Questões - AFA 2015 | Gabarito e resoluções

QUESTO ANULADA!! (AFA - 2015) Considere num mesmo sistema cartesiano ortogonal as funes reais f, g e h tais que: f funo quadrtica cujo vrtice V simtrico do ponto P( 0, 27), em relao ao eixo ; g funo afim que passa pelos pontos Q( ,1 12) e R( 3,0); os pontos Q e R tambm pertencem funo f; h uma funo constante cujo grfico intercepta o grfico da funo g no ponto de abscissa -7; Analise os grficos das funes f, g e h e marque a alternativa correta. a) se, e somente se, b)A funo real dada por jest definida se, e somente se, c)Se ento d)tal que QUESTO ANULADA!!

(AFA - 2015) Considere o polinmio e marque a alternativa FALSA.

(AFA - 2015) Na figura abaixo, tem-se um cubo cuja aresta mede centmetros; as superfcies e ,contidas nas faces desse cubo, so limitadas por arcos de circunferncias de raio centmetros e centros em, respectivamente, e , e . O O volume do slido formado por todos os segmentos de reta com extremidades em e , paralelos a e de bases e , , em , igual a

(AFA - 2015) Considere os nmeros complexos , , e em que, e e as relaes: O menor argumento de todos os complexos que satisfazem, simultaneamente, as relaes I e II

(AFA - 2015) Alex possui apenas moedas de 25 centavos, de 50 centavos e de 1 real, totalizando 36 moedas. Sabe-se que a soma do nmero de moedas de 25 centavoscom o dobro do nmero de moedas de 50 centavos igual diferena entre 82 e 5 vezes o nmero de moedas de 1 real. Nessas condies correto afirmar que

(AFA - 2015) Considere as seguintes simbologias em relao matriz M: Da equaoem que A e (B+C) so matrizes quadradas de ordem n e inversveis, afirma-se que So corretas

(AFA - 2015) Um jogo decidido com um nico lanamento do dado cuja planificao est representada abaixo. Participam desse jogo quatro pessoas: Carlos, que vencer o jogo se ocorrer face preta ou menor que 3; Jos vencer se ocorrer face branca e nmero primo; Vicente vencer casoocorra face preta e nmero par; Antnio vencer se ocorrer face branca ou nmero menor que 3. Nessas condies, correto afirmar que

(AFA - 2015) Considere a funo real definida por ,em que e Analise as alternativas abaixo e marque a FALSA,

(AFA - 2015) Considere o grfico da funo real g : A A abaixo e marque (V) verdadeiro ou (F) falso. ( ) A funo g possui exatamente duas razes. ( ) g(4) = -g(-3) ( ) Im(g) = {-3} ]-2, 4[ ( ) A funo definida por h(x) = g(x) + 3 no possui raiz. ( ) (g g g ...g)(-2) = 2 A sequncia correta

(AFA -2015) Considere no plano cartesiano um tringulo equiltero ABC em que: os vrtices B, de abscissa positiva, e C, de abscissa negativa, esto sobre o eixo OX; possui baricentro no ponto Considere tambm, nesse mesmo plano cartesiano, a circunferncia 1inscrita ecircunferncia2circunscrita ao tringulo ABC. Analise as proposies abaixo e escreva (V) para verdadeira e (F) para falsa. ( )A reta r, suporte do lado AB, passa pelo ponto (-1, b), em que b o dobro do oposto do coeficiente angular de r ( )O crculo delimitado por 2contm o ponto ( )O ponto da bissetriz dos quadrantes mpares de abscissapertence a1 A sequncia correta

(AFA - 2015) No Atlas de Desenvolvimento Humano no Brasil 2013 constam valores do ndice de Desenvolvimento Humano Municipal (IDHM) de todas as cidades dos estados brasileiros. O IDHM um nmero que varia entre 0 e 1. Quanto mais prximo de 1, maior o desenvolvimento humano de um municpio, conforme escala a seguir. Abaixo esto relacionados o IDHM de duas cidades de Minas Gerais em condies extremas, Monte Formoso e Uberlndia, e uma em situao intermediria, Barbacena. Analisando os dados acima, afirma-se que I. o municpio de maior crescimento do IDHM, nos perodos considerados, Monte Formoso. II. na ltima dcada, Barbacena apresentou maior evoluo do IDHM que Uberlndia. III. uma tabela que relaciona cidade, poca e faixa de IDHM pode ser representada corretamente como: So corretas:

(AFA - 2015) TEXT I JOBS AT HIGH RISK It is an invisible force that goes by many names.Computerization. Automation. Artificial intelligence. Technology. Innovation. And, everyones favorite,ROBOTS. Whatever name you prefer, some form of it hasbeen stimulating progress and killing jobs from tailors to paralegals for centuries9. But this time is different:nearly half of American jobs today could be automated in a decade or two. The question is: which half? Another way of posing the same question is:Where do machines work better than people?7Tractors are more powerful than farmers8. Robotic arms are stronger and more tireless than assembly-line workers. But in the past 30 years, software and robots havesucceeded replacing aarticular kind of occupation: the average-wage, middle-skill, routine-heavy worker, especially in manufacturing and office administration. Indeed, its projected that the next wave ofcomputer progress1will continue to endanger humanwork where it already has: manufacturing, administrativesupport, retail, and transportation. Most remaining factory jobs are likely to diminish over the next decades. Cashiers, counter clerks, and telemarketers are similarly endangered. On the other hand, health care workers, people responsible for our safety10, and management positions are the least likely to be automated6. Thenext big thing We might be on the edge of an innovating moment in robotics and artificial intelligence. Although the past 30 years have reduced the middle, high- and low-skill jobs have actually increased, as if protected from the invading armies of robots by their own moats.Higher-skill workers have been protected by a kind ofsocial-intelligence moat. Computers are historically good at executing routines, but theyre bad at finding patterns,communicating with people, and making decisions,which is what managers are paid to do. This is whysome people think managersare, for the moment, one ofthe largest categories immune to the fast wave of AI. Meanwhile, lower-skill workers have beenprotected by the Moravec moat. Hans Moravec was a futurist who pointed out that machine technology copieda savant infant: Machines could do long math equations instantly and beat anybody in chess, but they cant answer a simple question or walk up a flight of stairs. Asa result, not skilled work done by people without much education (like home health care workers, or fast-foodattendants) have been saved, too. The human half In the 19th century, new manufacturing technology replaced what was then skilled labor. In thesecond half of the 20th century, however, software technology took the place of median-salaried office work.The first wave showed that machines are better at assembling things. The second showed that machinesare better at organizing things. Now data analytics andself-driving cars suggest they might be better at pattern recognition and driving. So what are we better at? The safest industries and jobs are dominated by managers4, health-care workers, and a super-category that includes education, media, and community service.One conclusion to draw from this is that humans are, and will always be, superior at working with, and caringfor other humans11. In this light, automation doesnt makethe world worse. Far from it: it creates new opportunitiesfor human creativity12. But robots are already creeping into diagnostics and surgeries. Schools are already experimenting with software that replaces teaching hours. The fact thatsome industries have been safe from automation for the last three decades3doesnt guarantee that theyll be safefor the next one. It would be anxious enough if we knew exactly which jobs are next in line for automation. The truth is scarier5. We dont really have a clue.2 (Adapted from http://www.businessinsider.com/robots-overtakingamerican-jobs-2014-1) Glossary: savant infant a child with great knowledge and ability to assemble to make something by joining separate parts to creep to move slowly, quietly and carefully One of the purposes of the text is to show that

