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Nome: nº. ano: data: / /

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((((((((33333333ºººººººº TTTTTTTTRRRRRRRRIIIIIIIIMMMMMMMMEEEEEEEESSSSSSSSTTTTTTTTRRRRRRRREEEEEEEE –––––––– 22222222000000001111111166666666)))))))) Ensino Fundamental

6º Ano

� Orientações gerais

Olá pessoal, a data da nossa avaliação PARCIAL está se aproximando e é muito importante se preparar com antecedência.

Utilize os exercícios do livro, da Khan e do caderno de atividades suplementares para revisar o

conteúdo que foi estudado. Se você não realizou esses exercícios nos momentos solicitados pela professora, agora é o momento para realizar essas tarefas.

Além disso, 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.

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

professora antes da avaliação. � Orientações para o dia da Avaliação Parcial

Data da avaliação parcial: 14/10/2016. Material necessário: lápis, borracha, caneta azul ou preta, corretivo e régua. Erros ortográficos: serão avaliados e descontados. Como fazer a avaliação: leia as questões com muita atenção antes de começar a responder;

distribua o tempo e associe cada exercício a uma das estratégias estudadas para resolver os problemas; desenvolva-a por escrito aplicando passo a passo o procedimento de resolução, fazendo os cálculos cuidadosamente e deixando-os registrados de forma organizada e legível; utilize a borracha sempre que precisar. Antes de entregar a avaliação revise os processos de resolução e faça as correções necessárias; não se esqueça de responder aos questionamentos.

Tenha um ótimo estudo!

PPRROOFFEESSSSOORRAASS:: CCHHRRII SSTTII AANNEE MMOOLLII NNAA EE MM II CCHHEELLLLEE MMAACCHHAADDOO..

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Compreender e utilizar a notação decimal para indicar quantidades não inteiras no cotidiano. Identificar, representar e conceituar uma fração decimal. Ler e comparar números decimais. Transformar números decimais em fração e vice-versa. Aplicar as propriedades dos números decimais para tornar os cálculos mais práticos. Representar números decimais na reta numérica.

CAPÍTULO 9 - NÚMEROS DECIMAIS

Resolver situações problemas com números decimais.

1) Observe o gráfico abaixo.

TTeelleeffoonneess cceelluullaarreess eemm ooppeerraaççããoo nnoo BBrraassii ll ((eemm mmii llhhõõeess))

Anos Fonte: Anatel

a) Escreva por extenso a quantidade de celulares em operação no Brasil em 2004. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ b) Qual é o crescimento do número de celulares de 2002 para 2004? Escreva por extenso. ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3


22)) EEssccaallaa RRiicchhtteerr

A quantidade de energia liberada por um terremoto é medida pela escala Richter. De forma geral, terremotos com magnitude até 3,5 ou menos são raramente percebidos; de 3,5 a 6,0 são sentidos e causam poucos danos; entre 6,1 e 6,9 podem ser destrutivos e causar danos em um raio de cem quilômetros do epicentro; entre 7,0 e 7,9 causam danos sérios em áreas maiores e de 8,0 em diante são destrutivos por um raio de centenas de quilômetros.

Sandra e Paulo estão pesquisando a respeito dos fortes terremotos de 8,0 ou mais na escala Richter. Na tabela abaixo estão alguns locais onde ocorreu esse tipo de catástrofe.

Terremotos

Data Local Pontos na escala Richter

1755 Lisboa (Portugal) 8,75

1906 San Francisco (EUA) 8,3

1950 Assan (Índia) 8,7

1977 Indonésia 8,0

1985 Cidade do México (México) 8,1

a) Em qual desses lugares ocorreu o terremoto mais arrasador? E o menos?

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

b) Ponha em ordem decrescente os locais onde os terremotos aconteceram.

