ingles_mat_afa2005_c11

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COMANDO DA AERONÁUTICA 
DEPARTAMENTO DE ENSINO DA AERONÁUTICA 
ACADEMIA DA FORÇA AÉREA 
 
CONCURSO DE ADMISSÃO AO 
1O ANO DA AFA 2005 
 
 
PROVA DE LÍNGUA INGLESA E MATEMÁTICA 
21 de AGOSTO de 2004 
 
Transcreva este dado para o seu cartão de respostas 
CÓDIGO DA PROVA: 11 
 
ATENÇÃO! 
 
Esta prova contém 60 questões: Língua Inglesa (1 a 30) e 
Matemática (31 a 60). Confira se todas as questões estão 
perfeitamente legíveis. 
 
 
Read the text below and answer questions 01 and 02. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
01 - Mark the option that completes the text in the best way. 
 
It’s a ________ indicated for people ________ have 
________ diseases. ________ it’s necessary caution because 
according to the contra-indications , the ones ________ have 
penicillin hypersensitivity ________ take it. 
It’s important ________ the side effects. Thus, take 
the right dose in order to get ________. 
 
a) prescription / whom / any / Therefore / whose / can’t / 
remembering / best. 
b) recipe / that / some / But / Who / shouldn’t / to remind / 
well. 
c) piece of information / who / some / However / that / 
mustn’t / to remember / better. 
d) piece of advice / whose / any / Although / which / 
mightn’t / reminding / good. 
 
02 - Which sentence(s) below is (are) grammatically correct 
according to the context and the use of If Clause? 
 
I - If you have any contra-indication in relation to penicillin 
hypersensitivity, it’s better not to take it. 
II - It will be supposed that the results won’t be so 
efficient, if the patient wouldn’t take the medicine at 
least 30 minutes before food. 
III - If the side-effects of this remedy were nausea and 
diarrhea rashes it were prudent doesn’t make use of it. 
IV - It won’t be necessary to use the liquid ampicillin if the 
users would prefer to make use of this by intramuscular 
injection. 
V - If the patient is going to be a child under 10 years, he 
or she should have used just half adult dose. 
 
a) Only IV and V. c) Only I. 
b) Only III. d) Only II and IV. 
 
 
Considering the extracts of some texts, answer questions 03, 
and 04 
 
I - The woods were visible from the back windows and it 
was clear why the house was called Commonwood 
House, because there were views of the common from 
all sides. 
II - The hospital where Maggie in Little Dorrit was treated 
for fever is able to provide its impoverished patients 
with fruit and soft drinks... 
III - Most of the work was completed before the start of the 
nineteenth century. Thus the next chapter will focus on 
how land was farmed in Northamptonshire and 
Bedfordshire in the eighteenth century. Changes after 
1700 will not be discussed. 
IV - Immediately after an assault, rape or robbery, victims 
or witnesses can usually summon up a mental image of 
the assailant. But the time they sit down with a sketch 
artist at the police station, their memories often have 
faded. 
(Adapted from Time) 
 
03 - In which extract(s) above you cannot find Passive 
Construction(s)? 
 
a) Only in extracts I and III. 
b) Only in extracts II and IV. 
c) Only in extract IV. 
d) Only in extract III. 
 
 
04 - What are the real topics mentioned in the extracts you’ve 
just read above? 
 
I - The reason why the house was called Commonwood 
House. 
II - The fact that a hospital can feed the poor patient with 
good supply. 
III - How a great part of a work was completed in the 
nineteenth century, how it was farmed in some places 
and the changes they suffered. 
IV - There’s an evidence that after an assault or robbery, 
the victims get frightened of telling the police the true 
facts. 
 
a) I and IV. c) II, III and IV. 
b) I and II. d) I and III. 
 
Ampicilim 
 
Indications: urinary-tract infections, otitis media, sinusitis, 
chronic bronchitis. 
Cautions: history of allergy: renal impairment: erythematous 
rashes common in glandular fever. 
Interactions: Appendix 1 (penicillin) 
Contra-indications: penicillin hypersensitivity. 
Side-effects: nausea, diarrhea: rashes (discontinue 
treatment): rarely, antibiotic-associated colitis. 
Dose: by mouthy, 0.25 – 1 g every six hours, at least 30 
minutes before food. 
By intramuscular injection or intravenous injection or infusion, 
500mg every 4-6 hours: higher doses in meningitis. 
CHILD under 10 years, any route, half adult dose. 
Formatado: Inglês (EUA)
Formatado: Inglês (EUA)
Formatado: Inglês (EUA)
AFA 2005 PROVA DE LÍNGUA INGLESA E MATEMÁTICA - CÓDIGO 11 2 
Read the ad and answer question 05. 
 
