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Sejam g e ƒ funções reais, determine a área da região
limitada pelo eixo y, por g(x) = -|x - 3| + 4 e pela assíntota de 
e assinale a opção correta.
Sejam A,B,C,D e X pontos do ℝ3. Considere o tetraedro ABCD e a função real ƒ , dada por 
Sabendo
que o número real m é o valor para que 
pertença ao plano BCD, calcule ƒ'(-m ) e assinale a opção correta.
Nas proposições abaixo, coloque V (Verdadeiro) ou F (Falso) e assinale a opção que apresenta a sequência correta.
( ) Existe pelo menos um a ∈ ℝ e a ≠ 0, para que as curvas y = ax2 e x2 + 2y2 = 1 não se interceptem ortogonalmente.
( ) A negação da proposição (∃x ∈ A ) (p (x)) → (∀x ∈ A ) (~q (x)) é (∃x ∈ A)(p (x)) ∧ (∃x ∈ A)(q (x)).
( ) Se 
, então M2 = 2.
( ) Seja z um número complexo e i a unidade imaginária. Se z = |z|e10, então |eiz| = e|z|sen(0).
A Imagem de 
dada por f(x) = 2cos2(x) +
sen (2x) - 1, é [a, b]. Seja π o plano que passa pelo ponto
A(9,-1,0) e é paralelo aos vetores 
= (0,1,0) e 
= (1,1,1). Calcule a menor distância do ponto P(b/a ,a,1)
ao plano π e assinale a opção correta.
Seja P(x,y) um ponto da elipse 
de focos F1 e
F2 e excentricidade e. Calcule 
e assinale a opção
correta.
Se 
seja k o determinante da matriz 
sendo assim, é correto afirmar que o coeficiente de xk-1 no desenvolvimento de 
é
Complete the paragraph with a proper preposition.
I’m Hannah and I work _______ an Office in London.
During the week, I get up_______six-thirty. I go_______
work by subway, but_______Sundays I like waking up
late because I don’t work_______weekends.
Choose the right option to fill in the gaps with the correct prepositions.
Complete the sentences with the correct use of the Simple Past and the Past Continuous.
- I was waiting for the bus when I___________ (see) her.
- The children ___________ (argue) when the teacher arrived.
- Everyone___________ (listen) to music when the lights ___________. (go) out.
To fill in the gaps respectively, mark the right option.
Complete the dialogue using the right form of the adjectives.
A: Would you like to go to the beach on Friday?
B: Actually, I think Saturday is ___________________ for
me. Friday is my___________________ day.
Choose the item that respectively completes the gaps.
Complete the sentences using an article when necessary.
I- Is Mario_________ honest man?
II- The students wear_________ uniform here.
III- _________ Smiths live next to the supermarket.
IV- __________ Brasília was made the capital ia 1960.
Choose the correct option.
Match the questions to the answers.
(1) Are you on vacation?
(2) Where's she from?
(3) Are you and Ana married?
(4) Is Julie Italian?
( ) Yes, we are.
( ) She’s from Italy.
( ) No, she isn’t.
( ) No, I'm not.
Choose the option with the correct order.
Read the sentences below.
I- Can you give me some information ,please?
II- Those women are my teachers.
III- He doesn't have much money.
IV- Life is great!
Choose the option which defines the underlined nouns as U (uncountable) or C (countable).
Read the sentences below.
I- I work hardly every day.
II- My classmates speak French very well.
III- Ana drives incredibly fast.
IV- Our father is a very carefully driver.
Choose the option according to the correct use of the adverbs and modifiers.
Read the Information in the box below.
The Vikings
Raiders, travelers or brave explorers?
The Vikings sailed the seas, attacked towns, and stole treasures all over Europe between 800 and 1100. They started from Scandinavia and attacked many countries in Europe. They settled in Britain, Ireland and France. They also crossed the Atlantic Ocean and arrived in Iceland and Greenland. They discovered North America but they also traveled east to Russia and south to Arabia.
They were good farmers and excelient shipbuilders. They used their ships for war. They also used them to carry people and goods to new lands. In winter, when there was not much farm work to do, they stayed home and did other interesting jobs. Men made swords to use them in battle. The Vikings liked swords so much they often decorated them with gold and gave them names. Women cooked and made clothes, shoes, and jewelry for themselves,______ children and husbands.
In 866 the Vikings captured an Anglo-Saxon town. They called it Jorvik and it was the capital of the Viking kingdom for 200 years. They made Jorvik rich and one of the most famous cities in Britain. Some years ago, archeologists discovered part of that Viking town in York, the modern city of Jorvik. They found many things such as jewelry, coins and clothes. If you ever go to York and you want to traveli back in time and see how the Vikings lived, visit the Jorvik Centre!
Adapted from Wilson, D. M. (1987) The Vikings, Activity Book, British Museum Press http://www.pi-schools.gr/books/gymnasio/aggl_a_prox/ergas/043-060.pdf
The Vikings used their ships to
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