(AFA - 2015) TEXT I JOBS AT HIGH RISK It is an invisible force that goes by many names.Computerization. Automation. Artificial intelligence. Technology. Innovation. And, everyones favorite,ROBOTS. Whatever name you prefer, some form of it hasbeen stimulating progress and killing jobs from tailors to paralegals for centuries9. But this time is different:nearly half of American jobs today could be automated in a decade or two. The question is: which half? Another way of posing the same question is:Where do machines work better than people?7Tractors are more powerful than farmers8. Robotic arms are stronger and more tireless than assembly-line workers. But in the past 30 years, software and robots havesucceeded replacing aarticular kind of occupation: the average-wage, middle-skill, routine-heavy worker, especially in manufacturing and office administration. Indeed, its projected that the next wave ofcomputer progress1will continue to endanger humanwork where it already has: manufacturing, administrativesupport, retail, and transportation. Most remaining factory jobs are likely to diminish over the next decades. Cashiers, counter clerks, and telemarketers are similarly endangered. On the other hand, health care workers, people responsible for our safety10, and management positions are the least likely to be automated6. Thenext big thing We might be on the edge of an innovating moment in robotics and artificial intelligence. Although the past 30 years have reduced the middle, high- and low-skill jobs have actually increased, as if protected from the invading armies of robots by their own moats.Higher-skill workers have been protected by a kind ofsocial-intelligence moat. Computers are historically good at executing routines, but theyre bad at finding patterns,communicating with people, and making decisions,which is what managers are paid to do. This is whysome people think managersare, for the moment, one ofthe largest categories immune to the fast wave of AI. Meanwhile, lower-skill workers have beenprotected by the Moravec moat. Hans Moravec was a futurist who pointed out that machine technology copieda savant infant: Machines could do long math equations instantly and beat anybody in chess, but they cant answer a simple question or walk up a flight of stairs. Asa result, not skilled work done by people without much education (like home health care workers, or fast-foodattendants) have been saved, too. The human half In the 19th century, new manufacturing technology replaced what was then skilled labor. In thesecond half of the 20th century, however, software technology took the place of median-salaried office work.The first wave showed that machines are better at assembling things. The second showed that machinesare better at organizing things. Now data analytics andself-driving cars suggest they might be better at pattern recognition and driving. So what are we better at? The safest industries and jobs are dominated by managers4, health-care workers, and a super-category that includes education, media, and community service.One conclusion to draw from this is that humans are, and will always be, superior at working with, and caringfor other humans11. In this light, automation doesnt makethe world worse. Far from it: it creates new opportunitiesfor human creativity12. But robots are already creeping into diagnostics and surgeries. Schools are already experimenting with software that replaces teaching hours. The fact thatsome industries have been safe from automation for the last three decades3doesnt guarantee that theyll be safefor the next one. It would be anxious enough if we knew exactly which jobs are next in line for automation. The truth is scarier5. We dont really have a clue.2 (Adapted from http://www.businessinsider.com/robots-overtakingamerican-jobs-2014-1) Glossary: savant infant a child with great knowledge and ability to assemble to make something by joining separate parts to creep to move slowly, quietly and carefully According to the first paragraph, robots can be _____ by many names

(AFA - 2015) TEXT I JOBS AT HIGH RISK It is an invisible force that goes by many names.Computerization. Automation. Artificial intelligence. Technology. Innovation. And, everyones favorite,ROBOTS. Whatever name you prefer, some form of it hasbeen stimulating progress and killing jobs from tailors to paralegals for centuries9. But this time is different:nearly half of American jobs today could be automated in a decade or two. The question is: which half? Another way of posing the same question is:Where do machines work better than people?7Tractors are more powerful than farmers8. Robotic arms are stronger and more tireless than assembly-line workers. But in the past 30 years, software and robots havesucceeded replacing aarticular kind of occupation: the average-wage, middle-skill, routine-heavy worker, especially in manufacturing and office administration. Indeed, its projected that the next wave ofcomputer progress1will continue to endanger humanwork where it already has: manufacturing, administrativesupport, retail, and transportation. Most remaining factory jobs are likely to diminish over the next decades. Cashiers, counter clerks, and telemarketers are similarly endangered. On the other hand, health care workers, people responsible for our safety10, and management positions are the least likely to be automated6. Thenext big thing We might be on the edge of an innovating moment in robotics and artificial intelligence. Although the past 30 years have reduced the middle, high- and low-skill jobs have actually increased, as if protected from the invading armies of robots by their own moats.Higher-skill workers have been protected by a kind ofsocial-intelligence moat. Computers are historically good at executing routines, but theyre bad at finding patterns,communicating with people, and making decisions,which is what managers are paid to do. This is whysome people think managersare, for the moment, one ofthe largest categories immune to the fast wave of AI. Meanwhile, lower-skill workers have beenprotected by the Moravec moat. Hans Moravec was a futurist who pointed out that machine technology copieda savant infant: Machines could do long math equations instantly and beat anybody in chess, but they cant answer a simple question or walk up a flight of stairs. Asa result, not skilled work done by people without much education (like home health care workers, or fast-foodattendants) have been saved, too. The human half In the 19th century, new manufacturing technology replaced what was then skilled labor. In thesecond half of the 20th century, however, software technology took the place of median-salaried office work.The first wave showed that machines are better at assembling things. The second showed that machinesare better at organizing things. Now data analytics andself-driving cars suggest they might be better at pattern recognition and driving. So what are we better at? The safest industries and jobs are dominated by managers4, health-care workers, and a super-category that includes education, media, and community service.One conclusion to draw from this is that humans are, and will always be, superior at working with, and caringfor other humans11. In this light, automation doesnt makethe world worse. Far from it: it creates new opportunitiesfor human creativity12. But robots are already creeping into diagnostics and surgeries. Schools are already experimenting with software that replaces teaching hours. The fact thatsome industries have been safe from automation for the last three decades3doesnt guarantee that theyll be safefor the next one. It would be anxious enough if we knew exactly which jobs are next in line for automation. The truth is scarier5. We dont really have a clue.2 (Adapted from http://www.businessinsider.com/robots-overtakingamerican-jobs-2014-1) Glossary: savant infant a child with great knowledge and ability to assemble to make something by joining separate parts to creep to move slowly, quietly and carefully The expression wave of computer progress (reference 1) has the same idea as

