Questões: Universidade do Estado de Santa Catarina (UDESC) — com gabarito

A medida do lado de um quadrado é igual a 1. Unindo-se os pontos médios de seus lados obtém-se um segundo quadrado. Unindo-se os pontos médios dos lados desse novo quadrado obtém-se um terceiro quadrado, como ilustra a Figura 2, e assim sucessivamente. Os lados desses quadrados formam uma progressão geométrica infinita.



Seja r a reta que passa pelo ponto P (2 - √2,0 ) e tendo coeficiente angular igual à soma da progressão geométrica infinita formada pelos lados dos quadrados mostrados na Figura 2.

O ponto de interseção da reta r com o eixo das ordenadas é:

A expressão



é equivalente a:

A soma de todas as soluções da equação | log₂ (x)| = log₄ (8x) é igual a:

Seja S a soma dos seis primeiros termos de uma progressão geométrica de razão igual a 1/2 . Se log S  = 2 log 2 + log7, então o primeiro termo desta progressão é igual a:

Um estudante ganhou um carro novo de seus pais quando passou no vestibular. Como o pai já havia escolhido o modelo, na concessionária o estudante deveria decidir entre as opções duas ou quatro portas, com os possíveis equipamentos adicionais: ar condicionado; direção hidráulica; câmbio automático; freio ABS e airbag. Para o carro de duas portas, ele podia escolher três adicionais, enquanto que, para o carro de quatro portas, apenas dois adicionais. Como o pagamento foi à vista, a concessionária ofereceu de brinde uma das opções: rodas de liga leve ou equipamento de som. O número total de possibilidades do estudante, ao escolher o carro, foi:

        Text 2

01    Take a dive with hundreds of tropical fish, colorful coral and the world's biggest fish, the
        whale shark, at unspoilt Ningaloo Reef.
        The reef on Western Australia's mid north coast, has gained an impressive reputation as
        one of Earth's last ocean paradise.
05    It's one of the largest fringing reefs in the world and unlike many others; you can get to it
        just by stepping off the beach.
        The marine park stretches 260 kilometers from Bundegi Reef near the town of Exmouth to
        Amherst Point near Coral Bay in the south.
        It reaches nearly 20 kilometers seaward, encompassing a massive 5,000 square
10    kilometers of ocean with 500 species of tropical fish and 220 species of coral in all.
        Nothing can compare to the thrill of swimming beside a whale shark. These docile
        creatures visit the reef each year between April and June.
        Rare turtle species hatch here in late January and February. Watch this amazing natural
        phenomenon on special guided, eco-interactive trails.
15    Accommodation in the area is comfortable and ranges from camping and backpacker style
        to chalets, motels, eco-retreats and self catering apartments.
        It's not all about the water at Ningaloo - go four wheel driving to Cape Range National
        Park to see amazing red rock canyons and gorges.
        Getting there is easy - take a two hour flight north of Perth, or give yourself two days to
        drive there from the capital.
        (www.westernaustralia.com)

According to Text 2, answer the questions below:




According to the text:

...four wheel, in ... four wheel driving ... (line 17); ... two hour; in ... two hour flight ... (line 19); are:

        Text 2

01    Take a dive with hundreds of tropical fish, colorful coral and the world's biggest fish, the
        whale shark, at unspoilt Ningaloo Reef.
        The reef on Western Australia's mid north coast, has gained an impressive reputation as
        one of Earth's last ocean paradise.
05    It's one of the largest fringing reefs in the world and unlike many others; you can get to it
        just by stepping off the beach.
        The marine park stretches 260 kilometers from Bundegi Reef near the town of Exmouth to
        Amherst Point near Coral Bay in the south.
        It reaches nearly 20 kilometers seaward, encompassing a massive 5,000 square
10    kilometers of ocean with 500 species of tropical fish and 220 species of coral in all.
        Nothing can compare to the thrill of swimming beside a whale shark. These docile
        creatures visit the reef each year between April and June.
        Rare turtle species hatch here in late January and February. Watch this amazing natural
        phenomenon on special guided, eco-interactive trails.
15    Accommodation in the area is comfortable and ranges from camping and backpacker style
        to chalets, motels, eco-retreats and self catering apartments.
        It's not all about the water at Ningaloo - go four wheel driving to Cape Range National
        Park to see amazing red rock canyons and gorges.
        Getting there is easy - take a two hour flight north of Perth, or give yourself two days to
        drive there from the capital.
        (www.westernaustralia.com)

According to Text 2, answer the questions below:




The sentence "Nothing can compare to the thrill of swimming beside a whale shark" , means:

