Prova EFOMM 2026 comentada: questões e gabarito

EFOMM2026Dia 2Questao 1MatemáticaBinômio de NewtonMedia

Em uma missão de logística transatlântica, a equipe de engenharia do cargueiro Atlântis VI, da Marinha Mercante Brasileira, foi encarregada de simular o desempenho do navio em diferentes condições climáticas e de carga. O objetivo era prever o comportamento do sistema de propulsão do navio ao atravessar uma região turbulenta do oceano Atlântico, conhecida por seus redemoinhos e correntes contrárias. Durante os testes, os engenheiros perceberam que a força de propulsão líquida, ou seja, a força efetiva que impulsiona o navio para frente, descontadas as forças de resistência da água, variava com o tempo de forma não linear. Eles modelaram essa variação utilizando uma função matemática que relacionava o tempo x, a carga embarcada e à resistência hidrodinâmica do casco. Após vários ajustes, chegaram à seguinte expressão:

(2 x - \frac{3}{x ^{2}})^{9}

Essa expressão representa a variação da força de propulsão líquida em função do tempo x, medida em unidades padronizadas ao longo da travessia. Sabendo que o termo independente de x (aquele que representa um valor constante da força, sem depender diretamente do tempo) é essencial para avaliar a estabilidade média do navio durante a travessia, os engenheiros solicitaram seu cálculo. Com base nesse modelo, qual é o valor do termo independente de x na expansão da expressão acima?

A)156381
B)132300
C)-124416
D)-145152
E)-967680

EFOMM2026Dia 1Questao 1InglêsGramáticaMedia

Choose the option with the grammatically correct sentence.

A)People have always been very kind with me.
B)Our boss would live to see a big increase of productivity.
C)Who is the man dressed with green?
D)I am not bad in Mathematics.
E)She will agree to your suggestion if you reduce the price.

EFOMM2026Dia 2Questao 2MatemáticaEstatísticaFacil

Em um estudo recente do Centro de Instrução Almirante Graça Aranha (CIAGA) sobre os hábitos de leitura dos alunos do primeiro e segundo ano da EFOMM (Escola de Formação de Oficiais da Marinha Mercante), foram avaliados os tempos médios diários que eles dedicam à leitura em suas disciplinas. Os dados coletados em uma amostra desses alunos revelaram que a média dos tempos de leitura diária é de 36 minutos, enquanto a maior parte deles dedica exatamente 30 minutos diários à leitura, o que representa a moda dos dados. O CIAGA considera que o conhecimento da mediana é crucial para entender a distribuição dos tempos de leitura, pois ela indica o valor central que divide o grupo ao meio, auxiliando na otimização dos planos de estudo. Com base nessas informações, estime o valor aproximado da mediana desse conjunto de dados de tempos de leitura, utilizando a relação empírica entre média, moda e mediana.

A)31 minutos.
B)32 minutos.
C)33 minutos.
D)34 minutos.
E)35 minutos.

EFOMM2026Dia 1Questao 2InglêsGramáticaMedia

Read the sentences below and choose the option that is grammatically correct.

A)Remember always to call him on Saturdays.
B)Tired though he was, he went on studying.
C)Here your shoes are.
D)It was an educational old idea.
E)They are too strong-minded people to give up.

EFOMM2026Dia 2Questao 3MatemáticaTaxas RelacionadasDificil

Um balde em forma de tronco de cone, com altura de 1 m, raio do fundo de 0,3 m e raio do topo de 0,6 m, está sendo preenchido com água a uma taxa constante de

5 m^{3} / min

. A água mantém a forma do tronco de cone enquanto enche o balde. A que taxa, aproximadamente, a altura da água está aumentando no instante em que ela atinge 0,5 m de altura?

A) $50/ π m/min$
B) $27, 5/ π m/min$
C) $25/ π m/min$
D) $12, 5/ π m/min$
E) $10/ π m/min$