Lockheed Martin and Sikorsky. Working together for three 
decades, this team ________(I) and integrated 
__________(II) any other team in the world. That includes 
the SH-60B, ________(III) the new MH-60R and MH60S 
programs. This __________(IV) delivers the proven Naval 
Hawk airframe with advanced multi-mission avionics 
capabilities to the U.S. Navy and navies worldwide – 
together we deliver ________(V) naval capability to 
________(VI) customers. 
 ( SiKorsKy ) 
A United Technology Company 
 
 
05 - Fill in the blanks correctly with grammatical subjects that 
have been asked in the questions below: 
 
I - Use the Present Perfect Tense of the verb to build. 
II - Use a Comparative form of Superiority. 
III - Use a Comparative form of Equality. 
IV - Use the right Possessive case of nouns. 
V - Use the Superlative form of an adjective. 
VI - Use the right Pronoun. 
 
a) has built / more naval helicopters than / as well as / 
team’s synergy / the best / our 
b) have build / many naval helicopters as / so good as / 
teams’ synergy / the better / ours 
c) had build / much more helicopters than / less well as / 
team synergy’s / more and more / us 
d) has builded / less helicopters than / not so bad as / team 
synegys’s / the most / we 
 
 
06 - Which responses would you choose for these questions in 
the dialog below to make it correct? 
 
Larry: “Paola has different customs. Is she organized? 
Sandy: “_______________” 
Larry: “Do you know where ____________ my new ring?” 
Sandy: “Maybe she’s lost it.” 
Doris: “_______________.” 
 
a) She may / she keeps / she should have 
b) She may be / she kept / she might have 
c) She is / does she keep / she might 
d) Yes / did she keep / she may be 
 
 
Read the text below and answer question 07. 
 
A woman was so fed up of having to wait two hours in a 
physician’s waiting room that she billed him $50 an hour for 
her wasted time – and amazingly, he agreed to pay! 
(adapted from The National Enquirer) 
 
 
07 - We could understand from the text that 
 
a) the unlucky woman obliged the man eventually to pay 
her an amount of money for she has been waiting for 
him long hours. 
b) surprisingly a doctor paid a woman for being waiting for 
him such a long time. 
c) the physicist had to apologize to his patient by paying 
her some money because she waited for him a lot. 
d) a cheerful woman got so impatient into the man’s room 
that she made him pay her fifty dollars. 
Read the text below and answer questions 08 to 09 
according to it. 
 
Before the 1930’s folk songs were almost unknown in 
American cities. By the end of World War II , in 1945, young 
people became interested in traditional songs. Perhaps they 
were tired of hit –parade tunes. Perhaps they wanted to 
hear meaningful songs that made sense of them. 
 
08 - How many different prepositions can you find in the 
paragraph? 
 
a) eight 
b) four 
c) five 
d) seven 
 
 
09 - Reading the sentence: “Perhaps they were tired of hit- 
parade tunes”, we can conclude that 
 
a) the Americans weren’t used to listening to new songs on 
the radio but only the live ones. 
b) the American people wanted to hear a different sort of 
rhythm that valued their traditions and was related to 
their way of living. 
c) they didn’t like folk songs and after the Second World 
War these songs became recognized around the world . 
d) in America , they just listened to songs that were 
produced intheir cities and the traditional ones had no 
sense of them. 
 
 
Read the text below and answer questions 10 to 13 
according to it. 
 
 
One day in 1895 a German scientist named Wilhelm 
Roentgen discovered an astonishing thing. He 
______________ with the electron rays, shooting them at a 
coated glass screen. Roentgen happened to pass his hands 
between the rays and the screen. To his amazement, the 
shadow of the bones inside his hand ________________ 
instead ! Most of the rays _______________ right through 
the flesh of his hand lighting the screen, but enough of them 
were stopped by the bones to produce a clear shadow of the 
hand’s skeleton. Roentgen ______________ the X-ray. 
(From ATOMS – The Golden Library Of Knowledge) 
 
10 - Fill in the blanks in the text. Choose the best verbs to 
complete it 
 
a) experimented / appears / passes / discovered 
b) had experimented / appeared / has passed / has 
discovered 
c) is experimenting / is appearing / passed / was 
discovering 
d) was experimenting / appeared / were passing / had 
discovered 
 
 
 
 
 
 
 
 
 
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Formatado: Inglês (EUA)
AFA 2005 PROVA DE LÍNGUA INGLESA E MATEMÁTICA - CÓDIGO 11 3 
11 - The underlined words in the text are respectively 
 
a) gerund form / possessive pronoun / preposition / 
possessive adjective / preposition 
b) adjective / object pronoun / preposition / possessive 
adjective / conjunction 
c) noun / subject pronoun / conjunction / possessive 
pronoun / adverb 
d) continuous tense / adjective pronoun / adverb / 
possessive pronoun / preposition 
 
 
12 - The sentence: ”The rays were stopped by the bones to 
produce a clear shadow of the hand’s skeleton”, in the 
ACTIVE VOICE is 
 
a) To produce the rays by the bones the rays stopped a 
clear shadow of the hand’s skeleton. 
b) A clear shadow of the hand’s skeleton produced the 
bones by the rays stopped. 
c) The bones stopped the rays to produce a clear shadow of 
the hand’s skeleton. 
d) To produce a clear shadow the rays of the hand’s 
skeleton stopped the bones. 
 
