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Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Matemática |
Q3998746
Matemática
Considere uma função quadrática f(x), real de variável real, tal
que f(0) = 2 e f(−1) = f(3) = 0.
O valor máximo dessa função é
O valor máximo dessa função é
Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Matemática |
Q3998745
Matemática
Sejam x e y números naturais não nulos tais que 
A soma dos possíveis valores de x é
Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Matemática |
Q3998744
Matemática
Os números reais x e y são tais que x2 + y2 = 6x + 2y.
O maior valor possível de x é
Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Matemática |
Q3998743
Matemática
O conjunto C = {11, 13, 17, 19, 23, 25, ..., 95, 97} é formado pelos
números naturais de dois algarismos que não são múltiplos nem
de 2 e nem de 3.
A soma dos elementos de C é
A soma dos elementos de C é
Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Matemática |
Q3998742
Matemática
A figura a seguir mostra um corte em uma antena parabólica por
um plano que contém o seu eixo. A seção é uma parábola.
No sistema de coordenadas da figura o foco da antena é o ponto (0, y).
O valor de y é
No sistema de coordenadas da figura o foco da antena é o ponto (0, y).
O valor de y é
Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Matemática |
Q3998741
Matemática
O conjunto C é formado por todos os números inteiros N maiores
que 1000 e menores que 2000 com a seguinte propriedade: N é
formado por três algarismos diferentes, entre os quais um se
repete. Por exemplo, 1383, 1200 e 1451 são elementos de C.
O número de elementos de C é:
O número de elementos de C é:
Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Matemática |
Q3998740
Matemática
A figura abaixo mostra o cubo ABCDEFGH cuja aresta mede 60.
A distância do vértice A à reta EC é, aproximadamente, (
Use o necessário: √2 = 1,41; √3 = 1,73; √6 = 2,45)
A distância do vértice A à reta EC é, aproximadamente, (
Use o necessário: √2 = 1,41; √3 = 1,73; √6 = 2,45)
Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Matemática |
Q3998739
Matemática
Uma escola possui 2 professores de matemática, 3 professores de
português e 4 professores de ciências. Dois desses professores são
escolhidos por sorteio.
A probabilidade de que os dois professores sorteados sejam da mesma matéria é
A probabilidade de que os dois professores sorteados sejam da mesma matéria é
Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Matemática |
Q3998738
Matemática
O valor de 
Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Matemática |
Q3998737
Matemática
A reta r passa pelos pontos (−4, 2) e (2, 6).
O ponto da reta r que possui coordenadas iguais é
Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Matemática |
Q3998736
Matemática
O desenho abaixo representa uma operação de adição entre
quatro números naturais: A, AB, ABC e ABCD. Cada letra
representa um algarismo, letras diferentes representam
algarismos diferentes e A ≠ 0.
O valor de B ‒ C + D ‒ A é:
O valor de B ‒ C + D ‒ A é:
Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Matemática |
Q3998735
Matemática
Uma pirâmide regular tem base quadrada e suas faces laterais são
triângulos isósceles, cada um com base medindo 4 cm e dois lados
iguais medindo 6 cm cada um.
O volume dessa pirâmide em cm3 é aproximadamente
(Use se necessário: √3 = 1,73; √5 = 2,24; √7 = 2,65)
O volume dessa pirâmide em cm3 é aproximadamente
(Use se necessário: √3 = 1,73; √5 = 2,24; √7 = 2,65)
Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Matemática |
Q3998734
Estatística
Em uma das provas de certo concurso as notas dos dez candidatos
foram as seguintes:
7 | 7 | 7 | 7 | 7 | 7 | 7 | 8 | 9 | 10
O desvio padrão dessas notas é
7 | 7 | 7 | 7 | 7 | 7 | 7 | 8 | 9 | 10
O desvio padrão dessas notas é
Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Matemática |
Q3998733
Matemática
Maria ganhou certa quantia. Dessa quantia, retirou 30% para
colocar na poupança. Do restante, retirou 20% para compras de
que precisava e, do que sobrou, retirou 10% para a manutenção
da casa.