        Text 2

01    Take a dive with hundreds of tropical fish, colorful coral and the world's biggest fish, the
        whale shark, at unspoilt Ningaloo Reef.
        The reef on Western Australia's mid north coast, has gained an impressive reputation as
        one of Earth's last ocean paradise.
05    It's one of the largest fringing reefs in the world and unlike many others; you can get to it
        just by stepping off the beach.
        The marine park stretches 260 kilometers from Bundegi Reef near the town of Exmouth to
        Amherst Point near Coral Bay in the south.
        It reaches nearly 20 kilometers seaward, encompassing a massive 5,000 square
10    kilometers of ocean with 500 species of tropical fish and 220 species of coral in all.
        Nothing can compare to the thrill of swimming beside a whale shark. These docile
        creatures visit the reef each year between April and June.
        Rare turtle species hatch here in late January and February. Watch this amazing natural
        phenomenon on special guided, eco-interactive trails.
15    Accommodation in the area is comfortable and ranges from camping and backpacker style
        to chalets, motels, eco-retreats and self catering apartments.
        It's not all about the water at Ningaloo - go four wheel driving to Cape Range National
        Park to see amazing red rock canyons and gorges.
        Getting there is easy - take a two hour flight north of Perth, or give yourself two days to
        drive there from the capital.
        (www.westernaustralia.com)

According to Text 2, answer the questions below:




The word unlike in line 5, of the text, means:

        Text 2

01    Take a dive with hundreds of tropical fish, colorful coral and the world's biggest fish, the
        whale shark, at unspoilt Ningaloo Reef.
        The reef on Western Australia's mid north coast, has gained an impressive reputation as
        one of Earth's last ocean paradise.
05    It's one of the largest fringing reefs in the world and unlike many others; you can get to it
        just by stepping off the beach.
        The marine park stretches 260 kilometers from Bundegi Reef near the town of Exmouth to
        Amherst Point near Coral Bay in the south.
        It reaches nearly 20 kilometers seaward, encompassing a massive 5,000 square
10    kilometers of ocean with 500 species of tropical fish and 220 species of coral in all.
        Nothing can compare to the thrill of swimming beside a whale shark. These docile
        creatures visit the reef each year between April and June.
        Rare turtle species hatch here in late January and February. Watch this amazing natural
        phenomenon on special guided, eco-interactive trails.
15    Accommodation in the area is comfortable and ranges from camping and backpacker style
        to chalets, motels, eco-retreats and self catering apartments.
        It's not all about the water at Ningaloo - go four wheel driving to Cape Range National
        Park to see amazing red rock canyons and gorges.
        Getting there is easy - take a two hour flight north of Perth, or give yourself two days to
        drive there from the capital.
        (www.westernaustralia.com)

According to Text 2, answer the questions below:




What is the correct comparative of superiority form of the adjectives: comfortable, near, rare, easy.

          Text 1
01     There, in the pasture greenery,
         Sun mottling Nature's breast,
         It was the summer wind's song
         That filled me with its crest.
05     Emotion running rampant--
         Rivers to the sea--
         I could not even fathom the flood of you and me.

         But take me in your arms again
         And do not talk of time.
10     Let flesh rub flesh to parchment--
         Pale flowers crushed--
         And grind more mortar for my soul's room . . .
         Paint mirrors for my mind.

(Michela Curtis: www.poetry.com)


According to Text 1, answer the questions below:


The word its in line 4 of the text, refers to:

          Text 1
01     There, in the pasture greenery,
         Sun mottling Nature's breast,
         It was the summer wind's song
         That filled me with its crest.
05     Emotion running rampant--
         Rivers to the sea--
         I could not even fathom the flood of you and me.

         But take me in your arms again
         And do not talk of time.
10     Let flesh rub flesh to parchment--
         Pale flowers crushed--
         And grind more mortar for my soul's room . . .
         Paint mirrors for my mind.

(Michela Curtis: www.poetry.com)


According to Text 1, answer the questions below:


The words: its (in line 4), even (in line 7) and rampant (in line 5), are used in the text as:

          Text 1
01     There, in the pasture greenery,
         Sun mottling Nature's breast,
         It was the summer wind's song
         That filled me with its crest.
05     Emotion running rampant--
         Rivers to the sea--
         I could not even fathom the flood of you and me.

         But take me in your arms again
         And do not talk of time.
10     Let flesh rub flesh to parchment--
         Pale flowers crushed--
         And grind more mortar for my soul's room . . .
         Paint mirrors for my mind.

(Michela Curtis: www.poetry.com)


According to Text 1, answer the questions below:


Analyze the best answer to complete the following sentence, giving it the same meaning as in the text.

"Emotion running __________
Rivers to the sea
I could not even ___________ the __________ of you and me."

Mark the right alternative.

Assinale a alternativa incorreta, sobre o processo de imigração no Brasil, nos séculos XIX e XX.

É incorreto afirmar, em relação à América Latina:

Leia a citação abaixo.



Assinale a alternativa que indica o evento histórico a que se refere o texto.

É incorreto afirmar, considerando a situação do Brasil nos últimos 30 anos:

Sobre conflitos vividos na América Latina, é incorreto afirmar:

É incorreto afirmar, sobre o imperialismo do final do século XIX:

A fotossíntese é um processo de transformação de energia luminosa em energia química, realizada por organismos autotróficos.

Sobre a fotossíntese, é correto afirmar: