Prova ITA 2018 comentada: questões e gabarito

ITA20181a faseQuestao 1InglêsReading comprehension (atribuição de fala)Media

As questões de 1 a 6 referem-se ao texto a seguir: GOODBYE THINGS, HELLO MINIMALISM: CAN LIVING WITH LESS MAKE YOU HAPPIER? Fumio Sasaki owns a roll-up mattress, three shirts and four pairs of socks. After deciding to scorn possessions, he began feeling happier. He explains why. 1 Let me tell you a bit about myself. I'm 35 years old, male, single, never been married. I work as an 2 editor at a publishing company. I recently moved from the Nakameguro neighbourhood in Tokyo, where I 3 lived for a decade, to a neighbourhood called Fudomae in a different part of town. The rent is cheaper, but 4 the move pretty much wiped out my savings. 5 Some of you may think that I'm a loser: an unmarried adult with not much money. The old me would 6 have been way too embarrassed to admit all this. I was filled with useless pride. But I honestly don't care 7 about things like that any more. The reason is very simple: I'm perfectly happy just as I am. The reason? I got 8 rid of most of my material possessions. 9 Minimalism is a lifestyle in which you reduce your possessions to the least possible. Living with only 10 the bare essentials has not only provided superficial benefits such as the pleasure of a tidy room or the 11 simple ease of cleaning, it has also led to a more fundamental shift. It's given me a chance to think about 12 what it really means to be happy. 13 We think that the more we have, the happier we will be. We never know what tomorrow might bring, so 14 we collect and save as much as we can. This means we need a lot of money, so we gradually start judging 15 people by how much money they have. You convince yourself that you need to make a lot of money so you 16 don't miss out on success. And for you to make money, you need everyone else to spend their money. And 17 so it goes. 18 So I said goodbye to a lot of things, many of which I'd had for years. And yet now I live each day with a 19 happier spirit. I feel more content now than I ever did in the past. 20 I wasn't always a minimalist. I used to buy a lot of things, believing that all those possessions would 21 increase my self-worth and lead to a happier life. I loved collecting a lot of useless stuff, and I couldn't throw 22 anything away. I was a natural hoarder of knick-knacks that I thought made me an interesting person. 23 At the same time, though, I was always comparing myself with other people who had more or better 24 things, which often made me miserable. I couldn't focus on anything, and I was always wasting time. Alcohol 25 was my escape, and I didn't treat women fairly. I didn't try to change; I thought this was all just part of who I 26 was, and I deserved to be unhappy. 27 My apartment wasn't horribly messy; if my girlfriend was coming over for the weekend, I could do 28 enough tidying up to make it look presentable. On a usual day, however, there were books stacked 29 everywhere because there wasn't enough room on my bookshelves. Most I had thumbed through once or 30 twice, thinking that I would read them when I had the time. 31 The closet was crammed with what used to be my favourite clothes, most of which I'd only worn a few 32 times. The room was filled with all the things I'd taken up as hobbies and then gotten tired of. A guitar and 33 amplifier, covered with dust. Conversational English workbooks I'd planned to study once I had more free 34 time. Even a fabulous antique camera, which of course I had never once put a roll of film in. 35 It may sound as if I'm exaggerating when I say I started to become a new person. Someone said to 36 me: "All you did is throw things away," which is true. But by having fewer things around, I've started feeling 37 happier each day. I'm slowly beginning to understand what happiness is. 38 If you are anything like I used to be miserable, constantly comparing yourself with others, or just 39 believing your life sucks I think you should try saying goodbye to some of your things. [...] Everyone wants 40 to be happy. But trying to buy happiness only makes us happy for a little while. ——— De acordo com o texto, Fumio

A)já foi casado, mas está solteiro no momento.
B)morou em Nakameguro por 10 anos.
C)mudou-se de Tóquio recentemente.
D)é editor em uma agência de publicidade.
E)mudou-se porque precisava quitar dívidas.

ITA20181a faseQuestao 1FísicaGravitação (campo gravitacional e órbitas)Dificil

Considere uma estrela de nêutrons com densidade média de

5 \times 1 0^{14}

g/cm³, sendo que sua frequência de vibração radial

ν

é função do seu raio

R

, de sua massa

m

e da constante da gravitação universal

G

. Sabe-se que

ν

é dada por uma expressão monomial, em que a constante adimensional de proporcionalidade vale aproximadamente

1

. Então o valor de

ν

é da ordem de

A) $1 0^{- 2}$ Hz.
B) $1 0^{- 1}$ Hz.
C) $1 0^{0}$ Hz.
D) $1 0^{2}$ Hz.
E) $1 0^{4}$ Hz.

