle.

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Source: studylib.net

Date Published: 2/26/2021

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Past Tests – Easy as 3.14

The 2020 MathCounts National Competition was cancelled. 2019. School Competition. Sprint Round Target Round Team Round Competition Answers Solutions to Target …

+ 여기에 자세히 보기

Source: easy-as-314-final.savi05.repl.co

Date Published: 8/25/2022

View: 1081

MathCounts – Art of Problem Solving

MATHCOUNTS is a large national mathematics competition and mathematics coaching program that has … Sprint: 1-1.5 (School/Chapter), 2-2.5 (State/National)

+ 여기를 클릭

Source: artofproblemsolving.com

Date Published: 11/16/2021

View: 5270

mathcounts state PDF,Doc ,Images – PDFprof.com

PDF,PPT,images:mathcounts state · 2004 Sprint – MATHCOUNTS 2004 Chapter Competition Sprint Round · 1990 – 2000 MATHCOUNTS State Problems DISCUSSION · 1990 – 2000 …

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Source: www.pdfprof.com

Date Published: 10/10/2021

View: 4103

2013 Chapter Competition Solutions – PDF Free Download

The following pages prove solutions to the Sprint, Target and Team Rounds of the 013 MATHCOUNTS Chapter Competition. Though these solutions prove …

+ 여기에 표시

Source: docplayer.net

Date Published: 7/18/2022

View: 3290

주제와 관련된 이미지 mathcounts 2004 chapter sprint round solutions

주제와 관련된 더 많은 사진을 참조하십시오 Example Problems and Tips for the MATHCOUNTS Sprint Round. 댓글에서 더 많은 관련 이미지를 보거나 필요한 경우 더 많은 관련 기사를 볼 수 있습니다.

Example Problems and Tips for the MATHCOUNTS Sprint Round

주제에 대한 기사 평가 mathcounts 2004 chapter sprint round solutions

Author: Auxin Academy

Views: 조회수 457회

Likes: 좋아요 12개

Date Published: 2020. 6. 27.

Video Url link: https://www.youtube.com/watch?v=R_3v228XEQY

What is a good score for MATHCOUNTS chapter?

Coaches and students should view an individual written competition score of 23 (out of a possible 46) as highly commendable.

How hard is MATHCOUNTS?

This round is very fast-paced and requires speed and accuracy as well. The earlier problems are usually the easiest problems in the competition, and the later problems can be as hard as some of the Team Round questions. No calculators are allowed during this round.

How do I get better at MATHCOUNTS?

General Tips for MathCounts preparation Prepare with your friends. … The earlier you start your preparation, the better it is. … Try to work for 30-45 minutes 3-4 times a week during school time. … Do not time yourself the first time you solve a paper. … Apart from topic knowledge, improve your problem-solving skills.

What does the winner of MATHCOUNTS get?

The winning team will receive: Recognition on the MATHCOUNTS website and social media channels. First Place Medals (1 each for the 4 team members and Team Advisor, presented to the team at the MATHCOUNTS National Competition) $1,000 college scholarship (1 each for the 4 team members)

How do you qualify for the Mathcount nationals?

Only U.S. students in grades 6-8 are eligible to participate in MATHCOUNTS competitions. MATHCOUNTS defines a U.S. student as any student who either (1) attends a school located in a U.S. state or territory or (2) attends an overseas school that is affiliated with the U.S. Departments of Defense or State.

What grade level is MATHCOUNTS?

The MATHCOUNTS Foundation is a 501(c)(3) non-profit organization that reaches students in grades 6-8 in all US states and territories with 3 extracurricular math programs. Hundreds of thousands of students participate in our programs or use our resources each year. all students discover theirs.

How do I prepare for Mathcount state competition?

How do you prepare for the competition? And how we can help! Set aside time for training. … Practice, Practice, Practice. … Sign up for Alcumus on the AoPS website. … Study Smart. … Selecting the right level of challenge. … Know your approach. … Practice previous year competitions.

How many students compete in MATHCOUNTS?

Coaches of each school select up to 12 students from their school to advance to the chapter competition, with 4 of them competing on the official school team. The rest compete individually.

How much time do you need for MATHCOUNTS?

On average, students should expect to complete competitions within 1 1/2 to 2 hours. Once a student begins taking the competition (starting with agreeing to the Honor code), the student must complete the Sprint Round (40 minutes) and Target Rounds (4 rounds/6 minutes each).

Why is MATHCOUNTS important?

MATHCOUNTS works.

MATHCOUNTS builds the critical thinking and problem-solving skills necessary for success. In an independent study, 87% of MATHCOUNTS students said their confidence in their STEM abilities improved after participating in the Competition Series.

What is a good score on AMC 8?

On the AMC-8, out of the 25 questions on the test:

The average score was 10 right. Honor Roll (top 5%) was 18 right. Distinguished Honor Roll (top 1%) was 21 right.

What is a good score on the AMC 10?

High scores on the AMC 10 or 12 can qualify the participant for the American Invitational Mathematics Examination (AIME). On the AMC 10, the top 2.5% make it, typically around 100 to 115 points. On the AMC 12, the top 5% make it, typically around 85 to 95 points.

How does MATHCOUNTS trainer work?

Your bar on the top right tracks your round and rating. Your round is either School, State, Chapter, or National, and your rating for that round is a number from 1 to 46. Your rating goes up as you answer questions correctly and down as you answer questions incorrectly.

What is the website that solves any math problem?

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

How do you work out a quarter of 24?

One-fourth of 24 is 6. To get to this answer, use the following steps: Divide 24 by 4.

How do you double check in math?

Double check your final answer – This is an important step in solving any question. Once you find the solution, you always want to double check the answer by plugging it back into the original equation, and ensuring that it works.

s3. · PDF file2004 Chapter Competition Answer Key MATHCOUNTS Ò ‘2003 MATHCOUNTS Foundation, 1420 King Street, Alexandria, VA 22314 Optional units

2004Chapter Competition Answer Key MATHCOUNTS 2003 MATHCOUNTS Foundation, 1420 King Street, Alexandria, VA 22314 Optional units are indicated in parentheses. Standardabbreviations have been used for units of measure.Complete words or symbols are also acceptable.Square units or cube units may also be expressed asunits2 or units3. Note to coordinators: Answers to the TiebreakerRound problems appear in the Tiebreaker RoundBooklet. Founding Sponsors National SponsorsCNA Foundation The Dow Chemical Company Foundation National Society of Professional Engineers General Motors FoundationNational Council of Teachers of Mathematics Lockheed Martin National Aeronautics and Space AdministrationNEC Foundation of AmericaTexas Instruments Incorporated3M Foundation

MATHCOUNTS

Team Registration Each team will consist of exactly 4 students in grade 6 – 8 Teams must be comprised of active NSBE Jr. members Attendance at the 47th Annual Convention in Orlando, FL is required MATHCOUNTS® Competition Components MATHCOUNTS Written Competitions are designed to be completed in approximately two hours at Annual Convention: The SPRINT ROUND (40 minutes) consists of 30 problems. This round challenges students’ accuracy in completing all of the problems in a limited period of time. Calculators are not permitted. The TARGET ROUND (approximately 30 minutes) consists of eight problems presented to competitors in four pairs (6 minutes per pair). This round features multi-step problems that engage students in mathematical reasoning and problem-solving processes. Problems assume the use of calculators. The TEAM ROUND (20 minutes) consists of 10 problems that team members work to solve together. Team member interaction is permitted and encouraged. Problems assume the use of calculators. The MATHCOUNTS Final Countdown Round is designed for individual students to compete. A problem is presented to two students at a time. The question will be read aloud, as well as presented on a screen. Students can use a pencil and scratch paper. Students have 45 seconds to determine the answer and hit a buzzer when they are ready to answer. The other student can continue to work while their opponent is presenting. The student that correctly answers the most questions out of three moves on to the next round. Calculators are not permitted. Competition Rules Pencils and paper will be provided for students; however, students may bring their own pencils, pens and erasers if they wish. They may not use their own scratch paper or graph paper. Calculators are not permitted in the Sprint Round, but they are permitted in the Target, Team and Tiebreaker (if needed) Rounds. When calculators are permitted, students may use any calculator (including programmable and graphing calculators) that does not contain a QWERTY (typewriter-like) keypad. Calculators that have the ability to enter letters of the alphabet but do not have a keypad in a standard typewriter arrangement are acceptable. Smart phones, laptops, iPads®, iPods®, personal digital assistants (PDAs) and any other “smart” devices are not considered to be calculators and may not be used during competitions. Students may not use calculators to exchange information with another person or device during the competition. Coaches are responsible for ensuring that their students use acceptable calculators and students are responsible for providing their own calculators (and batteries).® Pagers, cell phones, iPods and other MP3 players should not be brought into the competition room. Failure to comply could result in dismissal from the competition. Should there be a rule violation or suspicion of irregularities, the MATHCOUNTS® coordinator or competition official has the obligation and authority to exercise his or her judgment regarding the situation and take appropriate action which might include disqualification of the suspected student(s) from the competition. Use of notes or other reference materials (including dictionaries and translation dictionaries) is not permitted. Communication with coaches is prohibited during rounds but is permitted during breaks. All communication between guests and students is prohibited during competition rounds. Communication between teammates is permitted only during the Team Round.

