art of problem solving 6th grade

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Art of Problem Solving (AoPS) Prealgebra F Fourth Printing New Edition

• ISBN-10 1934124214
• ISBN-13 978-1934124215
• Edition F Fourth Printing New
• Publisher AoPS Incorporated
• Publication date August 9, 2011
• Language English
• Dimensions 10.38 x 8.38 x 0.5 inches
• Print length 608 pages
• See all details

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About the author, product details.

• Publisher ‏ : ‎ AoPS Incorporated; F Fourth Printing New edition (August 9, 2011)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 608 pages
• ISBN-10 ‏ : ‎ 1934124214
• ISBN-13 ‏ : ‎ 978-1934124215
• Item Weight ‏ : ‎ 2.95 pounds
• Dimensions ‏ : ‎ 10.38 x 8.38 x 0.5 inches
• #152 in Textbooks (Special Features Stores)

About the authors

Richard rusczyk.

Richard Rusczyk founded Art of Problem Solving (AoPS) in 2003 to create interactive educational opportunities for avid math students. Richard is one of the co-authors of the Art of Problem Solving classic textbooks, author of Art of Problem Solving's Introduction to Algebra, Introduction to Geometry, and Precalculus textbooks, co-author of Art of Problem Solving's Intermediate Algebra and Prealgebra, one of the co-creators of the Mandelbrot Competition, and a past Director of the USA Mathematical Talent Search. He was a participant in National MATHCOUNTS, a three-time participant in the Math Olympiad Summer Program, and a USA Mathematical Olympiad winner (1989). He graduated from Princeton University in 1993, and worked as a bond trader for D.E. Shaw & Company for four years. AoPS marks Richard's return to his vocation: educating motivated students.

David Patrick

David Patrick has been an author and curriculum developer at Art of Problem Solving since 2004. He is the author of Art of Problem Solving's Introduction to Counting & Probability, Intermediate Counting & Probability, and Calculus textbooks, and co-author of AoPS's new Prealgebra textbook. He is also an instructor in AoPS's widely-acclaimed online school for high performing middle and high school students.

Dave earned the sole perfect score on the American High School Mathematics Examination (AHSME) in 1988 and was a USA Mathematical Olympiad winner that year. He attended the Research Science Institute (RSI) in 1987, and the Math Olympiad Summer Program in 1988, where he first met fellow student Richard Rusczyk. He also finished in the top 10 on the Putnam exam in 1991. Dave graduated from Carnegie Mellon in 1992 with a BS in Mathematics/Computer Science and an MS in Mathematics. He went on to earn his Ph.D. in mathematics from MIT in 1997. He was an acting Assistant Professor at the University of Washington from 1997 to 2001. Dave is originally from Western New York and is an alumnus of the SUNY Buffalo Gifted Math Program.

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Customers find the explanations and problems in the book excellent and easy to understand. They also say it's a fantastic approach to learning. However, opinions are mixed on the look, with some finding it great and not fancy, while others say it doesn't look good and the layout is bland.

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Customers find the explanations in the book excellent. They say it's a fantastic approach to learning, and the concepts are easy to understand. Readers also mention that the book covers seemingly simple topics with depth and insight.

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In the classic TV show Lost,  there's a computer into which you must enter a random string of numbers every 108 minutes without fail. We don't know what the numbers mean, or why it matters, just that it must be done. That's a nice metaphor for how we often approach math instruction. We don't know why 2+2=4, we just know that it does. Right?

Richard Rusczyk, former math competition winner, has created a math curriculum to combat that approach. Unlike on  Lost , there are very definite answers out there. In Art of Problem Solving students are taught why the rules are true rather than merely what they are. They get to learn math the way that mathematicians already know it; as a layered and rich discipline that isn't just about numbers, but about creative problem solving.  (Let that be your first warning that this is not "easy math.")

How It Works:

The books are fairly simple in format, but heavy on content. At the beginning of each chapter, students are asked to solve (or attempt to solve) an introductory problem set before they read about the concept being taught. They compare their solutions to the book's solution, and the book discusses where they may have gone wrong, and explores different paths to get to the solution. This type of "learning through mistakes" gives students an in-depth perspective on the problem itself.

The opening of each chapter typically has an optional math puzzle for students to play with, and a mathy sort of quote. The book takes a laidback approach to solving the exercises at the end. Assuming you have been doing the practice problems throughout the whole lesson, it advises you to work on the review problems until you can solve most of them (proving that you understood the chapter), and then move on. If you can't, go back and review the chapter again. 

