art of problem solving amc 10 2023

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Information overview, what is the amc 10/12.

The AMC 10 and AMC 12 are both 25-question, 75-minute, multiple-choice examinations in high school mathematics designed to promote the development and enhancement of problem-solving skills.

The AMC 10 is for students in 10th grade and below and covers the high school curriculum up to 10th grade. Students in grade 10 or below and under 17.5 years of age on the day of the contest can take the AMC 10. The AMC 12 covers the entire high school curriculum, including trigonometry, advanced algebra, and advanced geometry, but excluding calculus. Students in grade 12 or below and under 19.5 years of age on the day of the contest can take the AMC 12.

The AMC 10/12 provides an opportunity for high school students to develop positive attitudes towards analytical thinking and mathematics that can assist in future careers. The AMC 10/12 is the first in a series of competitions that eventually lead all the way to the International Mathematical Olympiad (see Invitational Competitions ).

The AMC 10/12 is also available in braille in print administration only and large print in online administration only.

Registration Deadlines and Competition Date

• AMC 10/12 A Early Bird Registration Deadline: Aug 18 - Sept 18, 2023
• AMC 10/12 A Regular Registration Deadline: Sept 19 - Oct 26, 2023
• AMC 10/12 A Late Registration Deadline: Oct 27 - Nov 3, 2023
• AMC 10/12 A Competition Date: November 8, 2023 from 8:00 am ET to 11:59 pm ET
• AMC 10/12 B Early Bird Registration Deadline: Aug 18 - Sept 25, 2023
• AMC 10/12 B Regular Registration Deadline: Sept 26 - Nov 2, 2023
• AMC 10/12 B Late Registration Deadline: Nov 3 - Nov 9, 2023
• AMC 10/12 B Competition Date: November 14, 2023 from 8:00 am ET to 11:59 pm ET

What is the difference between the A and B versions of the examinations?

Both the A and the B versions of the AMC 10 and the AMC 12 have the same number of questions, the same scoring, and the same rules for administration. The only differences are the competition dates and that each version has a distinct set of questions, although the two examinations are designed to be equal in difficulty and distribution of topics. Schools can order one or both versions of the tests, so long as they pay the appropriate registration fee for each competition date and purchase the competition bundles for each date.

Resources for Hosting the AMC 10/12 

This section includes all of the resources you need to host a successful AMC 10 and AMC 12 in your school. Download and read the AMC 10 and AMC 12 Teacher’s Manual for more details about how to host an AMC 10 and AMC 12 competition .

   2023-2024 AMC 10/12 A Teacher's Manual (PDF)   

   2023-2024 AMC 10/12 B Teacher's Manual (PDF)   

Administration Resources

Competition Managers can find all additional forms needed below.

• Registration and Administration Deadlines
• Hosting MAA Competitions Guide : Expands on the Teacher's Manual for Competition Managers who desire additional details.
• AMC 10/12 Registration Form 
• AMC 10/12 Additional Bundles Order Form : Used by Competition Managers who need to add competition bundle orders to an order that they have already placed. 
• Letter to Parents

STATISTICS FOR THE AMC 10/12

We are hosting our statistics through our new platform. Find the reports for the AMC 10/12 A & B below. Please note that we have amended the information we publicly provide in these statistics for student privacy.

   SUMMARY STATISTICS    

Preparing Your Students for the AMC 10/12

These resources will help you prepare your students for the types of questions found on the AMC 10/12 exam.

• AMC 10/12 Practice Questions
• Curriculum Inspirations Videos and essays for your classroom
• AMC Preparation Materials for Purchase

FAQs for the AMC 10/12

Q. What material is covered on the AMC 10 and 12?

A.  The AMC 10 covers mathematics normally associated with grades 9 and 10. The AMC 10 assumes knowledge of elementary algebra; basic geometry knowledge including the Pythagorean Theorem, area and volume formulas; elementary number theory; and elementary probability. What are excluded are trigonometry, advanced algebra, and advanced geometry. The AMC 12 covers the entire high school mathematics curriculum, including the above, as well as trigonometry, advanced algebra, and advanced geometry, but excludes calculus.

