Prova ITA 2017 comentada: questões e gabarito

ITA20171a faseQuestao 1QuímicaEletroquímica e oxirreduçãoFacil

Pode-se utilizar metais de sacrifício para proteger estruturas de aço (tais como pontes, antenas e cascos de navios) da corrosão eletroquímica. Considere os seguintes metais: I. Alumínio II. Magnésio III. Paládio IV. Sódio V. Zinco Assinale a opção que apresenta o(s) metal(is) de sacrifício que pode(m) ser utilizado(s).

A)Apenas I, II e V.
B)Apenas I e III.
C)Apenas II e IV.
D)Apenas III e IV.
E)Apenas V.

ITA20171a faseQuestao 1InglêsInterpretação de textoFacil

Leia o texto a seguir para responder à questão. FRAYING AT THE EDGES: A LIFE-CHANGING DIAGNOSIS IT BEGAN WITH what she saw in the bathroom mirror. On a dull morning, Geri Taylor padded into the shiny bathroom of her Manhattan apartment. She casually checked her reflection in the mirror, doing her daily inventory. Immediately, she stiffened with fright. Huh? What? She didn't recognize herself. She gazed saucer-eyed at her image, thinking: Oh, is this what I look like? No, that's not me. Who's that in my mirror? This was in late 2012. She was 69, in her early months getting familiar with retirement. For some time she had experienced the sensation of clouds coming over her, mantling thought. There had been a few hiccups at her job. She had been a nurse who climbed the rungs to health care executive. Once, she was leading a staff meeting when she had no idea what she was talking about, her mind like a stalled engine that wouldn't turn over. "Fortunately I was the boss and I just said, "Enough of that; Sally, tell me what you're up to,'" she would say of the episode. Certain mundane tasks stumped her. She told her husband, Jim Taylor, that the blind in the bedroom was broken. He showed her she was pulling the wrong cord. Kept happening. Finally, nothing else working, he scribbled on the adjacent wall which cord was which. Then there was the day she got off the subway at 14th Street and Seventh Avenue unable to figure out why she was there. So, yes, she had had inklings that something was going wrong with her mind. She held tight to these thoughts. She even hid her suspicions from Mr. Taylor, who chalked up her thinning memory to the infirmities of age. "I thought she was getting like me," he said. "I had been forgetful for 10 years." But to not recognize her own face! To Ms. Taylor, this was the "drop-dead moment" when she had to accept a terrible truth. She wasn't just seeing the twitches of aging but the early fumes of the disease. She had no further issues with mirrors, but there was no ignoring that something important had happened. She confided her fears to her husband and made an appointment with a neurologist. "Before then I thought I could fake it," she would explain. "This convinced me I had to come clean." In November 2012, she saw the neurologist who was treating her migraines. He listened to her symptoms, took blood, gave her the Mini Mental State Examination, a standard cognitive test made up of a set of unremarkable questions and commands. (For instance, she was asked to count backward from 100 in intervals of seven; she had to say the phrase: "No ifs, ands or buts"; she was told to pick up a piece of paper, fold it in half and place it on the floor beside her.) He told her three common words, said he was going to ask her them in a little bit. He emphasized this by pointing a finger at his head — remember those words. That simple. Yet when he called for them, she knew only one: Beach. In her mind, she would go on to associate it with the doctor, thinking of him as Dr. Beach. He gave a diagnosis of mild cognitive impairment, a common precursor to Alzheimer's disease. The first label put on what she had. Even then, she understood it was the footfall of what would come. Alzheimer's had struck her father, a paternal aunt and a cousin. She long suspected it would eventually find her. Quanto ao gênero textual, o texto pode ser classificado como

A)sinopse de romance.
B)romance autobiográfico.
C)romance biográfico.
D)laudo psiquiátrico.
E)resenha médica.

ITA20171a faseQuestao 1FísicaAnálise dimensionalMedia

Ondas gravitacionais foram previstas por Einstein em 1916 e diretamente detectadas pela primeira vez em 2015. Sob determinadas condições, um sistema girando com velocidade angular

ω

irradia tais ondas com potência proporcional a

G c^{β} Q^{γ} ω^{δ}

, em que

G

é a constante de gravitação universal;

c

, a velocidade da luz; e

Q

, uma grandeza que tem unidade em kg·m². Assinale a opção correta.

A) $β = - 5, γ = 2, δ = 6$
B) $β = - 3/5, γ = 4/3, δ = 4$
C) $β = - 10/3, γ = 5/3, δ = 5$
D) $β = 0, γ = 1, δ = 3$
E) $β = - 10, γ = 3, δ = 9$

ITA20171a faseQuestao 1MatemáticaOperações e otimizaçãoMedia

Sejam

X

e

Y

dois conjuntos finitos com

X \subset Y

e

X \neq = Y

. Considere as seguintes afirmações: I. Existe uma bijeção

f : X \to Y

. II. Existe uma função injetora

g : Y \to X

. III. O número de funções injetoras

f : X \to Y

é igual ao número de funções sobrejetoras

g : Y \to X

. É (são) verdadeira(s)

A)nenhuma delas.
B)apenas I.
C)apenas III.
D)apenas I e II.
E)todas.