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

4


3) Observe as frações e suas respectivas representações decimais:

I. 0001

3 = 0,003

II. 100

3672 = 23,67

III. 00010

129 = 0,0129

IV. 10

267 = 2,67

� Utilizando as igualdades acima, escolha a alternativa que indica as corretas: a) I e II.

b) I e IV.

c) I, II e III.

d) I, II, III e IV. 4) Examine o gráfico abaixo e responda às perguntas:

5


a) O que indicam os valores do eixo horizontal? ____________________________________________________________________________________________________________________________________________________________ b) O que indicam os valores do eixo vertical? ____________________________________________________________________________________________________________________________________________________________ c) Nesse período, em qual ano o dólar teve maior cotação? ____________________________________________________________________________________________________________________________________________________________ d) Em que período o dólar comercial manteve sua cotação em crescimento? ____________________________________________________________________________________________________________________________________________________________ e) Em que período o dólar comercial apresentou decréscimo em sua cotação? ____________________________________________________________________________________________________________________________________________________________ 5) Escreva a representação decimal das frações, identificando se são decimais exatos ou dízimas periódicas:

a) 4

21 = b)

9

77 =

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

c) 9

31 = d) 90

36 =

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

6


6) (SARESP-SP) Dentre as sentenças matemáticas abaixo, a única verdadeira é

a) 0,225 > 0,23. b) 0,5 > 0,50. c) 0,5 · 0,2 = 1. d) 0,4 < 10

5 < 0,6.

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 7) Observe como João fez para escrever o número 1,28 na forma de fração: ⇒ De maneira semelhante, escreva os números decimais na forma de fração irredutível. a) 0,36 ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ b) 9,75 ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ c) 22,2 ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ d) 1,625 ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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8) Escreva os seguintes números na forma numérica, ou seja, com algarismos: a) Quatro milésimos: ______________ b) Vinte e três centésimos: ___________ c) Trinta e cinco inteiros e trinta e cinco milésimos: ____________ d) Oito décimos de milésimo: ___________ 9) (SARESP) Dona Cláudia faz uma mistura de cereais para o café da manhã. Ela prepara uma lata de cada vez, colocando: � Nessa mistura, qual é o produto que aparece em maior quantidade? E o que aparece em menor quantidade? ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 10) Relacione a representação decimal da 2ª coluna de acordo com a representação fracionária da 1ª.

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11) No ábaco, também podemos representar números decimais. A vírgula separa a parte decimal da parte inteira. Observe o número indicado em cada ábaco e escreva-o na forma decimal, fracionária e por extenso. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Efetuar e compreender as operações de adição, subtração, multiplicação e divisão, envolvendo números decimais. Calcular a fração geratriz de uma dízima periódica e vice-versa. Aplicar o conceito de conversão de valores monetários corretamente.

CAPÍTULO 10 - OPERAÇÕES COM

NÚMEROS DECIMAIS Resolver situações problemas com números decimais envolvendo as

quatro operações matemáticas.

1) No esquema a seguir está indicada a distância de A até B e a distância de B até C, em centímetros. Calcule a distância de A até C. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

7,09 2,91

A B C

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2) Veja as distâncias, em quilômetros, de Vila Antonieta a Brejo Alegre e a distância de Vila Antonieta a Cravolândia. Observando os dados, descubra a distância de Brejo Alegre a Cravolândia. ____________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ 3) O gráfico mostra a venda de veículos de uma indústria fictícia, em determinado período de tempo.

VVeennddaa ddee vveeííccuullooss ((eemm mmii ll uunniiddaaddeess))

a) Em qual mês desse período a venda de veículos foi maior? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ b) Em março de 2007 foram vendidos mais veículos do que em agosto de 2007. Quantos veículos a mais? ____________________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

6,95

Vila Antonieta Brejo Alegre Cravolândia

9,1

10


c) Qual o total de veículos vendidos nos cinco últimos meses de 2006? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ d) Calcule o total de veículos vendidos por essa indústria nos cinco primeiros meses de 2007. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 4) A balança está em equilíbrio. Que número decimal devemos pôr no lugar da interrogação?

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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5) João tem R$84,30. Pedro tem R$31,50 mais que João, e José tem R$54,25 mais que Pedro. Quanto têm os três juntos? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 6) Esta é a tabela de preços da cantina de uma escola.

