1

Nome: n.º. ano: data: / /

AATTIIVVIIDDAADDEE DDEE OORRIIEENNTTAAÇÇÃÃOO DDEE EESSTTUUDDOOSS PPAARRAA AA

AAVVAALLIIAAÇÇÃÃOO TTRRIIMMEESSTTRRAALL

((22ºº TTRRIIMMEESSTTRREE –– 22001166))

Ensino Fundamental

7º Ano

Olá pessoal, a data da nossa avaliação TRIMESTRAL está se aproximando (22/8/2016) e é

muito importante se preparar com antecedência. A preparação para a avaliação de matemática

deve consistir numa revisão depois de já ter compreendido e revisto a matéria. Parte da revisão

em matemática consiste em fazer novos exercícios que requeiram a aplicação dos conceitos já

estudados.

Procure um lugar agradável e ao estudar tenha organização, concentração e dedicação. Utilize

o caderno, os livros, o portal SAS e a Khan Academy como fontes de pesquisa para revisar o

conteúdo estudado. Ao realizar os exercícios, não se esqueça de registrar (anotar) todos os

cálculos, procedimentos de resolução ou suas dúvidas de forma organizada e legível.

Analise os erros cometidos na avaliação parcial (você poderá refazer os exercícios que

apresentaram dificuldade e confrontar com o gabarito disponibilizado no Ning).

Estude antecipadamente, para ter a oportunidade de esclarecer suas dúvidas em aula com a

professora antes da avaliação.

Tenha um ótimo estudo! Profª Michelle Machado

OBJETIVOS:

Revisar e retomar os conceitos e procedimentos que foram avaliados na parcial;

Estudar e sistematizar o conteúdo que será avaliado na trimestral.

CONTEÚDO:

Operações com os números racionais: adição, subtração, multiplicação, divisão, potenciação e

radiciação; (CAPÍTULO 5)

Expressões numéricas envolvendo as operações com os números racionais; (CAPÍTULO 5)

Potência com expoentes negativos; (CAPÍTULO 5)

Propriedades da potenciação; (CAPÍTULO 5)

Geratriz de uma dízima periódica; (CAPÍTULO 5)

Expressões algébricas; (CAPÍTULO 6)

Valor numérico de uma expressão algébrica; (CAPÍTULO 6)

Equação do 1º grau com uma incógnita; (CAPÍTULO 6)

Equação do 1º grau com duas incógnitas e sua representação gráfica; (CAPÍTULO 7)

Plano cartesiano, par ordenado e produto cartesiano; (CAPÍTULO 7)

Sistemas de equações do 1º grau com duas incógnitas; (CAPÍTULO 8)

Tratamento da informação envolvendo o conteúdo estudado. (CAPÍTULOS: 5, 6, 7 e 8)

2

Nome: n.º. ano: data: / /

EXERCÍCIOS

1) Sendo 2

3

8

5A e

4

3

3

2B , calcule

2BA .

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2) Determine o valor de A, de acordo com o esquema abaixo:

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3) O valor de 3

5

3

1

2

1 é

a) 3

1. b)

4

1. c)

2

1. d)

5

3.

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3

Nome: n.º. ano: data: / /

4) Maria calculou o valor da expressão:

22

2

1

4

3

2

1

2

3e Pedro, o valor da expressão:

7

1

2

11

2

12

. Podemos afirmar que o valor que Pedro encontrou é igual à raiz quadrada

do valor que Maria encontrou? Justifique sua resposta com os cálculos.

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5) Qual o valor de x abaixo?

4

1

4

38,0

2

1x

a) 20

19 b)

20

1 c)

10

1 d)

10

19

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4

Nome: n.º. ano: data: / /

6) (FUVEST-SP) O valor da expressão ab1

ba para a =

2

1 e b =

3

1 é

a) 0. b) 1. c) 5. d) 6.

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7) O valor da expressão

1

4

1

8

3

2

175,0 é

a) 7

2. b)

8

7. c)

7

8. d)

2

7.

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5

Nome: n.º. ano: data: / /

8) A expressão

53

2

1

2

1 é igual a

a) 40. b) 40

1. c) – 40. d)

8

2

1.

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9) Efetuando as operações indicadas e simplificando a expressão 08,025

425,1

04,025

16, temos

a) 6

25. b)

2

3. c)

5

6. d)

9

16. e) 1.