13 - It’s correct to say that the text 
 
a) relates an accidental discovery of the x-ray by a German 
scientist, describing how the experiment was done and 
its unexpected result. 
b) details the production of clear shadows at a coated glass, 
appearing the scientist’s skeleton on the screen. 
c) describes how Roentgen was shooting electron rays on 
his hand lighting the bones and the way it made him 
astonished. 
d) shows how an amazing experiment could make a 
scientist become famous only trying to reflect the 
shadow of the flesh of his both hands. 
 
Read the paragraphs below and answer questions 14 and 15, 
according to it. 
 
Once upon a time, suspicious husbands and wives 
called in private detectives to check on a cheating spouse. 
But in today's high-tech world, where the Internet fuels 
online chatting and many affairs, a market for electronic 
spying has developed. 
Web sites describe a variety of products that can be 
used for tracking a spouse's e-mails and online chats, 
including a great variety of vehicle trackers and computer 
spying programs. Founded by a California man whose wife of 
23 years left him after meeting a man online, 
Chatcheaters.com averages 400 visitors (mostly women) a 
day. 
(Adapted form Online Detectives, Speak Up, ed. 202, 
mar. 2004) 
 
 
 
 
 
 
 
 
 
 
 
 
14 - Mark the option that shows the correct statements according 
to the reading: 
 
I - Spying activities have improved as well as the 
technology. 
II - Chatcheaters is a web site that concerns unfaithful 
matters. 
III - The news is a result of a wife who was left for a 
younger woman. 
IV - The Internet has become a way of finding partners. 
 
a) All the statements are correct. 
b) Only statements I and II are correct. 
c) Only statement III is incorrect. 
d) Statements II and III are incorrect. 
 
 
15 - The underlined expressions from the text (once upon a time 
and but) mean according to the context, respectively: 
 
a) something happened a long time ago / opposite 
information 
b) repeated action / connecting phrases 
c) at the same time / explaining why 
d) sometimes but not often / showing surprise 
 
Read the part of the lyrics and answer questions 16 and 17: 
 
Slip inside the eye of your mind 
Don't you know you might find 
A better place to play 
You said that you've never been 
But all the things that you've seen 
They slowly fade away 
(Don’t look back in anger – Oasis) 
 
 
16 - Mark the option that justifies the use of the underlined 
verbal tense in the context: 
 
a) indefinite time 
b) reported speech 
c) finished action 
d) beginning of an action 
 
 
17 - The sentence “They slowly fade away” means: 
 
a) The places are sometimes harmful to people. 
b) The things gradually disappear. 
c) Persons in love may die. 
d) Minds are mainly confused. 
 
 
18 - Complete the dialog with the appropriate sequence of 
prepositions/adverbs: 
 
Mike: “Have you ________ traveled abroad?” 
Joshua: “Unfortunately, ________. ________ I’ve started 
studying a foreign language I want this kind of effective 
practice. I hope I won’t have to wait ________ a long time.” 
 
a) ever / yet / Already / since 
b) already / never / Ever / for 
c) ever / never / Since / for 
d) already / yet / For / since 
 
 
Formatado: Inglês (EUA)
Formatado: Inglês (EUA)
Formatado: Inglês (EUA)
AFA 2005 PROVA DE LÍNGUA INGLESA E MATEMÁTICA - CÓDIGO 11 4 
Read the text below and answer question 19 according to it. 
 
For seven frustrating years, Ayrton Senna’s dream of a 
victory at home, in the Brazilian Grand Prix, eluded him. He 
finally won the race in 1991, but only after a cliffhanger 
finish and typical heroics. He was leading comfortably, with 
only a few kilometers to go, when the gearbox of his car 
jammed.By the last lap only one gear was functioning, but 
Senna wrestled his McLaren-Honda to the checkered flag. So 
exhausted he could barely lift his arms, grimacing from the 
pain, he hoisted the trophy and the flag. 
(Adapted from Speak up) 
 
 
19 - In the sentence “So exhausted he could barely lift his arms, 
grimacing from the pain, he hoisted the trophy and the flag”, 
the underlined word is 
 
a) a verb expressing that he could just put his hands high to 
show happiness. 
b) an adverb and it means that Senna was able only to lift 
his arms grimacing from the pain. 
c) an adjective which shows how painful his movement of 
grimacing his face was. 
d) a pronoun used to explain how Senna presents the flag 
in order to show his hoisted victory. 
 
