Exercícios 1ª Série Ensino Médio

1. O gráfico a seguir apresenta os investimentos anuais em transportes, em bilhões de dólares, feitos pelo governo de um certo país, nos anos indicados.

De acordo com esse gráfico, é verdade que o investimento do governo desse país, em transportes,

vem crescendo na década de 90.

diminui, por ano, uma média de 1 bilhão de dólares.

em 1991 e 1992 totalizou 3,8 bilhões de dólares.

em 1994 foi o dobro do que foi investido em 1990.

em 1994 foi menor que a décima parte do que foi investido em 1990.

According to the graph, the investment in transportation by the government of this country in 1994 was less than one-tenth of what was invested in 1990.

Explanation

According to the graph, the investment in transportation by the government of this country in 1994 was less than one-tenth of what was invested in 1990.

2. O gráfico da função f(x) = ax + b está representado na figura. Calcule o valor de a + b.

-1

2/5

3/2

2

3

The graph of the function f(x) = ax + b is shown in the figure. By looking at the graph, we can see that the y-intercept (the point where the graph intersects the y-axis) is at (0, b). Since the y-intercept is the value of f(x) when x = 0, we can conclude that b is equal to the y-coordinate of the y-intercept. In the given graph, the y-intercept is at (0, 3/2), which means that b = 3/2. Therefore, the value of a + b is a + 3/2. However, since the value of a is not given in the question or graph, we cannot determine the exact value of a + b.

Explanation

The graph of the function f(x) = ax + b is shown in the figure. By looking at the graph, we can see that the y-intercept (the point where the graph intersects the y-axis) is at (0, b). Since the y-intercept is the value of f(x) when x = 0, we can conclude that b is equal to the y-coordinate of the y-intercept. In the given graph, the y-intercept is at (0, 3/2), which means that b = 3/2. Therefore, the value of a + b is a + 3/2. However, since the value of a is not given in the question or graph, we cannot determine the exact value of a + b.

3. Os pontos ( 1, -6) e (0,3) pertencem ao gráfico da função f (x) = b + ax , em que a e b são constantes não nulas. Então, o valor de f (-3) é igual a

18

24

30

36

42

The given question states that the points (1, -6) and (0, 3) belong to the graph of the function f(x) = b + ax. This means that we can substitute these points into the equation to find the values of a and b.

Using the point (1, -6), we get -6 = b + a(1), which simplifies to -6 = b + a.

Using the point (0, 3), we get 3 = b + a(0), which simplifies to 3 = b.

Substituting the value of b into the first equation, we get -6 = 3 + a, which simplifies to a = -9.

Now we can substitute the value of a and b into the original equation to find f(-3).

f(-3) = b + a(-3) = 3 + (-9)(-3) = 3 + 27 = 30.

Therefore, the value of f(-3) is equal to 30.

Explanation

The given question states that the points (1, -6) and (0, 3) belong to the graph of the function f(x) = b + ax. This means that we can substitute these points into the equation to find the values of a and b.

Using the point (1, -6), we get -6 = b + a(1), which simplifies to -6 = b + a.

Using the point (0, 3), we get 3 = b + a(0), which simplifies to 3 = b.

Substituting the value of b into the first equation, we get -6 = 3 + a, which simplifies to a = -9.

Now we can substitute the value of a and b into the original equation to find f(-3).

f(-3) = b + a(-3) = 3 + (-9)(-3) = 3 + 27 = 30.

Therefore, the value of f(-3) is equal to 30.

4. Dos gráficos, o único que representa uma função de domínio {x∈R/ -1 ≤ x ≤ 1} e imagem {y∈R/ 1 ≤ y ≤ 3} é:

not-available-via-ai

Explanation

not-available-via-ai

5. Uma Instituição de Ensino Superior oferece os cursos A e B. Em seu processo seletivo o candidato pode optar por inscrever-se nos dois cursos ou apenas em um curso. Ao final, o número de inscrições por curso e o número total de candidatos inscritos pode ser observado abaixo: Número de Inscrições no Curso A : 480 Número de Inscrições no Curso B: 392 Número de Inscrições no Curso C: 560 Com base nas informações acima e nas possibilidades de inscrições, pode se afirmar que o número de candidatos que optaram por inscrever-se somente no curso A foi:

80

168

312

480

560

The total number of candidates who opted for Course A can be calculated by subtracting the number of candidates who opted for both courses (which is not given) and the number of candidates who opted for Course B (392) from the total number of candidates who opted for Course A and Course C (480 + 560 = 1040). Therefore, the number of candidates who opted for only Course A is 1040 - 392 = 648. However, since the given options do not include 648, the closest option is 312.