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10) A expressão 3

2

3

1

2

11

é igual a

a) 4

1. b)

15

28. c)

15

13. d)

5

12.

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6

Nome: n.º. ano: data: / /

11) Classifique as sentenças a seguir em verdadeira (V) ou falsa (F). Depois corrija as falsas,

fazendo os cálculos corretos.

a) 28,084,7 (____)

b) 2564

14

(____)

c) 343

216

7

63

(____)

d) 2

1

16

4 (____)

12) O valor de ...111,0

...777,1 é

a) 4,444… b) 4. c) 4,777… d) 3. e) 3

4.

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13) A soma 1,333… + 0,1666… é igual a

a) 2

1. b)

2

3. c)

2

5. d)

3

4. e)

3

5.

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7

Nome: n.º. ano: data: / /

14) (UFRN) O valor de ...666,0

2 é

a) 0,333…

b) 3.

c) 3,333…

d) 1,333…

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15) O resultado de 5

10

3

2

2

1...333,0 é

a) 3

1. b)

6

7. c) 0,666… d)

2

1. e)

2

3.

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8

Nome: n.º. ano: data: / /

16) A expressão 3

1...666,0...333,1 é igual a

a) 9

11. b)

3

7. c)

21

11. d)

21

20.

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17) Transforme em fração irredutível as dízimas periódicas a seguir, conforme o solicitado:

a) 0,8333… b) 1,1222… c) 0,2161616…

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18) Sendo n um número expresso por 247 222 , qual é o valor de n?

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9

Nome: n.º. ano: data: / /

19) Dados 5472 1010.10a e

752107 44.4.4b , determine o valor 3

ba .

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20) A expressão

253

3

1

3

1

3

1 é igual a

a)

10

3

1. b) 30. c)

30

1. d)

6

3

1.

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21) A expressão ―a metade da soma de um número inteiro com seu sucessivo‖, simbolicamente,

pode ser representada por

a) x

2x. b)

2

x + x + 1. c)

2

x + 1. d)

2

)1x(x.

22) Nas expressões a seguir, a letra x representa um número. Identifique cada expressão escrita

na linguagem comum com a expressão algébrica correspondente, escrevendo o número romano e

a letra que estão associados a elas.

I) O dobro do quadrado de x.

II) O quadrado do dobro de x.

III) A diferença entre o dobro de x e 3.

IV) O dobro da diferença entre x e 3.

V) A divisão da soma de x com 3 por 2.

VI) A soma dos quadrados dos números x e 3.

VII) O quadrado da soma dos números x e 3.

10

Nome: n.º. ano: data: / /

a) 2x – 3 b) x2 + 3

2 c) (2x)

2 d) (x + 3)

2 e) 2x

2 f)

2

3x g) 2(x – 3)

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23) A expressão algébrica que representa a situação ―o quadrado da soma de dois números, mais

5 unidades‖ é

a) x + y + 52.

b) (x + y + 5)2.

c) (x + y)2 + 5.

d) x2 + y + 5

2.

24) Calcule o valor numérico das expressões algébricas:

a) 8x5 , para 15

1x

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b) b5a 2, se

3

2a e

45

1b

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c) y2x , para 4

1x e

3

1y

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11

Nome: n.º. ano: data: / /

25) Considere a balança em equilíbrio na figura.

O valor representado pela letra x é _________.

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26) Observe o gráfico.

Sabendo que a produção de leite em março foi de 13 800 litros e em abril, de 12 000 litros,

qual foi a produção de leite em janeiro?

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27) Calcule x tal que 4

1

2

x

3

1.

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12

Nome: n.º. ano: data: / /

28) Resolva a equação: x3

16x

2

1.

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29) Se 3

1

20

1x15

5

x2, então o valor de 13x é

a) 1. b) 2. c) 3. d) 4.