ITA20171a faseQuestao 2MatemáticaTrigonometria e vetoresMedia

O número de soluções da equação

(1 + sec θ) (1 + cossec θ) = 0

, com

θ \in [- π, π]

, é

A)0.
B)1.
C)2.
D)3.
E)4.

ITA20171a faseQuestao 2FísicaEstática e máquinas simplesMuito dificil

Um bastão rígido e uniforme, de comprimento

L

, toca os pinos

P

e

Q

fixados numa parede vertical, interdistantes de

a

, conforme a figura. O coeficiente de atrito entre cada pino e o bastão é

μ

, e o ângulo deste com a horizontal é

α

. Assinale a condição em que se torna possível o equilíbrio estático do bastão.

A) $L \geq a (1 + \frac{tan α}{μ})$
B) $L \geq a (- 1 + \frac{tan α}{μ})$
C) $L \geq a (1 + \frac{tan α}{2 μ})$
D) $L \geq a (- 1 + \frac{tan α}{2 μ})$
E) $L \geq \frac{a}{2} (1 + \frac{tan α}{μ})$

ITA20171a faseQuestao 2QuímicaEstequiometriaDificil

A reação do mercúrio metálico com excesso de ácido sulfúrico concentrado a quente produz um gás mais denso do que o ar. Dois terços deste gás são absorvidos e reagem completamente com uma solução aquosa de hidróxido de sódio, formando 12,6 g de um sal. A solução de ácido sulfúrico utilizada tem massa específica igual a 1,75 g·cm⁻³ e concentração de 80 % em massa. Assinale a alternativa que apresenta o volume consumido da solução de ácido sulfúrico, em cm³.

A)11
B)21
C)31
D)41
E)51

ITA20171a faseQuestao 2InglêsInterpretação de textoMedia

Leia o texto a seguir para responder à questão. FRAYING AT THE EDGES: A LIFE-CHANGING DIAGNOSIS IT BEGAN WITH what she saw in the bathroom mirror. On a dull morning, Geri Taylor padded into the shiny bathroom of her Manhattan apartment. She casually checked her reflection in the mirror, doing her daily inventory. Immediately, she stiffened with fright. Huh? What? She didn't recognize herself. She gazed saucer-eyed at her image, thinking: Oh, is this what I look like? No, that's not me. Who's that in my mirror? This was in late 2012. She was 69, in her early months getting familiar with retirement. For some time she had experienced the sensation of clouds coming over her, mantling thought. There had been a few hiccups at her job. She had been a nurse who climbed the rungs to health care executive. Once, she was leading a staff meeting when she had no idea what she was talking about, her mind like a stalled engine that wouldn't turn over. "Fortunately I was the boss and I just said, "Enough of that; Sally, tell me what you're up to,'" she would say of the episode. Certain mundane tasks stumped her. She told her husband, Jim Taylor, that the blind in the bedroom was broken. He showed her she was pulling the wrong cord. Kept happening. Finally, nothing else working, he scribbled on the adjacent wall which cord was which. Then there was the day she got off the subway at 14th Street and Seventh Avenue unable to figure out why she was there. So, yes, she had had inklings that something was going wrong with her mind. She held tight to these thoughts. She even hid her suspicions from Mr. Taylor, who chalked up her thinning memory to the infirmities of age. "I thought she was getting like me," he said. "I had been forgetful for 10 years." But to not recognize her own face! To Ms. Taylor, this was the "drop-dead moment" when she had to accept a terrible truth. She wasn't just seeing the twitches of aging but the early fumes of the disease. She had no further issues with mirrors, but there was no ignoring that something important had happened. She confided her fears to her husband and made an appointment with a neurologist. "Before then I thought I could fake it," she would explain. "This convinced me I had to come clean." In November 2012, she saw the neurologist who was treating her migraines. He listened to her symptoms, took blood, gave her the Mini Mental State Examination, a standard cognitive test made up of a set of unremarkable questions and commands. (For instance, she was asked to count backward from 100 in intervals of seven; she had to say the phrase: "No ifs, ands or buts"; she was told to pick up a piece of paper, fold it in half and place it on the floor beside her.) He told her three common words, said he was going to ask her them in a little bit. He emphasized this by pointing a finger at his head — remember those words. That simple. Yet when he called for them, she knew only one: Beach. In her mind, she would go on to associate it with the doctor, thinking of him as Dr. Beach. He gave a diagnosis of mild cognitive impairment, a common precursor to Alzheimer's disease. The first label put on what she had. Even then, she understood it was the footfall of what would come. Alzheimer's had struck her father, a paternal aunt and a cousin. She long suspected it would eventually find her. Quanto à narrativa, o texto é apresentado

A)por narrador externo, que utiliza discursos direto e indireto.
B)pela personagem principal, que relata ao leitor suas limitações cognitivas.
C)por uma personagem que traz também a voz da personagem principal.
D)pelo médico que busca apresentar informações sobre Geri Taylor.
E)pela própria narradora, quando ainda tinha consciência dos fatos de sua vida.