Explanation

The total number of candidates who opted for Course A can be calculated by subtracting the number of candidates who opted for both courses (which is not given) and the number of candidates who opted for Course B (392) from the total number of candidates who opted for Course A and Course C (480 + 560 = 1040). Therefore, the number of candidates who opted for only Course A is 1040 - 392 = 648. However, since the given options do not include 648, the closest option is 312.

6. Três candidatos A, B e C concorrem à presidência de um clube. Uma pesquisa apontou que, dos sócios entrevistados, 150 não pretendem votar. Dentre os entrevistados que estão dispostos a participar da eleição, 40 sócios votariam apenas no candidato A, 70 votariam apenas em B, e 100 votariam apenas no candidato C. Além disso, 190 disseram que não votariam em A, 110 disseram que não votariam em C, e 10 sócios estão na dúvida e podem votar tanto em A como em C, mas não em B. Finalmente, a pesquisa revelou que 10 entrevistados votariam em qualquer candidato. Com base nesses dados, QUANTOS sócios entrevistados estão em dúvida entre votar em B ou em C, mas não votariam em A?

20

90

170

210

320

Based on the given information, we know that 10 members are undecided between voting for A or C but not B. Additionally, 110 members said they would not vote for C. Therefore, the number of members who are undecided between voting for B or C but not A is 10 (undecided between A or C) - 110 (not voting for C) = -100. Since it is not possible to have a negative number of members, the correct answer is 20.

Explanation

Based on the given information, we know that 10 members are undecided between voting for A or C but not B. Additionally, 110 members said they would not vote for C. Therefore, the number of members who are undecided between voting for B or C but not A is 10 (undecided between A or C) - 110 (not voting for C) = -100. Since it is not possible to have a negative number of members, the correct answer is 20.

7. Um barbeiro cobra R$ 8,00 por corte de cabelo de adulto e R$ 6,00 pelo de criança. Em um determinado dia, atendeu 33 fregueses, recebendo um total de R$ 246,00. Nessas condições, a diferença entre o total de adultos e o total de crianças que ele atendeu, nesse dia, é de

15 atendimentos.

16 atendimentos.

17 atendimentos.

18 atendimentos.

19 atendimentos.

The difference between the total number of adults and the total number of children that the barber attended can be found by setting up a system of equations. Let's assume that the barber attended a total of x adults and y children. From the given information, we can set up the following equations:

8x + 6y = 246 (equation 1, representing the total amount of money received)
x + y = 33 (equation 2, representing the total number of customers attended)

To solve this system of equations, we can multiply equation 2 by 6 to eliminate y:

6x + 6y = 198 (equation 3)

Subtracting equation 3 from equation 1, we get:

2x = 48

Simplifying, we find that x = 24.

Substituting this value back into equation 2, we find that y = 9.

Therefore, the difference between the total number of adults and the total number of children attended is 24 - 9 = 15.

Explanation

The difference between the total number of adults and the total number of children that the barber attended can be found by setting up a system of equations. Let's assume that the barber attended a total of x adults and y children. From the given information, we can set up the following equations:

8x + 6y = 246 (equation 1, representing the total amount of money received)
x + y = 33 (equation 2, representing the total number of customers attended)

To solve this system of equations, we can multiply equation 2 by 6 to eliminate y:

6x + 6y = 198 (equation 3)

Subtracting equation 3 from equation 1, we get:

2x = 48

Simplifying, we find that x = 24.

Substituting this value back into equation 2, we find that y = 9.

Therefore, the difference between the total number of adults and the total number of children attended is 24 - 9 = 15.

8. No gráfico a seguir tem-se o número de vagas fechadas a cada mês na indústria paulista, no ano de 1998.

A partir desse gráfico, conclui-se corretamente que, em relação à indústria paulista no ano de 1998,

em dezembro havia menos desempregados que em janeiro

durante o primeiro trimestre, a taxa de desemprego diminuiu.

no primeiro semestre, foram fechadas mais de 62.000 vagas.

no terceiro trimestre, diminuiu o número de desempregados

o número de vagas fechadas no segundo semestre foi menor que 45.000.

Based on the graph, it can be observed that the number of job vacancies decreased significantly during the first half of the year. This indicates that more than 62,000 job vacancies were closed in the first semester of 1998.

Explanation

Based on the graph, it can be observed that the number of job vacancies decreased significantly during the first half of the year. This indicates that more than 62,000 job vacancies were closed in the first semester of 1998.