Produto Preço

Refrigerante R$2,50

Biscoito R$1,65

Doce R$1,75

Sanduíche R$4,75

Salgadinho R$1,90

� Um aluno comprou 1 refrigerante, 2 doces e 1 sanduíche. Quanto gastou? ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 7) A diferença entre dois números é 18,4, e o menor número é 7,4. Qual é o outro número? ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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8) Complete o quadrado mágico:

2,1 1,9

1,8

1,7

� Lembre-se: Em um quadrado mágico, a soma dos três números de cada linha, coluna ou diagonal sempre dá o mesmo resultado. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 9) (FGV-SP) As tarifas praticadas por duas agências de locação de automóveis para veículos idênticos são: � Para um percurso diário de 110km, qual agência oferece o menor preço? ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Agência A

R$14,40 por dia mais

R$1,67 por km rodado

Agência B

R$14,10 por dia mais

R$1,70 por km rodado

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10) Certo banco oferece a seguinte modalidade de tarifa para o uso de cheques: o cliente paga R$4,00 para receber o talão de cheques no seu domicílio e paga R$0,30 por folha de cheque utilizada, até 20 folhas; a partir da 21ª, paga R$1,10 por folha utilizada. Quanto o cliente paga pelo uso de 23 folhas de cheque? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 11) (OLIMPÍADA DE MATEMÁTICA-CE) O dono de uma mercearia comprou 5 caixas de rapadura por R$80,00. Cada caixa tem 20 rapaduras e ele vendeu cada uma a R$1,10. a) Quanto ele lucrou em cada rapadura? __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ b) Quanto ele lucrou nas 5 caixas de rapadura? __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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12) Para ir ao trabalho e voltar dele, Fabíola gasta, a cada 5 dias, R$34,00. Então, em 18 dias, mantido o preço da condução, ela gastará a) R$121,40. b) R$120,40. c) R$122,40. d) R$124,40. ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 13) (SARESP) O resultado da divisão de 4,5 por 0,3 é a) 0,15. b) 1,35. c) 1,5. d) 15. ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 14) (SARESP) Dividindo 1,25 por 0,5 obtemos a) 1,05. b) 1,5. c) 2,05. d) 2,5. ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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15) Classifique as dízimas periódicas a seguir em simples ou composta. Depois determine a sua fração geratriz. a) 0,888… b) 2,333… c) 0,161616… __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ d) 0,1555… e) 1,1222… f) 0,22555… __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

16) A expressão 1,333… + 0,666… + 3

1 é igual a

a) 9

11. b)

3

7. c)

21

11. d)

21

20.

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

16


17) A soma 1,333… + 0,1666… é igual a

a) 2

1. b)

2

3. c)

2

5. d)

3

4. e)

3

5.

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 18) Calcule as adições e subtrações seguintes: a) 12,54 + 2,76 = b) 1,25 + 0,5 = c) 12,865 + 1,8 = __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ d) 0,4 + 0,035 = e) 4 + 1,35 = f) 12,456 + 7,844 = ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ g) 0,125 + 0,88 = h) 7 + 0,5 = i) 125 + 24,5 = ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

17


j) 12,012 + 0,988 = k) 12,54 – 9,7 = l) 1,25 – 0,128 = ______________________________________________________________________________

______________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ m) 12,865 – 1,86 = n) 0,9 – 0,035 = o) 4 – 1,25 = ____________________________________________________________________________________________________________________________________________________________

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ p) 12,456 – 7,856 = q) 0,125 – 0,8 = r) 13 – 0,5 = ____________________________________________________________________________________________________________________________________________________________

____________________________________________________________________________________________________________________________________________________________

______________________________________________________________________________

____________________________________________________________________________________________________________________________________________________________

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ s) 125 – 27,5 = t) 12,012 – 1,212 = ______________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

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19) Calcule as multiplicações e divisões seguintes: a) 12,5 × 9 = b) 1,25 × 0,12 = ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ c) 12 × 1,8 = d) 0,9 × 0,35 = -____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ e) 4 × 1,25 = f) 1,2 × 8,5 = ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ g) 0,125 × 8 = h) 13 × 0,5 = __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