Da quantia inicial, Maria ficou ainda com cerca de
Da quantia inicial, Maria ficou ainda com cerca de
Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Matemática |
Q3998732
Matemática
A figura a seguir mostra um quadrado e um pentágono regular com o lado AB em comum.
O ângulo DCB mede
Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Matemática |
Q3998731
Matemática
André e Bruno são irmãos e possuem suas poupanças que, juntas,
dão 1200 reais. Eles compraram um jogo contribuindo, cada um,
com a mesma quantia. Essa quantia é equivalente à quarta parte
da poupança de André e, também, equivalente à sexta parte da
poupança de Bruno mais 25 reais.
O preço do jogo comprado pelos irmãos foi de
O preço do jogo comprado pelos irmãos foi de
Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Matemática |
Q3998730
Matemática
A expressão 
é igual a
é igual a
Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Inglês |
Q3998594
Inglês
Texto associado
Read Text V and answer the question that follows.
Text V
Structural and pedagogical problems
hinder the use of technology
Three out of four teachers in Brazil show support for the use
of artificial intelligence (AI) as a teaching tool. They also say that
the technology has impacted education both positively, with faster
access to information, and negatively, as students lose their focus.
The data can be found in an unprecedented survey by Semesp
Institute, an organization that represents higher education
providers. The study was carried out between March 18 and 31
with 444 public and private school teachers from kindergarten to
high school located in all regions of Brazil.
In the study, 74.8 percent of respondents partially or totally
agree with the use of artificial intelligence in teaching. Despite this,
just over a third (39.2%) of them said they always use it as a
teaching tool.
Even though educators believe it is important to use AI, they
also report structural and pedagogical problems that prevent or
hinder its employment. Further issues were reported in
connection with its excessive use, especially by pupils. Among
these problems are the lack of internet at school, the lack of
training for teachers and also greater difficulty in holding students’
attention.
“I sense students have become more dependent on research
tools and immediate answers and have a hard time having
resilience and patience and acting as problem solvers,” an
anonymous teacher who took part in the survey said.
Another one said: “Technology has advanced, but sometimes
access to it at school is not satisfactory. Poor internet connection.
The computer lab is a restricted space. No Microsoft Office in the
mobile lab. The use of cell phones is impractical as students have
no internet. Now, even the internet is restricted to teachers.”
Just under half of the teachers (45.7%) declared that both
teachers and students have access to computers and the internet
where they teach. Another seven percent answered there is still
no access to technology in their schools.
Teachers also report that technology has made students lose
their focus. “The school can’t keep up with the use of new technologies at the speed that the students can, which leads to a
mismatch between the lesson taught and the lesson that the
students want. The unbridled use of social media and the high level
of exposure of young people to these networks have undermined
teachers’ contact with students,” one of the teachers stated.
From: https://agenciabrasil.ebc.com.br/en/educacao/noticia/2024-05/three-outfour-teachers-brazil-advocate-ai-teaching-tool
The key goal of integrating technology into the Brazilian National
Curriculum is to:
Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Inglês |
Q3998593
Pedagogia
Texto associado
Read Text V and answer the question that follows.
Text V
Structural and pedagogical problems
hinder the use of technology
Three out of four teachers in Brazil show support for the use
of artificial intelligence (AI) as a teaching tool. They also say that
the technology has impacted education both positively, with faster
access to information, and negatively, as students lose their focus.
The data can be found in an unprecedented survey by Semesp
Institute, an organization that represents higher education
providers. The study was carried out between March 18 and 31
with 444 public and private school teachers from kindergarten to
high school located in all regions of Brazil.
In the study, 74.8 percent of respondents partially or totally
agree with the use of artificial intelligence in teaching. Despite this,
just over a third (39.2%) of them said they always use it as a
teaching tool.
