Prova ITA 2015 comentada: questões e gabarito

ITA20151a faseQuestao 1QuímicaQuímica analítica: solubilidade e identificação de saisFacil

Assinale a opção que apresenta os instrumentos de medição de volume mais indicados para a realização de uma titulação.

A)Bureta e erlenmeyer
B)Proveta e erlenmeyer
C)Pipeta volumétrica e erlenmeyer
D)Proveta e béquer
E)Pipeta volumétrica e béquer

ITA20151a faseQuestao 1InglêsInterpretação de textoMedia

Leia o texto a seguir para responder à questão. THE MAN IN THE CONVERTIBLE One morning, well after I was diagnosed with cancer, I got an email from Robbee Kosak, Carnegie Mellon’s vice president for advancement. She told me a story. She said she had been driving home from work the night before, and she found herself behind a man in a convertible. It was a warm, gorgeous, early-spring evening, and the man had his top down and all his windows lowered. His arm was hanging over the driver’s side door, and his fingers were tapping along to the music on his radio. His head was bobbing along, too, as the wind blew through his hair. Robbee changed lanes and pulled a little closer. From the side, she could see that the man had a slight smile on his face, the kind of absentminded smile a person might have when he’s all alone, happy in his own thoughts. Robbee found herself thinking: “Wow, this is the epitome of a person appreciating this day and this moment.” The convertible eventually turned the corner, and that’s when Robbee got a look at the man’s full face. “Oh my God,” she said to herself. “It’s Randy Pausch!” She was so struck by the sight of me. She knew that my cancer diagnosis was grim. And yet, as she wrote in her email, she was moved by how contented I seemed. In this private moment, I was obviously in high spirits. Robbee wrote in her email: “You can never know how much that glimpse of you made my day, reminding me of what life is all about.” I read Robbee’s email several times. I came to look at it as a feedback loop of sorts. It has not always been easy to stay positive through my cancer treatment. When you have a dire medical issue, it’s tough to know how you’re really faring emotionally. I had wondered whether a part of me was acting when I was with other people. Maybe at times I forced myself to appear strong and upbeat. Many cancer patients feel obliged to put up a brave front. Was I doing that, too? But Robbee had come upon me in an unguarded moment. I’d like to think she saw me as I am. She certainly saw me as I was that evening. Her mail was just a paragraph, but it meant a great deal to me. She had given me a window into myself. I was still fully engaged. I still knew life was good. I was doing OK. Fonte: PAUSCH, R. The last lecture. New York, Hyperion, 2008. p.64-65. O autor do texto

A)utiliza a dissertação e a descrição como tipologia textual predominante.
B)é narrador observador e mescla discursos direto, indireto e indireto livre.
C)usa foco narrativo em primeira pessoa configurando o texto autobiográfico.
D)utiliza linguagem coloquial nos diálogos para externar seus sentimentos.
E)recorre a figuras de pensamento para compor o gênero dramático.

ITA20151a faseQuestao 1FísicaOndulatóriaFacil

Um fio de comprimento

L

e massa específica linear

μ

é mantido esticado por uma força

F

em suas extremidades. Assinale a opção com a expressão do tempo que um pulso demora para percorrê-lo.

A) $\frac{2 L F}{μ}$
B) $\frac{F}{2 π Lμ}$
C) $L \frac{μ}{F}$
D) $\frac{L}{π} \frac{μ}{F}$
E) $\frac{L}{2 π} \frac{μ}{F}$

ITA20151a faseQuestao 1MatemáticaSequências e progressõesDificil

Considere as seguintes afirmações sobre números reais: I. Se a expansão decimal de

x

é infinita e periódica, então

x

é um número racional. II.

n = 0 \sum \infty \frac{1}{( 2 - 1 ) 2 ^{n}} = \frac{2}{1 - 2 2}

. III.

ln 3 e^{2} + (lo g_{3} 2) (lo g_{4} 9)

é um número racional. É(são) verdadeira(s):

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

ITA20151a faseQuestao 2MatemáticaNúmeros complexosDificil

Sejam

A

,

B

e

C

os subconjuntos de

C

definidos por

A = {z \in C : ∣ z + 2 - 3 i ∣ < 19}

,

B = {z \in C : ∣ z + i ∣ < 7/2}

e

C = {z \in C : z^{2} + 6 z + 10 = 0}

. Então,

(A ∖ B) \cap C

é o conjunto

A) ${- 1 - 3 i, - 1 + 3 i}$
B) ${- 3 - i, - 3 + i}$
C) ${- 3 + i}$
D) ${- 3 - i}$
E) ${- 1 + 3 i}$

ITA20151a faseQuestao 2FísicaEletrostáticaFacil

Uma pequena esfera metálica, de massa

m

e carga positiva

q

, é lançada verticalmente para cima com velocidade inicial

v_{0}

em uma região onde há um campo elétrico de módulo

E

, apontando para baixo, e um gravitacional de módulo

g

, ambos uniformes. A máxima altura que a esfera alcança é

A) $\frac{v _{0}^{2}}{2 g}$
B) $\frac{q E}{m v _{0}}$
C) $\frac{v _{0}}{q m E}$
D) $\frac{m v _{0}^{2}}{2 ( q E + m g )}$
E) $\frac{3 m E q v _{0}}{8 g}$

ITA20151a faseQuestao 2QuímicaAtomísticaFacil

Cinco amostras idênticas de um mesmo metal são aquecidas a diferentes temperaturas até à incandescência. Assinale a opção que apresenta a cor da amostra submetida a uma maior temperatura.

A)Vermelho
B)Laranja
C)Amarelo
D)Verde
E)Branco

ITA20151a faseQuestao 2InglêsInterpretação de textoFacil

Leia o texto a seguir para responder à questão. THE MAN IN THE CONVERTIBLE One morning, well after I was diagnosed with cancer, I got an email from Robbee Kosak, Carnegie Mellon’s vice president for advancement. She told me a story. She said she had been driving home from work the night before, and she found herself behind a man in a convertible. It was a warm, gorgeous, early-spring evening, and the man had his top down and all his windows lowered. His arm was hanging over the driver’s side door, and his fingers were tapping along to the music on his radio. His head was bobbing along, too, as the wind blew through his hair. Robbee changed lanes and pulled a little closer. From the side, she could see that the man had a slight smile on his face, the kind of absentminded smile a person might have when he’s all alone, happy in his own thoughts. Robbee found herself thinking: “Wow, this is the epitome of a person appreciating this day and this moment.” The convertible eventually turned the corner, and that’s when Robbee got a look at the man’s full face. “Oh my God,” she said to herself. “It’s Randy Pausch!” She was so struck by the sight of me. She knew that my cancer diagnosis was grim. And yet, as she wrote in her email, she was moved by how contented I seemed. In this private moment, I was obviously in high spirits. Robbee wrote in her email: “You can never know how much that glimpse of you made my day, reminding me of what life is all about.” I read Robbee’s email several times. I came to look at it as a feedback loop of sorts. It has not always been easy to stay positive through my cancer treatment. When you have a dire medical issue, it’s tough to know how you’re really faring emotionally. I had wondered whether a part of me was acting when I was with other people. Maybe at times I forced myself to appear strong and upbeat. Many cancer patients feel obliged to put up a brave front. Was I doing that, too? But Robbee had come upon me in an unguarded moment. I’d like to think she saw me as I am. She certainly saw me as I was that evening. Her mail was just a paragraph, but it meant a great deal to me. She had given me a window into myself. I was still fully engaged. I still knew life was good. I was doing OK. Fonte: PAUSCH, R. The last lecture. New York, Hyperion, 2008. p.64-65. De acordo com as informações no texto, Robbee Kosak

A)descreveu detalhadamente o cenário do seu primeiro encontro com Randy Pausch.
B)sentiu-se atraída pelo veículo de Randy Pausch devido à alta velocidade dele.
C)escreveu palavras motivadoras a Randy Pausch porque desejava reanimá-lo.
D)caracterizou o motorista do veículo como uma pessoa satisfeita e de bem com a vida.
E)ocupava o cargo de Vice-Presidente na empresa presidida por Randy Pausch.

ITA20151a faseQuestao 3QuímicaRadioatividade e meia-vidaMedia

O elemento Plutônio-238 é utilizado para a geração de eletricidade em sondas espaciais. Fundamenta-se essa utilização porque esse isótopo tem

A)longo tempo de meia-vida e é emissor de partículas beta.
B)longo tempo de meia-vida e é emissor de partículas gama.
C)longo tempo de meia-vida e é emissor de partículas alfa.
D)longo tempo de meia-vida e é emissor de partículas delta.
E)tempo de meia-vida curto e é emissor de partículas alfa.