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13

Nome: n.º. ano: data: / /

30) Resolva as equações a seguir:

1x420x29x7

3x3x3x5

31xx24

c)

b)

a)

1x245x43x2

2x341x2x

2x46x2

f)

e)

d)

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14

Nome: n.º. ano: data: / /

31) Resolva as equações:

3

1x2x

5

1x

52

x7

4

x

152

x

3

x

c)

b)

a)

2

1

8

5x

10

x2

2x32x3

2

3x2

13x

2

1

f)

e)

d)

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15

Nome: n.º. ano: data: / /

32) Resolva as situações problemas a seguir, utilizando equações. Não se esqueça de registrar as

informações e responder à questão proposta.

a) Numa caixa há bolas vermelhas e bolas azuis num total de 570. Se o número de bolas

vermelhas é o quíntuplo do de bolas azuis, então o número de bolas vermelhas é

_________________.

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b) Em uma escola há uma quadra esportiva cujo perímetro é 96 metros,

sendo a medida do comprimento da quadra 12 metros maior que a da

largura. Determine qual é o comprimento e a largura dessa quadra.

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c) O triplo de um número, menos 10, é igual ao próprio número mais 70. Qual é esse número?

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16

Nome: n.º. ano: data: / /

d) A soma de dois números consecutivos é 31. Quais são esses números?

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e) A soma de um número com sua quinta parte é 2. Qual é o número?

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33) Dez caixas fechadas de parafusos mais 100 parafusos soltos pesam o mesmo que 15 caixas

fechadas mais 20 parafusos soltos. O número de parafusos em cada caixa é

a) 12. b) 16. c) 20. d) 24.

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34) Os 2 700 alunos matriculados numa escola estão assim distribuídos: no período da manhã há

520 alunos mais do que no período da tarde e, à noite, há 290 alunos menos do que no período da

manhã. O número de alunos do período da manhã dessa escola é ___________________.

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17

Nome: n.º. ano: data: / /

35) O número s do sapato que uma pessoa calça está relacionado com o comprimento p, em

centímetros, do seu pé, pela fórmula:

Qual é o comprimento do pé de uma pessoa que calça sapatos de número 41?

a) 27,2cm b) 29,5cm c) 30,8cm d) 35,32cm

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36) Numa lanchonete, a despesa de R$102,00 foi dividida entre três amigos, conforme mostra o

gráfico a seguir:

De acordo com o gráfico, responda quantos reais pagou cada amigo.

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18

Nome: n.º. ano: data: / /

37) Sendo 16,8,4,2A e 9,6,3B , determine os seguintes conjuntos:

a) A × B

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b) A2

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38) Complete a tabela a seguir com os pares ordenados, de modo que eles sejam solução da

equação 3x + y = 1.

x y Par ordenado (x, y)

(– 2, 7)

–1

0 1

1

2

CÁLCULOS:

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19

Nome: n.º. ano: data: / /

Agora complete o plano cartesiano abaixo e represente cada um desses pontos nele. Depois

trace a reta suporte que é o gráfico dessa equação. (Utilize régua.)

39) Sabendo que os pares ordenados (a + 1, 4 – b) e (2a – 3, 3b + 8) são iguais, determine o valor

de a–2

+ b3.

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40) Complete a tabela a seguir com os pares ordenados, de modo que eles sejam solução da

equação x + y = 2.

x y Par ordenado (x, y)

– 3

2

0

(5, –1)

20

Nome: n.º. ano: data: / /

Agora represente cada um desses pontos no plano cartesiano e trace seu gráfico. (Utilize régua.)

41) (FUVEST-SP) Resolva o sistema: 2yx

3yx2 (método da substituição).

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21

Nome: n.º. ano: data: / /

42) Cada par ordenado que aparece nas fichas é solução de um dos sistemas abaixo. Identifique o

par ordenado com o sistema correspondente. (Resolva os sistemas pelo método da adição.)

1,2 1,2 2,1 1,2

5yx2

1y3x

0y2x

7yx3

3yx

1y3x2

1yx3

5y2x

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22

Nome: n.º. ano: data: / /

43) Se p e q são tais que:

12pq

4pq,

então 2pq vale

a) 32. b) 30. c) 10. d) 12.

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44) Resolva os sistemas de duas equações do 1º grau com duas incógnitas a seguir:

a) )adiçãodamétodo(5y2x3

9yx5

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b) )ãosubstituiçdamétodo(8yx2

2y5x4

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23

Nome: n.º. ano: data: / /

45) Leia o problema e faça o que se pede:

Júlia guardou durante um mês, num cofre, moedas de 25 e 10 centavos. Ao abri-lo, constatou

que possuía 210 moedas num total de R$35,70. Quantas moedas de 25 centavos Júlia guardou?

a) Assinale qual dos sistemas abaixo permite resolver esse problema.