Q. Who is eligible to take the AMC 10 and the AMC 12?

A.  Students with a passion for problem-solving who are in grade 10 or below and under 17.5 years of age on the day of the contest can take the AMC 10. Students in grade 12 or below and under 19.5 years of age on the day of the contest can take the AMC 12.

Q. Who can proctor the competition?

A.  Only competition manager proctoring is allowed. Parents or guardians cannot proctor students. Starting 2022-2023, their competition manager will proctored students in person. Competition Managers will be contacted if there is any suspicion of cheating or unapproved resources.  View Disqualification and Cheating policies here . For further questions on AMC 8 proctoring policy, contact the MAA AMC at  [email protected]

Q. Can the AMC 10/12 competition be proctored to different math classes during various time slots on the official administration date(s), or do all the students have to take the competition at the same time?

A. Competition managers must administer competitions during their valid competition window . The valid competition window for this cycle is 8:00 AM to 11:59 PM Eastern Standard time (GMT +5) on the official USA competition dates. See competition dates . Competition managers may choose to administer the competition at separate times to different sections of students; however, for competition integrity and security, the MAA AMC strongly encourages competition managers to administer the competition to all participating students at the same time.

Q. How do I request a rescore of my answer forms?     

A. Use the  AMC 10/12 Rescoring Request Form to request a rescore. There is a $35 charge for each participant's answer form that is rescored. The official answers will be the ones blackened on the answer form. All participant answer forms returned for grading will be recycled 80 days after the AMC 10/12 competition date.

Q. Can I order more bundles even if I’ve already registered my school for the AMC 10/12?

A .  Yes , you can use the  Additional Bundles Order Form  to order more. Orders for additional bundles will be accepted until the deadline for participating domestic institutions located within the United States and Canada. 

Q. Can a student take both competitions?

A.  Yes, as long as a student is eligible to take the appropriate competitions. That is, a 10th grader or below can take both AMC 10 A and the AMC 10 B, the AMC 12 A and the AMC 12 B, etc., and an 11th or 12th grader can take the AMC 12 A and the AMC 12 B. However, the school must register for both dates and order bundles for each competition.

Q. What if a school registers for one date and then wants to change the registration to another?

A.  Although we discourage a change in date because of potential confusion, a date change is permitted under certain circumstances. If the competition materials have not been shipped and time permits according to the registration schedule, a school can pay the corresponding change in registration fee (plus any change in bundles) to change contest dates. Credit cards must pay additional fees when a date change is requested to expedite changes. Please email [email protected] to process this change.

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2023 AMC 12B Problems/Problem 1

• 2 Solution 1
• 3 Solution 2 (unnecessary numerical values)
• 4 Solution 3
• 5 Video Solution by Math-X (First understand the problem!!!!)
• 6 Video Solution (Quick and Easy!)
• 7 Video Solution by SpreadTheMathLove
• 8 Video Solution
• 9 Video Solution by Interstigation
• 10 See also

~Sir Ian Seo the Great & lprado

Solution 2 (unnecessary numerical values)

~Ishaan Garg

~Technodoggo

Video Solution by Math-X (First understand the problem!!!!)

https://youtu.be/EuLkw8HFdk4?si=kYOwfMyrV1Wwtdev&t=62

Video Solution (Quick and Easy!)

https://youtu.be/toJBKTrPiRY

~Education, the Study of Everything

Video Solution by SpreadTheMathLove

https://www.youtube.com/watch?v=SUnhwbA5_So

Video Solution

https://youtu.be/HFHOTVvU3yQ

~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)

Video Solution by Interstigation

https://youtu.be/gDnmvcOzxjg?si=cYB6uChy7Ue0UT4L

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The Mind-Expanding Value of Arts Education

As funding for arts education declines worldwide, experts ponder what students — and the world at large — are losing in the process.

By Ginanne Brownell

This article is part of our special report on the Art for Tomorrow conference that was held in Florence, Italy.