EFOMM2026Dia 1Questao 3InglêsInterpretação de textoMedia

Text I Read the text below and answer questions 3, 4 and 5. The universe is not locally real By Daniel Garisto One of the most unsettling discoveries in the past half a century is that the universe is not locally real. In this context, "real" means that objects have definite properties independent of observation - an apple can be red even when no one is looking. "Local" means that objects can be influenced only by their surroundings and that any influence cannot travel faster than the light. Investigations at the frontier of quantum physics have found that these things cannot both be true. Instead the evidence shows that objects are not influenced solely by their surroundings, and they may also lack definite properties prior to measurement. This is, of course, deeply contrary to our everyday experiences. As Albert Einstein once bemoaned to a friend, "Do you really believe the moon is not there when you are not looking at it?" To adapt a phrase from author Douglas Adams, the demise of local realism has made a lot of people very angry and has been widely regarded as a bad move. Blame for this achievement has now been laid squarely on the shoulders of three physicists: John Clauser, Alain Aspect and Anton Zeilinger. They equally split the 2022 Nobel Prize in Physics "for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science" ("Bell inequalities" refers to the pioneering work of Northern Ireland physicist John Stewart Bell, who laid the foundations for the 2022 Physics Nobel in the early 1960s). Colleagues agreed that the trio had it coming, deserving this reckoning for overthrowing reality as we know it. "It was long overdue," says Sandu Popescu, a quantum physicist at the University of Bristol in England. "Without any doubt, the prize is well deserved." "The experiments beginning with the earliest one of Clauser and continuing along show that this stuff isn't just philosophical, it's real - and like other real things, potentially useful," says Charles H. Bennett, and eminent quantum researcher at IBM. "Each Year I thought, 'Oh, maybe this is the year,'" says David Kaiser, a physicist and historian at the Massachusetts Institute of Technology. In 2022 "it really was. It was very emotional - and very thrilling." The journey from fringe to favor was a long one. From about 1940 until as late as 1990, studies of so-called quantum foundations were often treated as philosophy at best and crackpottery at worst. Many scientific journals refused to publish papers on the topic, and academic positions indulging such investigations were nearly impossible to come by. In 1985 Popescu's adviser warned him against a Ph.D. in the subject. "He said, 'Look, if you do that, you will have fun for five years, and then you will be jobless,'" Popescu says. Today quantum information science is among the most vibrant subfields in all of physics. (Adapted from: Scientific American, 2023) Choose the correct option according to the text.

A)The fact that the universe might not behave in a way that is both local and real is considered a comforting discovery.
B)Quantum foundations have never been regarded as nonscientific.
C)The theoretical underpinnings of research carried out by John Clauser, Alain Aspect, and Anton Zeilinger were not established in the 21st century.
D)"Local" relates to the intrinsic properties of an object as they are accurately observed.
E)The demise of local realism has made people angry because "local realism" is diametrically opposed to what we experience in daily life.

EFOMM2026Dia 1Questao 4InglêsVocabulário em contextoMedia

Text I Read the text below and answer questions 3, 4 and 5. The universe is not locally real By Daniel Garisto One of the most unsettling discoveries in the past half a century is that the universe is not locally real. In this context, "real" means that objects have definite properties independent of observation - an apple can be red even when no one is looking. "Local" means that objects can be influenced only by their surroundings and that any influence cannot travel faster than the light. Investigations at the frontier of quantum physics have found that these things cannot both be true. Instead the evidence shows that objects are not influenced solely by their surroundings, and they may also lack definite properties prior to measurement. This is, of course, deeply contrary to our everyday experiences. As Albert Einstein once bemoaned to a friend, "Do you really believe the moon is not there when you are not looking at it?" To adapt a phrase from author Douglas Adams, the demise of local realism has made a lot of people very angry and has been widely regarded as a bad move. Blame for this achievement has now been laid squarely on the shoulders of three physicists: John Clauser, Alain Aspect and Anton Zeilinger. They equally split the 2022 Nobel Prize in Physics "for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science" ("Bell inequalities" refers to the pioneering work of Northern Ireland physicist John Stewart Bell, who laid the foundations for the 2022 Physics Nobel in the early 1960s). Colleagues agreed that the trio had it coming, deserving this reckoning for overthrowing reality as we know it. "It was long overdue," says Sandu Popescu, a quantum physicist at the University of Bristol in England. "Without any doubt, the prize is well deserved." "The experiments beginning with the earliest one of Clauser and continuing along show that this stuff isn't just philosophical, it's real - and like other real things, potentially useful," says Charles H. Bennett, and eminent quantum researcher at IBM. "Each Year I thought, 'Oh, maybe this is the year,'" says David Kaiser, a physicist and historian at the Massachusetts Institute of Technology. In 2022 "it really was. It was very emotional - and very thrilling." The journey from fringe to favor was a long one. From about 1940 until as late as 1990, studies of so-called quantum foundations were often treated as philosophy at best and crackpottery at worst. Many scientific journals refused to publish papers on the topic, and academic positions indulging such investigations were nearly impossible to come by. In 1985 Popescu's adviser warned him against a Ph.D. in the subject. "He said, 'Look, if you do that, you will have fun for five years, and then you will be jobless,'" Popescu says. Today quantum information science is among the most vibrant subfields in all of physics. (Adapted from: Scientific American, 2023) In "[...] academic positions indulging such investigations were nearly impossible to come by", the word "indulging" can be correctly replaced — with no change in meaning — by:

A)suppressing.
B)restraining.
C)denying.
D)supporting.
E)withholding.

EFOMM2026Dia 2Questao 4MatemáticaSequências e Raciocínio LógicoDificil

Considere que você está participando de um desafio de lógica proposto pela EFOMM (Escola de Formação de Oficiais da Marinha Mercante), uma instituição de ensino superior militar do Brasil, responsável pela formação de Oficiais da Marinha Mercante. Para testar suas habilidades de raciocínio lógico e numérico, foi criada a sequência S(n), definida pelas seguintes etapas: • Liste todos os números PARES de 2 até n. • Elimine todos os múltiplos de 6 (exceto o 6), depois os múltiplos de 8 (exceto o 8), e os múltiplos de 10 (exceto o 10). • Atribua a cada número sobrevivente, na ordem crescente, uma letra da sigla EFOMM, repetindo-a ciclicamente. Por exemplo: • S(1) = 2 → E • S(2) = 4 → F • S(3) = 6 → O • S(4) = 8 → M • S(5) = 10 → M • S(6) = 14 → E Qual é a letra, destacada nas opções abaixo, que está associada ao número 2026 dentro da sequência de sobreviventes?

A) $E FOMM$
B) $E F OMM$
C) $EF O MM$
D) $EFO M M$
E) $EFOM M$

EFOMM2026Dia 1Questao 5InglêsVocabulário em contextoFacil

Text I Read the text below and answer questions 3, 4 and 5. The universe is not locally real By Daniel Garisto One of the most unsettling discoveries in the past half a century is that the universe is not locally real. In this context, "real" means that objects have definite properties independent of observation - an apple can be red even when no one is looking. "Local" means that objects can be influenced only by their surroundings and that any influence cannot travel faster than the light. Investigations at the frontier of quantum physics have found that these things cannot both be true. Instead the evidence shows that objects are not influenced solely by their surroundings, and they may also lack definite properties prior to measurement. This is, of course, deeply contrary to our everyday experiences. As Albert Einstein once bemoaned to a friend, "Do you really believe the moon is not there when you are not looking at it?" To adapt a phrase from author Douglas Adams, the demise of local realism has made a lot of people very angry and has been widely regarded as a bad move. Blame for this achievement has now been laid squarely on the shoulders of three physicists: John Clauser, Alain Aspect and Anton Zeilinger. They equally split the 2022 Nobel Prize in Physics "for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science" ("Bell inequalities" refers to the pioneering work of Northern Ireland physicist John Stewart Bell, who laid the foundations for the 2022 Physics Nobel in the early 1960s). Colleagues agreed that the trio had it coming, deserving this reckoning for overthrowing reality as we know it. "It was long overdue," says Sandu Popescu, a quantum physicist at the University of Bristol in England. "Without any doubt, the prize is well deserved." "The experiments beginning with the earliest one of Clauser and continuing along show that this stuff isn't just philosophical, it's real - and like other real things, potentially useful," says Charles H. Bennett, and eminent quantum researcher at IBM. "Each Year I thought, 'Oh, maybe this is the year,'" says David Kaiser, a physicist and historian at the Massachusetts Institute of Technology. In 2022 "it really was. It was very emotional - and very thrilling." The journey from fringe to favor was a long one. From about 1940 until as late as 1990, studies of so-called quantum foundations were often treated as philosophy at best and crackpottery at worst. Many scientific journals refused to publish papers on the topic, and academic positions indulging such investigations were nearly impossible to come by. In 1985 Popescu's adviser warned him against a Ph.D. in the subject. "He said, 'Look, if you do that, you will have fun for five years, and then you will be jobless,'" Popescu says. Today quantum information science is among the most vibrant subfields in all of physics. (Adapted from: Scientific American, 2023) In "As Albert Einstein once bemoaned to a friend [...]", the word "bemoan" means:

A)to complain or express sadness about something.
B)to show that you really mean the opposite of what you are saying.
C)to express admiration and approval for something or someone.
D)to speak very quietly, using the breath but not the voice, so that only the person close to you can hear you.
E)to shout something or make a loud noise, usually when you are angry, in pain, or excited.

EFOMM2026Dia 2Questao 5MatemáticaGeometria planaMedia

Um terreno triangular equilátero possui, em seu interior, uma árvore plantada. As distâncias perpendiculares dessa árvore até cada um dos três lados do terreno medem 3 m, 4 m e 5 m. Qual a área do terreno em metros quadrados?