Art of Problem Solving

Many AoPS Community members and online school students have been participants at National MATHCOUNTS, including many Nationals Countdown Round participants in the past decade. MATHCOUNTS is a large national mathematics competition and mathematics coaching program that has served millions of middle school students since 1984. Sponsored by the CNA Foundation, National Society of Professional Engineers, the National Council of Teachers of Mathematics, and others including Art of Problem Solving, the focus of MATHCOUNTS is on mathematical problem solving. Students are eligible for up to three years, but cannot compete beyond their eighth grade year. MATHCOUNTS Region: USA Type: Free Response Difficulty: 0.5 – 2.5 Difficulty Breakdown: Countdown : 0.5 (School/Chapter), 1 (State/National) Sprint : 1-1.5 (School/Chapter), 2-2.5 (State/National) Target: 1.5 (School), 2 (Chapter), 2-2.5 (State/National) MATHCOUNTS Resources MATHCOUNTS Books Art of Problem Solving’s Introductory subject textbooks are ideal for students preparing for MATHCOUNTS, as are AoPS Volume 1 and Competition Math for Middle School MATHCOUNTS Classes Art of Problem Solving hosts a Basic and an Advanced MATHCOUNTS course. The AoPS Introduction-level subject courses also include a great deal of MATHCOUNTS preparation. Many AoPS instructors are former National MATHCOUNTS Mathletes. MATHCOUNTS Online MATHCOUNTS Curriculum MATHCOUNTS curriculum includes arithmetic, algebra, counting, geometry, number theory, probability, and statistics. The focus of MATHCOUNTS curriculum is in developing mathematical problem solving skills. Before 1990, MATHCOUNTS chose particular areas of mathematics to highlight each year before changing the focus of the competition more broadly to problem solving. Past State Team Winners 1984: Virginia 1985: Florida 1986: California 1987: New York 1988: New York 1989: North Carolina 1990: Ohio 1991: Alabama 1992: California 1993: Kansas 1994: Pennsylvania 1995: Indiana 1996: Wisconsin 1997: Massachusetts 1998: Wisconsin 1999: Massachusetts 2000: California 2001: Virginia 2002: California 2003: California 2004: Illinois 2005: Texas 2006: Virginia 2007: Texas 2008: Texas 2009: Texas 2010: California 2011: California 2012: Massachusetts 2013: Massachusetts 2014: California 2015: Indiana 2016: Texas 2017: Texas 2018: Texas 2019: Massachusetts 2020: CANCELLED 2021: New Jersey 2022: New Jersey MATHCOUNTS Competition Structure Sprint Round 30 problems are given all at once. Students have 40 minutes to complete the Sprint Round. This round is very fast-paced and requires speed and accuracy as well. The earlier problems are usually the easiest problems in the competition, and the later problems can be as hard as some of the Team Round questions. No calculators are allowed during this round. Target Round 8 problems given 2 at a time. Students have 6 minutes to complete each set of two problems. Students may not go back to previous rounds (or forwards to future rounds) even if they finish before time is called. Calculators are allowed for the Target Round. Usually comprised of one “confidence booster” and one hard problem. Team Round 10 problems in 20 minutes for a team of 4 students. These problems typically include some of the most difficult problems of the competition. Use of a calculator is allowed (and required for some questions). Countdown Round High scoring individuals compete head-to-head until a champion is crowned. People compete from off a screen taking 45 seconds or less to finish the problem. The Countdown round is run differently in various different chapter, state, and national competitions. In the national competitions, it is the round that determines the champion. Calculators are not allowed, but scratch paper will be provided. Chapter and State Competitions In the chapter and state competitions, the countdown round is not mandatory. However, if it is deemed official by the chapter or state, the following format must be used: The 10th place written finisher competes against the 9th place written finisher. A problem is displayed, and both competitors have 45 seconds to answer the question, and the first competitor to correctly answer the question receives one point. The person who gets the most correct out of three questions (not necessarily two out of three) is the winner. The winner of the first round goes up against the 8th place finisher. The winner of the second round goes up against the 7th place finisher. This process is continued until the countdown round reaches the top four written competitors. Starting then, the first person to get three questions correct wins (as opposed to the best-out-of-three rule). If the countdown round is unofficial, any format may be used, and if it is unofficial it will not determine your placement towards the final results and may be determined by another format. Single-elimination bracket-style tournaments are common. National Competition At the national competition, there are some structural changes to the countdown round. The top 12 (not the top 10) written finishers make it to the countdown round, and the format is changed from a ladder competition to a single-elimination tournament where the top four written competitors get a bye. This setup makes it far more likely for a 12th place finisher to become champion, and it makes it less likely for a first-place written finisher to become champion, equalizing the field. But even then, a 12th place written competitor will have less of a chance to become champion than the top 4, because the top 4 get a bye. Until the semi-finals, the scoring is best out of five advances. In the first round and the second round, the person to correctly answer the most out of 5 questions wins. However, at the semifinals, the rules slightly change— the first person to correctly answer four questions wins. Ciphering Round In some states, (most notably Florida) there is an optional ciphering round. Very similar to countdown (in both difficulty and layout), a team sends up a representative to go against all representatives from the other teams. A problem is shown on a screen and students work fast to answer the problem. The students give their answer and after 45 seconds the answer is shown and the answers are checked to see if they are right. The fastest correct answer gets five points, the next fastest gets 4, etc. There are 4 questions per individual and teams send up 4 people. A perfect score is then 80. Often times the questions take clever reading skills. For example, one question was “How much dirt is in a 3 ft by 3 ft by 4 ft hole?” The answer was 0 because there is no dirt in a hole. Masters Round Top students give in-depth explanations to challenging problems. This round was optional at the state level competition and mandatory at the national competition (up to 2011). At nationals the top two on the written and countdown participate. In 2012, it was replaced by the Reel Math Challenge (now called the Math Video Challenge). Scoring and Ranking An individual’s score is their total number of correct sprint round answers plus 2 times their total number of correct target round answers. This total is out of a maximum of points. A team’s score is the individual scores of its members divided by 4 plus 2 points for every correct team round answer, making a team’s maximum possible score 66 points. Therefore, it is possible to win with a relatively low team score and a phenomenal individual score, as the team score is only roughly 30% of the total team score. Note that when there are less than four members the score will become less. MATHCOUNTS Competition Levels School Competition Students vie for the chance to make their school teams. Problems at this level are generally the easiest and most basic in curriculum. Chapter Competition Chapter competitions serve as a selection filter for state competitions. A few states don’t need to host chapter competitions due to a small population size. State Competition The top 4 students in each state form the state team for the national competition. The coach of the top school team at the state level is invited to coach the state team at the national competition. Interestingly, the coach of a state team is not necessarily the coach of any of the state’s team members. State competition competitors may be determined from the Chapter competition, based on the population of that particular state. National Competition National Competition Sites For many years, the National MATHCOUNTS competition was held in Washington, D.C. More recently, the competition has changed venues often. The 2022 competition was held in Washington, D.C. The 2021 competition was an online event. The 2020 competition was canceled due to the COVID-19 pandemic, but was due to be held in Orlando, Florida. The 2019 competition was held in Orlando, Florida. The 2018 competition was held in Washington, D.C. The 2017 competition was held in Orlando, Florida. The 2016 competition was held in Washington, D.C. The 2015 competition was held in Boston, Massachusetts. The 2014 competition was held in Orlando, Florida. The 2013 competition was held in Washington, D.C. The 2012 competition was held in Orlando, Florida. The 2011 competition was held in Washington, D.C. The 2009 and 2010 competitions were held in Orlando, Florida. The 2008 competition was held in Denver, Colorado. The 2007 competition was held in Fort Worth, Texas. The 2006 competition was held in Arlington, Virginia. The 2005 competition was held in Detroit, Michigan. The 2004 competition was held in Washington, D.C. The 2002 and 2003 competitions were held in Chicago, Illinois. What comes after MATHCOUNTS? Give the following competitions a try and take a look at the List of United States high school mathematics competitions.

How to Prepare for MathCounts

MathCounts is a middle school math competition for grades 6-8. Students cannot compete beyond grade 8. It is fun to compete because unlike AMC 8, this has multiple rounds and levels. Different skills are also tested. Some of the rounds allow the use of calculators so they test your problem-solving skills heavily and move so much beyond smart arithmetic. How to Register for MathCounts Topics for MathCounts What to expect in MathCounts or MathCounts format Scoring in MathCounts MathCounts preparation For school and chapter level For State and National Level General Tips During the MathCounts exam How to Register for MathCounts Through school: Usually students can register for Math Counts only through school. A lot of schools only let you participate if you belong to the school’s math club. As an individual: In 2020-21, they opened up individual registrations. Students can participate as an individual only if their school does not participate. (Not sure if they will continue this though. Will update as soon as I learn about this). Topics for MathCounts Since this is for grades 6-8, students are expected to know the Middle School Math, Geometry and a part of Algebra 2 well. The following list is just a guide and is not exhaustive. Some common topics 1. Number Theory a. divisibility rules, b. LCM and GCF, c. modular arithmetic, d. base number arithmetic and e. number sense. 2. Algebra a. fractions, decimals, ratios and percents, b. exponents and radicals c. equations and inequalities, d. functions, quadratics, and more 3. Geometry a. angles, b. Pythagorean theorem and special right triangles c. perimeter and area of 2D shapes including circles d. surface area and volumes of 3D shapes, e. co-ordinate geometry f. similar triangles 4. Counting and Probability a. nPr and nCr (permutations and combinations) b. Pascals triangle c. Binomial theorem d. Probability e. Geometrical probability What to expect in MathCounts MathCounts usually is 4 levels – School, Chapter, State and National. In 2020-21, they introduced a Chapter Invitational Level because of individual registrations. Since all the individual participants directly went to Chapter level, they added an extra round to filter out. So it was School, Chapter, Chapter Invitational, State and Nationals. In each of the levels, we have 4 rounds – Sprint, Target, Team and Countdown. None of the rounds are multiple choice. Sprint Round: Consists of 30 questions to be answered in 40 minutes. No calculators are allowed. Students have to write the correct answer in the correct format in the blank provided. Target Round: Consists of 8 problems. Students are given 2 problems at a time ( a set) and they get 6 minutes to solve the set. Time is not carried over, so it is wise to take up the time and check your work if you have some time left. Team Round: Consists of 10 problems and students are given 20 minutes to solve them. Students work with their 4 member team to solve these problems. How they split the problems depends on the team’s strength and weaknesses. Countdown Round: Two competitors compete head on with each other. They are given less than 45 seconds per question. It’s a buzzer round. One of the most tense rounds I’ve seen 🙂 A particular school, chapter and state might or might not do the countdown round. But this is the round that determines the National Champion. Here’s a sample of National Countdown round you can watch at youtube. Scoring in MathCounts: Your individual score is the sum of sprint and target rounds. Each question in sprint is worth 1 point and each question in target and team rounds is worth 2 points. So 30+16=46 points. The team score is the sum of individual scores divided by 4, plus 2 points for each correct answer in the team round. It is not the average of the individual scores. This is because even if your team has only 3 members they will divide the sum of individual scores by 4. Hence it is always good to have 4 members in your team. Materials/ Resources to Prepare for MathCounts I coach kids for all middle school competitions and here are some of the resources that I use/ suggest to prepare for Math Counts. See if your school has a math club. Most of the schools that host the competition does. If not try to see if you can start one with the help of a teacher. A lot of schools will let you participate only if you belong to the school’s math club as well. Math Counts handbook: Math Counts releases its own Handbook. For the 2020-21 handbook you can click here. It will give you an idea of what topics to expect and the type of questions. If your school is registered and has a coach, these are the worksheets they usually give you. Past Exam Question Papers: Math Counts has one year’s question paper available for free. You can download it from their website. The previous years question papers can be bought from their online store. They also have a book on MathCounts Practice Problems that you can use for extra practice 🙂 Resources from Math Counts website: Go to their website and hover over resources. You’ll find a trainer app, video resources, online problem library, problem of the week etc. for practice. For online practice I especially liked the MathCounts Trainer App . Books from Art of Problem Solving: If you’re a beginner to the competition get the Pre-Algebra by AOPS. If you’re familiar with the topics then get the Volume 1 from AOPS. To be really thorough and for state/ national rounds you should practice from their Intro to Algebra, Geometry, Number Theory and Intro to Probability books. Courses by Art of Problem Solving: They have beginners and advanced courses specifically for AMC 8 and Math Counts. MathCounts preparation For school and chapter level School level is the easiest one and chapter is not too difficult either. Even if you are a beginner, you can get through this with dedication and sufficient practice. Start with the school competition exam paper. That’s the easiest. If you’re extremely comfortable with the questions, move on to Chapter level papers. This will also tell you where you need to focus. Based on that you can start with hard core preparation. If you get fewer than 20 on a school sprint test, start with the Pre-Algebra book by AOPS. You can then move on to Algebra, Counting Probability and Geometry books. Work through the current year’s school handbook. It does help you practice a variety of topics in a short time. Know all your perfect squares till 25 squared and all your primes till 200. These will help you save time. Unless your chapter is ultra competitive, doing the past papers, the handout and Pre-Algebra book should get you through. For State and National Level If you can get a score of 25+ in chapter level competition go to Volume 1 book and go through it chapter by chapter. If you are stuck in any chapter, review that by going to the respective book. Mathcounts State Competition Preparation books (5 Volumes) by myMathCounts is also definitely useful. You can also practice questions from AMC 10. If you’ve done all this and still want more practice, try getting question papers from other middle and high school math competitions and do them as well. It’s always good to get a variety of questions. General Tips for MathCounts preparation Prepare with your friends. You can bounce off ideas and it’ll make the preparation fun as well. The earlier you start your preparation, the better it is. Summer is usually a great time to prepare because you have a lot of time to dedicate. Try to work for 30-45 minutes 3-4 times a week during school time. Summers aim for at least 1 hour a day for 4 days a week. Some kids do residential math camps and they work 6 hours a day for 3 weeks straight. What makes this fun is doing it with friends/ like minded people. Do not time yourself the first time you solve a paper. Take however long it requires. Sometimes struggling with a question for an hour will help you learn more than doing 10 questions that you already kind of know how to do. Apart from topic knowledge, improve your problem-solving skills. While doing the AOPS books, if you encounter a problem you have trouble with, do try out various ways before giving up. Like I said in the previous point, your struggles help you learn more. I highly encourage my students to not give up. Look at the hints but looking at the answer should be the last resort. Since Target and Team rounds allow the use of calculators, learn how to use it. I’ve seen students spend a lot of time preparing for Sprint without doing much of Target and Team and hence do not use calculators much. Be comfortable using your calculator! Prepare an excel sheet marking the questions you got right and wrong. After you solve a few years papers, look into it to see if you can find a pattern. Do you consistently get problems from a particular topic wrong? Work on that. Or do you have trouble with the last few problems? Try setting your Alcumus level to “Hard” or “Insanely Hard” and try out the ropics. Once you go to Chapter level you need to choose a strong team and team captain. Your team should get used to solving problems together and you should be prepared on how to deal with the team round and what works for you before you enter the Chapter level competition. If you want more help in preparation you can always hire a coach/ tutor to guide and help you through it. A coach will always look at your strengths and weaknesses and guide you accordingly. During the MathCounts exam Sleep well the night before. You should have established a good night routine much before the competition. A good bedtime routine will help you throughout your life. Do some breathing exercises to calm down. Adrenaline rush is good for solving problems but too much stress is not good. Be relaxed. You’ve done all the preparation and now it is just fun time 🙂 Sprint Round: The first 15-20 questions should be easy even in State Round. It should take you about 10 minutes for the first 20 (or at least 15) questions. So depending on how much you want to score, you should make sure that you get all of those right. You can then move on to the harder ones. Target Round: The first 5-6 questions should be easy. Since you are given only 2 questions at a time and 6 minutes to solve them, make sure you utilise it fully. Do not return the answer sheet even if you finish early. Check your work and if you still have time left over, take rest. Use your calculator where necessary. I’ve seen my students so used to doing everything by hand they forget to use calculators. I keep reminding them to use it. All the best for your competition! Glad that you are thinking through this early. It does require a year (or more) to prepare. If you liked this article and it was useful please do share it with your friends and in social media. Do you have any other tips that has worked for you? Do let me know in the comments below. #MathCounts #MiddleSchoolMathCompetition #prepareForMathCounts About Me: Hi, I’m Vasudha, an Online Math Tutor. I help prepare students for all Elementary and Middle school Math Competitions. If you’d like to talk to me about preparing your child for math competitions please do contact me here .