Awuor Onguru says that if it were not for her continued exposure to arts education as a child, she never would have gotten into Yale University.

Growing up in a lower-middle-class family in Nairobi, Kenya, Ms. Onguru, now a 20-year-old junior majoring in English and French, started taking music lessons at the age of four. By 12, she was playing violin in the string quartet at her primary school, where every student was required to play an instrument. As a high school student on scholarship at the International School of Kenya, she was not only being taught Bach concertos, she also became part of Nairobi’s music scene, playing first violin in a number of local orchestras.

During her high school summer breaks, Ms. Onguru — who also has a strong interest in creative writing and poetry — went to the United States, attending the Interlochen Center for the Arts ’ creative writing camp, in Michigan, and the Iowa Young Writers’ Studio . Ms. Onguru, who recently returned to campus after helping organize Yale Glee Club’s spring tour in Kenya, hopes to become a journalist after graduation. She has already made progress toward that goal, serving as the opinion editor for the Yale Daily News, and getting her work published in Teen Vogue and the literary journal Menacing Hedge.

“Whether you’re in sports, whether you end up in STEM, whether you end up in government, seeing my peers — who had different interests in arts — not everyone wanted to be an artist,” she said in a video interview. “But they found places to express themselves, found places to be creative, found places to say things that they didn’t know how else to say them.”

Ms. Onguru’s path shows what a pivotal role arts education can play in a young person’s development. Yet, while the arts and culture space accounts for a significant amount of gross domestic product across the globe — in the United Kingdom in 2021, the arts contributed £109 billion to the economy , while in the U.S., it brought in over $1 trillion that year — arts education budgets in schools continue to get slashed. (In 2021, for instance, the spending on arts education in the U.K. came to an average of just £9.40 per pupil for the year .)

While experts have long espoused the idea that exposure to the arts plays a critical role in primary and secondary schooling, education systems globally have continually failed to hold it in high regard. As Eric Booth, a U.S.-based arts educator and a co-author of “Playing for Their Lives: The Global El Sistema Movement for Social Change Through Music,” said: “There are a whole lot of countries in the world that don’t have the arts in the school, it just isn’t a thing, and it never has been.”

That has led to the arts education trajectory heading in a “dark downward spiral,” said Jelena Trkulja, senior adviser for academic and cultural affairs at Qatar Museums , who moderated a panel entitled “When Arts Education is a Luxury: New Ecosystems” at the Art for Tomorrow conference in Florence, Italy, organized by the Democracy & Culture Foundation, with panels moderated by New York Times journalists.

Part of why that is happening, she said, is that societies still don’t have a sufficient and nuanced understanding of the benefits arts education can bring, in terms of young people’s development. “Arts education is still perceived as an add-on, rather than an essential field creating essential 21st-century skills that are defined as the four C’s of collaboration, creativity, communication and critical thinking,” Dr. Trkulja said in a video interview, “and those skills are being developed in arts education.”

Dennie Palmer Wolf, principal researcher at the U.S.-based arts research consultancy WolfBrown , agreed. “We have to learn to make a much broader argument about arts education,” she said. “It isn’t only playing the cello.”

It is largely through the arts that we as humans understand our own history, from a cave painting in Indonesia thought to be 45,000 years old to “The Tale of Genji,” a book that’s often called the world’s first novel , written by an 11th-century Japanese woman, Murasaki Shikibu; from the art of Michelangelo and Picasso to the music of Mozart and Miriam Makeba and Taylor Swift.

“The arts are one of the fundamental ways that we try to make sense of the world,” said Brian Kisida, an assistant professor at the University of Missouri’s Truman School of Public Affairs and a co-director of the National Endowment for the Arts-sponsored Arts, Humanities & Civic Engagement Lab . “People use the arts to offer a critical perspective of their exploration of the human condition, and that’s what the root of education is in some ways.”