Even though educators believe it is important to use AI, they
also report structural and pedagogical problems that prevent or
hinder its employment. Further issues were reported in
connection with its excessive use, especially by pupils. Among
these problems are the lack of internet at school, the lack of
training for teachers and also greater difficulty in holding students’
attention.
“I sense students have become more dependent on research
tools and immediate answers and have a hard time having
resilience and patience and acting as problem solvers,” an
anonymous teacher who took part in the survey said.
Another one said: “Technology has advanced, but sometimes
access to it at school is not satisfactory. Poor internet connection.
The computer lab is a restricted space. No Microsoft Office in the
mobile lab. The use of cell phones is impractical as students have
no internet. Now, even the internet is restricted to teachers.”
Just under half of the teachers (45.7%) declared that both
teachers and students have access to computers and the internet
where they teach. Another seven percent answered there is still
no access to technology in their schools.
Teachers also report that technology has made students lose
their focus. “The school can’t keep up with the use of new technologies at the speed that the students can, which leads to a
mismatch between the lesson taught and the lesson that the
students want. The unbridled use of social media and the high level
of exposure of young people to these networks have undermined
teachers’ contact with students,” one of the teachers stated.
From: https://agenciabrasil.ebc.com.br/en/educacao/noticia/2024-05/three-outfour-teachers-brazil-advocate-ai-teaching-tool
The Brazilian National Curriculum (BNCC) proposes that
technology and digital skills should be:
Ano: 2026
Banca:
FGV
Órgão:
Prefeitura de São José dos Campos - SP
Prova:
FGV - 2026 - Prefeitura de São José dos Campos - SP - Professor II - Inglês |
Q3998592
Inglês
Texto associado
Read Text V and answer the question that follows.
Text V
Structural and pedagogical problems
hinder the use of technology
Three out of four teachers in Brazil show support for the use
of artificial intelligence (AI) as a teaching tool. They also say that
the technology has impacted education both positively, with faster
access to information, and negatively, as students lose their focus.
The data can be found in an unprecedented survey by Semesp
Institute, an organization that represents higher education
providers. The study was carried out between March 18 and 31
with 444 public and private school teachers from kindergarten to
high school located in all regions of Brazil.
In the study, 74.8 percent of respondents partially or totally
agree with the use of artificial intelligence in teaching. Despite this,
just over a third (39.2%) of them said they always use it as a
teaching tool.
Even though educators believe it is important to use AI, they
also report structural and pedagogical problems that prevent or
hinder its employment. Further issues were reported in
connection with its excessive use, especially by pupils. Among
these problems are the lack of internet at school, the lack of
training for teachers and also greater difficulty in holding students’
attention.
“I sense students have become more dependent on research
tools and immediate answers and have a hard time having
resilience and patience and acting as problem solvers,” an
anonymous teacher who took part in the survey said.
Another one said: “Technology has advanced, but sometimes
access to it at school is not satisfactory. Poor internet connection.
The computer lab is a restricted space. No Microsoft Office in the
mobile lab. The use of cell phones is impractical as students have
no internet. Now, even the internet is restricted to teachers.”
Just under half of the teachers (45.7%) declared that both
teachers and students have access to computers and the internet
where they teach. Another seven percent answered there is still
no access to technology in their schools.
Teachers also report that technology has made students lose
their focus. “The school can’t keep up with the use of new technologies at the speed that the students can, which leads to a
mismatch between the lesson taught and the lesson that the
students want. The unbridled use of social media and the high level
of exposure of young people to these networks have undermined
teachers’ contact with students,” one of the teachers stated.
From: https://agenciabrasil.ebc.com.br/en/educacao/noticia/2024-05/three-outfour-teachers-brazil-advocate-ai-teaching-tool
The text concludes that uncontrolled exposure to social media has
shown to be:
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