19


i) 125 × 27,5 = j) 12 × 1,2 = ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 20) Calcule mentalmente as multiplicações seguintes: a) 1,234 × 10 = _________________________ b) 1,234 × 100 = ______________________ c) 1,234 × 1 000 = _______________________ d) 13,76 × 10 = _______________________ e) 13,76 × 100 = ________________________ f) 13,76 × 1 000 = _____________________ g) 13,76 × 10 000 = _____________________ h) 0,75 × 10 = ________________________ i) 0,75 × 100 = _________________________ j) 0,75 × 1 000 = ______________________ k) 0,005 × 10 = ________________________ l) 0,005 × 100 = _______________________ m) 0,005 × 1 000 = _____________________ n) 0,005 × 10 000 = ____________________ 21) Calcule mentalmente as divisões seguintes: a) 123,4 ÷ 10 = _____________________ b) 123,4 ÷ 100 = ___________________________ c) 123,4 ÷ 1 000 = __________________ d) 13,76 ÷ 10 = ____________________________ e) 13,76 ÷ 100 = ____________________ f) 13,76 ÷ 1 000 = __________________________ g) 13,76 ÷ 10 000 = _________________ h) 7,5 ÷ 10 = ______________________________ i) 7,5 ÷ 100 = _______________________ j) 7,5 ÷ 1 000 = ____________________________ k) 25 ÷ 10 = ________________________ l) 25 ÷ 1 000 = _____________________________ m) 25 ÷ 100 = _______________________ n) 25 ÷ 10 000 = ___________________________

20


22) Calcule as expressões: a) 17,352 – 15,2 + 8,3 = 35,25 – (4,85 – 1,23 + 17,9) = ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ b) 15 – (3,25 + 2,7 – 4,08) – 10 = ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ c) 20,3 – [4,75 – (1,2 + 2,38)] + 5,1= ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

21


d) –0,25 · 0,15 = ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ e) 7,5 · 3,8 + 3,5 · 0,5 = ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ f) 5,75 · 2,05 – 3,01 · 2,04 = ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ g) 2 · (3,15 – 2,08) + 4 · (2,04 · 3,05) = ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

22


23) Calcule: a) 5 : 0,4 = b) 7 : 0,35 = ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ c) 8 : 3,2 = d) 9 : 0,06 = __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ e) 4 : 0,16 = f) 1 : 2,5 = ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ g) 2,08 : 0,8 = h) 1,2 : 0,24 = ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

23


i) 9,81 : 0,9 = j) 7,44 : 0,6 = ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ k) 5,4 : 2,7 = l) 0,063 : 0,09 = ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 24) Escreva a representação decimal das frações, identificando se são decimais exatos ou dízimas periódicas:

a) 4

21 = b)

20

77 =

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ _____________________________________________________________________________ __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

24


c) 6

11 = d) 2

8

1 =

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

e) 9

31 = f)

90

29 =

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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1) Escreva as porcentagens a seguir na forma em que se pede: a) 45% na forma de fração irredutível → ________________ b) 80% na forma de número decimal → _________________ c) 8% na forma de número decimal → __________________ d) 120% na forma de fração irredutível → _______________ 2) Passe cada valor para a porcentagem correspondente.

a) 20

7 = ________ b) 0,04 = _______

c) 150

42= ________ d) 2,3 = _________

3) Complete a tabela:

PORCENTAGEM 25% 3% 16%

NÚMERO DECIMAL

0,25 0,35 0,08 0,7

FRAÇÃO 100

25

4

3

100

1

4) Uma casa de R$80 000,00 foi vendida com um lucro de 27%. Qual foi o preço da venda? __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Relacionar a representação percentual com a representação fracionária. Calcular a porcentagem de uma dada quantidade.

CAPÍTULO 11 -PORCENTAGEM

Resolver problemas que envolvam porcentagem.

26


5) (SARESP) O losango abaixo foi dividido em partes iguais.

⇒ A parte pintada corresponde a que porcentagem do losango todo? a) 4% b) 25% c) 40% d) 50% _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 6) Calcule: a) 8% de 13 500 c) 19% de 12 600 ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ b) 1,5% de 500 d) 120% de 30 ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 7) Na loja “Compre Aqui”, um modelo de televisor tem o preço de R$820,00 e pode ser comprado de duas formas: • à vista, com desconto correspondente a 20% do preço; • a prazo, com entrada correspondente a 10% do preço e o saldo acrescido de 30% de seu valor, pago em 5 parcelas iguais.