MATHCOUNTS Foundation

You can purchase online resources or books to access additional MATHCOUNTS competition problems. Click the buttons at the left to learn more. We sell resources to help cover the cost of the free materials and programs we provide, so purchasing MATHCOUNTS materials helps support the work we do!

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Easy as 3.14 A MathCounts Preparation Website More Resources Though I have tried my hardest to incoroporate a lot of concepts, problems, and tips in this website, there is always more to explore in mathematics and beyond, so below is a list of super helpful resources: Past Tests 2020 School Competition Chapter Competition State Competition The 2020 MathCounts National Competition was cancelled. 2019 School Competition Chapter Competition State Competition National Competition (not available at this time) 2018 School Competition Chapter Competition State Competition Team Round (unavailable at this time) National Competition (not available at this time) 2017 School Competition Sprint Round Team Round Competition Solutions Chapter Competition State Competition National Competition Competition Solutions 2016 School Competition Chapter Competition State Competition National Competition 2015 School Competition Chapter Competition State Competition National Competition Competition Solutions 2014 School Competition Chapter Competition State Competition National Competition Competition Solutions 2013 School Competition Chapter Competition State Competition National Competition Competition Solutions 2012 School Competition Chapter Competition State Competition National Competition Competition Solutions 2011 School Competition Chapter Competition State Competition National Competition Competition Solutions 2010 School Competition Chapter Competition State Competition National Competition Competition Solutions 2009 School Competition Chapter Competition State Competition National Competition Competition Solutions 2008 School Competition Chapter Competition State Competition National Competition Competition Solutions 2007 Chapter Competition State Competition National Competition Competition Solutions 2006 Chapter Competition State Competition National Competition Competition Solutions 2005 School Competition Chapter Competition State Competition National Competition Competition Solutions 2004 School Competition Chapter Competition State Competition National Competition Competition Solutions 2003 School Competition Chapter Competition State Competition National Competition Competition Solutions 2002 School Competition Chapter Competition State Competition National Competition 2001 School Competition Chapter Competition State Competition National Competition Competition Solutions 2000 School Competition Chapter Competition State Competition National Competition Countdown round

Art of Problem Solving

Many AoPS Community members and online school students have been participants at National MATHCOUNTS, including many Nationals Countdown Round participants in the past decade. MATHCOUNTS is a large national mathematics competition and mathematics coaching program that has served millions of middle school students since 1984. Sponsored by the CNA Foundation, National Society of Professional Engineers, the National Council of Teachers of Mathematics, and others including Art of Problem Solving, the focus of MATHCOUNTS is on mathematical problem solving. Students are eligible for up to three years, but cannot compete beyond their eighth grade year. MATHCOUNTS Region: USA Type: Free Response Difficulty: 0.5 – 2.5 Difficulty Breakdown: Countdown : 0.5 (School/Chapter), 1 (State/National) Sprint : 1-1.5 (School/Chapter), 2-2.5 (State/National) Target: 1.5 (School), 2 (Chapter), 2-2.5 (State/National) MATHCOUNTS Resources MATHCOUNTS Books Art of Problem Solving’s Introductory subject textbooks are ideal for students preparing for MATHCOUNTS, as are AoPS Volume 1 and Competition Math for Middle School MATHCOUNTS Classes Art of Problem Solving hosts a Basic and an Advanced MATHCOUNTS course. The AoPS Introduction-level subject courses also include a great deal of MATHCOUNTS preparation. Many AoPS instructors are former National MATHCOUNTS Mathletes. MATHCOUNTS Online MATHCOUNTS Curriculum MATHCOUNTS curriculum includes arithmetic, algebra, counting, geometry, number theory, probability, and statistics. The focus of MATHCOUNTS curriculum is in developing mathematical problem solving skills. Before 1990, MATHCOUNTS chose particular areas of mathematics to highlight each year before changing the focus of the competition more broadly to problem solving. Past State Team Winners 1984: Virginia 1985: Florida 1986: California 1987: New York 1988: New York 1989: North Carolina 1990: Ohio 1991: Alabama 1992: California 1993: Kansas 1994: Pennsylvania 1995: Indiana 1996: Wisconsin 1997: Massachusetts 1998: Wisconsin 1999: Massachusetts 2000: California 2001: Virginia 2002: California 2003: California 2004: Illinois 2005: Texas 2006: Virginia 2007: Texas 2008: Texas 2009: Texas 2010: California 2011: California 2012: Massachusetts 2013: Massachusetts 2014: California 2015: Indiana 2016: Texas 2017: Texas 2018: Texas 2019: Massachusetts 2020: CANCELLED 2021: New Jersey 2022: New Jersey MATHCOUNTS Competition Structure Sprint Round 30 problems are given all at once. Students have 40 minutes to complete the Sprint Round. This round is very fast-paced and requires speed and accuracy as well. The earlier problems are usually the easiest problems in the competition, and the later problems can be as hard as some of the Team Round questions. No calculators are allowed during this round. Target Round 8 problems given 2 at a time. Students have 6 minutes to complete each set of two problems. Students may not go back to previous rounds (or forwards to future rounds) even if they finish before time is called. Calculators are allowed for the Target Round. Usually comprised of one “confidence booster” and one hard problem. Team Round 10 problems in 20 minutes for a team of 4 students. These problems typically include some of the most difficult problems of the competition. Use of a calculator is allowed (and required for some questions). Countdown Round High scoring individuals compete head-to-head until a champion is crowned. People compete from off a screen taking 45 seconds or less to finish the problem. The Countdown round is run differently in various different chapter, state, and national competitions. In the national competitions, it is the round that determines the champion. Calculators are not allowed, but scratch paper will be provided. Chapter and State Competitions In the chapter and state competitions, the countdown round is not mandatory. However, if it is deemed official by the chapter or state, the following format must be used: The 10th place written finisher competes against the 9th place written finisher. A problem is displayed, and both competitors have 45 seconds to answer the question, and the first competitor to correctly answer the question receives one point. The person who gets the most correct out of three questions (not necessarily two out of three) is the winner. The winner of the first round goes up against the 8th place finisher. The winner of the second round goes up against the 7th place finisher. This process is continued until the countdown round reaches the top four written competitors. Starting then, the first person to get three questions correct wins (as opposed to the best-out-of-three rule). If the countdown round is unofficial, any format may be used, and if it is unofficial it will not determine your placement towards the final results and may be determined by another format. Single-elimination bracket-style tournaments are common. National Competition At the national competition, there are some structural changes to the countdown round. The top 12 (not the top 10) written finishers make it to the countdown round, and the format is changed from a ladder competition to a single-elimination tournament where the top four written competitors get a bye. This setup makes it far more likely for a 12th place finisher to become champion, and it makes it less likely for a first-place written finisher to become champion, equalizing the field. But even then, a 12th place written competitor will have less of a chance to become champion than the top 4, because the top 4 get a bye. Until the semi-finals, the scoring is best out of five advances. In the first round and the second round, the person to correctly answer the most out of 5 questions wins. However, at the semifinals, the rules slightly change— the first person to correctly answer four questions wins. Ciphering Round In some states, (most notably Florida) there is an optional ciphering round. Very similar to countdown (in both difficulty and layout), a team sends up a representative to go against all representatives from the other teams. A problem is shown on a screen and students work fast to answer the problem. The students give their answer and after 45 seconds the answer is shown and the answers are checked to see if they are right. The fastest correct answer gets five points, the next fastest gets 4, etc. There are 4 questions per individual and teams send up 4 people. A perfect score is then 80. Often times the questions take clever reading skills. For example, one question was “How much dirt is in a 3 ft by 3 ft by 4 ft hole?” The answer was 0 because there is no dirt in a hole. Masters Round Top students give in-depth explanations to challenging problems. This round was optional at the state level competition and mandatory at the national competition (up to 2011). At nationals the top two on the written and countdown participate. In 2012, it was replaced by the Reel Math Challenge (now called the Math Video Challenge). Scoring and Ranking An individual’s score is their total number of correct sprint round answers plus 2 times their total number of correct target round answers. This total is out of a maximum of points. A team’s score is the individual scores of its members divided by 4 plus 2 points for every correct team round answer, making a team’s maximum possible score 66 points. Therefore, it is possible to win with a relatively low team score and a phenomenal individual score, as the team score is only roughly 30% of the total team score. Note that when there are less than four members the score will become less. MATHCOUNTS Competition Levels School Competition Students vie for the chance to make their school teams. Problems at this level are generally the easiest and most basic in curriculum. Chapter Competition Chapter competitions serve as a selection filter for state competitions. A few states don’t need to host chapter competitions due to a small population size. State Competition The top 4 students in each state form the state team for the national competition. The coach of the top school team at the state level is invited to coach the state team at the national competition. Interestingly, the coach of a state team is not necessarily the coach of any of the state’s team members. State competition competitors may be determined from the Chapter competition, based on the population of that particular state. National Competition National Competition Sites For many years, the National MATHCOUNTS competition was held in Washington, D.C. More recently, the competition has changed venues often. The 2022 competition was held in Washington, D.C. The 2021 competition was an online event. The 2020 competition was canceled due to the COVID-19 pandemic, but was due to be held in Orlando, Florida. The 2019 competition was held in Orlando, Florida. The 2018 competition was held in Washington, D.C. The 2017 competition was held in Orlando, Florida. The 2016 competition was held in Washington, D.C. The 2015 competition was held in Boston, Massachusetts. The 2014 competition was held in Orlando, Florida. The 2013 competition was held in Washington, D.C. The 2012 competition was held in Orlando, Florida. The 2011 competition was held in Washington, D.C. The 2009 and 2010 competitions were held in Orlando, Florida. The 2008 competition was held in Denver, Colorado. The 2007 competition was held in Fort Worth, Texas. The 2006 competition was held in Arlington, Virginia. The 2005 competition was held in Detroit, Michigan. The 2004 competition was held in Washington, D.C. The 2002 and 2003 competitions were held in Chicago, Illinois. What comes after MATHCOUNTS? Give the following competitions a try and take a look at the List of United States high school mathematics competitions.

mathcounts state

0. 1. 2. 3. 4. 5. 6. 7. 8. 9. Page 2. Copyright MATHCOUNTS Inc. 2018. All rights reserved. 2019 State Target Round. An architectural scale drawing of a The following pages provide solutions to the Sprint Target and Team Rounds of the 2022 MATHCOUNTS State Competition. These solutions provide creative and Note to coordinators: Answers to the Tiebreaker Round problems appear in the Tiebreaker Round Booklet. 2020 MATHCOUNTS. National Competition Sponsor. TITLE If you complete the problems before time is called use the time remaining to check your answers. Scorer’s Initials. Problem 1. Problem 2. 2020 MATHCOUNTS. Copyright MATHCOUNTS Inc. 2021. All rights reserved. Name. DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. Copyright MATHCOUNTS Inc. 2021. All rights reserved. Name. DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. [PDF] MATHCOUNTS Individual and Team Scores from the State Individual Scores — There are fewer scores than individuals because there were ties MATHCOUNTS Individual and Team Scores from the State Competition PDF [PDF] 2019 State Competition Sprint Round Problems 1−30 – MathCounts What is the sum of all the integers x for which x2 + 4x ≤ 1? Page 6 Copyright MATHCOUNTS, Inc 2018 All rights reserved 2019 State Sprint Round PDF [PDF] STATE MATHCOUNTS RULES and INSTRUCTIONS – North Dakota receive State MATHCOUNTS participation certificates D MATHCOUNTS Sessions -The sprint round will commence at 9:00 a m at the Ramkota Hotel PDF [PDF] 2015 State Competition Solutions – Scarsdale Public Schools The following pages provide solutions to the Sprint, Target and Team Rounds of the 2015 MATHCOUNTS® State Competition Though these solutions provide PDF [PDF] 2015 State Competition Sprint Round Problems 1−30 – Scarsdale Copyright MATHCOUNTS, Inc 2015 All rights reserved 2015 State Sprint Round 1 ______ 2 ______ 3 ______ 4 ______ 5 ______ 6 ______ PDF [PDF] MATHCOUNTS® State Competition Answer Key MATHCOUNTS® ©2005 MATHCOUNTS Foundation, 1420 King Street, Alexandria, VA 22314 New this year: The appropriate PDF [PDF] 2018 State Competition Target Round Problems 1 & 2 Texas Instruments Incorporated 3Mgives Art of Problem Solving NextThought 2018 MATHCOUNTS National Competition Sponsor Scorer’s Initials Problem 1 PDF [PDF] 2018 State Competition Solutions The following pages provide solutions to the Sprint, Target and Team Rounds of the 2018 MATHCOUNTS® State Competition These solutions provide creative PDF

2013 Chapter Competition Solutions

Transcription 1 013 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 would be able to answer a particular Target Round problem in less 3 minutes? Are you wondering how we could have possibly thought that a Mathlete would be able to answer a particular Team Round problem with less that 10 sheets of scratch paper? The following pages provide solutions to the Sprint, Target and Team Rounds of the 013 MATHCOUNTS Chapter Competition. Though these solutions provide creative and concise ways of solving the problems from the competition, there are certainly numerous other solutions that also lead to the correct answer, and may even be more creative or more concise! We encourage you to find numerous solutions and representations for these MATHCOUNTS problems. Special thanks to volunteer author Mady Bauer for sharing these solutions with us and the rest of the MATHCOUNTS community! 2 013 Chapter Competition Sprint Round 1. Marti, who lives in New York, calls Kathy, who lives in Honolulu. Marti calls at 6:30 p.m. in New York. The chart shows that when it is noon in New York it is 7 AM in Honolulu. That means that Honolulu is 5 hours earlier than New York. 6:30 p.m. 5 = 1:30 p.m. Ans.. What is the value of ? 1 + ( + 4) + ( ) + ( ) + ( ) + ( ) = = 683 Ans names are read at a rate of 1 name every 10 seconds. This means that = 6 names are read every minute. Therefore, it will take = 115 minutes. 115 Ans. 4. According to the bar graph, Ms. Pinski s class collected 9 red apples, 3 yellow apples and 8 green apples. There are 9 3 = 6 more red apples than yellow apples. 6 Ans. 5. The perimeter of a rectangle is 18 cm. The length of the rectangle is one-third of its perimeter so what is the width? Let l represent the length of the rectangle and w represent its width. We have l = (1/3) 18 = 6. Using the perimeter formula, we have l + w = 18 ( 6) + w = w = 18 w = 6 w = 3 Ans. 6. One-half of the sum of n and 8 is 7. Find n. Let s rewrite this as an equation and solve: ½(n + 8) = 7 n + 8 = 14 n = 6 Ans. 7. When (37 45) 15 is simplified, what is the units digit? Consider the units digits of 37 and 45. Since 7 5 = 35, the units digit of is 5. Since 15 also has a units digit of 5, subtracting results in a units digit of 0. Ans. 8. One witness says the suspect is 5 years old and 69 inches tall. A second witness says the suspect is 35 years old and 74 inches tall. And a third witness says the suspect is 35 years old and 65 inches tall. Each witness correctly identified the suspect s age or height but not both. Let a represent the suspect s age and b represent the suspect s height. We must find a + b. Let s assume the first witness identified the suspect s correct age, 5 years old. That means the other two witnesses were wrong about the age, so they must have correctly identified the suspect s height. But they gave two different values for the height. So, the first witness must have correctly identified the suspect s height of 69 inches, and the suspect is 35 years old. Therefore, a = 35, b = 69 and a + b = 104 Ans. 9. The rabbit jumps halfway to a carrot. If the rabbit lands within 6 inches of the carrot he will eat it. If the rabbit is originally 1 feet away, how many times must the rabbit jump in order to eat the carrot? After the first jump, the rabbit s distance 3 from the carrot is 6 feet. After the second jump, it s 3 feet. After the third jump, it s 1.5 feet, or 18 inches. After the fourth jump, it s 9 inches. After the fifth jump, it s 4.5 inches, which means the rabbit has a rather tasty carrot. 5 Ans. 10. Mellie has 6 pairs of pants and 10 shirts. She buys more pairs of pants. How many more outfits can Mellie make now? Each new pair of pants can be paired with each of the 10 shirts, to make a total of 10 = 0 additional outfits. 0 Ans. 11. Two equilateral triangles are drawn in a square. Find the measure of each obtuse angle in the rhombus formed by the intersection of the triangles. The rhombus formed by the intersection of the triangles has two opposite angles of 60. The other two angles are both the same size. Let x represent the measure of one of the two unknown angles in the rhombus. Since the sum of the interior angles of a quadrilateral is 360, we have x = 360 x + 10 = 40 x = 40 x = 10 Ans. 1. For 7 lbs of Mystery Meat and 4 lbs of Tastes Like Chicken the cost is $78. Tastes Like Chicken costs $3 more per pound than Mystery Meat. So how much does a pound of Mystery Meat cost? Let m represent the cost per pound of Mystery Meat, and c represent the cost per pound of Tastes Like Chicken. We have two equations: 7m + 4c = 78 and c = m + 3. Substitute and solve to get 7m + 4(m + 3) = 78 7m + 4m + 1 = 78 11m = 66 m = 6 Ans. 13. The perimeter of a rectangle is cm. The area is 4 cm. What is the smaller of the two integer dimensions of the rectangle? Let l represent the length of the rectangle and w represent its width. Then (l + w) = and l + w = 11. We also know lw = 4. The factors of 4 are: Of these, only 3 and 8 add to 11. The smaller of the two integer dimensions must be 3. Ans. 14. Mr. Cansetti s home is 7.5 blocks from the police station. The post office is 6 blocks from the grocery store and 3.5 blocks from the police station. The order in which the buildings are is Mr. Cansetti s home, the post office, the police station and then the grocery store. How far is it from his home to the store? The post office is 3.5 blocks from the police station. Therefore, the police station is =.5 blocks from the grocery store. From Mr. Cansetti s home to the post office is = 4 blocks. Now we can add it all up: 4 blocks (home to post office) blocks (post office to police) +.5 blocks (police to 4 grocery) is 10 blocks. 10 Ans. 15. Hank has less than 100 pigs. 5 pigs to a pen results in 3 pigs left over. 7 pigs to a pen results in 1 pig left over. 3 pigs to a pen results in 0 pigs left over. Let x represent Hank s number of pigs. We know that x is divisible by 3 and ends in 3 or 8 since there is a remainder of 3 when x is divided by 5. Given that when x divided by 7 leaves a remainder of 1, we must be looking for a number ending in or 7 that is divisible by 7. Those numbers less than 100 are 7, 4, and 77. Add 1 to each and choose the one that is divisible by 3. That must be 77. We have = 78. Checking, we see that 78 is divisible by 3, 78 7 = 11r1 and 78 5 = 15r3. 78 Ans people can paint 5 rooms in days. How long does it take 6 people to paint 15 rooms. It follows that 6 people can paint 10 rooms in days, and 6 people can paint 5 rooms in 1 day. Therefore, 6 people can paint 15 rooms in 3 days. 3 Ans. 17. A square dartboard has 5 smaller shaded squares. The side of dartboard is 4 times the side of a shaded square. What s the probability that a dart lands in a shaded area? Let x represent the length of a shaded area. Then x is the area of one of the shaded squares and 5x is the entire shaded area. The length of the side of the dartboard, then, is 4x, which means that the area of the dartboard is 16x. The probability of landing in a shaded area is 5x /16x = 5/16 Ans. 18. A line passes through the points (, 8) and (5, 13). When the equation of the line is written in the form y = mx + b, what is the product of m and b. Recall that m = (y y 1 )/ (x x 1 ). So, we have m = (8 ( 13))/( 5) = 1/( 7) = 3. Now substituting y = 8, x = and m = 3 into y = mx + b, we have 8 = 3( ) + b 8 = 6 + b b = m b = 3 = 6 Ans. 19. A sign has a shape consisting of a semicircle and an isosceles triangle. The rectangle measures ft by 4 ft. The shaded regions will be removed. BE = 3BG and AB is parallel to CE. Find the area of the resulting region. Since FG = and FH = HG = 1, it follows that the semicircle with diameter AB has a radius of 1 and area π/. GB is the same length as the radius so it is also 1. Therefore, EB = 4 1 = 3, and the area of ΔABD is ½ 3 = 3. Thus, the total area of the isosceles triangle and the semicircle is: 3 + π/ = Ans. 0. A license plate has three letters followed by 3 digits. The first two letters must be consonants, excluding Y. How many different license plates are there? There are 6 letters in the alphabet. 5 There are 5 vowels in the alphabet and we can t use Y. There are 6 6 = 0 choices for the first two letters and 6 choices for the third letter. There are 10 choices for each of the three digits. Therefore, the number of license plates is = 10,400,000 Ans. 1. A right square pyramid has a base with a perimeter of 36 cm and a height of 1 cm. One-third of the distance from the base, the pyramid is cut by a plane parallel to its base. What is the volume of the top pyramid? The volume of a square pyramid is (1/3)Bh, where B is the area of the base. With a perimeter of 36, each side of the base is 9. Since the plane cuts the pyramid at 1/3 of the distance from the base to the apex, it means that the height of the top pyramids is /3 the height of the larger pyramid, or (/3) 1 = 8. That also means the length of each side of the base of the top pyramid is (/3) 9 = 6. Therefore, the volume of the top pyramid is (1/3) = 96 Ans.. Four integers are chosen from 1 to 10, with repetition allowed. What is the greatest possible difference between the mean and median? To minimize the median we choose 1, 1, 1, 10. Then the median is 1, and the mean is 13/4. The difference is (13/4) (4/4) = 9/4 Ans. 3. If Jay takes one of Mike s books, then he will be carrying twice as many books as Mike. But if Mike takes one of Jay s books, they will each be carrying the same number. We need to find out how many books Mike is carrying. Let m represent the number of books Mike is carrying, j represent the number of books Jay is carrying. We have j + 1 = (m 1) j + 1 = m j = m 3 When Mike takes one of Jay s books: m + 1 = j 1 m = j m = (m 3) = m 5 m = 5 Ans. 4. A rectangular prism has a volume of 70 cm 3. Its surface area is 484 cm and all edge lengths are integers. We must determine what the longest segment is that can be drawn to connect two vertices. Let w, h and l represent the prism s width, height and length, respectively. We have lwh = 70 and (lw + lh + wh) = 484 lw + lh + wh = 4 Let s factor 70 so that we can determine what l, w and h are. 70 = = Let s check the surface area: (8 9) + (8 10) + (9 10) = = 4 So we have a rectangular prism similar to the one shown here: B C A 6 AB is the length of the longest segment connecting two vertices. Notice that triangle ABC is a right triangle. Segment AC is also the hypotenuse of a right triangle with sides of length 8 and 9. So (AC) = = = 145. It follows that (AB) = (AC) + 10 (AB) = (AB) = 45 AB = 45 = 7 5 Ans. 5. Avi and Hari agree to meet between 5:00 p.m. and 6:00 p.m. The first person who arrives will wait for the other for only 15 minutes. Find the probability that the two of them actually meet. If Avi gets there between 5:00 and 5:45, Hari still has a 15 minute window to arrive. The probability that Avi gets there between 5:00 and 5:45 is 3/4. The probability that Hari arrives in the next 15 minute window is 1/4. So the probability that Avi gets there in the first 45 minutes and Hari gets there within the next 15 minutes is (3/4) (1/4) = 3/16. Similarly, the probability that Hari gets there between 5:00 and 5:45 and Avi arrives within the next 15 minutes is 3/16. This leaves dealing with the last 15 minutes. There is a probability of (1/4) (1/4) = 1/16 that both Avi and Hari arrive during those last 15 minutes. (3/16) + (3/16) + (1/16) = 7/16 Ans. 6. Old sodas were replaced by new sodas that were 0% larger. The price of the new soda is 0% less than the price of the old soda. What is the ratio of the cost per ounce of the old soda to the new soda? Let x represent the number of ounces that were in the old soda, and y represent the price of the old soda. The cost per ounce of the old soda is y/x. At a volume that is 0% larger, the new sodas are (6/5)x ounces. The price of the new soda is (4/5)y. The cost per ounce for the new soda is (4/5)y]/[(6/5)x] = (4/6) (y/x) = (/3) (y/x). Therefore, the ratio of the cost per ounce of the old soda to the new soda is (y/x)/[(/3) (y/x)] = 1/(/3) = 3/ Ans. 7. Alana and Bob can complete a job in hours. Bob and Cody can do the job in 3 hours. Alana and Cody can do the same job in 4 hours. How many hours will it take all three working together to complete the job? Since Alana and Bob can complete a job in hours, they can complete 1/ the job in one hour. Body and Cody can do the job in 3 hours. So, they can complete 1/3 of the job in one hour. Since Alana and Cody can do the same job in 4 hours they can complete 1/4 of the job in 1 hour. This means that sets of Alana, Bob and Cody could do (1/) + (1/3) + (1/4) = (6/1) + (4/1) + (3/1) = 13/1 of the job in one hour. One set of Alana, Bob and Cody can do (13/1) (1/) = 13/4 of the job in one hour. It will take them 1/(13/4) = 4/13 hours. 4/13 Ans. 8. What fraction of the first 100 triangular numbers is evenly divisible by 7? The nth triangular number is the sum of 1 through n. So let s look at the first several and see if we can see a pattern. 1, 3, 6, 10, 15, 1, 8, 36, 45, 55, 66, 7 78, 91,105, 10, 136, 153, 171, 190, 10, 1 Looking at this we can see that the 6 th and 7 th triangular numbers, 1 and 8, are divisible by 7. The 13 th and 14 th triangular numbers, 105 and 10, are also divisible by 7, as are the 0 th and 1 st triangular numbers, 10 and 1. We have a pattern. There are triangular numbers divisible by 7 in every 7 numbers. There are 100/7 14 sets of 7 numbers. In each set we have and they are always the last two of the 7 numbers. Therefore, we don t have to worry about the 99 th and 100 th triangular numbers. They will not be divisible by 7. That s 14 = 8 out of 100, which is 7/5 Ans. 9. Point A of a clock is at the tip of the minute hand. Point B is at the tip of the hour hand. Point A is twice as far from the center of the clock as point B. We must find the ratio of the distance that point B travels in 3 hours to the distance that point A travels in 9 hours. The distance that the hour hand travels when it makes a complete revolution is πr, where r is the distance between the tip of the hour hand and the center of the clock. The distance that the minute hand travels when it makes a complete revolution is 4πr. The minute hand of a clock travels around the whole clock once per hour or one entire revolution. So point A travels 9 4πr = 36πr in the 9 hours. Point B travels only 1/1 of the way around the clock per hour or 360/1 = 30. So, in 3 hours it travels 90 or 1/4 of a revolution, which is (1/4) πr = (1/)πr. The ratio we must find is: ((1/)πr)/(36πr) = 1/7 Ans. 30. What percent of the interval with endpoints 5 and 5 consists of real numbers x satisfying the inequality x + 1 > 8/(x 1)? Let s create a table trying the integers from 5 to 5: x x + 1 8/(x 1) 5 4 8/6 = 4/ /5 3 8/4 = 1 8/ / = /1 = 8 1 8/0 = undefined 3 8/1 = / = / /4 = This information is represented on the number line below: Consider the 10 intervals from 5 to 5. Only 6 of these 10 intervals consist of values that satisfy the given inequality. That s, 6/10 = 60% Ans. Target Round 1. The distance between any two adjacent dots is one unit. Find the area of the shaded polygon. The shaded polygon has been divided into 6 smaller pieces. The area of each: A: (1/) 1 = 1 B: (1/) 3 1 = 1.5 C: (1/) 4 1 = 8 D: 3 4 = 1 E: (1/) 4 1 = F: (1/) 4 1 = Total area: = 0.5 Ans.. A mug is filled with a mixture that is 15 ml of hot chocolate and 35 ml of cream. What percent of the mixture is hot chocolate? There are = 50 ml in the entire mixture. So, hot chocolate accounts for 15/50 = 3/10 = 30% Ans. 3. A lottery has 0 million combinations. How many tickets would you need to purchase each second to buy all 0 million combinations in 1 week? There are = 604,800 seconds in one week. So, we have 0,000, ,800 = Ans. 4. Find the mean of all possible positive three-digit integers in which no digit is repeated and all digits are prime. Prime digits are, 3, 5 and 7. There are 3! = 6 combinations of {,3,5}, {, 3, 7}, {, 5, 7} and {3, 5, 7}. Starting with we have: 35, 53, 37, 73, 57 and 73. Starting with 3 we have: 35, 35, 37, 37, 357 and 375. Starting with 5 we have: 53, 53, 57, 57, 537 and 573. Starting with 7 we have: 73, 73, 75, 75, 735 and 753. If we were to add up all the numbers, the units column would contain 6 s, 6 3s, 6 5s and 6 7s. That s ( 6) + (3 6) + (5 6) + (7 6) = = 10. That gives us a in the units column, and we carry 10 over to the tens column. In the tens column you also have 6 of each number. So that s a sum of 10 plus the 10 we carried over, or 11. That means a in the tens column and we carry over 11. Similarly, there are 6 of each number in the hundreds column. That s a sum of 10 plus the 11 we carried over, or 113. The 3 is in the hundreds column so the sum is actually 11,3. The mean is 11,3/4 = Ans. 5. Ray s age is half his sister s age. Ray s age is also the square root of one-third of his grandfather s age. In 5 years, Ray will be two-thirds as old as his sister will be. We need to find the ratio of Ray s sister s age to his grandfather s age. Let r, s and g represent Ray s, Ray s sister s and Ray s grandfather s ages, respectively. Now let s create the equations. We have r = (1/)s r = (1/3)g r + 5 = (/3)(s + 5) (1/)s + 5 = (/3)s + 10/3 Multiply both sides by 6 yields 3s + 30 = 4s + 0 s = 10 r = 5 r = 5 = (1/3)g g = 5 3 = 75 s/g = 10/75 = /15 Ans. 6. Alex added the page numbers of a book and got a total of 888. But there is a page missing. We must find the page number on the final page. The sum of the pages numbers is n 1 + n = 888. Since the sum of the consecutive integers from 1 to n is (n/) (n + 1), we can write (n/) (n + 1) = 888. This isn t entirely accurate because 888 doesn t include the two 9 page numbers from the missing sheet. Multiplying by to get rid of the fractions, we get n(n + 1) = 1776, and n + n 1776 = 0. We could try and solve this, but remember, the sum isn t accurate. What this does show us is that the difference between the two roots is 1. Notice that So, let s look at the sum of the first 4 numbers. We have (4/) 43 = 1 43 = 903, and = 15. Well, 15 = so that must be the page that is missing. Therefore, the last page must be 4. 4 Ans. And And And A circular spinner has 7 sections of equal size. Each is colored either red or blue. In how many ways can the spinner be colored? Where you have to be careful is understanding that if you use an odd number of switches (from red to blue or vice versa) the first and last groups of sections are next to each other so the first and last groups are no longer distinct. So we re looking for even numbers of integers that sum to 7 with the exception of all 7 sections being one color. Let s start with 6 different groups or: There are versions (where the red and blue sections are switched). And Now two groups: And finally all of the same color: There are no other combinations of 6 groups so let s consider 4 groups 10 That s a total of 0. Ans. 8. A square is inscribed in a circle of radius 5 units. There are smaller squares, one in each of the regions bounded by a side of the square and the circle as shown. We must find the area of the large square and the four smaller squares. First, let s determine the side of the large square. If we draw a diagonal in the square, that is the diameter of the circle, or 10. Let s represent the side length of the large square. Based on the properties of right triangles, we know that 10 = s ; thus, s = 5. Now, let s draw a right triangle whose long leg and hypotenuse originate at the center of the circle, one extending to the midpoint of the edge of one of the small squares, as shown, and one extending to a point of the same small square that is on the circle. The short leg is a segment connecting the other two (which is half of the side of the small square). which is half the length of a side of the small square, is x. Using the Pythagorean Theorem, we have x + [(5 )/ + x] = 5 x + 4x + (10 )x + 5/ = 5 5x + (10 )x + 5/ = 5 10x + (0 )x + 5 = 50 10x + (0 )x 5 = 0 x + (4 )x 5 = 0 Let s use the quadratic equation to solve this. b ± b 4ac x = a where a =, b = 4 and c = 5. We have x = x = ± ) () 4 (4 4()( 5) 4 ± x = 3 = So, x = = 4 ± 6 4 =, and the area of each small square is ( ) =. There are 4 of these squares for a total area of 4 = 8. The area of the large square with side length 5 is (5 ) = 50. Therefore, the total area of the five squares is = 58 Ans. Let x represent the side length of the small square. The length of the long leg is half the length of the large square plus the length of the small square or (5 )/ + x. The length of the hypotenuse is just the radius of the circle, or 5. The length of the short leg, Team Round 1. Greenland is 840,000 square miles. Iceland is only 39,800 square miles. Greenland is 3 times the size of Texas. So what percent of Texas would be covered by Iceland? 840,000 3 = 80,000 11 39,800 80, % Ans.. A square and a regular hexagon share a common side. Find the sum of the degree measures of angles 1 and. Let x and y represent the measures of angles 1 and, respectively. Let z represent the measure of the third angle of that triangle, so x + y = 180 z. In a regular hexagon, each interior angle is 10. Adjacent to the hexagon we have an angle of 90. That means z = 360 ( ) = = 150. So, x + y = = 30 Ans. 3. A trip costs $9000 for the bus plus $15 per student. Each student pays $375. We must find how many students must go on the trip so that the total amount paid is equal to the total cost of the trip. Let x represent the number of students who must go on the trip. Then x = 375x 50x = 9000 x = 36 Ans. 4. Triangle ABC has vertices at A( 3, 4), B(5, 0) and C(1, 4). What is the x-coordinate of the point where the median from C intersects AB? Since [5 ( 3)]/ = 8/ = 4, the x-coordinate is = 1 Ans. 5. The sum of three primes is 15. The difference between the largest and smallest prime is 50. We must find the largest possible median of these three prime numbers. OK. Let s list all the primes up to 15., 3, 5, 7, 11, 13, 17, 19, 3, 9, 31 37, 41, 43, 47, 53, 57, 61, 67, 71, 73 79, 83, 89, 97, 101, 103, 107, 109, 113 Let s make a list of pairs of primes that are 50 apart. We have {3, 53}, {11, 61}, {17, 67}, {3, 73}, {9, 79}, {47, 97}, {53, 103}, {57, 107}. Some of these choices have a sum greater than 15. Eliminating those leaves us with {3, 53}, {11, 61}, {17, 67}, {3, 73}, (9, 79}. Now let s determine which of these two primes will result in a third prime to make them all sum up to = 56; = 69; too large and not a prime = 7; 15 7 = 53 which is a prime = 84; = 41 which is a prime = 96; = 9 which is a prime = 108; = 17 which is less than 9 So we have choices of {11, 53, 61}, {17, 41, 67} and {3, 9, 73} The median of the first set is 53. The median of the second set is 41. The median of the third set is 9. The greatest is 53 Ans. 6. What is the probability that a randomly selected integer from 1 to 81, inclusive is equal to the product of two one-digit numbers? Any number less than or equal to 81 is the product of two one-digit numbers except two-digit primes. Let s see how many primes there are from 10 to 81: 11, 13, 17, 19, 3, 9, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79 That s a total of 18 primes. Add to this any other numbers that are multiples of these primes: 11:, 33, 44, 55, 66, 77 or 6 more 12 13: 6, 39, 5, 65, 78 or 5 more 17: 34, 51, 68 or 3 more 19: 38, 57, 76 or 3 more 3: 46, 69 or more 9: 58 or 1 more 31: 6 or 1 more 37: 74 or 1 more That s a total of = more. But we re not done yet: There are also a few integers that are multiples of 3 or more digits: 50 = = = = = 5 That s a total of 5 more. That brings the total number of = 45 numbers between 1 and 81, inclusive that cannot be written as the product of two one-digit numbers. Therefore, there are = 36 that are. That s a probability of 36/81 = 4/9 Ans. Another way to solve this problem is using the following multiplication table: 7. We have two sticks, one of length a cm and one of length b cm. With a stick whose length is strictly between 8 and 6 cm a triangle can be constructed. We must find the product ab. The length of the third side of a triangle is always less than the sum of the lengths of the two other sides. The length of the third side must also be greater than the difference of the lengths of the two sides a and b. Therefore, a b = 8 and a + b = 6. Solving this system by adding the two equations, we get a = 4, and a = 17. That means b = 6 17 = 9. Therefore, ab = 17 9 = 153 Ans. 8. A 3-inch by 8-inch sheet of paper and a -inch by 1-inch sheet of paper have the same area. Using just one cut (not necessarily straight), the 3-inch by 8-inch sheet can be divided into two pieces that can be rearranged to completely cover the -inch by 1-inch sheet. Find the length of the cut. The perfect squares are located on the diagonal. Since any products located below the perfect square in each column will be duplicates, they ve been grayed out. Also, 4, 6, 8, 9, 1, 18, 16, 4 and 36 are duplicates, so they ve been grayed out as well. What s left are the 36 different numbers from 1 to 81, inclusive, that are the product of two one-digit numbers. Again, that s a probability of 36/81 = 4/9 Ans. If we cut the 3-by-8 sheet into symmetric L shapes, it should work. Superimposing those cuts onto the 13 -by-1 sheet: The cut is = 9 inches. 9 Ans. 9. d = ,003 + Each additional term after the second has one more interior 0. The last term has 30 digits. So what is the sum of the digits of d? Adding the 30 3s in the units column we get 3 30 = 90. So, d has a 0 in the units column, and we carry the 9 to the tens column. In the tens column, the sum of the 3 and 8 0s, plus the 9 that was carried is 1. So, d has a in the tens column, and we carry the 1 to the hundreds column. Now in the hundreds column the sum of the 3 and 7 0s, plus the one that was carried is 4. So, d has a 4 in the hundreds column. The sum in each of the remaining 7 columns is 3. Therefore, the sum of the digits of d is (7 3) = 87 Ans. 10. A bullet train travels 10 km/h. A freight train travels 90 km/h on a parallel track. From the time the bullet train catches up to the back of the freight train to the time the back of the bullet train pulls even with the front of the freight train 4 seconds elapse. Freight trains are three times as long as bullet trains. So how many seconds would it take two bullet trains, each traveling at 10 km/h to pass by each other completely, when moving in opposite directions? A bullet train that travels 10 km/h travels 10/(60 60) = 7/10 km/sec. A freight train that travels 90 km/h travels 90/(60 60) = 3/10 km/sec. So, when the bullet train starts approaching the freight train to pass, it does so at a rate of (7/10) (3/10) = 1/30 km/sec. It takes 4 seconds for the back of the bullet train to pull even with the front of the freight train. This means that the front of the bullet train passes the entire freight train and has continued on the full length of the bullet train. Let f and b represent the lengths of the freight train and bullet train, respectively. We have f = 3b. The number of kilometers that the bullet train travels when its rear has pulled even with the front of the freight train is 4 (1/30) = 4/5 km. So, f + b = 4/5 3b + b = 4/5 4b = 4/5 b = 1/5 km Given that the two bullet trains are nose to nose, every second the front of the one bullet train moves (7/10) = 7/60 km towards the back of the other bullet train. It will take (1/5)/(7/60) = (1/5) (60/7) = 1/7 seconds for the front of the first bullet train to reach the back of the second bullet train. It will take another 1/7 seconds for the end of the first bullet train to reach the end of the second bullet train. The time for the two bullet trains to completely pass one another is (1/7) + (1/7) = 4/7 = Ans.