210y25x10

70,35yx(I)

70,35y10,0x25,0

210yx(II)

70,35y10x25

210yx(III)

b) Resolva o sistema e responda à questão do problema.

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46) Somando as idades de Luciano e a de seu pai dá 84 anos. A diferença entre as suas idades é

de 26 anos. Qual é a idade de Luciano?

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24

Nome: n.º. ano: data: / /

47) (FAAP-SP) Num terreno há galinhas e coelhos num total de 95 cabeças e 226 pés. Quantos

animais há de cada espécie?

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48) Uma prova de múltipla escolha com 60 questões foi corrigida da seguinte forma: o aluno

ganhava 5 pontos por questão que acertava e perdia 1 ponto por questão errada ou deixada em

branco. Se um aluno totalizou 210 pontos, o número de questões que ele acertou é

a) 25. b) 30. c) 35. d) 40. e) 45.

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49) (FAAP-SP) Pagou-se uma compra no valor de R$ 950,00 com notas de R$ 10,00 e R$ 50,00,

num total de 47 notas. Quantas notas de cada espécie foram usadas no pagamento?

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25

Nome: n.º. ano: data: / /

50) Resolva os sistemas a seguir, utilizando qualquer um dos métodos estudados.

y512x2x310y6

8y2x46y3x5a)

83

y

2

x

12

19

4

y3

6

x5

b)

2y5x3

12

y

3

x

c) 1,4

2

y

5

x2

0y4x5

d)

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26

Nome: n.º. ano: data: / /

51) Lucas comprou 3 canetas e 2 lápis pagando R$7,20. Danilo comprou 2 canetas e 1 lápis

pagando R$4,40. Assinale com X qual é o sistema de equações do 1º grau que melhor representa

essa situação e responda qual é o preço de cada lápis e de cada caneta.

20,2yx

60,3yxa)

40,4yx2

20,7y2x3b)

40,4yx2

20,7y2x3c)

40,4yx

20,7yx3d)

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52) D. Pedro II foi aclamado segundo imperador do Brasil com x anos de idade e iniciou um

reinado que só terminou com a República, y anos depois. Determine com que idade D. Pedro II

iniciou seu reinado e quantos anos reinou, resolvendo as equações: x – y = –52 e 10x – y = 2.

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53) Qual é o valor de yx

yx 2

, dado o sistema 1y2x3

4y3x2?

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27

Nome: n.º. ano: data: / /

54) Resolva os problemas a seguir, utilizando sistemas de equações do 1º grau com duas

incógnitas.

a) Em um sítio há cavalos e galinhas. No total, há 97 cabeças e 264 pés.

Quantos são os cavalos e quantas são as galinhas?

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b) A soma de dois números é 21 e sua diferença é 51. Quais são esses números?

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55) Santos Dumont, o gênio que seduziu Paris. Alberto Santos Dumont é um daqueles estranhos

heróis nacionais que todo brasileiro conhece — mas pouco ou nada se sabe sobre ele. O que a

história oficial diz é que ele foi o Pai da Aviação. E que, a bordo do esquálido 14-Bis, movido a

um pequeno motor de Antoniette de 50 cavalos, sobrevoou o Campo de Bagatelle, em Paris, no

dia 23 de outubro de 1906. Neto de francês, nasceu em Cabangu, sul de Minas Gerais, cidade que

hoje leva o seu nome, em 20 de julho de 1873. Estudou no Rio de Janeiro e em Campinas, depois

foi para Paris, aonde chegou em 1892, com apenas 19 anos.

(Fonte: A conquista da matemática. José Ruy Giovanni, Benedito Castrucci, José Ruy Giovanni Junior.

São Paulo: FTD, 2002- retirado do Globo Ciência, out 1996)

28

Nome: n.º. ano: data: / /

Para homenagear Santos Dumont, vamos recordar seu mais importante feito, por meio de um

problema:

A multidão presente ao campo de Bagatelle aclamou Santos Dumont, quando o 14-Bis voou,

aproximadamente, x metros, durante y segundos. Determine a distância percorrida pelo 14-Bis e o

seu tempo de voo, sabendo que:

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