Read the text below and answer questions 20 and 21 
according to it. 
 
“Houve um momento de silêncio, em que Augusto 
passeou pela sala inquieto. Finalmente, veio sentar-se de 
novo junto de Leopoldo. 
 É verdade – disse , não é a minha cabeça, a causa 
está no coração. Não posso mais esconder meus 
sentimentos. Leopoldo, aquela menina, que aborreci no 
primeiro instante, quando a vi de joelhos, banhando os pés 
de sua ama, plantou no meu coração um sentimento muito 
forte. Amo-a! Tudo naquela ilha fatal se combinou para 
enfeitiçar-me, tudo!” 
(MACEDO, Joaquim Manoel de, A Moreninha ) 
 
 
20 - From the paragraph above we may conclude that Augusto 
 
a) from the moment the girl was bathing her mistress feet 
on, he couldn’t help loving her even after he had bored 
her. 
b) loved watching the girl’s moistening her mother’s feet 
that’s why he got so impressed with her. 
c) walked around the room trying to explain how deep his 
feeling in relation to that girl was. 
d) fell in love with the girl because she was washing her 
baby-sitter’s feet and he had regretted to hurt her 
feelings. 
 
 
21 - “Não posso mais esconder meus sentimentos, Leopoldo.” 
The Indirect Speech of this sentence inEnglish is 
 
a) Leopoldo said to Augusto that he mustn’t hid his feelings. 
b) Leopoldo asked Augusto if his feelings shouldn’t be 
hidden by him. 
c) Augusto said that he wouldn’t hid his feelings at all. 
d) Augusto told Leopoldo that his feelings could not be 
hidden anymore. 
 
 
22 - All the sequences of nouns below are in the plural form, 
except one. Mark it. 
 
a) sheep / series / women / loaves / fruit 
b) means / children / mice / lice / wolves 
c) geese / thieves / oxen / buzzes / feet 
d) news / electronics / measles / nephew / widower 
 
 
Observe the cartoon below and answer questions 23 and 24 
according to it 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
"I don't care what planet you're from. You can't run around 
Earth stark naked!" 
 
23 - Which sentence has the same idea as the modal can’t in the 
dialogue above? 
 
a) You don’t have to run around Earth... 
b) You mustn’t run around Earth... 
c) You needn’t run around Earth... 
d) You aren’t able to run around Earth... 
 
 
24 - What’s the best definition for the sentence “I don’t care” in 
the context? 
 
a) It’s a difficult situation if someone is naked in front of 
me. 
b) I don’t have to take care of people who walk naked. 
c) It really upsets me when someone comes naked from 
another planet. 
d) It’s not important if someone comes from a different 
planet. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Formatado: Inglês (EUA)
Formatado: Inglês (EUA)
Formatado: Inglês (EUA)
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AFA 2005 PROVA DE LÍNGUA INGLESA E MATEMÁTICA - CÓDIGO 11 5 
25 - Mark the alternative that best completes the text below: 
 
“Would you like to travel back in time and see knights in 
armor fighting battles? Or go forward to the 21st century and 
see the world of the future? 
 
Time travel ________ the dream of science-fiction writers 
for many years. Perhaps the first story about time travel was 
The Time Machine by H.G. Wells, but there has been many 
more stories, films and TV series since then. In the movie 
BACK TO THE FUTURE, Michael J. Fox plays a teenager who 
accidentally travels back 30 years in time. There he meets 
his parents, ________ are still teenagers and ________ in 
love yet. 
He has to help them get together, because if they don’t 
get married, he _______ exist! When he gets back to the 
present, he finds that he has improved their lives – and his 
own. 
You may think that time travel is just fantasy, but some 
scientists believe it’s possible – at least traveling into the 
future. 
(adapted from the Internet) 
 
a) was / that / have fallen / wouldn’t 
b) has been / who / haven’t fallen / won’t 
c) is / whom / have fallen / won’t 
d) have been / in which / haven’t fallen / would 
 
 
26 - In the text above, the pronoun they in the 8th line refers to: 
 
a) H.G.Wells and Michael J. Fox 
b) M.J.Fox’s parents in the film 
c) The science-fiction writers 
d) The films about science-fiction 
 
 
Read the dialogue and answer questions 27 and 28 
 
A: “Sue has been playing volleyball a lot recently”! 
B: “That’s because she wants to be a professional.” 
 