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## MATHCOUNTS

Team Registration Each team will consist of exactly 4 students in grade 6 – 8

Teams must be comprised of active NSBE Jr. members

Attendance at the 47th Annual Convention in Orlando, FL is required MATHCOUNTS® Competition Components MATHCOUNTS Written Competitions are designed to be completed in approximately two hours at Annual Convention: The SPRINT ROUND (40 minutes) consists of 30 problems. This round challenges students’ accuracy in completing all of the problems in a limited period of time. Calculators are not permitted. The TARGET ROUND (approximately 30 minutes) consists of eight problems presented to competitors in four pairs (6 minutes per pair). This round features multi-step problems that engage students in mathematical reasoning and problem-solving processes. Problems assume the use of calculators. The TEAM ROUND (20 minutes) consists of 10 problems that team members work to solve together. Team member interaction is permitted and encouraged. Problems assume the use of calculators. The MATHCOUNTS Final Countdown Round is designed for individual students to compete. A problem is presented to two students at a time. The question will be read aloud, as well as presented on a screen. Students can use a pencil and scratch paper. Students have 45 seconds to determine the answer and hit a buzzer when they are ready to answer. The other student can continue to work while their opponent is presenting. The student that correctly answers the most questions out of three moves on to the next round. Calculators are not permitted.

Competition Rules Pencils and paper will be provided for students; however, students may bring their own pencils, pens and erasers if they wish. They may not use their own scratch paper or graph paper. Calculators are not permitted in the Sprint Round, but they are permitted in the Target, Team and Tiebreaker (if needed) Rounds. When calculators are permitted, students may use any calculator (including programmable and graphing calculators) that does not contain a QWERTY (typewriter-like) keypad. Calculators that have the ability to enter letters of the alphabet but do not have a keypad in a standard typewriter arrangement are acceptable. Smart phones, laptops, iPads®, iPods®, personal digital assistants (PDAs) and any other “smart” devices are not considered to be calculators and may not be used during competitions. Students may not use calculators to exchange information with another person or device during the competition. Coaches are responsible for ensuring that their students use acceptable calculators and students are responsible for providing their own calculators (and batteries).® Pagers, cell phones, iPods and other MP3 players should not be brought into the competition room. Failure to comply could result in dismissal from the competition. Should there be a rule violation or suspicion of irregularities, the MATHCOUNTS® coordinator or competition official has the obligation and authority to exercise his or her judgment regarding the situation and take appropriate action which might include disqualification of the suspected student(s) from the competition. Use of notes or other reference materials (including dictionaries and translation dictionaries) is not permitted. Communication with coaches is prohibited during rounds but is permitted during breaks. All communication between guests and students is prohibited during competition rounds. Communication between teammates is permitted only during the Team Round.

## Art of Problem Solving

Many AoPS Community members and online school students have been participants at National MATHCOUNTS, including many Nationals Countdown Round participants in the past decade. MATHCOUNTS is a large national mathematics competition and mathematics coaching program that has served millions of middle school students since 1984. Sponsored by the CNA Foundation, National Society of Professional Engineers, the National Council of Teachers of Mathematics, and others including Art of Problem Solving, the focus of MATHCOUNTS is on mathematical problem solving. Students are eligible for up to three years, but cannot compete beyond their eighth grade year.

MATHCOUNTS Region: USA Type: Free Response Difficulty: 0.5 – 2.5 Difficulty Breakdown: Countdown : 0.5 (School/Chapter), 1 (State/National)

Sprint : 1-1.5 (School/Chapter), 2-2.5 (State/National)

Target: 1.5 (School), 2 (Chapter), 2-2.5 (State/National)

MATHCOUNTS Resources

MATHCOUNTS Books

Art of Problem Solving’s Introductory subject textbooks are ideal for students preparing for MATHCOUNTS, as are AoPS Volume 1 and Competition Math for Middle School

MATHCOUNTS Classes

Art of Problem Solving hosts a Basic and an Advanced MATHCOUNTS course. The AoPS Introduction-level subject courses also include a great deal of MATHCOUNTS preparation. Many AoPS instructors are former National MATHCOUNTS Mathletes.

MATHCOUNTS Online

MATHCOUNTS Curriculum

MATHCOUNTS curriculum includes arithmetic, algebra, counting, geometry, number theory, probability, and statistics. The focus of MATHCOUNTS curriculum is in developing mathematical problem solving skills.

Before 1990, MATHCOUNTS chose particular areas of mathematics to highlight each year before changing the focus of the competition more broadly to problem solving.

Past State Team Winners

1984: Virginia

1985: Florida

1986: California

1987: New York

1988: New York

1989: North Carolina

1990: Ohio

1991: Alabama

1992: California

1993: Kansas

1994: Pennsylvania

1995: Indiana

1996: Wisconsin

1997: Massachusetts

1998: Wisconsin

1999: Massachusetts

2000: California

2001: Virginia

2002: California

2003: California

2004: Illinois

2005: Texas

2006: Virginia

2007: Texas

2008: Texas

2009: Texas

2010: California

2011: California

2012: Massachusetts

2013: Massachusetts

2014: California

2015: Indiana

2016: Texas

2017: Texas

2018: Texas

2019: Massachusetts

2020: CANCELLED

2021: New Jersey

2022: New Jersey

MATHCOUNTS Competition Structure

Sprint Round

30 problems are given all at once. Students have 40 minutes to complete the Sprint Round. This round is very fast-paced and requires speed and accuracy as well. The earlier problems are usually the easiest problems in the competition, and the later problems can be as hard as some of the Team Round questions. No calculators are allowed during this round.

Target Round

8 problems given 2 at a time. Students have 6 minutes to complete each set of two problems. Students may not go back to previous rounds (or forwards to future rounds) even if they finish before time is called. Calculators are allowed for the Target Round. Usually comprised of one “confidence booster” and one hard problem.

Team Round

10 problems in 20 minutes for a team of 4 students. These problems typically include some of the most difficult problems of the competition. Use of a calculator is allowed (and required for some questions).

Countdown Round

High scoring individuals compete head-to-head until a champion is crowned. People compete from off a screen taking 45 seconds or less to finish the problem. The Countdown round is run differently in various different chapter, state, and national competitions. In the national competitions, it is the round that determines the champion. Calculators are not allowed, but scratch paper will be provided.

Chapter and State Competitions

In the chapter and state competitions, the countdown round is not mandatory. However, if it is deemed official by the chapter or state, the following format must be used:

The 10th place written finisher competes against the 9th place written finisher. A problem is displayed, and both competitors have 45 seconds to answer the question, and the first competitor to correctly answer the question receives one point. The person who gets the most correct out of three questions (not necessarily two out of three) is the winner.

The winner of the first round goes up against the 8th place finisher.

The winner of the second round goes up against the 7th place finisher.

This process is continued until the countdown round reaches the top four written competitors. Starting then, the first person to get three questions correct wins (as opposed to the best-out-of-three rule).

If the countdown round is unofficial, any format may be used, and if it is unofficial it will not determine your placement towards the final results and may be determined by another format. Single-elimination bracket-style tournaments are common.

National Competition

At the national competition, there are some structural changes to the countdown round. The top 12 (not the top 10) written finishers make it to the countdown round, and the format is changed from a ladder competition to a single-elimination tournament where the top four written competitors get a bye. This setup makes it far more likely for a 12th place finisher to become champion, and it makes it less likely for a first-place written finisher to become champion, equalizing the field. But even then, a 12th place written competitor will have less of a chance to become champion than the top 4, because the top 4 get a bye. Until the semi-finals, the scoring is best out of five advances.

In the first round and the second round, the person to correctly answer the most out of 5 questions wins. However, at the semifinals, the rules slightly change— the first person to correctly answer four questions wins.