The exercises also include "starred" challenge problems that are more difficult. These have hints, and students are expected to at least give them a try but not to stress too much about solving them right away. The text takes a mathematician's view of solving problems. Sometimes you have to let a problem sit and come back to it later with fresh eyes. Working on it progressively is acceptable.

It also recommends that you don't look at the solutions manual until you've absolutely exhausted your ability to solve the problem -- but that you certainly read the solution after you find the answer in case the book solves it a different way.

The emphasis of the texts are on knowing why the rules are true rather than merely memorizing the rules. The tone is fairly conversational and shows a true interest for the subject matter. The design isn't too flashy, and will engage those already interested in math for math's sake, or at least those who need a challenge. 

Our Honest Opinion:

Traditional American math education is flawed (a generally agreed upon fact). Students don't learn how to solve problems. They learn how to input formulas and output solutions. A student could tell you how to solve for X, but often couldn't tell you why it works. It just does . That's math. You don't question it. And the faster you are at identifying the formula and correctly applying it, the better you are at math, but in a purely robotic way.

Math, therefore becomes a memorization game instead of a uniquely creative activity. And the makers of Art of Problem Solving are fighting back against that mindset. Math is not about memorizing one-size-fits-all formulas, but about creative problem solving with multiple paths towards an ending solution. The more ways you can find to solve a problem, the more deeply you'll understand the solution. This is true for any problem.

Creative problem solving is understandably difficult and will stretch students in ways they may be unused to being stretched. So though we are fans of this method, it's certainly not for everyone. Formulas do have their place, and most people will grow up using the math they need. But if your student is ready for a brain workout, ready to eschew traditional ideas on math proficiency, and can handle spending a long time on a single problem, then this just might be the program that will give them the tools to creatively solve problems not just in math, but in life.

The Art of Problem Solving  curriculum may be used in this order:

• Pre-Algebra
• Introduction to Algebra
• Introduction to Counting & Probability
• Introduction to Geometry
• Introduction to Number Theory
• Intermediate Algebra
• Intermediate Counting & Probability
• Pre-Calculus

The texts Art of Problem Solving Volumes 1 & 2 are not part of the series. They are problem solving textbooks meant to get students ready for math contests like MATHCOUNTS or the Math Olympiad. 

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• Grade 6 Lessons

Challenging Math Problems for 6th Graders

Introduction

Importance of challenging math problems for 6th graders.

• The Transition to Higher-Level Thinking : 6th grade is a pivotal year in your education journey. You’re expected to transition from basic arithmetic to more complex mathematical concepts here. Challenging math problems provide the perfect opportunity for you to begin this transition confidently.
• Preparation for Advanced Courses : High school is pretty close, and the foundation you build in 6th grade will help you immensely. Tackling challenging math problems now means you’ll be well-prepared for the algebra, geometry, and even calculus challenges down the line.
• Develop Problem-Solving Skills : Real-world problems are sometimes complicated. By solving challenging math problems , you’re learning math and training yourself to think critically and find solutions in tricky situations. These skills are invaluable both in and out of the classroom.
• Engagement and Excitement : Sure, routine practice is necessary. But let’s be honest, it can get dull. Complex math problems bring an element of excitement to learning. They can feel more like puzzles, making learning math much more engaging.

Benefits of solving challenging math problems

• Boosts Confidence : Whenever you solve a complex problem, you’re proving to yourself that you can tackle tough challenges. This success builds a sense of achievement and confidence that can spill over into other subjects and areas of life.
• Encourages Perseverance : Not all problems can be solved on the first try, and that’s okay! By persisting through challenging math problems, you’re learning the valuable lesson of perseverance. In time, you’ll see that patience and determination can lead to impressive outcomes.
• Improves Test Scores : Challenging math problems often resemble the questions you’ll encounter on standardized tests and essential exams. Regular practice will make these tests less daunting and can help improve your overall scores.
• Strengthens Math Foundation : When you dive deep into complex problems, you reinforce your mathematical foundation. This understanding is crucial, as math is a cumulative subject — each new concept builds on the previous ones.
• Fosters a Love for Math : It’s exciting when you overcome a math challenge! These victories can transform how you view math. Instead of seeing it as a hurdle, you’ll recognize it as an area where you can excel and enjoy the learning process.