(AFA - 2015) TEXT I JOBS AT HIGH RISK It is an invisible force that goes by many names.Computerization. Automation. Artificial intelligence. Technology. Innovation. And, everyones favorite,ROBOTS. Whatever name you prefer, some form of it hasbeen stimulating progress and killing jobs from tailors to paralegals for centuries9. But this time is different:nearly half of American jobs today could be automated in a decade or two. The question is: which half? Another way of posing the same question is:Where do machines work better than people?7Tractors are more powerful than farmers8. Robotic arms are stronger and more tireless than assembly-line workers. But in the past 30 years, software and robots havesucceeded replacing aarticular kind of occupation: the average-wage, middle-skill, routine-heavy worker, especially in manufacturing and office administration. Indeed, its projected that the next wave ofcomputer progress1will continue to endanger humanwork where it already has: manufacturing, administrativesupport, retail, and transportation. Most remaining factory jobs are likely to diminish over the next decades. Cashiers, counter clerks, and telemarketers are similarly endangered. On the other hand, health care workers, people responsible for our safety10, and management positions are the least likely to be automated6. Thenext big thing We might be on the edge of an innovating moment in robotics and artificial intelligence. Although the past 30 years have reduced the middle, high- and low-skill jobs have actually increased, as if protected from the invading armies of robots by their own moats.Higher-skill workers have been protected by a kind ofsocial-intelligence moat. Computers are historically good at executing routines, but theyre bad at finding patterns,communicating with people, and making decisions,which is what managers are paid to do. This is whysome people think managersare, for the moment, one ofthe largest categories immune to the fast wave of AI. Meanwhile, lower-skill workers have beenprotected by the Moravec moat. Hans Moravec was a futurist who pointed out that machine technology copieda savant infant: Machines could do long math equations instantly and beat anybody in chess, but they cant answer a simple question or walk up a flight of stairs. Asa result, not skilled work done by people without much education (like home health care workers, or fast-foodattendants) have been saved, too. The human half In the 19th century, new manufacturing technology replaced what was then skilled labor. In thesecond half of the 20th century, however, software technology took the place of median-salaried office work.The first wave showed that machines are better at assembling things. The second showed that machinesare better at organizing things. Now data analytics andself-driving cars suggest they might be better at pattern recognition and driving. So what are we better at? The safest industries and jobs are dominated by managers4, health-care workers, and a super-category that includes education, media, and community service.One conclusion to draw from this is that humans are, and will always be, superior at working with, and caringfor other humans11. In this light, automation doesnt makethe world worse. Far from it: it creates new opportunitiesfor human creativity12. But robots are already creeping into diagnostics and surgeries. Schools are already experimenting with software that replaces teaching hours. The fact thatsome industries have been safe from automation for the last three decades3doesnt guarantee that theyll be safefor the next one. It would be anxious enough if we knew exactly which jobs are next in line for automation. The truth is scarier5. We dont really have a clue.2 (Adapted from http://www.businessinsider.com/robots-overtakingamerican-jobs-2014-1) Glossary: savant infant a child with great knowledge and ability to assemble to make something by joining separate parts to creep to move slowly, quietly and carefully In the sentence Hans Moravec was a futurist who pointed out that machine technology copied a savant infant [...] the pronoun who can be replaced, with no change in meaning, by