Ciphering Round

In some states, (most notably Florida) there is an optional ciphering round. Very similar to countdown (in both difficulty and layout), a team sends up a representative to go against all representatives from the other teams. A problem is shown on a screen and students work fast to answer the problem. The students give their answer and after 45 seconds the answer is shown and the answers are checked to see if they are right. The fastest correct answer gets five points, the next fastest gets 4, etc. There are 4 questions per individual and teams send up 4 people. A perfect score is then 80. Often times the questions take clever reading skills. For example, one question was “How much dirt is in a 3 ft by 3 ft by 4 ft hole?” The answer was 0 because there is no dirt in a hole.

Masters Round

Top students give in-depth explanations to challenging problems. This round was optional at the state level competition and mandatory at the national competition (up to 2011). At nationals the top two on the written and countdown participate. In 2012, it was replaced by the Reel Math Challenge (now called the Math Video Challenge).

Scoring and Ranking

An individual’s score is their total number of correct sprint round answers plus 2 times their total number of correct target round answers. This total is out of a maximum of points.

A team’s score is the individual scores of its members divided by 4 plus 2 points for every correct team round answer, making a team’s maximum possible score 66 points. Therefore, it is possible to win with a relatively low team score and a phenomenal individual score, as the team score is only roughly 30% of the total team score. Note that when there are less than four members the score will become less.

MATHCOUNTS Competition Levels

School Competition

Students vie for the chance to make their school teams. Problems at this level are generally the easiest and most basic in curriculum.

Chapter Competition

Chapter competitions serve as a selection filter for state competitions. A few states don’t need to host chapter competitions due to a small population size.

State Competition

The top 4 students in each state form the state team for the national competition. The coach of the top school team at the state level is invited to coach the state team at the national competition. Interestingly, the coach of a state team is not necessarily the coach of any of the state’s team members. State competition competitors may be determined from the Chapter competition, based on the population of that particular state.

National Competition

National Competition Sites

For many years, the National MATHCOUNTS competition was held in Washington, D.C. More recently, the competition has changed venues often.

The 2022 competition was held in Washington, D.C.

The 2021 competition was an online event.

The 2020 competition was canceled due to the COVID-19 pandemic, but was due to be held in Orlando, Florida.

The 2019 competition was held in Orlando, Florida.

The 2018 competition was held in Washington, D.C.

The 2017 competition was held in Orlando, Florida.

The 2016 competition was held in Washington, D.C.

The 2015 competition was held in Boston, Massachusetts.

The 2014 competition was held in Orlando, Florida.

The 2013 competition was held in Washington, D.C.

The 2012 competition was held in Orlando, Florida.

The 2011 competition was held in Washington, D.C.

The 2009 and 2010 competitions were held in Orlando, Florida.

The 2008 competition was held in Denver, Colorado.

The 2007 competition was held in Fort Worth, Texas.

The 2006 competition was held in Arlington, Virginia.

The 2005 competition was held in Detroit, Michigan.

The 2004 competition was held in Washington, D.C.

The 2002 and 2003 competitions were held in Chicago, Illinois.

What comes after MATHCOUNTS?

Give the following competitions a try and take a look at the List of United States high school mathematics competitions.

## How to Prepare for MathCounts

MathCounts is a middle school math competition for grades 6-8. Students cannot compete beyond grade 8. It is fun to compete because unlike AMC 8, this has multiple rounds and levels. Different skills are also tested. Some of the rounds allow the use of calculators so they test your problem-solving skills heavily and move so much beyond smart arithmetic.

How to Register for MathCounts

Topics for MathCounts

What to expect in MathCounts or MathCounts format

Scoring in MathCounts

MathCounts preparation

For school and chapter level

For State and National Level

General Tips

During the MathCounts exam

How to Register for MathCounts

Through school: Usually students can register for Math Counts only through school. A lot of schools only let you participate if you belong to the school’s math club.

As an individual: In 2020-21, they opened up individual registrations. Students can participate as an individual only if their school does not participate. (Not sure if they will continue this though. Will update as soon as I learn about this).

Topics for MathCounts

Since this is for grades 6-8, students are expected to know the Middle School Math, Geometry and a part of Algebra 2 well. The following list is just a guide and is not exhaustive.

Some common topics

1. Number Theory

a. divisibility rules,

b. LCM and GCF,

c. modular arithmetic,

d. base number arithmetic and

e. number sense.

2. Algebra

a. fractions, decimals, ratios and percents,

b. exponents and radicals

c. equations and inequalities,

d. functions, quadratics, and more

3. Geometry

a. angles,

b. Pythagorean theorem and special right triangles

c. perimeter and area of 2D shapes including circles

d. surface area and volumes of 3D shapes,

e. co-ordinate geometry

f. similar triangles

4. Counting and Probability

a. nPr and nCr (permutations and combinations)

b. Pascals triangle

c. Binomial theorem

d. Probability

e. Geometrical probability

What to expect in MathCounts

MathCounts usually is 4 levels – School, Chapter, State and National. In 2020-21, they introduced a Chapter Invitational Level because of individual registrations. Since all the individual participants directly went to Chapter level, they added an extra round to filter out. So it was School, Chapter, Chapter Invitational, State and Nationals.

In each of the levels, we have 4 rounds – Sprint, Target, Team and Countdown. None of the rounds are multiple choice.

Sprint Round: Consists of 30 questions to be answered in 40 minutes. No calculators are allowed. Students have to write the correct answer in the correct format in the blank provided.

Target Round: Consists of 8 problems. Students are given 2 problems at a time ( a set) and they get 6 minutes to solve the set. Time is not carried over, so it is wise to take up the time and check your work if you have some time left.

Team Round: Consists of 10 problems and students are given 20 minutes to solve them. Students work with their 4 member team to solve these problems. How they split the problems depends on the team’s strength and weaknesses.

Countdown Round: Two competitors compete head on with each other. They are given less than 45 seconds per question. It’s a buzzer round. One of the most tense rounds I’ve seen 🙂

A particular school, chapter and state might or might not do the countdown round. But this is the round that determines the National Champion.

Here’s a sample of National Countdown round you can watch at youtube.

Scoring in MathCounts:

Your individual score is the sum of sprint and target rounds. Each question in sprint is worth 1 point and each question in target and team rounds is worth 2 points. So 30+16=46 points.

The team score is the sum of individual scores divided by 4, plus 2 points for each correct answer in the team round. It is not the average of the individual scores. This is because even if your team has only 3 members they will divide the sum of individual scores by 4. Hence it is always good to have 4 members in your team.

Materials/ Resources to Prepare for MathCounts

I coach kids for all middle school competitions and here are some of the resources that I use/ suggest to prepare for Math Counts.

See if your school has a math club. Most of the schools that host the competition does. If not try to see if you can start one with the help of a teacher. A lot of schools will let you participate only if you belong to the school’s math club as well. Math Counts handbook: Math Counts releases its own Handbook. For the 2020-21 handbook you can click here. It will give you an idea of what topics to expect and the type of questions. If your school is registered and has a coach, these are the worksheets they usually give you. Past Exam Question Papers: Math Counts has one year’s question paper available for free. You can download it from their website. The previous years question papers can be bought from their online store. They also have a book on MathCounts Practice Problems that you can use for extra practice 🙂 Resources from Math Counts website: Go to their website and hover over resources. You’ll find a trainer app, video resources, online problem library, problem of the week etc. for practice. For online practice I especially liked the MathCounts Trainer App . Books from Art of Problem Solving: If you’re a beginner to the competition get the Pre-Algebra by AOPS. If you’re familiar with the topics then get the Volume 1 from AOPS. To be really thorough and for state/ national rounds you should practice from their Intro to Algebra, Geometry, Number Theory and Intro to Probability books. Courses by Art of Problem Solving: They have beginners and advanced courses specifically for AMC 8 and Math Counts.

MathCounts preparation

For school and chapter level

School level is the easiest one and chapter is not too difficult either. Even if you are a beginner, you can get through this with dedication and sufficient practice.

Start with the school competition exam paper. That’s the easiest. If you’re extremely comfortable with the questions, move on to Chapter level papers. This will also tell you where you need to focus. Based on that you can start with hard core preparation. If you get fewer than 20 on a school sprint test, start with the Pre-Algebra book by AOPS. You can then move on to Algebra, Counting Probability and Geometry books. Work through the current year’s school handbook. It does help you practice a variety of topics in a short time. Know all your perfect squares till 25 squared and all your primes till 200. These will help you save time.

Unless your chapter is ultra competitive, doing the past papers, the handout and Pre-Algebra book should get you through.

For State and National Level

If you can get a score of 25+ in chapter level competition go to Volume 1 book and go through it chapter by chapter. If you are stuck in any chapter, review that by going to the respective book. Mathcounts State Competition Preparation books (5 Volumes) by myMathCounts is also definitely useful. You can also practice questions from AMC 10. If you’ve done all this and still want more practice, try getting question papers from other middle and high school math competitions and do them as well. It’s always good to get a variety of questions.

General Tips for MathCounts preparation

Prepare with your friends. You can bounce off ideas and it’ll make the preparation fun as well. The earlier you start your preparation, the better it is. Summer is usually a great time to prepare because you have a lot of time to dedicate. Try to work for 30-45 minutes 3-4 times a week during school time. Summers aim for at least 1 hour a day for 4 days a week. Some kids do residential math camps and they work 6 hours a day for 3 weeks straight. What makes this fun is doing it with friends/ like minded people. Do not time yourself the first time you solve a paper. Take however long it requires. Sometimes struggling with a question for an hour will help you learn more than doing 10 questions that you already kind of know how to do. Apart from topic knowledge, improve your problem-solving skills. While doing the AOPS books, if you encounter a problem you have trouble with, do try out various ways before giving up. Like I said in the previous point, your struggles help you learn more. I highly encourage my students to not give up. Look at the hints but looking at the answer should be the last resort. Since Target and Team rounds allow the use of calculators, learn how to use it. I’ve seen students spend a lot of time preparing for Sprint without doing much of Target and Team and hence do not use calculators much. Be comfortable using your calculator! Prepare an excel sheet marking the questions you got right and wrong. After you solve a few years papers, look into it to see if you can find a pattern. Do you consistently get problems from a particular topic wrong? Work on that. Or do you have trouble with the last few problems? Try setting your Alcumus level to “Hard” or “Insanely Hard” and try out the ropics. Once you go to Chapter level you need to choose a strong team and team captain. Your team should get used to solving problems together and you should be prepared on how to deal with the team round and what works for you before you enter the Chapter level competition. If you want more help in preparation you can always hire a coach/ tutor to guide and help you through it. A coach will always look at your strengths and weaknesses and guide you accordingly.

During the MathCounts exam

Sleep well the night before. You should have established a good night routine much before the competition. A good bedtime routine will help you throughout your life.

Do some breathing exercises to calm down. Adrenaline rush is good for solving problems but too much stress is not good. Be relaxed. You’ve done all the preparation and now it is just fun time 🙂

Sprint Round: The first 15-20 questions should be easy even in State Round. It should take you about 10 minutes for the first 20 (or at least 15) questions. So depending on how much you want to score, you should make sure that you get all of those right. You can then move on to the harder ones.

Target Round: The first 5-6 questions should be easy. Since you are given only 2 questions at a time and 6 minutes to solve them, make sure you utilise it fully. Do not return the answer sheet even if you finish early. Check your work and if you still have time left over, take rest.

Use your calculator where necessary. I’ve seen my students so used to doing everything by hand they forget to use calculators. I keep reminding them to use it.

All the best for your competition! Glad that you are thinking through this early. It does require a year (or more) to prepare. If you liked this article and it was useful please do share it with your friends and in social media.

Do you have any other tips that has worked for you? Do let me know in the comments below.

#MathCounts #MiddleSchoolMathCompetition #prepareForMathCounts

About Me:

Hi, I’m Vasudha, an Online Math Tutor. I help prepare students for all Elementary and Middle school Math Competitions. If you’d like to talk to me about preparing your child for math competitions please do contact me here .

## MATHCOUNTS COMPETITION SERIES

The Competition Series has 4 levels of competition—school, chapter, state and national. Each level of competition is comprised of 4 rounds—Sprint, Target, Team and Countdown Round. Altogether the rounds are designed to take about 3 hours to complete. Click the buttons to the left to learn a little more about what each round looks like.

