Prova de 2019: Universidade Estadual de Campinas (UNICAMP) — questões com gabarito

A figura a seguir exibe um pentágono em que quatro lados consecutivos têm comprimentos a, b, c e d. Se a sequência (a, b, c, d) é uma progressão geométrica de razão q > 1, então tan 0 é igual a

Considere um paralelepípedo retângulo, cujas arestas têm comprimento 6 cc, 8 cc e 10 cc, e um triângulo cujos vértices são os centros (intersecção das diagonais) de três faces de dimensões distintas, como ilustra a figura a seguir. O perímetro P desse triângulo é tal que

Leia o texto a seguir e observe a figura do Homem Vitruviano.

Ao longo da vida, cada vez mais, Leonardo da Vinci passou a perceber que a matemática era a chave para transformar suas observações em teorias. Não existe certeza na ciência em que a matemática não possa ser aplicada, declarou.

(Adaptado de Walter Isaacson, Leonardo da Vinci. Rio de Janeiro: Intrínseca, 2017, p. 52.)

Assinale a alternativa que expressa adequadamente a correlação entre o texto e a imagem.

A propaganda através de inscrições e desenhos em muros e paredes é uma parte integrante da Paris revolucionária de Maio de 1968. Ela se tornou uma atividade de massa, parte e parcela do método de autoexpressão da Revolução.

Considerando o texto e a imagem anteriores, assinale a alternativa correta sobre o movimento de Maio de 1968.

Touching thermal-paper receipts could extend BPA retention in the body

When people handle receipts printed on thermal paper containing the endocrine disruptor bisphenol A (BPA), the toxic chemical could linger in the body for a week or more. Jonathan W. Martin of Stockholm University and Jiaying Liu of the University of Alberta asked six male volunteers to handle paper containing isotopically labeled BPA for five minutes. The volunteers then put on nitrile gloves, wore them for two hours, removed them, and washed their hands with soap. Afterward, the researchers measured the labeled BPA and its metabolites in the volunteers’ urine regularly for two days and then once again a week later. The study only traced the isotopically labeled (deuterated) BPA and its metabolites, so any additional BPA exposure from other sources was not monitored.

(Deirdre Lockwood, Touching thermal-paper receipts could extend BPA retention in the body. Chemical & Engineering News, 04/09/2017.)

O texto discorre sobre uma pesquisa cujo objetivo foi

Largest prime number discovered: with more than 23m digits

Known simply as M77232917, the figure is arrived at by calculating two to the power of 77,232,917 and subtracting one, leaving a gargantuan string of 23,249,425 digits. The result is nearly one million digits longer than the previous record holder discovered in January 2016. The number belongs to a rare group of so-called Mersenne prime numbers, named after the 17th century French monk Marin Mersenne. Like any prime number, a Mersenne prime is divisible only by itself and one, but is derived by multiplying twos together over and over before taking away one. The previous record-holding number was the 49th Mersenne prime ever found, making the new one the 50th.

(Adaptado de Ian Sample, “Largest prime number discovered: with more than 23m digits”. The Guardian, 04/ 01/2018.)

Considerando as informações contidas no excerto anterior, qual dos números a seguir é um primo de Mersenne?

O post anterior aponta

Este cartum foi criado pelo norte-americano Bruce Beattie, em 2011. Nele, o cartunista faz uso da ironia para

We raise girls to cater to the fragile egos of men. We teach girls do shrink themselves, to make themselves smaller. We tell girls ‘You can have ambition, but not too much’. ‘You should aim to be successful, but not too successful, otherwise you will threaten the man’. (…) We teach girls shame – ‘Close your legs, cover yourself!’. We make them feel as though by being born female, they’re already guilty of something. And so, girls grow up to be women who cannot see they have desire. They grow up to be women who silence themselves. They grow up to be women who cannot say what they truly think. And they grow up – and this is the worst thing we do to girls – to be women who turn pretense into an art form.

(Adaptado da palestra “We should all be feminists”, 15/07/2009. Disponível em https://www.youtube.com/watch?v=hg3umXU_qWc&t=797s. Acessado em 14/05/2018.)

O texto anterior reproduz trechos de uma palestra proferida pela escritora nigeriana Chimamanda Adichie em 2009. Segundo a autora, o fato de serem criadas para agradar aos homens faz com que as mulheres

Os dizeres da camiseta

‘Yes, I’m Italian – but I’m not loud, I don’t gesticulate and I’m not good with pizza’

Elena Ferrante

I love my country, but I have no patriotic spirit and no national pride. What’s more, I digest pizza poorly, I eat very little spaghetti, I don’t speak in a loud voice, I don’t gesticulate, I hate all mafias, I don’t exclaim “Mamma mia!” National characteristics are simplifications that should be contested. Being Italian, for me, begins and ends with the fact that I speak and write in the Italian language.

Put that way it doesn’t seem like much, but really it’s a lot. A language is a compendium of the history, geography, material and spiritual life, the vices and virtues, not only of those who speak it, but also of those who have spoken it through the centuries. When I say that I’m Italian because I write in Italian, I mean that I’m fully Italian in the only way that I’m willing to attribute to myself a nationality. I don’t like the other ways, especially when they become nationalism, chauvinism, and imperialism.

(Adaptado de Elena Ferrante, ‘Yes, I´m Italian – but I´m not loud, I don´t gesticulate and I´m not good with pizza’, The Guardian, 24/02/2018.)

Transcrevem-se, a seguir, versos de canções brasileiras e de um poema de Vinícius de Moraes. Assinale a alternativa que melhor exemplifica as afirmações de Elena Ferrante.