ITA20181a faseQuestao 1MatemáticaGeometria planaMedia

Os lados de um triângulo de vértices

A

,

B

e

C

medem

A B = 3

cm,

B C = 7

cm e

C A = 8

cm. A circunferência inscrita no triângulo tangencia o lado

\overline{A B}

no ponto

N

e o lado

\overline{C A}

no ponto

K

. Então, o comprimento do segmento

\overline{N K}

, em cm, é

A) $2$ .
B) $22$ .
C) $3$ .
D) $23$ .
E) $\frac{7}{2}$ .

ITA20181a faseQuestao 1QuímicaQuímica orgânicaMedia

Aminoácidos são compostos orgânicos que contêm um grupo amino e um grupo carboxílico. Nos α-aminoácidos, os dois grupos encontram-se nas extremidades da molécula e entre eles há um átomo de carbono, denominado carbono-α, que também está ligado a um grupo R, conforme a figura. Considere os seguintes aminoácidos: I. Alanina, em que R = CH₃. II. Asparagina, em que R = CH₂CONH₂. III. Fenilalanina, em que R = CH₂C₆H₅. IV. Glicina, em que R = H. V. Serina, em que R = CH₂OH. Assinale a opção que contém o(s) aminoácido(s) que possui(em) grupo(s) R polar(es).

Imagens anexadas

A)Alanina e Fenilalanina.
B)Asparagina e Glicina.
C)Asparagina e Serina.
D)Fenilalanina.
E)Glicina, Fenilalanina e Serina.

ITA20181a faseQuestao 2FísicaComposição de movimentosMedia

Numa quadra de vôlei de

18

m de comprimento, com rede de

2, 24

m de altura, uma atleta solitária faz um saque com a bola bem em cima da linha de fundo, a

3, 0

m de altura, num ângulo

θ

de

1 5^{\circ}

com a horizontal, conforme a figura, com trajetória num plano perpendicular à rede. Desprezando o atrito, pode-se dizer que, com

12

m/s de velocidade inicial, a bola

Imagens anexadas

A)bate na rede.
B)passa tangenciando a rede.
C)passa a rede e cai antes da linha de fundo.
D)passa a rede e cai na linha de fundo.
E)passa a rede e cai fora da quadra.

ITA20181a faseQuestao 2MatemáticaPolinômios e identidadesMedia

Se

x

é um número real que satisfaz

x^{3} = x + 2

, então

x^{10}

é igual a

A) $5 x^{2} + 7 x + 9$ .
B) $3 x^{2} + 6 x + 8$ .
C) $13 x^{2} + 16 x + 12$ .
D) $7 x^{2} + 5 x + 9$ .
E) $9 x^{2} + 3 x + 10$ .

ITA20181a faseQuestao 2QuímicaAtomísticaMedia

Considere as seguintes proposições a respeito dos valores, em módulo, da energia de orbitais atômicos 2s e 2p: I. |E₂ₛ| = |E₂ₚ| para o átomo de hidrogênio. II. |E₂ₛ| = |E₂ₚ| para o íon de hélio carregado com uma carga positiva. III. |E₂ₛ| > |E₂ₚ| para o átomo de lítio. Das proposições acima, está(ão) CORRETA(S)