Sprint Round Focuses on speed and accuracy. Students have 40 minutes to complete 30 math problems without a calculator. Chapter-level example: By switching two of the digits of the number 123,456, Rodrigo obtains a new number that is 1980 more than the original. What is the product of the two digits Rodrigo switched? (answer: 15)

Target Round Focuses on problem-solving and mathematical reasoning. Students receive 4 pairs of problems and have 6 minutes to complete each pair, assuming the use of a calculator. State-level example: One evening, Varun finishes reading a novel that he has been reading for several days and finds the ending so exciting that he immediately begins reading the novel’s sequel. Each novel has pages numbered consecutively, starting with page 1. Each novel has fewer than 1000 pages. If Varun reads a total of 42 pages in one sitting and the sum of the page numbers he reads in that sitting is 2018, what is the number of the last page of the first novel? (Answer: Page 265)

Team Round Focuses on problem-solving and collaboration. Students have 20 minutes to complete 10 math problems, assuming the use of a calculator. Only the 4 students on a school’s team can take this round officially. State-level example: Jackie sold two cars for $25,000 each. The first car sold for a profit of 22%, and the second sold at a loss of 7%. What was the total percent profit on the sale of the two cars? Express your answer to the nearest hundredth. (Answer: 5.54%)

## Art of Problem Solving

Many AoPS Community members and online school students have been participants at National MATHCOUNTS, including many Nationals Countdown Round participants in the past decade. MATHCOUNTS is a large national mathematics competition and mathematics coaching program that has served millions of middle school students since 1984. Sponsored by the CNA Foundation, National Society of Professional Engineers, the National Council of Teachers of Mathematics, and others including Art of Problem Solving, the focus of MATHCOUNTS is on mathematical problem solving. Students are eligible for up to three years, but cannot compete beyond their eighth grade year.

MATHCOUNTS Region: USA Type: Free Response Difficulty: 0.5 – 2.5 Difficulty Breakdown: Countdown : 0.5 (School/Chapter), 1 (State/National)

Sprint : 1-1.5 (School/Chapter), 2-2.5 (State/National)

Target: 1.5 (School), 2 (Chapter), 2-2.5 (State/National)

MATHCOUNTS Resources

MATHCOUNTS Books

Art of Problem Solving’s Introductory subject textbooks are ideal for students preparing for MATHCOUNTS, as are AoPS Volume 1 and Competition Math for Middle School

MATHCOUNTS Classes

Art of Problem Solving hosts a Basic and an Advanced MATHCOUNTS course. The AoPS Introduction-level subject courses also include a great deal of MATHCOUNTS preparation. Many AoPS instructors are former National MATHCOUNTS Mathletes.

MATHCOUNTS Online

MATHCOUNTS Curriculum

MATHCOUNTS curriculum includes arithmetic, algebra, counting, geometry, number theory, probability, and statistics. The focus of MATHCOUNTS curriculum is in developing mathematical problem solving skills.

Before 1990, MATHCOUNTS chose particular areas of mathematics to highlight each year before changing the focus of the competition more broadly to problem solving.

Past State Team Winners

1984: Virginia

1985: Florida

1986: California

1987: New York

1988: New York

1989: North Carolina

1990: Ohio

1991: Alabama

1992: California

1993: Kansas

1994: Pennsylvania

1995: Indiana

1996: Wisconsin

1997: Massachusetts

1998: Wisconsin

1999: Massachusetts

2000: California

2001: Virginia

2002: California

2003: California

2004: Illinois

2005: Texas

2006: Virginia

2007: Texas

2008: Texas

2009: Texas

2010: California

2011: California

2012: Massachusetts

2013: Massachusetts

2014: California

2015: Indiana

2016: Texas

2017: Texas

2018: Texas

2019: Massachusetts

2020: CANCELLED

2021: New Jersey

2022: New Jersey

MATHCOUNTS Competition Structure

Sprint Round

30 problems are given all at once. Students have 40 minutes to complete the Sprint Round. This round is very fast-paced and requires speed and accuracy as well. The earlier problems are usually the easiest problems in the competition, and the later problems can be as hard as some of the Team Round questions. No calculators are allowed during this round.

Target Round

8 problems given 2 at a time. Students have 6 minutes to complete each set of two problems. Students may not go back to previous rounds (or forwards to future rounds) even if they finish before time is called. Calculators are allowed for the Target Round. Usually comprised of one “confidence booster” and one hard problem.

Team Round

10 problems in 20 minutes for a team of 4 students. These problems typically include some of the most difficult problems of the competition. Use of a calculator is allowed (and required for some questions).

Countdown Round

High scoring individuals compete head-to-head until a champion is crowned. People compete from off a screen taking 45 seconds or less to finish the problem. The Countdown round is run differently in various different chapter, state, and national competitions. In the national competitions, it is the round that determines the champion. Calculators are not allowed, but scratch paper will be provided.

Chapter and State Competitions

In the chapter and state competitions, the countdown round is not mandatory. However, if it is deemed official by the chapter or state, the following format must be used:

The 10th place written finisher competes against the 9th place written finisher. A problem is displayed, and both competitors have 45 seconds to answer the question, and the first competitor to correctly answer the question receives one point. The person who gets the most correct out of three questions (not necessarily two out of three) is the winner.

The winner of the first round goes up against the 8th place finisher.

The winner of the second round goes up against the 7th place finisher.

This process is continued until the countdown round reaches the top four written competitors. Starting then, the first person to get three questions correct wins (as opposed to the best-out-of-three rule).

If the countdown round is unofficial, any format may be used, and if it is unofficial it will not determine your placement towards the final results and may be determined by another format. Single-elimination bracket-style tournaments are common.

National Competition

At the national competition, there are some structural changes to the countdown round. The top 12 (not the top 10) written finishers make it to the countdown round, and the format is changed from a ladder competition to a single-elimination tournament where the top four written competitors get a bye. This setup makes it far more likely for a 12th place finisher to become champion, and it makes it less likely for a first-place written finisher to become champion, equalizing the field. But even then, a 12th place written competitor will have less of a chance to become champion than the top 4, because the top 4 get a bye. Until the semi-finals, the scoring is best out of five advances.

In the first round and the second round, the person to correctly answer the most out of 5 questions wins. However, at the semifinals, the rules slightly change— the first person to correctly answer four questions wins.

Ciphering Round

In some states, (most notably Florida) there is an optional ciphering round. Very similar to countdown (in both difficulty and layout), a team sends up a representative to go against all representatives from the other teams. A problem is shown on a screen and students work fast to answer the problem. The students give their answer and after 45 seconds the answer is shown and the answers are checked to see if they are right. The fastest correct answer gets five points, the next fastest gets 4, etc. There are 4 questions per individual and teams send up 4 people. A perfect score is then 80. Often times the questions take clever reading skills. For example, one question was “How much dirt is in a 3 ft by 3 ft by 4 ft hole?” The answer was 0 because there is no dirt in a hole.

Masters Round

Top students give in-depth explanations to challenging problems. This round was optional at the state level competition and mandatory at the national competition (up to 2011). At nationals the top two on the written and countdown participate. In 2012, it was replaced by the Reel Math Challenge (now called the Math Video Challenge).

Scoring and Ranking

An individual’s score is their total number of correct sprint round answers plus 2 times their total number of correct target round answers. This total is out of a maximum of points.

A team’s score is the individual scores of its members divided by 4 plus 2 points for every correct team round answer, making a team’s maximum possible score 66 points. Therefore, it is possible to win with a relatively low team score and a phenomenal individual score, as the team score is only roughly 30% of the total team score. Note that when there are less than four members the score will become less.

MATHCOUNTS Competition Levels

School Competition

Students vie for the chance to make their school teams. Problems at this level are generally the easiest and most basic in curriculum.

Chapter Competition

Chapter competitions serve as a selection filter for state competitions. A few states don’t need to host chapter competitions due to a small population size.

State Competition

The top 4 students in each state form the state team for the national competition. The coach of the top school team at the state level is invited to coach the state team at the national competition. Interestingly, the coach of a state team is not necessarily the coach of any of the state’s team members. State competition competitors may be determined from the Chapter competition, based on the population of that particular state.

National Competition

National Competition Sites

For many years, the National MATHCOUNTS competition was held in Washington, D.C. More recently, the competition has changed venues often.

The 2022 competition was held in Washington, D.C.

The 2021 competition was an online event.

The 2020 competition was canceled due to the COVID-19 pandemic, but was due to be held in Orlando, Florida.

The 2019 competition was held in Orlando, Florida.

The 2018 competition was held in Washington, D.C.

The 2017 competition was held in Orlando, Florida.

The 2016 competition was held in Washington, D.C.

The 2015 competition was held in Boston, Massachusetts.

The 2014 competition was held in Orlando, Florida.

The 2013 competition was held in Washington, D.C.

The 2012 competition was held in Orlando, Florida.

The 2011 competition was held in Washington, D.C.

The 2009 and 2010 competitions were held in Orlando, Florida.

The 2008 competition was held in Denver, Colorado.

The 2007 competition was held in Fort Worth, Texas.

The 2006 competition was held in Arlington, Virginia.

The 2005 competition was held in Detroit, Michigan.

The 2004 competition was held in Washington, D.C.

The 2002 and 2003 competitions were held in Chicago, Illinois.

What comes after MATHCOUNTS?

Give the following competitions a try and take a look at the List of United States high school mathematics competitions.

## mathcounts state

0. 1. 2. 3. 4. 5. 6. 7. 8. 9. Page 2. Copyright MATHCOUNTS Inc. 2018. All rights reserved. 2019 State Target Round. An architectural scale drawing of a

The following pages provide solutions to the Sprint Target and Team Rounds of the 2022 MATHCOUNTS State Competition. These solutions provide creative and

Note to coordinators: Answers to the Tiebreaker Round problems appear in the Tiebreaker Round Booklet. 2020 MATHCOUNTS. National Competition Sponsor. TITLE

If you complete the problems before time is called use the time remaining to check your answers. Scorer’s Initials. Problem 1. Problem 2. 2020 MATHCOUNTS.

Copyright MATHCOUNTS Inc. 2021. All rights reserved. Name. DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO.

Copyright MATHCOUNTS Inc. 2021. All rights reserved. Name. DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO.

[PDF] MATHCOUNTS Individual and Team Scores from the State Individual Scores — There are fewer scores than individuals because there were ties MATHCOUNTS Individual and Team Scores from the State Competition

## repl.it

Easy as 3.14 A MathCounts Preparation Website

More Resources

Though I have tried my hardest to incoroporate a lot of concepts, problems, and tips in this website, there is always more to explore in mathematics and beyond, so below is a list of super helpful resources:

Past Tests

2020

School Competition

Chapter Competition

State Competition

The 2020 MathCounts National Competition was cancelled.

2019

School Competition

Chapter Competition

State Competition

National Competition (not available at this time)

2018

School Competition

Chapter Competition

State Competition

Team Round (unavailable at this time)

National Competition (not available at this time)

2017

School Competition

Sprint Round

Team Round

Competition Solutions

Chapter Competition

State Competition

National Competition

Competition Solutions

2016

School Competition

Chapter Competition

State Competition

National Competition

2015

School Competition

Chapter Competition

State Competition

National Competition

Competition Solutions

2014

School Competition

Chapter Competition

State Competition

National Competition

Competition Solutions

2013

School Competition

Chapter Competition

State Competition

National Competition

Competition Solutions

2012

School Competition

Chapter Competition

State Competition

National Competition

Competition Solutions

2011

School Competition

Chapter Competition

State Competition

National Competition

Competition Solutions

2010

School Competition

Chapter Competition

State Competition

National Competition

Competition Solutions

2009

School Competition

Chapter Competition

State Competition

National Competition

Competition Solutions

2008

School Competition

Chapter Competition

State Competition

National Competition

Competition Solutions

2007

Chapter Competition

State Competition

National Competition

Competition Solutions

2006

Chapter Competition

State Competition

National Competition

Competition Solutions

2005

School Competition

Chapter Competition

State Competition

National Competition

Competition Solutions

2004

School Competition

Chapter Competition

State Competition

National Competition

Competition Solutions

2003

School Competition

Chapter Competition

State Competition

National Competition

Competition Solutions

2002

School Competition

Chapter Competition

State Competition

National Competition

2001

School Competition

Chapter Competition

State Competition

National Competition

Competition Solutions

2000

School Competition

Chapter Competition

State Competition

National Competition

Countdown round

## 키워드에 대한 정보 mathcounts 2004 chapter sprint round solutions

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