And yet, the arts don’t lend themselves well to hard data, something educators and policymakers need to justify classes in those disciplines in their budgets. “Arts is this visceral thing, this thing inside you, the collective moment of a crescendo,” said Heddy Lahmann , an assistant professor of international education at New York University, who is conducting a global study examining arts education in public schools for the Community Arts Network. “But it’s really hard to qualify what that is.”

Dr. Lahmann’s early research into the decrease in spending by public schools in arts education points to everything from the lack of trained teachers in the arts — partly because those educators are worried about their own job security — to the challenges of teaching arts remotely in the early days of the Covid pandemic. And, of course, standardized tests like the Program for International Student Assessment, which covers reading, math and science, where countries compete on outcomes. “There’s a race to get those indicators,” Dr. Lahmann said, “and arts don’t readily fit into that.” In part, that is because standardized tests don’t cover arts education .

“It’s that unattractive truth that what gets measured gets attended to,” said Mr. Booth, the arts educator who co-authored “Playing for Their Lives.”

While studies over the years have underscored the ways that arts education can lead to better student achievement — in the way that musical skills support literacy, say, and arts activities lead to improved vocabulary, what have traditionally been lacking are large-scale randomized control studies. But a recent research project done in 42 elementary and middle schools in Houston, which was co-directed by Dr. Kisida and Daniel H. Bowen, a professor who teaches education policy at Texas A&M, is the first of its kind to do just that. Their research found that students who had increased arts education experiences saw improvements in writing achievement, emotional and cognitive empathy, school engagement and higher education aspirations, while they had a lower incidence of disciplinary infractions.

As young people are now, more than ever, inundated with images on social media and businesses are increasingly using A.I., it has become even more relevant for students these days to learn how to think more critically and creatively. “Because what is required of us in this coming century is an imaginative capacity that goes far beyond what we have deliberately cultivated in the schooling environment over the last 25 years,” said Mariko Silver, the chief executive of the Henry Luce Foundation, “and that requires truly deep arts education for everyone.”

‘We’re Still Here’: How AMC Theatres Is Struggling With $4.5 Billion in Debt and Surviving Thanks to Taylor Swift, Viral Popcorn Buckets and More

Adam Aron , the CEO of AMC Theatres , gives me a choice.

Popular on Variety

At CinemaCon, where cinema owners are treated like gods, Aron is a big deal. But outside the smoke-filled walls of Caesars, it’s hard to envy him. He’s running the world’s largest theater chain at a time when it faces questions about its survival — and he’s doing it as the movie business is flailing, having been shellacked by COVID and then two labor strikes. Since the pandemic, Aron has cycled through nine lives and then some, while averting the dreaded “B” word — bankruptcy — a fate that befell competitors like Cineworld and Alamo Drafthouse. 

Privately, studio executives and rival exhibitors would love to see AMC file for Chapter 11. It’s not a case of schadenfreude. Given its stature, AMC is seen as the barometer for the industry’s financial health. This upsets other theater owners because they have more pristine balance sheets and feel the company’s current woes are a drag on the sector. The next two years will be crucial, as AMC has more than $2.8 billion of maturities due in 2026. Because of the looming deadline, the company is reportedly weighing debt-extension proposals. 

“Adam wants to avoid bankruptcy, and it sounds like investors are open to renegotiating debt,” says Alicia Reese, VP of Equity Research at Wedbush Securities. “But there’s so much noise about AMC’s lack of profitability that unfairly implies an unhealthy industry. Studios and rivals want to reduce that noise.” 

The pandemic exacerbated things, but AMC’s debt dilemma is largely self-created. Aron became CEO in 2016, having previously overseen the Philadelphia 76ers and Norwegian Cruise Line. He quickly transformed the company into a global powerhouse, acquiring Carmike Cinemas, London-based Odeon & UCI Cinemas and Nordic Cinema Group — deals that didn’t always pay off.  

“Hindsight is tough,” says Eric Wold, senior analyst with B. Riley Securities. “In terms of Adam’s desire to get bigger and have more control over the industry, it was smart. He now has a lot of pull with studios.” 