A) $483 m^{2}$
B) $363 m^{2}$
C) $243 m^{2}$
D) $242 m^{2}$
E) $122 m^{2}$

EFOMM2026Dia 1Questao 6InglêsInterpretação de textoMedia

Text II Read the text below and answer the questions 6, 7 and 8. The search for 'meaning' at work By Kate Morgan Ask workers what the most important thing is to them in a job, and first on the list generally is pay cheque - perhaps obviously. But in a very close second, as data is beginning to show; people want their work to have meaning. A 2020 McKinsey & Company surveyed showed 82% of employees believe it's important their company has a purpose; ideally, one that contributes to society and creates meaningful work. And when a company has purpose, its people do, too. Separate McKinsey research from 2022 showed 70% of employees say their personal sense of purpose is defined by their work, and when that work feels meaningful, they perform better, are much more committed and are about half as likely to go looking for a new job. The search for meaning at work is a relatively new idea, says Aaron De Smet, a senior partner at McKinsey. The Industrial Revolution, he says, made work very "transactional": people worked and got paid money to live, with no greater purpose required or expected. But over time, as decent working conditions and a pay cheque became simple fundamentals, workers began to want more. In 2018, a survey of American professionals showed nine out of 10 workers would trade a percentage of their earnings for work that felt more meaningful. This drive for meaning is especially true of the newest generation to enter the workforce; in a survey of Gen Z workers from jobs site Monster, 70% of respondents ranked purpose as more important than pay. As people's jobs have become a significant part of their identities - and the way they spend most of their time - occupations have also become the place where they hope to derive at least some of their life's meaning. People might define meaning in many ways, whether that's working in a glossy 'dream job' or using particular skills to perform a necessary role. But however people frame meaning, experts say that in the workplace of the future, making people feel that what they're doing matters, matters more than ever. The modern search for meaning at work The desire for meaningful work has been a slow and steady evolution that's happened as society has become, on the whole, wealthier. As people's basic needs for food and shelter were met, and the nature of work changed, people began to want more from their daily grinds. In many industries, the more rote, repetitive jobs have disappeared. "Automation is happening pretty quickly, which is why I think things are now coming to this tipping point where meaning matters a lot," says De Smet. Stephanie Bot, a clinical psychologist and co-founder of Workright, a Toronto-based workplace mental-health consultancy, notes that for a lot of people, identity has become closely tied to work. What we do, in many ways, defines who we are. "As the type of jobs we're in have evolved, people are now looking for a greater sense of self," she says. It makes people feel like their lives have meaning, she adds, when their work does. People also spend most of their time at work - it's the activity that takes up the biggest chunk of waking hours - and even when they're not actively working, many people are still thinking about work. The majority of younger people, in particular, report that it's difficult to disengage. It becomes even more important, then, that this place people spend most of their time and mental energy mean something. "If people don't have outside time to get those needs met elsewhere," says Bot, "they need to get more out of work." In the wake of the pandemic, meaningful work has become more important to people than ever before. It was a catalyst that realigned many people's priorities. "Two-thirds of US employees said Covid caused them to reflect on their purpose in life," says De Smet, of 2021 McKinsey research. "Everybody took this moment to step back and reassess. People were taking stock of their lives, and asking, 'Does what I do matter? I should really spend my time on things that matter." People's search for meaning in their work contributed to the Great Resignation - a phenomenon that's seen workers leave their jobs in droves throughout the past two years. "Some people said, 'I'm not getting enough meaning from work, I want to work somewhere my purpose is more fulfilled by the work I do'," says De Smet. "Or, they said, 'I don't feel the work I do is important to anyone. I want to go somewhere it feels like my work is valued by my organisation'." (Adapted from: https://www.bbc.com/) Choose the correct option according to the text.

A)Transactional jobs entail the idea of ensuring the employees' sense of worthiness.
B)Most members of Generation Z believe purpose outweighs pay.
C)Having a meaningful job is something ordinarily wanted before anything else.
D)Occupying glamorous positions is not considered a part of many possible definitions of meaningful jobs.
E)'Great Resignation' can be defined as people's willingness to fight for their dream jobs.

EFOMM2026Dia 2Questao 6MatemáticaTrigonometria e vetoresDificil

A soma dos quadrados das funções circulares seno, cosseno e tangente do arco

\frac{2 π}{5}

, sabendo-se que o lado do pentágono regular estrelado, inscrito em um círculo de raio unitário, é

\frac{1}{2} 10 + 25

, vale:

A) $2 (3 + \frac{1}{2} 5)$
B) $3 (2 + 5)$
C) $2 (3 + 5)$
D) $3 + 5$
E) $2 + 5$

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