ITA20171a faseQuestao 3QuímicaEstudo dos gasesMedia

Um frasco fechado contém dois gases cujo comportamento é considerado ideal: hidrogênio molecular e monóxido de nitrogênio. Sabendo que a pressão parcial do monóxido de nitrogênio é igual a 3/5 da pressão parcial do hidrogênio molecular, e que a massa total da mistura é de 20 g, assinale a alternativa que fornece a porcentagem em massa do hidrogênio molecular na mistura gasosa.

A)4%
B)6%
C)8%
D)10%
E)12%

ITA20171a faseQuestao 3MatemáticaSequências e progressõesMedia

Sejam

a, b, c, d \in R

. Suponha que

a, b, c, d

formem, nesta ordem, uma progressão geométrica e que

a, b /2, c /4, d - 140

formem, nesta ordem, uma progressão aritmética. Então, o valor de

d - b

é

A) $- 140$ .
B) $- 120$ .
C) $0$ .
D) $120$ .
E) $140$ .

ITA20171a faseQuestao 3InglêsInterpretação de textoFacil

Leia o texto a seguir para responder à questão. FRAYING AT THE EDGES: A LIFE-CHANGING DIAGNOSIS IT BEGAN WITH what she saw in the bathroom mirror. On a dull morning, Geri Taylor padded into the shiny bathroom of her Manhattan apartment. She casually checked her reflection in the mirror, doing her daily inventory. Immediately, she stiffened with fright. Huh? What? She didn't recognize herself. She gazed saucer-eyed at her image, thinking: Oh, is this what I look like? No, that's not me. Who's that in my mirror? This was in late 2012. She was 69, in her early months getting familiar with retirement. For some time she had experienced the sensation of clouds coming over her, mantling thought. There had been a few hiccups at her job. She had been a nurse who climbed the rungs to health care executive. Once, she was leading a staff meeting when she had no idea what she was talking about, her mind like a stalled engine that wouldn't turn over. "Fortunately I was the boss and I just said, "Enough of that; Sally, tell me what you're up to,'" she would say of the episode. Certain mundane tasks stumped her. She told her husband, Jim Taylor, that the blind in the bedroom was broken. He showed her she was pulling the wrong cord. Kept happening. Finally, nothing else working, he scribbled on the adjacent wall which cord was which. Then there was the day she got off the subway at 14th Street and Seventh Avenue unable to figure out why she was there. So, yes, she had had inklings that something was going wrong with her mind. She held tight to these thoughts. She even hid her suspicions from Mr. Taylor, who chalked up her thinning memory to the infirmities of age. "I thought she was getting like me," he said. "I had been forgetful for 10 years." But to not recognize her own face! To Ms. Taylor, this was the "drop-dead moment" when she had to accept a terrible truth. She wasn't just seeing the twitches of aging but the early fumes of the disease. She had no further issues with mirrors, but there was no ignoring that something important had happened. She confided her fears to her husband and made an appointment with a neurologist. "Before then I thought I could fake it," she would explain. "This convinced me I had to come clean." In November 2012, she saw the neurologist who was treating her migraines. He listened to her symptoms, took blood, gave her the Mini Mental State Examination, a standard cognitive test made up of a set of unremarkable questions and commands. (For instance, she was asked to count backward from 100 in intervals of seven; she had to say the phrase: "No ifs, ands or buts"; she was told to pick up a piece of paper, fold it in half and place it on the floor beside her.) He told her three common words, said he was going to ask her them in a little bit. He emphasized this by pointing a finger at his head — remember those words. That simple. Yet when he called for them, she knew only one: Beach. In her mind, she would go on to associate it with the doctor, thinking of him as Dr. Beach. He gave a diagnosis of mild cognitive impairment, a common precursor to Alzheimer's disease. The first label put on what she had. Even then, she understood it was the footfall of what would come. Alzheimer's had struck her father, a paternal aunt and a cousin. She long suspected it would eventually find her. De acordo com o texto,

A)Geri Taylor ficou abatida com o diagnóstico de Alzheimer e declarou ter sido nocauteada pela doença.
B)Jim Taylor procurou o médico para conversar sobre os esquecimentos da esposa.
C)o neurologista teve certeza da doença de Geri Taylor porque ela não conseguiu contar de 0 a 100.
D)Geri Taylor foi diagnosticada com um problema cognitivo que normalmente precede o Alzheimer.
E)Jim Taylor preferiu não contar ao médico sobre as doenças degenerativas na família da esposa.

ITA20171a faseQuestao 3FísicaDinâmicaDificil

Na figura, o vagão move-se a partir do repouso sob a ação de uma aceleração

a

constante. Em decorrência, desliza para trás o pequeno bloco apoiado em seu piso de coeficiente de atrito

μ

. No instante em que o bloco percorrer a distância

L

, a velocidade do bloco, em relação a um referencial externo, será igual a

A) $\frac{g L}{a - μg}$
B) $\frac{g L}{a + μg}$
C) $\frac{μg L}{a - μg}$
D) $\frac{μg 2 L}{a - μg}$
E) $\frac{μg 2 L}{a + μg}$

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