By rising to the challenge and embracing the tough problems that come your way in 6th grade, you’re setting yourself up for success, growth, and a lot of mathematical fun. Keep pushing your limits, and you’ll be amazed at what you can achieve!

Algebraic Expressions and Equations

Evaluating algebraic expressions.

– **Explore the power of variables**: Welcome to the world of algebra! In 6th grade, you’ll encounter algebraic expressions with variables like x and y. You’ll learn how to substitute values for variables and solve problems by evaluating these expressions.

• Practice order of operations : Evaluating algebraic expressions involves following the correct order of operations. It would help if you remembered PEMDAS (Parentheses, Exponents, Multiplication, Division from left to right, and Addition and Subtraction from left to right). It helps ensure that you simplify expressions correctly.
• Develop logical thinking : Evaluating expressions requires logical thinking. You’ll need to break down the problem, identify the variables and substitute values, and perform the operations correctly. This process helps develop logical reasoning skills and trains your mind to think step-by-step.
• Connect to real-life situations : Algebraic expressions can represent real-world situations. You’ll learn to analyze and interpret situations mathematically by evaluating these expressions. This skill will be valuable as you encounter more complex problems in higher grades.

Solving equations with variables

– **Become a problem solver**: Equations with variables may seem intimidating initially, but they are opportunities to become problem-solving superheroes. By solving these equations, you’ll learn how to find the value(s) of the variable(s) that make the equation true.

• Practice balancing both sides : Solving equations requires balancing both sides. You’ll use inverse operations to isolate the variable and find the solution. This process helps reinforce the concept of equality and strengthens your grasp of foundational mathematical skills.
• Apply critical thinking : Solving equations involves critical thinking and analyzing patterns. You’ll use problem-solving skills to determine the best strategies and steps to solve the equation. This process fosters your ability to think critically and solve problems in various contexts.
• Prepare for advanced math : Solving equations is a fundamental skill that lays the groundwork for more complex algebraic concepts in higher grades. By mastering the art of equation solving in 6th grade , you’ll be ready to tackle advanced topics like linear, quadratic, and systems of equations in the future.

By confidently exploring algebraic expressions and equations in 6th grade, you’ll gain a solid foundation in algebra and set yourself up for success in future math courses. Embrace the challenge, persevere through the problems, and see how algebra can become your mathematical superpower!

Finding the area of complex shapes

– **Unlock the secrets of shapes**: Welcome to the world of geometry! In 6th grade, you’ll dive into the fascinating field of finding the area of complex shapes. By mastering this skill, you can calculate the space inside various polygons and irregular shapes.

• Break down complex shapes : Finding the area of complex shapes requires breaking them down into simpler shapes. You’ll learn how to decompose shapes like rectangles, triangles, and circles and find their areas. Then, you’ll add or subtract these areas to determine the total area of the complex shape.
• Apply formulas and measurements : Geometry is all about using formulas and measurements. You’ll explore formulas like A = bh for the area of rectangles, A = 1/2 base x height for triangles, and A = πr^2 for circles. By applying these formulas and using accurate measurements, you’ll be able to find the area of complex shapes with precision.
• Connect math to the real world : The ability to find the area of complex shapes is valuable for the classroom; it has practical, real-world applications. Whether planning to tile a floor, estimate the amount of paint needed for a wall, or design a garden layout, understanding geometry will help you make accurate calculations and measurements.

Working with volume and surface area

– **Discover the dimensions of 3D objects**: Besides finding the area of 2D shapes, 6th-grade geometry introduces you to volume and surface area concepts. These concepts provide insights into the 3D world around us and allow us to quantify the amount of space objects occupy.

• Calculate volume : Volume measures the space inside a 3D object. You’ll learn to calculate the volume of shapes like rectangular prisms and cylinders using V = lwh and V = πr^2h. Understanding volume will enable you to determine how much liquid can be held in a container or the capacity of a building.
• Find surface area : Surface area is the sum of all the areas of a 3D object’s faces. You’ll explore formulas such as SA = 2lw + 2lh + 2wh for rectangular prisms and SA = 2πrh + 2πr^2 for cylinders. By calculating surface area, you’ll understand how much material is required to cover an object or the amount of paint needed to coat it.
• Apply problem-solving skills : Working with volume and surface area involves problem-solving skills. You’ll face real-world scenarios where you must determine the volume of irregular shapes or find the surface area to optimize material usage. These challenges will enhance your critical thinking abilities and sharpen your problem-solving skills.

