Which of the following series is conditionally convergent?
(A) $\sum _ { k = 1 } ^ { \infty } ( - 1 ) ^ { k } \frac { 5 } { k ^ { 3 } + 1 }$
(B) $\sum _ { k = 1 } ^ { \infty } ( - 1 ) ^ { k } \frac { 5 } { k + 1 }$
(C) $\sum _ { k = 1 } ^ { \infty } ( - 1 ) ^ { k } \frac { 5 k } { k + 1 }$
(D) $\sum _ { k = 1 } ^ { \infty } ( - 1 ) ^ { k } \frac { 5 k ^ { 2 } } { k + 1 }$

The figure above shows the graph of the polar curve $r = 2 + 4 \sin \theta$. What is the area of the shaded region?
(A) 2.174
(B) 2.739
(C) 13.660
(D) 37.699

The graph of the function $f$ is shown above. Which of the following statements is false?
(A) $\lim _ { x \rightarrow 2 } f ( x )$ exists.
(B) $\lim _ { x \rightarrow 3 } f ( x )$ exists.
(C) $\lim _ { x \rightarrow 4 } f ( x )$ exists.
(D) $\lim _ { x \rightarrow 5 } f ( x )$ exists.
(E) The function $f$ is continuous at $x = 3$.

Question 168
Um recipiente em forma de paralelepípedo retângulo tem dimensões internas de 50 cm $\times$ 40 cm $\times$ 30 cm. A capacidade desse recipiente, em litros, é
(A) 6 (B) 12 (C) 60 (D) 120 (E) 600

Question 177
A figura mostra um trapézio $ABCD$ com $AB \parallel CD$, $AB = 10$ cm, $CD = 6$ cm e altura $h = 4$ cm.
[Figure]
A área desse trapézio, em cm², é
(A) 24 (B) 28 (C) 32 (D) 36 (E) 40

Question 179
Uma esfera tem raio de 3 cm. O volume dessa esfera, em cm³, é
(A) $9\pi$ (B) $12\pi$ (C) $27\pi$ (D) $36\pi$ (E) $108\pi$

A empresa Recicla Tudo coletou, em um determinado mês, 1 200 kg de material reciclável, sendo 30\% de papel, 20\% de plástico, 20\% de vidro e 30\% de metal. No mês seguinte, a empresa coletou 1 500 kg de material reciclável, com a mesma distribuição percentual. Qual foi o aumento, em quilograma, na coleta de papel do primeiro para o segundo mês?
(A) 60 (B) 75 (C) 90 (D) 100 (E) 120

Uma torneira despeja água em um reservatório cilíndrico de base circular com raio de 1 m e altura de 2 m. A torneira enche o reservatório em 4 horas. Qual é a vazão da torneira, em metros cúbicos por hora? Considere $\pi \approx 3{,}14$.
(A) 1,57 (B) 3,14 (C) 6,28 (D) 12,56 (E) 25,12

O gráfico a seguir representa a evolução do número de usuários de internet no Brasil entre 2005 e 2010.
Com base no gráfico, o percentual de crescimento no número de usuários de internet no Brasil, de 2005 a 2010, foi de aproximadamente
(A) 100\% (B) 120\% (C) 140\% (D) 160\% (E) 180\%

Um comerciante comprou um produto por R\$\,80,00 e o vendeu com um lucro de 25\%. Após algum tempo, ele comprou o mesmo produto por R\$\,100,00 e o vendeu com um lucro de 20\%. A diferença entre os preços de venda do produto nas duas situações é de
(A) R\$\,5,00 (B) R\$\,10,00 (C) R\$\,15,00 (D) R\$\,20,00 (E) R\$\,25,00

A figura mostra um triângulo retângulo com catetos medindo 3 cm e 4 cm.
A área do quadrado construído sobre a hipotenusa desse triângulo é de
(A) 7 cm$^2$ (B) 12 cm$^2$ (C) 25 cm$^2$ (D) 49 cm$^2$ (E) 144 cm$^2$

Um capital de R\$\,5\,000,00 é aplicado a uma taxa de juros simples de 2\% ao mês. Após 6 meses, o montante obtido será de
(A) R\$\,5\,100,00 (B) R\$\,5\,300,00 (C) R\$\,5\,500,00 (D) R\$\,5\,600,00 (E) R\$\,5\,700,00

O volume de uma esfera de raio 3 cm é
(A) $9\pi$ cm$^3$ (B) $12\pi$ cm$^3$ (C) $27\pi$ cm$^3$ (D) $36\pi$ cm$^3$ (E) $54\pi$ cm$^3$

High-performance sport today has produced a question still without an answer: What is the limit of the human body? The original marathoner, the Greek of legend, died of fatigue from running 42 kilometers. American Dean Karnazes, crossing the California plains alone, managed to run ten times more in 75 hours.
A Physical Education teacher, while discussing with the class the text about the American marathoner's capacity, drew on the board a straight track of 60 centimeters, which would represent the referred route.
If Dean Karnazes' route were also on a straight track, what would be the scale between the track made by the teacher and the one covered by the athlete?
(A) 1:700
(B) 1:7000
(C) 1:70 000
(D) 1:700 000
(E) 1:7000000

The rhombus represented in Figure 1 was formed by the union of the centers of four tangent circles, with radii of the same measure.
By doubling the radius of two of the circles centered at opposite vertices of the rhombus and still maintaining the tangency configuration, a situation is obtained as illustrated by Figure 2.
The perimeter of the rhombus in Figure 2, when compared to the perimeter of the rhombus in Figure 1, had an increase of
(A) 300\%.
(B) $200\%$.
(C) 150\%.
(D) 100\%.
(E) $50\%$.

José, Carlos and Paulo must transport a certain quantity of oranges on their bicycles. They decided to divide the route to be traveled into two parts, and at the end of the first part they would redistribute the quantity of oranges that each one carried depending on each one's fatigue. In the first part of the route José, Carlos and Paulo divided the oranges in the proportion 6:5:4, respectively. In the second part of the route José, Carlos and Paulo divided the oranges in the proportion $4:4:2$, respectively.
Knowing that one of them carried 50 more oranges in the second route, what is the quantity of oranges that José, Carlos and Paulo, in that order, transported in the second part of the route?
(A) 600, 550, 350
(B) 300, 300, 150
(C) 300, 250, 200
(D) 200, 200, 100
(E) $100, 100, 50$

On a blog of miscellaneous content, music, mantras and diverse information, ``Halloween Tales'' were posted. After reading, visitors could give their opinion by marking their reactions as: ``Fun'', ``Scary'' or ``Boring''. At the end of one week, the blog recorded that 500 distinct visitors accessed this post.
The following graph presents the result of the survey.
The blog administrator will draw a book among the visitors who gave their opinion on the ``Halloween Tales'' post.
Knowing that no visitor voted more than once, the probability that a person chosen at random among those who voted marked that the ``Halloween Tales'' story is ``Boring'' is most closely approximated by
(A) 0.09.
(B) 0.12.
(C) 0.14.
(D) 0.15.
(E) 0.18.

Arthur wishes to buy a piece of land from Cléber, who offers him the following payment options:

• Option 1: Pay in full, for $\mathrm{R}\$ 55000.00$;
• Option 2: Pay in installments, giving a down payment of $\mathrm{R}\$ 30000.00$, and another installment of $\mathrm{R}\$ 26000.00$ six months from now.
• Option 3: Pay in installments, giving a down payment of $\mathrm{R}\$ 20000.00$, plus an installment of $\mathrm{R}\$ 20000.00$, six months from now and another of $\mathrm{R}\$ 18000.00$ twelve months from the purchase date.
• Option 4: Pay in installments giving a down payment of R\$15000.00 and the remainder in 1 year from the purchase date, paying $\mathrm{R}\$ 39000.00$.
• Option 5: Pay in installments, one year from now, the amount of $\mathrm{R}\$ 60000.00$.

Arthur has the money to pay in full, but evaluates whether it would not be better to invest the money from the full payment amount (or even a smaller amount) in an investment, with a return of 10\% per semester, withdrawing the amounts as the installments of the chosen option became due.
After evaluating the situation from a financial point of view and the conditions presented, Arthur concluded that it was more financially advantageous to choose option
(A) 1.
(B) 2.
(C) 3.
(D) 4.
(E) 5.