ITA20151a faseQuestao 3MatemáticaNúmeros complexosMedia

Seja

z = (\frac{1 + 3 i}{1 - 3 i})^{10}

. Então, o valor de

2 arcsin (Re (z)) + 5 arctg (2 Im (z))

é igual a

A) $- \frac{2 π}{3}$
B) $- \frac{π}{3}$
C) $\frac{2 π}{3}$
D) $\frac{4 π}{3}$
E) $\frac{5 π}{3}$

ITA20151a faseQuestao 3FísicaDinâmicaDificil

Uma massa puntiforme é abandonada, com impulso inicial desprezível, do topo de um hemisfério maciço em repouso sobre uma superfície horizontal. Ao descolar-se da superfície do hemisfério, a massa terá percorrido um ângulo

θ

em relação à vertical. Esse experimento é realizado nas três condições seguintes: I. O hemisfério é mantido preso à superfície horizontal e não há atrito entre a massa e o hemisfério. II. O hemisfério é mantido preso à superfície horizontal, mas há atrito entre a massa e o hemisfério. III. O hemisfério e a massa podem deslizar livremente pelas respectivas superfícies. Sendo

θ_{I}

,

θ_{I I}

e

θ_{I I I}

os respectivos ângulos medidos, pode-se afirmar que

A) $θ_{I I} < θ_{I}$ e $θ_{I I I} < θ_{I}$ .
B) $θ_{I I} < θ_{I}$ e $θ_{I I I} > θ_{I}$ .
C) $θ_{I I} > θ_{I}$ e $θ_{I I I} < θ_{I}$ .
D) $θ_{I I} > θ_{I}$ e $θ_{I I I} > θ_{I}$ .
E) $θ_{I} = θ_{I I I}$ .

ITA20151a faseQuestao 3InglêsVocabulário e GramáticaMedia

Leia o texto a seguir para responder à questão. THE MAN IN THE CONVERTIBLE One morning, well after I was diagnosed with cancer, I got an email from Robbee Kosak, Carnegie Mellon’s vice president for advancement. She told me a story. She said she had been driving home from work the night before, and she found herself behind a man in a convertible. It was a warm, gorgeous, early-spring evening, and the man had his top down and all his windows lowered. His arm was hanging over the driver’s side door, and his fingers were tapping along to the music on his radio. His head was bobbing along, too, as the wind blew through his hair. Robbee changed lanes and pulled a little closer. From the side, she could see that the man had a slight smile on his face, the kind of absentminded smile a person might have when he’s all alone, happy in his own thoughts. Robbee found herself thinking: “Wow, this is the epitome of a person appreciating this day and this moment.” The convertible eventually turned the corner, and that’s when Robbee got a look at the man’s full face. “Oh my God,” she said to herself. “It’s Randy Pausch!” She was so struck by the sight of me. She knew that my cancer diagnosis was grim. And yet, as she wrote in her email, she was moved by how contented I seemed. In this private moment, I was obviously in high spirits. Robbee wrote in her email: “You can never know how much that glimpse of you made my day, reminding me of what life is all about.” I read Robbee’s email several times. I came to look at it as a feedback loop of sorts. It has not always been easy to stay positive through my cancer treatment. When you have a dire medical issue, it’s tough to know how you’re really faring emotionally. I had wondered whether a part of me was acting when I was with other people. Maybe at times I forced myself to appear strong and upbeat. Many cancer patients feel obliged to put up a brave front. Was I doing that, too? But Robbee had come upon me in an unguarded moment. I’d like to think she saw me as I am. She certainly saw me as I was that evening. Her mail was just a paragraph, but it meant a great deal to me. She had given me a window into myself. I was still fully engaged. I still knew life was good. I was doing OK. Fonte: PAUSCH, R. The last lecture. New York, Hyperion, 2008. p.64-65. Assinale a oração que não contém expressão ou termo qualificador.

A)It was a warm, gorgeous, early-spring evening... (linha 4)
B)She was so struck by the sight of me. (linha 13)
C)...she was moved by how contented I seemed. (linha 14)
D)...I was obviously in high spirits. (linhas 14 e 15)
E)She certainly saw me as I was that evening. (linhas 22 e 23)

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