By confidently exploring geometry concepts in 6th grade, you’ll enhance your spatial reasoning skills and develop a solid foundation in 2D and 3D measurements. Embrace the thrill of unraveling the secrets of shapes and see how geometry can become a powerful tool in understanding the world around you.

Fractions and Decimals

Comparing and ordering fractions and decimals.

– **Understanding the value of fractions and decimals**: Welcome to the world of fractions and decimals! In 6th grade, you’ll learn how to compare and order these numerical representations. By mastering this skill, you can confidently understand and manipulate numbers that are less than 1 or have decimal parts.

• Comparing fractions and decimals : Comparing fractions and decimals involves understanding their numerical value . You’ll learn techniques like finding a common denominator for fractions and identifying place values for decimals. These skills will enable you to determine which fraction or decimal is greater or lesser in value.
• Ordering fractions and decimals : Once you can compare fractions and decimals, you can order them from least to most excellent or vice versa. This skill allows you to organize numbers logically, making it easier to understand and analyze data, solve problems, and make accurate estimations.

Converting fractions to decimals and vice versa

– **Unlocking the power of conversion**: Converting fractions to decimals and vice versa is crucial in 6th-grade mathematics. It allows you to translate between different numerical representations and provides flexibility in solving problems and manipulating numbers.

• Converting fractions to decimals : Fractions can be converted by dividing the numerator (top number) by the denominator (bottom number). You’ll practice this process and learn to express fractions as decimals, terminating and repeating. Decimal representation provides a different perspective, making comparisons and calculations easier in some cases.
• Converting decimals to fractions : Decimals, on the other hand, can be converted to fractions by identifying the place value of each digit. You’ll learn techniques to express decimals as fractions, simplifying them to their lowest terms. Fractional representation allows you to work with exact values and can be helpful in measurements or ratios.

By confidently exploring fractions and decimals in 6th grade, you’ll enhance your mathematical abilities and develop a solid foundation in number sense and operations. Embrace the power of these numerical representations and see how they can become essential tools in understanding and solving real-life problems. Keep practicing and sharpening your skills; soon, you’ll be on your way to mastering fractions and decimals!

Ratios and Proportions

Solving ratio problems.

– **Understanding and using ratios**: Get ready to dive into the world of ratios in 6th-grade math! Ratios compare the relative sizes or quantities of two or more values. You can analyze relationships and solve real-life problems by understanding how to work with ratios.

• Writing ratios in different forms : Ratios can be expressed differently, such as using the “:” as a fraction or verbally. You’ll learn how to write ratios correctly and choose the appropriate form based on the context of the problem.
• Simplifying ratios : Ratios can be simplified by dividing both sides by their most significant common factor . Simplifying ratios makes them easier to work with and analyze, especially when dealing with complex or large numbers .

Applying proportions in real-life situations

– **Understanding proportions**: Proportions are another important concept in 6th-grade math. They are used to represent and solve problems involving equivalent ratios. Understanding proportions allows you to find the missing value in a proportion, compare quantities, and solve various real-life problems.

• Solving proportion problems : Proportions can be solved using cross-multiplication or setting up equivalent fractions . You’ll learn different methods to solve proportion problems and apply these techniques to various scenarios.
• Real-life applications : Proportions have numerous real-life applications, such as scaling recipes, calculating distances on maps, or determining the missing side lengths in similar geometric figures. You’ll explore these applications and see how proportions can be used to solve practical problems.

Mastering ratios and proportions in 6th grade, you’ll develop essential problem-solving skills and gain a deeper understanding of numerical relationships. Remember to practice regularly and apply these concepts to real-life situations to strengthen your mathematical abilities. With determination and perseverance, you’ll become proficient in solving ratio problems and applying proportions, opening doors to countless opportunities for mathematical exploration and problem-solving. Keep up the great work!