27


⇒ Carlos e Heitor compraram esse aparelho, o primeiro à vista e o outro a prazo. Quanto Heitor pagou mais que Carlos? _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 8) No início de maio um lojista diminuiu em 5% o preço de um ventilador que custava R$200,00. Carla comprou o ventilador e pagou com duas notas de 100 reais. Quanto Carla recebeu de troco? _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ 9) O gerente de uma empresa recebeu a incumbência de distribuir um prêmio de R$2 400,00 entre três funcionários, de acordo com a eficiência em vendas de cada um. Se um deles recebeu 20% desse valor e um outro recebeu 55%, quantos reais recebeu o terceiro? __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 10) Laís comprou uma bicicleta por R$250,00 e deseja vendê-la com o lucro de 25% para compensar alguns gastos que teve com a sua manutenção. Qual o preço de venda dessa bicicleta? ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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11) (SARESP-SP) Dos 100 alunos de uma escola, 25 são palmeirenses e 35 são santistas. Qual é a porcentagem de alunos que torcem para outros times? ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 12) Os alunos do 6º ano fizeram uma estimativa para 200 pessoas com base no estudo abaixo. ⇒ De acordo com o gráfico, quantas pessoas responderam “Estilo de vida”? ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 13) Das 14 toneladas diárias da coleta seletiva de lixo, 37% são de alumínio (latas de refrigerante e cerveja). Com o quilo de alumínio ao preço de R$0,70, a arrecadação no final de um dia é a) R$2 394,00. b) R$3 626,00. c) R$4 497,00. d) R$5 362,00. ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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14) Comprei um objeto por R$1 250,00, a ser pago do seguinte modo: a) Qual é o valor da entrada? __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ b) Qual é o valor de cada prestação? __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 15) Numa cidade, o preço da passagem de ônibus subiu de R$3,00 para R$3,54. Qual foi a taxa porcentual de aumento? __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

1155%% ddee eennttrraaddaa ee oo

rreessttaannttee eemm 66

pprreessttaaççõõeess iigguuaaiiss

30


16) (UFPB) Em uma eleição, um candidato recebeu 20

7 dos votos dos eleitores. Portanto, o

porcentual de votos obtidos por esse candidato foi de a) 35%. b) 20%. c) 7%. d) 14%. e) 27%. __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 17) Um funcionário de uma empresa recebeu a quantia de R$315,00 a mais no seu salário, referente a um aumento de 12,5%. Sendo assim, o seu salário atual é de a) R$2 205,00. b) R$2 520,00. c) R$2 835,00. d) R$2 913,00. e) R$3 050,00. _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 18) A tabela a seguir mostra os rendimentos mensais com as respectivas alíquotas e deduções do imposto de renda (I. R.).

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⇒ Nesse período, o salário mensal de Renata era de R$2 500,00. Então, Renata (A) era isenta. (B) deve pagar R$375,00 de I. R. (C) deve pagar R$495,00 de I. R. (D) deve pagar R$687,50 de I. R. ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 19) Numa pesquisa em que 2 673 pessoas foram entrevistadas com o seguinte questionamento: “O que leva as pessoas a se mudarem para os condomínios fechados fora das grandes cidades?” as respostas foram organizadas no gráfico a seguir:

⇒ Após análise do gráfico, pode-se afirmar que, aproximadamente, a) 321 pessoas mudam por causa do conforto. b) 588 pessoas mudam por causa da tranquilidade. c) 749 pessoas mudam por causa do espaço. d) 1 016 pessoas mudam por causa da segurança. ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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Identificar o ponto, a reta e o plano como elementos fundamentais da Geometria, aplicando a notação adequada de cada um. Identificar semirretas e segmentos de reta e aplicar a notação adequada às suas representações. Classificar retas e segmentos de reta segundo sua posição relativa.

CCAAPPÍÍ TTUULLOO 1122 -- GGEEOOMMEETTRRII AA II

Classificar ângulos quanto à abertura. 1) Em cada item, trace todas as possíveis retas que passem por dois pontos dados: a) Pontos A e B.

Quantas retas foram traçadas? _____________________________________________________ Quantos pontos, no mínimo, são necessários para determinar uma reta? ______________________________________________________________________________ b) Pontos A, B e C.

