Autor: Paulo Ricardo | Publicado: 2013-06-02T16:50:00-07:00


E. M. EDILSON VIGNOLI MARINS



EXERCÍCIOS DE REVISÃO PARA A AVALIAÇÃO DO 2º
BIMESTRE / 2013

9º ANO





1.
Ao quadrado de um número você adiciona 7 e obtém sete vezes o número, menos 3.
A forma normal da equação de 2º grau que pode formar com os dados desse
problema é:

a)
x² – 7x + 10 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; c)
7x² – x + 10

b)
– x² + 7x + 10&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; d)
– 7x² + x + 10



2.
O valor da raiz quadrada de 0,444... é:

a)
0,222...&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; b) 0,333...&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; c) 0,444...&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; d) 0,666...



3.
Uma cultura de certa bactéria, mantida sob condições ideais, triplica o seu
volume a cada dia. Se o volume no primeiro dia é de 9 cm³, o volume no quinto
dia será:

a)
405 cm³&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; b) 729 cm³&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; c) 939 cm³&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; d) 2187 cm³




4.
Num congresso havia 50 pessoas, entre homens e mulheres. Quantos homens e
quantas mulheres estavam presentes, sabendo que o produto das quantidades dos
dois grupos é igual a 621 e que a quantidade de mulheres é maior do que a
quantidade de homens.


DICA:
utilize o método da equação do 2º grau para calcular.



a)
23 mulheres e 27 homens.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; c)
37 homens e 13 mulheres.

b)
27 mulheres e 23 homens.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; d)
13 homens e 37 mulheres.





5.
A equação x² – 10x + 24 = 0 tem as
seguintes soluções no conjunto dos números reais:

a)
somente 5&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; c)
– 5

b)
somente 10&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; d)
5 e 10



6.
O menor das raízes da equação x²+ x – 12
= 0 é:

a)
3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; b) 4&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; c) – 3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; d) – 4



7.
A equação x² – 3x = 10 admite a:

a)
raiz – 2.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; b) raiz – 5.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; c) raiz 2.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; d) raiz 4.



8.
O conjunto verdade em R da equação 3 (x²
- 1) = 2x (x + 1) é:

a)
{1, 3}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; b) {1, – 3}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; c) {– 1, 3}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; d) {– 1, – 3}



9.
Uma das raízes da equação 0,1x² – 0,7x + 1 = 0 é:

a)
0,2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; b) 0,5&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; c) 7&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; d) 2



10.
Durante um jogo de futebol, a bola foi chutada para cima a uma velocidade
inicial de 25m/s. A bola atingirá 20m de altura em:

Dado:
h = v × t – g × t² , sendo:

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2

h
= altura

v
= velocidade inicial

g
= aceleração da gravidade ͠͠= 10m/s²

t
= tempo



a)
na subida (1º segundo) e na descida (5º segundo).

b)
na subida (1º segundo) e na descida (4º segundo).

c)
na subida (3º segundo) e na descida (5º segundo).

d)
na subida (1º segundo) e na descida (3º segundo).



11.
A área seguinte é 64 cm². Nessas condições as dimensões do retângulo seguinte
é:

 

  
 

  
  
 


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– 6



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; x + 6



a)
16 cm e 10 cm.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; c)
64 cm e 36 cm.
b)
16 cm e 36 cm.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; d)
16 cm e 4 cm.




12.
Um salão retangular tem área de 204 m² e seu comprimento tem 5 m a mais do que
sua largura. As dimensões desse salão são:


a)
17m e 12m&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; c)
21m e 16m

b)
19m e 24m&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; d)
24m e 8,5m




13.
Em um retângulo, a área pode ser obtida multiplicando-se o comprimento pela
largura. Em determinado retângulo que tem 54 m² de área, o comprimento é
expresso por (x – 1) cm, enquanto a largura é expressa por (x – 4) cm. Nessas
condições, escreva na forma normal a equação do 2º grau que se pode formar com
esses dados.




14.
As seguintes equações estão escritas na forma ax² + bx + c = 0. Nessas
condições, resolva as seguintes equações:

a)
x² – 6x – 16 = 0





b)
6x² – x – 5 = 0





c)
25x² + 10x + 1 = 0





d)
y² – 16y – 64 = 0






15.
O número p de partidas que devem ser
disputadas em um torneio de voleibol, com turno e returno, pode ser calculado
pela fórmula p = x(x – 1), em que x indica o número de equipes que
participam desse torneio. Se um torneio tem um total de 380 jogos, quantas
equipes participam desse torneio?




16.
O quadrado de um número real inteiro é igual a sete vezes o número, menos 6.
Qual é esse número?



17.
Coloque na forma ax² + bx + c = 0 as
seguintes equações do 2º grau:

a)
5x + 3x² = 4x – 7



b)
(x – 2) (x + 1) = 3




18.
Sabe-se que a é a raiz quadrada exata
de 4096, b é a raiz quarta exata de
1296 e c é a raiz cúbica exata de
3375. Qual é o valor da expressão a +
b + c?





19.
A medida do lado de um quadrado é expressa por (3x – 1) cm, e a área desse
quadrado é 64 cm². Qual é a equação do 2º grau, escrita na forma reduzida, que
se pode obter com os dados desse problema?





20.
O quadrado da diferença entre os números reais x e 3 é igual a 5 vezes o número
x, menos 1. Qual é a equação do 2º grau, escrita na forma reduzida, que se pode
escrever com esses dados?





21.
As medidas dos lados de um terreno retangular estão indicadas, em metros, na
figura abaixo. Se a área desse terreno é 899 m², quais as medidas dos lados
desse terreno?




 

  
 

  
  
 


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&nbsp;&nbsp;(x
– 1) m







&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (x
+ 1) m



22.
Leia as informações:



O
quadrado de um número real positivo x é igual a 81.

O
quíntuplo de um número real positivo y é igual ao seu quadrado.



Qual
é o valor da expressão x + y?





23.Imagine que a primeira figura é um quadrado e a segunda é um retângulo. O quadrado e o retângulo seguinte têm a mesma área.



&nbsp;&nbsp;

 

  
  
  
  
 

  
  
  &nbsp;x
  
 


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" strokecolor="black [3213]">
 
<![endif]--><!--[if !vml]-->



<!--[endif]-->&nbsp;
&nbsp;16

&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;x&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp; x + 5







a)
Qual a medida do lado e o perímetro do quadrado?



b)
Qual o perímetro do retângulo?





24.
Um estacionamento retangular tem 23 m de comprimento por 12 m de largura. O
proprietário deseja aumentar a área para 476 m², acrescentando duas faixas
laterais de mesma largura. Qual deve ser a medida da largura da faixa
acrescida?



(OBS.: OBSERVE O DESENHO DO CADERNO)

 

  




25.
O triplo do quadrado de um número aumentado do próprio número resulta a
diferença entre 92 e o décuplo do número. Escreva na forma normal a equação do
2º grau que se pode escrever com esses dados.





FONTE:

<!--[if !supportLists]-->·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->A Conquista da Matemática ( José Ruy
Giovanni Jr. &amp; Benedicto Castrucci) – 2009. Editora FTD.

<!--[if !supportLists]-->·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->Praticando Matemática (Álvaro Andrini) –
1989. Editora do Brasil.


<!--[if !supportLists]-->·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->Novo Praticando Matemática (Álvaro
Andrini &amp; Maria José Vasconcellos) – 2002. Editora do Brasil.