A rectangular fabric lining brings on its label the information that it will shrink after the first wash while maintaining, however, its shape. The following figure shows the original measurements of the lining and the size of the shrinkage (x) in length and (y) in width. The algebraic expression that represents the area of the lining after being washed is $(5-x)(3-y)$.
Under these conditions, the area lost from the lining after the first wash will be expressed by
(A) $2xy$
(B) $15 - 3x$
(C) $15 - 5y$
(D) $-5y - 3x$
(E) $5y + 3x - xy$

The minimum capacity, in BTU/h, of an air conditioning unit for environments without sun exposure, can be determined as follows:

• $600 \mathrm{BTU}/\mathrm{h}$ per $\mathrm{m}^{2}$, considering up to two people in the environment;
• for each additional person in this environment, add 600 BTU/h;
• add another 600 BTU/h for each electrical appliance in operation in the environment.

An air conditioning unit will be installed in a room, without sun exposure, with dimensions $4\mathrm{~m} \times 5\mathrm{~m}$, in which four people remain and which has a television set in operation.
The minimum capacity, in BTU/h, of this air conditioning unit should be
(A) 12000.
(B) 12600.
(C) 13200.
(D) 13800.
(E) 15000.

The mechanical resistance $S$ of a wooden beam, in the form of a rectangular parallelepiped, is directly proportional to its width (b) and to the square of its height (d) and inversely proportional to the square of the distance between the beam's supports, which coincides with its length ($x$), as illustrated in the figure. The constant of proportionality k is called the resistance of the beam.
The expression that translates the resistance S of this wooden beam is
(A) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b} \cdot \mathrm{d}^{2}}{\mathrm{x}^{2}}$
(B) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b} \cdot \mathrm{d}}{\mathrm{x}^{2}}$
(C) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b} \cdot \mathrm{d}^{2}}{\mathrm{x}}$
(D) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b}^{2} \cdot \mathrm{d}}{\mathrm{x}}$
(E) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b} \cdot 2\mathrm{d}}{2\mathrm{x}}$

The principal of a school invited the 280 third-year students to participate in a game. Suppose there are 5 objects and 6 characters in a house with 9 rooms; one of the characters hides one of the objects in one of the rooms of the house. The objective of the game is to guess which object was hidden by which character and in which room of the house the object was hidden.
All students decided to participate. Each time a student is drawn and gives their answer. The answers must always be different from the previous ones, and the same student cannot be drawn more than once. If the student's answer is correct, they are declared the winner and the game is ended.
The principal knows that some student will get the answer right because there are
(A) 10 more students than possible distinct answers.
(B) 20 more students than possible distinct answers.
(C) 119 more students than possible distinct answers.
(D) 260 more students than possible distinct answers.
(E) 270 more students than possible distinct answers.

A biologist measured the height of five different trees and represented them on the same grid, using different scales, as indicated in the figure below.

I	II	III	IV	V
1:100	2:100	2:300	1:300	2:300

Which tree has the greatest actual height?
(A) I
(B) II
(C) III
(D) IV
(E) V

In a game there are two urns with 10 balls of the same size in each urn. The table below indicates the quantities of balls of each color in each urn.

Color	Urn 1	Urn 2
Yellow	4	0
Blue	3	1
White	2	2
Green	1	3
Red	0	4

A turn consists of: $1^{\circ}$) the player makes a guess about the color of the ball that will be drawn by them from urn 2; $2^{\circ}$) they randomly draw a ball from urn 1 and place it in urn 2, mixing it with those already there; $3^{\circ}$) then they also randomly draw a ball from urn 2; $4^{\circ}$) if the color of the last ball drawn is the same as the initial guess, they win the game.
Which color should be chosen by the player so that they have the greatest probability of winning?
(A) Blue.
(B) Yellow.
(C) White.
(D) Green.
(E) Red.

Water meters are markers of water consumption in residences and commercial establishments. There are several models of water meter displays, some of which have a combination of a display and two pointer clocks. The number formed by the first four digits of the display gives the consumption in $\mathrm{m}^{3}$, and the last two digits represent, respectively, the hundreds and tens of liters of water consumed. One of the pointer clocks indicates the quantity in liters, and the other in tenths of liters, as illustrated in the figure below.
Considering the information indicated in the figure, the total water consumption recorded on this water meter, in liters, is equal to
(A) 3534.85.
(B) 3544.20.
(C) 3534850.00.
(D) 3534859.35.
(E) 3534850.39.