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

ITA20181a faseQuestao 2InglêsReading comprehension (atribuição de fala)Media

As questões de 1 a 6 referem-se ao texto a seguir: GOODBYE THINGS, HELLO MINIMALISM: CAN LIVING WITH LESS MAKE YOU HAPPIER? Fumio Sasaki owns a roll-up mattress, three shirts and four pairs of socks. After deciding to scorn possessions, he began feeling happier. He explains why. 1 Let me tell you a bit about myself. I'm 35 years old, male, single, never been married. I work as an 2 editor at a publishing company. I recently moved from the Nakameguro neighbourhood in Tokyo, where I 3 lived for a decade, to a neighbourhood called Fudomae in a different part of town. The rent is cheaper, but 4 the move pretty much wiped out my savings. 5 Some of you may think that I'm a loser: an unmarried adult with not much money. The old me would 6 have been way too embarrassed to admit all this. I was filled with useless pride. But I honestly don't care 7 about things like that any more. The reason is very simple: I'm perfectly happy just as I am. The reason? I got 8 rid of most of my material possessions. 9 Minimalism is a lifestyle in which you reduce your possessions to the least possible. Living with only 10 the bare essentials has not only provided superficial benefits such as the pleasure of a tidy room or the 11 simple ease of cleaning, it has also led to a more fundamental shift. It's given me a chance to think about 12 what it really means to be happy. 13 We think that the more we have, the happier we will be. We never know what tomorrow might bring, so 14 we collect and save as much as we can. This means we need a lot of money, so we gradually start judging 15 people by how much money they have. You convince yourself that you need to make a lot of money so you 16 don't miss out on success. And for you to make money, you need everyone else to spend their money. And 17 so it goes. 18 So I said goodbye to a lot of things, many of which I'd had for years. And yet now I live each day with a 19 happier spirit. I feel more content now than I ever did in the past. 20 I wasn't always a minimalist. I used to buy a lot of things, believing that all those possessions would 21 increase my self-worth and lead to a happier life. I loved collecting a lot of useless stuff, and I couldn't throw 22 anything away. I was a natural hoarder of knick-knacks that I thought made me an interesting person. 23 At the same time, though, I was always comparing myself with other people who had more or better 24 things, which often made me miserable. I couldn't focus on anything, and I was always wasting time. Alcohol 25 was my escape, and I didn't treat women fairly. I didn't try to change; I thought this was all just part of who I 26 was, and I deserved to be unhappy. 27 My apartment wasn't horribly messy; if my girlfriend was coming over for the weekend, I could do 28 enough tidying up to make it look presentable. On a usual day, however, there were books stacked 29 everywhere because there wasn't enough room on my bookshelves. Most I had thumbed through once or 30 twice, thinking that I would read them when I had the time. 31 The closet was crammed with what used to be my favourite clothes, most of which I'd only worn a few 32 times. The room was filled with all the things I'd taken up as hobbies and then gotten tired of. A guitar and 33 amplifier, covered with dust. Conversational English workbooks I'd planned to study once I had more free 34 time. Even a fabulous antique camera, which of course I had never once put a roll of film in. 35 It may sound as if I'm exaggerating when I say I started to become a new person. Someone said to 36 me: "All you did is throw things away," which is true. But by having fewer things around, I've started feeling 37 happier each day. I'm slowly beginning to understand what happiness is. 38 If you are anything like I used to be miserable, constantly comparing yourself with others, or just 39 believing your life sucks I think you should try saying goodbye to some of your things. [...] Everyone wants 40 to be happy. But trying to buy happiness only makes us happy for a little while. ——— Antes da mudança, Fumio acumulava bens materiais porque

A)queria vendê-los quando chegasse à velhice.
B)costumava julgar as pessoas pelos carros que possuíam.
C)queria desfrutar deles sem se preocupar com o futuro.
D)acreditava que as posses aumentariam a sua autoestima e felicidade.
E)desejava impressionar a mulher que amava por meio de suas posses.