• Understanding and using ratios : Let’s dive into ratios in 6th-grade math together! Ratios are a powerful tool for comparing two or more values’ relative sizes or quantities. Understanding how to work with ratios allows us to analyze relationships and solve real-life problems.
• Writing ratios in different forms : Ratios can be expressed differently, such as using the “:” as a fraction or verbally. We’ll learn how to write ratios correctly and choose the appropriate form based on the context of the problem.
• Simplifying ratios : Ratios can be simplified by dividing both sides by their most significant common factor. Simplifying ratios makes them easier to work with and analyze, especially when dealing with complex or large numbers.
• Understanding proportions : Proportions are another vital concept in 6th-grade math that we’ll conquer together. They are used to represent and solve problems involving equivalent ratios. Understanding proportions allows us to find the missing value in a proportion, compare quantities, and solve various real-life problems.
• Solving proportion problems : Proportions can be solved using cross-multiplication or setting up equivalent fractions. We’ll learn different methods to solve proportion problems and apply these techniques to various scenarios.
• Real-life applications : Proportions have numerous real-life applications that we’ll explore together. We can use them to scale recipes, calculate distances on maps, or determine the missing side lengths in similar geometric figures. It’s incredible how proportions can be used to solve practical problems!

By mastering ratios and proportions in 6th grade, we’ll develop essential problem-solving skills and gain a deeper understanding of numerical relationships. Remember, practice is critical in mastering these challenging math problems. Practicing regularly and applying these concepts to real-life situations will strengthen our mathematical abilities and open doors to countless opportunities for mathematical exploration and problem-solving. Keep up the great work as we continue this exciting mathematical journey together!

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The Art of Problem Solving Math

The Art of Problem Solving (AoPS) math courses for grades five through twelve were designed for high-performing math students. The publisher says on their website ,

 We present a much broader and deeper exploration of challenging mathematics than a typical math curriculum and show students how to apply their knowledge and problem-solving skills to difficult problems. We help students learn the critical problem-solving skills necessary for success at mathematics competitions (such as MATHCOUNTS and the AMC), top universities, and competitive careers.

Their courses cover much more than typical math courses for middle through high school. They have courses that cover the standard sequence at advanced levels, plus other courses that take students deeper into the math needed for physics, engineering, computer science, and other math-based careers.

 AoPS students often work a few years ahead of other students, which means that capable fifth or sixth graders might start with Prealgebra . Note that AoPS is the publisher of Beast Academy math courses for grades one through five, and those courses prepare students to move right into AoPS Prealgebra.

Courses and Format Options

AoPS lists five courses as part of their “Introductory Curriculum” for students up through tenth grade : Prealgebra, Introduction to Algebra, Introduction to Counting & Probability, Introduction to Geometry , and Introduction to Number Theory . Their “Intermediate Curriculum” for advanced high school students includes Intermediate Algebra, Intermediate Counting & Probability, Precalculus , and Calculus . Even so, students in a traditional program can still use these courses following a more typical timeline and concentrating on the required courses.

The website page for each course has two free diagnostic tests (PDFs) that help determine whether a student has the prerequisites for the course or whether they already have mastered what the course covers. These tests are accessed by clicking on “Are You Ready?” and “Do You Need This?” on each course’s description page.

Students do not need to complete all books in the series, but if they start the series in sixth grade, they should be able to complete most of them. Students who want to participate in math competitions might also be interested in AoPS books written specifically for that purpose: Competition Math for Middle School; the Art of Problem Solving, Volume 1: the Basics ; and the Art of Problem Solving, Volume 2: and Beyond . (The titles of the last two books do not begin with capital T.)

AoPS sells printed or online books or a combination of both. They also offer live, online options for all courses and a self-paced-online option for Prealgebra and Introductory Algebra A. (The online courses might be a great way for eager students to find the community support they need to enter competitions.)

The printed textbooks have separate solutions manuals with worked-out solutions for every problem. The online books include the solutions, and they also integrate the textbooks with interactions with the AoPS community, Alcumus (described below), and the free videos (also described below). The textbooks vary in length; those for the standard courses (except Calculus ) run from 528 to 720 pages, while other courses have from 256 to 400 pages.

Free videos are available online for Prealgebra, Introduction to Algebra , and Introduction to Counting & Probability . You can view these without having to pay or register. The videos do not replace the textbooks or online classes but supplement them. There are one or more videos for each lesson, all taught by Richard Rusczyk, a very engaging presenter as well as a former USA Mathematical Olympiad winner. I highly recommend watching them.

How the Courses Work

The courses divide the content into chapters, with several lessons within each chapter. Each lesson begins either with brief instruction or a set of three or more problems. Students should try to solve the problems on their own. The lesson continues with thorough explanations for how to solve each problem, and this is where most of the instruction is presented. This strategy very much reflects the title of the series, the Art of Problem Solving—students are focused on developing problem-solving skills as well as accuracy.