 
27 - Mark the option that best explains the use of the underlined 
verb tense. 
 
a) It expresses a habit or a regular past activity. 
b) It’s a situation that started and finished in the past. 
c) It’s an activity that started in the past and hasn’t finished 
yet. 
d) The action is happening right now and will go on in a 
near future. 
 
 
28 - Mark the correct question tag for the second sentence: 
 
a) Hasn’t that? c) Doesn’t she? 
b) Isn’t she? d) Doesn’t that? 
 
 
 
 
 
 
 
 
 
29 - Read the following article and answer questions 29 and 30 
according to it. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
The Origin of the Names of the Months 
 
January Janus, the Roman god of doors and gates 
Frebruary Februa, the Roman period of purification 
March Mars, Roman god of war 
April aprerire, the Latin word which means to 
open: 
April was the month when spring began 
May Maia, Roman goddess of growth 
June Juno, Roman goddess of marriage 
July After Julius Caesar 
August After Augustus Caesar, first emperor of 
Rome 
September septem, Latin for seven* 
October octo, Latin for eight* 
November novem, Latin for nine* 
December decem, Latin for ten* 
 
* September, October, November, and December were 
originally the seventh, eighth, ninth, and tenth months of 
the year. 
 
From the article we can conclude that: 
 
I - one third of the names were created to celebrate the 
gods or goddesses. 
II - astronomers wanted to praise only Caesar. 
III - there was a concern about cardinal numbers. 
IV - the names of the months have no relation to some 
ancient gods. 
 
a) only one of the sentences is correct. 
b) only two of them are incorrect. 
c) only three of them are correct. 
d) all of them are correct. 
 
 
30 - The preposition FOR referred to the months from September 
to December in the text is used to show 
 
a) a period of time. 
b) how some words are derived from Latin. 
c) a relation among all months and numbers. 
d) the ways in which Latin and English were not linked. 
 
 
 
 
 
 
 
Formatado: Inglês (EUA)
Formatado: Inglês (EUA)
AFA 2005 PROVA DE LÍNGUA INGLESA E MATEMÁTICA - CÓDIGO 11 6 
MATEMÁTICA 
 
 
31 - Considere um subconjunto A contido em �* e constituído 
por y elementos dos quais 
 
13 são múltiplos de 4 
7 são múltiplos de 10 
5 são múltiplos de 20 e 
9 são números ímpares. 
 
É correto dizer que y é um número 
 
a) par menor que 19 c) primo maior que 21 
b) ímpar entre 10 e 20 d) múltiplo de 12 
 
 
32 - Seja: A = {x � �* | 
x
24
= n e n � �} 
Seja: B = {x � �+ | 
9x2
4x3
+
+
 – 1 < 0} 
 
É correto afirmar que 
 
a) B – A = {0} c) BA ⊃ 
b) A ∪ B tem 8 elementos d) A ∩ B = B 
 
 
33 - Considere P1, P2, P3, P4, ..., Pn os n primeiros números 
naturais primos consecutivos com n ≥ 5. Se 
n
n
4
4
3
3
2
21 P.....P.P.P.Px = e y = P1.P2.P3.P4 . ... . Pn, 
então o número total de divisores positivos de 
y
x
é dado por 
 
a) (n + 1)! c) n! + 1 
b) n! d) (n – 1)! 
 
 
34 - Considere i2 = –1 e α ∈ [0, 2π], 
2
π≠α e 
2
3π≠α 
Se z = tg α + i, então a soma dos valores de α para os 
quais |z| = 2 é igual a 
 
a) 2π c) 4π 
b) 3π d) 5π 
 
 
35 - Considere o número complexo z tal que i2zz −=+ , onde 
1i −= e identifique entre as opções abaixo, as que são 
corretas. 
 
(01) O afixo de z é ponto do 1o quadrante. 
(02) 
1002
4
3
z 




 − é real positivo. 
(04) O menor inteiro positivo n para o qual 
n
4
1
z 




 + é real 
negativo pertence ao intervalo ]2, 5[ 
 
A soma das opções corretas é igual a 
 
a) 6 c) 3 
b) 5 d) 2 
 
 
36 - Escolha a opção INCORRETA. 
 
a) O polinômio P(x) = x5 – 12x4 + 2x3 – 1 tem pelo menos 
uma raiz real. 
b) Toda equação polinomial de grau n admite, no máximo, n 
raízes reais. 
c) Toda equação polinomial de grau n admite exatamente n 
raízes complexas. 
d) Se α e β são números reais positivos e a equação 
αx3 – αx2 + βx – β = 0 admite duas raízes simétricas, 
então todas as suas raízes são reais. 
 
 
37 - Três crianças A, B e C vão dividir entre si 450 balas da 
seguinte maneira: A recebe uma bala; B, duas e C, três. 
Repetindo-se o processo, A recebe quatro balas; B, cinco e 
C, seis e, novamente, A recebe sete e assim por diante, até 
que não haja mais balas para continuar o processo. A 
criança seguinte, então, receberá as balas restantes. 
 