Despite its financial challenges, AMC is still a buyer, picking up several high-performing leases formerly operated by Arclight, Pacific Theatres and Bow Tie Cinemas that shuttered during COVID. And Aron is open to expanding again. Would he buy Alamo Drafthouse, the Texas-based circuit that’s like church to cinephiles and is exploring a sale ? 

“We would be willing to grow AMC through acquisition going forward if we can find the right theaters at the right price,” Aron says, adding that he “won’t talk about individual theaters.” 

That AMC is even afloat right now, let alone entertaining another spending spree, is due to a financial deus ex machina that’s bizarre even by Hollywood standards. In 2021, as movie theaters were struggling to stay open and Wall Street was betting against the business’s recovery, the “meme stock” frenzy — fueled by young retail investors, many of whom were more interested in sticking it to hedge funds seeking to short-sell the stock than they were supporting the big screen — sent the circuit’s stock price to the moon. It miraculously allowed AMC to improve its financial situation and renegotiate its massive debt obligations. Shares subsequently fell back to earth and are trading at slightly under $5.

He not only communicates with them on social media; he also embraces their ideas, which include accepting bitcoin and crypto payments for tickets and concessions. Those investors, who call themselves “Apes,” hail Aron as “the Silverback.” (It’s a reference to “The Planet of the Apes,” a movie in which primates overthrow humans.) And Aron, a 69-year-old Harvard Business School graduate, has embraced the disruption with a showman’s flair.  

Being the center of attention comes naturally. At dinner, Aron interjects as the waiter asks if we’ve ever dined at Carmine’s, famous for platters of food so big that a wrestler in bulking season would struggle to polish them off. “Can I help? Order a lot,” Aron says, “because the portion sizes are very small.” 

Aron is charming in a “dad joke-y” way, but Hollywood executives and rival exhibitors can’t decide whether he’s a business savant or the captain of the Titanic. Aron captured lightning in a bottle with the chain’s $25 million promotional campaign to get people back to the movies, in which he hired Nicole Kidman to tout the “magic” of the AMC theatrical experience and famously declare that “somehow, heartbreak feels good in a place like this.” Moviegoers committed her melodramatic speech to memory and petitioned when AMC attempted to shorten the commercial, which still plays before every showtime. But some feel that Aron puts the exhibition industry in the news for the wrong reasons — like in 2023, when he revealed he had been the victim of an “ elaborate criminal extortion ” by a woman who “threatened to release sexually explicit photographs of, and sexually explicitly communications” with the CEO. And despite the company’s economic hardships, he’s profiting handsomely; his total compensation in 2023 rose to $25.4 million in salary, stock and bonuses, according to public filings with the Securities and Exchange Commission.

Retail shareholders may have saved AMC from catastrophe, but there are dangers ahead. These include a lighter release calendar and underperforming blockbusters that sent the box office tumbling 20% behind 2023 and 40% behind pre-pandemic levels. 

Over the past four years, Aron has made attempts — some more unusual than others — to expand the company’s business outside of box office. AMC has invested in a Nevada-based gold and silver mining company, started selling popcorn in shopping malls, launched a branded credit card and partnered with Zoom so audience members can schedule conference calls from the comfort of their local multiplex. There’s also that “Dune” popcorn bucket (you know the one) that ignited the internet, to say nothing of the wildly successful AMC-distributed concert film “Taylor Swift: The Eras Tour.” 

AMC still needs to survive the next seven months. This year doesn’t look like it’ll match the grosses of 2023 — the best post-pandemic year but far below pre-COVID revenues. Last year’s strikes derailed the recovery as anticipated blockbusters were delayed while the industry shut down for months. Cinemas were collateral damage in the strikes, which Aron calls a “needless, self-inflicted wound.” He estimates theaters need six to nine months to recover.

“We’re aware of our current circumstances. Believe me,” he says. “But it’s not going to stay that way. It’s the first time in four years that I’ve been able to look ahead and say with some confidence that it’s not going to be atrocious.” 