ITA20181a faseQuestao 3InglêsReading comprehension (atribuição de fala)Media

As questões de 1 a 6 referem-se ao texto a seguir: GOODBYE THINGS, HELLO MINIMALISM: CAN LIVING WITH LESS MAKE YOU HAPPIER? Fumio Sasaki owns a roll-up mattress, three shirts and four pairs of socks. After deciding to scorn possessions, he began feeling happier. He explains why. 1 Let me tell you a bit about myself. I'm 35 years old, male, single, never been married. I work as an 2 editor at a publishing company. I recently moved from the Nakameguro neighbourhood in Tokyo, where I 3 lived for a decade, to a neighbourhood called Fudomae in a different part of town. The rent is cheaper, but 4 the move pretty much wiped out my savings. 5 Some of you may think that I'm a loser: an unmarried adult with not much money. The old me would 6 have been way too embarrassed to admit all this. I was filled with useless pride. But I honestly don't care 7 about things like that any more. The reason is very simple: I'm perfectly happy just as I am. The reason? I got 8 rid of most of my material possessions. 9 Minimalism is a lifestyle in which you reduce your possessions to the least possible. Living with only 10 the bare essentials has not only provided superficial benefits such as the pleasure of a tidy room or the 11 simple ease of cleaning, it has also led to a more fundamental shift. It's given me a chance to think about 12 what it really means to be happy. 13 We think that the more we have, the happier we will be. We never know what tomorrow might bring, so 14 we collect and save as much as we can. This means we need a lot of money, so we gradually start judging 15 people by how much money they have. You convince yourself that you need to make a lot of money so you 16 don't miss out on success. And for you to make money, you need everyone else to spend their money. And 17 so it goes. 18 So I said goodbye to a lot of things, many of which I'd had for years. And yet now I live each day with a 19 happier spirit. I feel more content now than I ever did in the past. 20 I wasn't always a minimalist. I used to buy a lot of things, believing that all those possessions would 21 increase my self-worth and lead to a happier life. I loved collecting a lot of useless stuff, and I couldn't throw 22 anything away. I was a natural hoarder of knick-knacks that I thought made me an interesting person. 23 At the same time, though, I was always comparing myself with other people who had more or better 24 things, which often made me miserable. I couldn't focus on anything, and I was always wasting time. Alcohol 25 was my escape, and I didn't treat women fairly. I didn't try to change; I thought this was all just part of who I 26 was, and I deserved to be unhappy. 27 My apartment wasn't horribly messy; if my girlfriend was coming over for the weekend, I could do 28 enough tidying up to make it look presentable. On a usual day, however, there were books stacked 29 everywhere because there wasn't enough room on my bookshelves. Most I had thumbed through once or 30 twice, thinking that I would read them when I had the time. 31 The closet was crammed with what used to be my favourite clothes, most of which I'd only worn a few 32 times. The room was filled with all the things I'd taken up as hobbies and then gotten tired of. A guitar and 33 amplifier, covered with dust. Conversational English workbooks I'd planned to study once I had more free 34 time. Even a fabulous antique camera, which of course I had never once put a roll of film in. 35 It may sound as if I'm exaggerating when I say I started to become a new person. Someone said to 36 me: "All you did is throw things away," which is true. But by having fewer things around, I've started feeling 37 happier each day. I'm slowly beginning to understand what happiness is. 38 If you are anything like I used to be miserable, constantly comparing yourself with others, or just 39 believing your life sucks I think you should try saying goodbye to some of your things. [...] Everyone wants 40 to be happy. But trying to buy happiness only makes us happy for a little while. ——— Sobre Fumio, é correto afirmar que

A)a mudança para o novo apartamento fez com que suas reservas financeiras aumentassem.
B)seu antigo apartamento era tão bagunçado que ele não podia sequer receber a namorada.
C)desperdiçava tempo e não conseguia manter o foco, antes de aderir ao minimalismo.
D)orgulhava-se de ter um salário mais alto do que todos os seus amigos.
E)era alcoólatra e violento com as pessoas, antes de mudar o estilo de vida.

ITA20181a faseQuestao 3FísicaDinâmicaMedia

Sobre uma prancha horizontal de massa desprezível e apoiada no centro, dois discos, de massas

m_{A}

e

m_{B}

, respectivamente, rolam com as respectivas velocidades

v_{A}

e

v_{B}

, constantes, em direção ao centro, do qual distam

L_{A}

e

L_{B}

, conforme a figura. Com o sistema em equilíbrio antes que os discos colidam, a razão

v_{A} / v_{B}

é dada por

Imagens anexadas

A) $1$ .
B) $\frac{m _{A}}{m _{B}}$ .
C) $\frac{m _{B}}{m _{A}}$ .
D) $\frac{L _{A} m _{A}}{L _{B} m _{B}}$ .
E) $\frac{L _{B} m _{B}}{L _{A} m _{A}}$ .

ITA20181a faseQuestao 3MatemáticaAnálise combinatóriaDificil

Sejam

a

e

b

números inteiros positivos. Se

a

e

b

são, nessa ordem, termos consecutivos de uma progressão geométrica de razão

\frac{1}{2}

e o termo independente de

(a x - \frac{b}{x})^{12}

é igual a

7920

, então

a + b

é

A) $2$ .
B) $3$ .
C) $4$ .
D) $5$ .
E) $6$ .

ITA20181a faseQuestao 3QuímicaPolaridade e forças intermolecularesMedia

Entre as substâncias CH₄, CH₃Cl, CH₂Br₂, CH₂Cl₂, CHBr₃ e CBr₄:

A)CBr₄ é a de maior ponto de ebulição.
B)CH₂Br₂ é mais volátil que o CH₂Cl₂.
C)CHBr₃ tem maior pressão de vapor que o CH₃Cl.
D)CH₄ é a de maior força de interação intermolecular.
E)quatro destas moléculas são apolares.

Prova ITA 2018: questões por disciplina

O que caiu na prova 2018

Questões da prova ITA 2018

Treine direto nas questões reais