Com base nessas informações, é correto afirmar que 
 
a) o número de balas restantes foi 29 e quem recebeu foi a 
criança B. 
b) as crianças A e C, juntas, receberam 300 balas. 
c) a criança B recebeu 10 balas a mais que a criança A. 
d) o maior número de balas que uma criança recebe antes 
da conclusão do processo é 15. 
 
 
38 - Uma prova consta de 3 partes, cada uma com 5 questões. 
Cada questão, independentemente da parte a que pertença,vale 1 ponto, sendo o critério de correção “certo ou errado”. 
O número de maneiras diferentes de se alcançar 10 pontos 
nessa prova, se devem ser resolvidas pelo menos 3 
questões de cada parte e 10 questões no total, é igual a 
 
a) 75 c) 1500 
b) 150 d) 1600 
 
 
39 - Dentro de uma caixa há nove etiquetas. Cada etiqueta 
recebe um número de 01 a 09, sem repetir nenhum. 
Retira-se três delas, uma a uma, sem reposição. A 
probabilidade de que os três números correspondentes às 
etiquetas retiradas sejam, nesta ordem, ÍMPAR – PAR – 
ÍMPAR ou PAR – ÍMPAR – PAR é de 
 
a) 
28
1
 c) 
81
20
 
b) 
18
5
 d) 
36
5
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
AFA 2005 PROVA DE LÍNGUA INGLESA E MATEMÁTICA - CÓDIGO 11 7 
40 - Analise as afirmativas abaixo e classifique-as em (V) 
verdadeiras ou (F) falsas. 
 
( ) No desenvolvimento de ( )7kx2 + , k ∈ �*, o coeficiente 
numérico do termo em x4 é quatro vezes o coeficiente 
numérico do termo em x3. Então k vale 
4
1
 
( ) Sejam m e p números inteiros positivos, tais que 
p1m ≥− . Então, 





+





−
−
+





−
−
p
m
1p
1m
2p
1m
 é igual a 





 +
p
1m
 
( ) Se 1023
n
n
...
3
n
2
n
1
n
=





++





+





+





, o valor de n é igual 
a 10 
 
A seqüência correta é 
 
a) V, V, V c) V, F, F 
b) F, F, V d) F, V, V 
 
41 - Considere α � [0,2π[ e π+π≠α k
2
, k � � e ln x, o logaritmo 
neperiano de x (x > 0). Calcule o valor do determinante 
)cos(sen
)sen(xln
sec
xln
D
α−α
α−
α= 
 
É correto afirmar que o valor de D 
 
a) depende do ângulo α 
b) nunca será nulo. 
c) será positivo ∗+∈∀ �x 
d) será negativo se 0 < x < 1 
 
 
42 - Considere o sistema 



=+−
=+−
nmzy6x3
6z10y4x2
 em que m e n são 
números reais e x, y e z são incógnitas. Para que este 
sistema seja possível e indeterminado deve-se ter 
 
a) m = 15 e n = 9 c) m ≠ 15 e n ≠ 9 
b) m = 15 e n qualquer d) m ≠ 15 e n = 9 
 
 
43 - Considere duas circunferências de mesmo raio, sendo 
x2 + y2 – 4x – 8y + 4 = 0 a equação da primeira e C2(4,2), o 
centro da segunda. Se a reta s contém uma corda comum a 
ambas circunferências, é FALSO que s 
 
a) é perpendicular à bissetriz dos quadrantes pares. 
b) tem declividade positiva. 
c) admite equação na forma segmentária. 
d) tem coeficiente linear nulo. 
 
 
44 - Dados os conjuntos A e B, tais que 
A = {(x, y) � �2 | x2 + y2 ≤ 9} e 
B = {(x, y) � �2 | x – y ≤ m, m � �} 
É correto afirmar que 
 
a) A e B são disjuntos se m = 23− 
b) A ∩ B ≠ ∅ se m ≥ 23 
c) A é subconjunto de B se |m| < 3 2 
d) A e B nunca terão apenas um ponto comum. 
45 - Analise as proposições abaixo, classificando-as em (V) 
verdadeiras ou (F) falsas. 
 