Quantas retas foram traçadas? _____________________________________________________ Quais retas passaram pelo ponto A? _________________________________________________

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2) Observe a figura e complete com os símbolos ∈ ou ∉:

3) Observe a figura e complete com os símbolos ⊂ ou ⊄:

4) Observe a figura e classifique as afirmações em V (verdadeira) ou F (falsa): 5) Quantos e quais são os segmentos de reta que formam a figura? ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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6) Observe as seguintes figuras:

⇒ Podemos classificar as figuras I, II e III respectivamente como: a) semirreta, reta e segmento de reta. b) reta, segmento de reta e semirreta.

c) segmento de reta, semirreta e reta. d) reta, semirreta e segmento de reta.

7) Nas figuras abaixo, foram desenhados pares de retas. Escreva se elas são retas paralelas ou retas perpendiculares.

8) Quantos ângulos há na figura abaixo? E quais são eles?

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 9) A medida de um ângulo obtuso é __________ do que a de um ângulo reto e ____________ do que a de um ângulo raso. Que palavras completam a frase corretamente? a) menor/ menor b) menor/ maior c) maior/ menor d) maior/ maior

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10) O que é um ângulo? E qual é o instrumento que utilizamos para medir um ângulo? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 11) Classifique os ângulos destacados em reto, agudo ou obtuso: 12)

______________________________________________________________________________ __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 13) Muitas situações do cotidiano exigem que se conheça a medida de um ângulo. Em outras, é necessário comparar ângulos e existem também aquelas nas quais a classificação dos ângulos se faz necessária. A postura correta em diversos esportes é de suma importância para um maior desempenho do atleta. Observe as figuras a seguir: Elas possuem, em comum, a classificação dos ângulos assinalados. Esses ângulos são

a) agudos. b) retos. c) obtusos. d) rasos.

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14) Observe o mapa do bairro de Todos os Santos.

⇒⇒⇒⇒ Complete com as palavras paralela, perpendicular e oblíqua. a) A rua dos Anjos é __________________ à rua Maria José. b) A rua São Sebastião é ________________ à rua dos Anjos. c) A rua do Natal é _________________ à avenida Três Marias. d) A rua dos Anjos é ________________ à rua Santa Quitéria. 15) Observe a figura:

a) Quais são as retas perpendiculares entre si? _________________________________________________________________________________________________________________________________ b) Quais são as paralelas entre si? _________________________________________________________________________________________________________________________________

16) Veja as figuras abaixo.

Em cada uma, escreva o nome (reta, semirreta ou segmento de reta) e como é representada.

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17) Dê a medida do ângulo em cada caso:

a) AÔB - ___________ b) AÔC - ___________ c) AÔD -____________ d) AÔE - ___________ e) AÔF - ___________ f) AÔG - ___________ 18) Responda às questões a seguir: a) O que é um ângulo obtuso? ______________________________________________________________________________ __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ b) O que é um ângulo agudo? ______________________________________________________________________________ __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ c) O que são retas perpendiculares? ______________________________________________________________________________ __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ d) O que são retas concorrentes? ______________________________________________________________________________ __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 19) Responda qual é a medida de um ângulo: reto: ______________ de meia-volta: ______________ de uma volta inteira: _______________

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20) Observe a figura ao lado e responda ao que se pede:

a) Quais pontos pertencem à reta s? __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ b) Indique um par de segmentos de reta consecutivos e colineares. __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ c) Indique um par de segmentos de reta consecutivos e não colineares. __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 21) Um projetista brasileiro prestou um concurso numa empresa multinacional. A prova estava toda em inglês. Num dos exercícios ele não entendeu o enunciado, mas tentou fazer apenas o que entendeu com as indicações a seguir:

a) b) c) d) � Agora observe estas indicações e desenhe cada uma delas. (Atenção: utilize a régua, OK!) a)

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b) c) d)

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22) (SARESP)

O relógio abaixo marca 9h.

� Assinale a alternativa que mostra corretamente qual a medida do ângulo formado pelos 2 ponteiros indicados na figura. a) 180° b) 90° c) 60° d) 45° 23) Trace uma reta s e considere nessa reta 4 pontos distintos: F, G, H e I. a) Quantas semirretas de s existem com origem nesses pontos? ____________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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b) Quantos e quais são os segmentos de reta com extremos nesses pontos? ____________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ 24) Observe a figura e responda à pergunta:

� Quais são os lados dos ângulos CÔD e BÔA respectivamente? ____________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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25) Observe as retas na figura abaixo e escreva os pontos que são colineares em cada uma delas:

____________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________

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