It helps that traditional studios, after a torrid affair with streaming, fell back in love with theaters. In 2020, during the worst of the pandemic, AMC and Universal feuded over the video-on-demand release of “Trolls World Tour.” It ended with the companies striking a historic deal to shorten the theatrical window from 90 days to roughly three weeks — sending shockwaves through a slow-to-change sector of the business. Now there’s a shift in attitude from the major distributors when assessing the value of the big screen; studios once again want their movies to enjoy a longer stay in theaters.   

“People were writing off the existence of theaters as some bizarre anachronism,” Aron says about pandemic-era disputes. “Then studios finally realized again, ‘Wait a second — there’s a shitload of money to be made in movie theaters.’”  

Despite the change of heart, studios are releasing fewer films. In response, AMC is filling in the gaps in the calendar: Aron once again shook up the industry in 2023 by beating out traditional studios to partner with Swift on “The Eras Tour” and Beyoncé’s concert film “Renaissance.”

Swift’s movie set all kinds of benchmarks, becoming the highest-grossing concert film ever, with $261 million globally. “And it was really good,” Aron says. “It got an ‘A+’ on CinemaScore and 98% on Rotten Tomatoes. It’s not like we threw together some garbage.” 

Aron expects that AMC will unveil “two to three” concert films a year and recently expanded the company’s distribution team, underscoring its commitment to releasing its own movies.  

Hollywood studios, which regularly work with AMC, aren’t thrilled about the chain’s foray into distribution, feeling that the exhibitor is encroaching on their territory. Theater owners, too, feel slighted by the arrangements with Swift and Beyoncé. AMC was the only chain to know about the existence of those films in advance, so it could put tickets on sale first. 

To soothe bruised feelings, before Beyoncé’s film went on sale, AMC gave its competition a super-secret heads-up: Don’t tell anyone , but be ready to put tickets on sale. 

“At least half a dozen movie circuits leaked the news,” Aron laments. “Beyoncé was seriously thinking about not doing the movie at all because the secret was blown. So, they didn’t keep their word.”  

Aron has other plans to revitalize the company’s languishing stock price. He wants to improve the moviegoing experience. To do that, he’ll deploy $200 million in capital annually to reinvest in theaters, which will renovate auditoriums with comfy recliner seats, upgrade projection systems and add premium large-format screens. AMC already boasts the largest North American footprint of the newly popular Imax screens. “Those are the seats that sell first,” he adds. 

Aron tends to speak in outlines, ticking off the one, two, three steps in his multipronged plan of attack. When it comes to appeasing shareholders, it’s twofold. “No. 1 is to make sure we survive since COVID. And we’ve done a pretty good or, I’d say, very good job at that. No. 2 is to deliver increased earnings going forward. We’re quite focused on that.”

He adds, “It’s generally smart for people in my role not to talk externally about the share price. I happen to be a very large AMC shareholder. So clearly I would prefer that the stock price be higher rather than lower.”  

According to Aron, AMC doesn’t need the box office to return to pre-COVID levels. He says the company has cut costs and let go of underperforming leases. “We’re focused on delivering more revenue and bottom-line profit,” he says. “At some point, the share price will take care of itself.”   

Another win: Customers have been spending more freely at the concession stand, which helps revenues. A big growth driver has been movie-themed merchandise, like a top hat for “Wonka” or a toy pink convertible for “Barbie.” In 2023, those collectibles delivered $54 million in sales. Aron expects 25 or more movie tie-ins in 2024.  

Thanks to those efforts, AMC went viral last year after the internet discovered the souvenir canister for “Dune: Part Two” looked more like a sex toy than a sandworm. The now-iconic bucket has been memed to hell and even immortalized on “Saturday Night Live” in a sketch about a teenager with other plans for the popcorn container. Aron tuned in, but he wasn’t impressed.

“It wasn’t their best skit,” Aron says. “It was great they did it. But you gotta remember that I’m so much older than you. When I think of ‘Saturday Night Live,’ I’m going back to John Belushi, Dan Aykroyd, Jane Curtin, Eddie Murphy. I have very high standards for comedy on ‘SNL.’”  

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