( ) Considere a circunferência λ e a hipérbole 2y2 – x2 = 8 
tendo mesmo centro. Se λ passa pelos focos da 
hipérbole, uma de suas equações é x2 + y2 = 12 
( ) Numa hipérbole equilátera, uma das assíntotas tem 
coeficiente angular igual a 
2
2
 
( ) A excentricidade da elipse x2 + 4y2 = 4 é igual a 
2
3
 
 
Tem-se a seqüência 
 
a) V, F, V c) F, V, F 
b) F, F, V d) V, V, F 
 
 
46 - Seja f a função real cujo gráfico se apresenta a seguir: 
 
 
 
 
 
 
 
 
 
 
 
 
 
Analisando o gráfico, é INCORRETO afirmar que 
 
a) f(f(1)) = f(0,5) 
b) f(x) + 1 > 0, ∀ x � � 
c) f(0) ≤ f(x), ∀ x � � 
d) se g(x) = f(x) – 1, então 




=−
2
5
f)2(g 
 
47 - Observe os gráficos abaixo, das funções f e g, definidas no 
intervalo [0,1] 
 
 
 
 
 
 
 
 
 
 
 
 
 
Com base nos gráficos, assinale a alternativa FALSA . 
 
a) g(f(0,4)) ≥ g(f(x)), ∀ x � [0,1] 
b) g(f(0,05)) > g(f(0,1)) 
c) g(g(x)) = x, ∀ x � [0,3; 0,8] 
d) g(f(0,6)) > g(f(1)) 
 
 
 
 
 
 
 
AFA 2005 PROVA DE LÍNGUA INGLESA E MATEMÁTICA - CÓDIGO 11 8 
48 - Dada a função real f definida por f(x) = x 2 , considere a 
função real g definida por g(x) = f(x+m) + k, sendo m e 
k � �. 
 
É INCORRETO afirmar que 
 
a) o gráfico da função g em relação ao gráfico da função f é 
deslocado k unidades para cima, se k > 0, e m unidades 
para a direita, se m < 0 
b) a equação do eixo de simetria da parábola que 
representa g é dada por x = m 
c) se m = 0 e k = 1, então o conjunto imagem de g é dado 
por Im = {y � � | y ≥ 1} 
d) se m = –2 e k = –3, então as coordenadas do vértice da 
parábola que representa g são (–m, k) 
 
49 - Considere as funções f, g e h, todas de domínio [ ]b,a e 
contra-domínio [ ]d,c , representadas através dos gráficos 
abaixo. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Com base nos gráficos, é correto afirmar que 
 
a) f é uma sobrejeção, g não é uma injeção, h é uma 
sobrejeção. 
b) f é uma sobrejeção, g é uma injeção, h não é uma 
sobrejeção. 
c) f é uma injeção, g não é uma sobrejeção, h é uma 
bijeção. 
d) f é uma bijeção, g não é uma injeção, h não é uma 
sobrejeção. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
50 - Considere a função f(x) = 



<≤−−
≤≤
0x2se,2
2x0se,1
 
A função g(x) = |f(x)| –1 terá o seguinte gráfico: 
 
a) c) 
 
 
 
 
 
 
 
 
 
b) d) 
 
 
 
 
 
 
 
 
 
 
51 - Os valores de x que satisfazem a equação 2x1x IIII =++ 
têm produto igual a 
 
a) 
256
81− c) 
16
9− 
b) 
64
27− d) 
4
3− 
 
 
52 - A soma dos números inteiros que satisfazem a sentença 
3 ≤ |2x – 3| < 6 é um número 
 
a) ímpar. c) divisível por 3 
b) primo. d) que é divisor de 7 
 
 
53 - Uma casa que custa R$ 50.000,00 à vista pode ser 
comprada conforme um dos dois financiamentos abaixo: 
 
I - 50% de entrada e o restante, ao final de 2 meses, com 
juros compostos de 5% ao mês. 
II - R$ 20.000,00 de entrada e uma parcela de 
R$ 36.300,00, ao final de x meses com juros 
compostos de 10% ao mês. 
 
De acordo com a situação acima, é FALSO afirmar que 
 
a) o financiamento I é mais vantajoso que o financiamento 
II 
b) o valor pago a prazo no financiamento II corresponde a 
72,6% do preço da casa à vista. 
c) o valor dos juros do financiamento I, corresponde a 5,2% 
do valor da casa à vista. 
d) quem optar pelo financiamento II pagará a parcela de 
R$ 36.300,00 ao final de dois meses. 
 
 
 
 
 
 
 
AFA 2005 PROVA DE LÍNGUA INGLESA E MATEMÁTICA - CÓDIGO 11 9 
54 - O domínio da função real definida por f(x) = xax 2xlog1 a −+ 
é 
 
a) a 22 ax −≤≤ se 0 < a < 1 
b) 0 < x 2a−≤ ou 2ax ≥ se 0 < a < 1 
c) a 1aseax 22 >≤≤ − 
d) x < a 2− ou x 2a> se a 1> 
 
 
55 - Sabendo que o gráfico abaixo é da função y = a + sen bx, 
pode-se afirmar que a + b é um número 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
a) par. c) divisor de 18 
b) primo. d) múltiplo de 7 
 
 
56 - Sabendo que 0 < x < 
2
π
, analise as proposições e 
classifique-as como verdadeiras (V) ou falsas (F). 
 