After studying the solutions, students have another set of problems to solve, a few of which are drawn from advanced math exams (no longer in use), such as the AHSME (American High School Mathematics Examination).

Lessons often use blue boxes to highlight key concepts, important ideas, and warnings about common mistakes.

There are Review Problems at the end of each chapter but no quizzes or tests for any of these courses. (The second diagnostic test for each course, titled “Do You Need This?,” could function as a final exam if needed.) The publisher’s explanation to me regarding this was: “Since our curriculum focuses on teaching students mathematical concepts and problem-solving skills, we believe that students who are using our textbooks have mastered the material if they can successfully solve the Review Problems at the end of each chapter.”

Alcumus, AoPS’s online learning system, is available for free to all students, even if they have not purchased any AoPS course. Alcumus adapts to the student’s performance, giving them problems to solve that are appropriate for their level—problems to solve in addition to those in their course. Alcumus can be used alongside the Introductory Curriculum courses, whether in print or online. (Students using courses from other publishers for pre-algebra through geometry should also find the program useful.) Alcumus provides ambitious students with work that will both reinforce and stretch their skills.

The AoPS website offers many other resources for advanced math students, including information about competitions, online forums, and training for competitions.

AoPS math courses should be fantastic for avid math students who are eager to learn and go deeper, but they also offer excellent and thorough instruction for the average student.

Pricing Information

When prices appear, please keep in mind that they are subject to change. Click on links where available to verify price accuracy.

See the publisher's website for options and prices.

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Publisher's Info

• Art of Problem Solving, Inc.
• PO Box 2185
• Alpine, CA 91903
• [email protected]
• https://artofproblemsolving.com/

Note: Publishers, authors, and service providers never pay to be reviewed. They do provide free review copies or online access to programs for review purposes.

Disclosure of Material Connection: Some of the links in the post above are "affiliate links." This means if you click on the link and purchase the item, I will receive an affiliate commission. Regardless, I only recommend products or services that I believe will add value to my readers. I am disclosing this in accordance with the Federal Trade Commission's 16 CFR, Part 255 "Guidelines Concerning the Use of Endorsements and Testimonials in Advertising."

Honors Language Arts 6A and 6B together prepare sixth graders (ages 11-12) for an advanced middle school language arts curriculum.

Live instructors help students develop writing and critical thinking skills and appreciation of language arts.

View the course syllabus for full class information and a list of topics.

This course is recommended for students entering Grade 6. We recommend students enroll in Language Arts courses at grade level.

Each 18-week term will cover 2 units, with each unit featuring a long-term project that integrates a variety of reading, writing, critical thinking, and grammar skills.

• Public Speaking : Students craft and deliver a speech using skills gained studying the origins of classic critical thinking and rhetoric.
• Creative Writing : Using advanced grammar concepts and studying how other writers make language work for them, students will create a collection of polished creative writing pieces.
• Research : Students develop strong research skills that will benefit them in any humanities classroom. They learn how to judge the quality of research sources, produce annotated bibliographies, and write feature articles that incorporate their research.
• Literary Analysis : Students will explore A Midsummer Night’s Dream by William Shakespeare. At the end of the unit, students memorize speeches from the play and use their public speaking and literary analysis skills to build strong performances.

Students must purchase the required books before the start of the course.

Our instructors hold classes virtually, in a small-sized (10-16 students) videoconferencing classroom.

Students should expect to spend about 60-90 minutes on homework every week. Homework will include practicing skills learned in class through short answer questions, long-term writing assignments connected to the unit project, and assigned reading in one of the four quarterly textbooks.

Visit our tuition page to learn more about our drop and refund policies.

Each course runs for 18 weeks, meeting for one 105-minute lesson per week.

AMC Problems and Solutions

You can find problems and solutions from the math contests run by the American Mathematics Competitions on the following pages:

• AMC 8 / AJHSME Problems and Solutions
• AMC 10 Problems and Solutions
• AMC 12 Problems and Solutions
• AHSME Problems and Solutions
• AIME Problems and Solutions
• USAMO Problems and Solutions
• USAJMO Problems and Solutions
• The AMC 8 was previously known as the AJHSME.
• The AMC 12 was previously known as the AHSME.
• Due to the changing format of the AHSME, different years of the AHSME may have different numbers of problems: some years have 50, others have 40, and still others have 30.
• Mathematics competitions resources
• Math contest books
• Math Contest Problems

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