( ) Se π=+α 2x , então, tg x = –tg α 
( ) Se 
2
x
π=+α , então, sec x = cossec α 
( ) Sendo sen 




 −π x
2
= 
5
3
, então cos ( )x−π =
5
3
 
( ) A função f(x) = sen 




 π−
2
x + 2 é idêntica a função 
g(x) = 2 – cos x 
 
Tem-se a seqüência 
 
a) V, V, V, V. c) F, V, F, F. 
b) V, F, F, F. d) V, V, F, V. 
 
 
57 - Considere m a raiz da equação 
cos2x + 3sen 2 x – senx – 3 = 0 no intervalo [ ]π2,0 . O 
número cotg m – sec 2m é 
 
a) 0 c) 1 
b) –1 d) 
3
3− 
 
 
 
 
58 - Considere o triângulo ABC, de lados 15AB = , 10AC = , 
12BC = e seu baricentro G. Traçam-se GE e GF paralelos 
a AB e AC, respectivamente, conforme a figura abaixo. O 
perímetro do triângulo GEF é um número que, escrito na 
forma de fração irredutível, tem a soma do numerador com o 
denominador igual a 
 
 
 
 
 
 
 
 
 
 
 
 
 
a) 43 c) 38 
b) 40 d) 35 
 
 
59 - Um recipiente no formato de uma superfície de um cone 
circular reto, conforme figura, tem a sua superfície lateral 
desenvolvida em um semicírculo de área igual a 18π cm2. 
Se tal recipiente, em seu interior, armazena um líquido até 
os 
3
2
 de sua altura, pode-se dizer que o volume do líquidoarmazenado, em cm3, é igual a 
 
 
 
 
 
 
 
 
 
 
 
 
a) 
3
32π
 c) 
3
38π
 
b) 32π d) 38π 
 
 
60 - A diagonal de um paralelepípedo reto retângulo mede 
3 cm35 e suas dimensões são proporcionais a 1, 3 e 5. A 
fração irredutível 
β
α
 que representa a razão entre a área 
total do paralelepípedo e seu volume é tal que 
 
a) α e β são dois números primos. 
b) 100=β+α 
c) 11=β−α 
d) β – α = –1 
 
 
CONCURSO DE ADMISSÃO À AFA 2005 
PROVAS DE LÍNGUA INGLESA E MATEMÁTICA 
GABARITO PROVISÓRIO 
CÓDIGO 11 CÓDIGO 12 CÓDIGO 13 
QUESTÃO RESPOSTA QUESTÃO RESPOSTA QUESTÃO RESPOSTA 
01 C 01 D 01 A 
02 C 02 D 02 A 
03 C 03 D 03 A 
04 B 04 C 04 D 
05 A 05 B 05 C 
06 B 06 C 06 D 
07 B 07 C 07 D 
08 B 08 C 08 D 
09 B 09 C 09 D 
10 D 10 A 10 B 
11 B 11 C 11 D 
12 C 12 D 12 A 
13 A 13 B 13 C 
14 C 14 D 14 A 
15 A 15 B 15 C 
16 A 16 B 16 C 
17 B 17 C 17 D 
18 C 18 D 18 A 
19 B 19 C 19 D 
20 A 20 B 20 C 
21 D 21 A 21 B 
22 D 22 A 22 B 
23 B 23 C 23 D 
24 D 24 A 24 B 
25 B 25 C 25 D 
26 B 26 C 26 D 
27 C 27 D 27 A 
28 C 28 D 28 A 
29 B 29 C 29 D 
30 B 30 C 30 D 
31 D 31 A 31 B 
32 A 32 B 32 C 
33 B 33 C 33 D 
34 C 34 D 34 A 
35 B 35 C 35 D 
36 D 36 A 36 B 
37 C 37 D 37 A 
38 C 38 D 38 A 
39 B 39 C 39 D 
40 D 40 A 40 B 
41 D 41 A 41 B 
42 A 42 B 42 C 
43 C 43 D 43 A 
44 B 44 C 44 D 
45 A 45 B 45 C 
46 B 46 C 46 D 
47 D 47 A 47 B 
48 B 48 C 48 D 
49 D 49 A 49 B 
50 A 50 B 50 C 
51 A 51 B 51 C 
52 C 52 D 52 A 
53 C 53 D 53 A 
54 A 54 B 54 C 
55 A 55 B 55 C 
56 D 56 A 56 B 
57 C 57 D 57 A 
58 B 58 C 58 D 
59 C 59 D 59 A 
60 D 60 A 60 B