In order to classify the best routes in a traffic application, a researcher proposes a model based on electrical circuits. In this model, the current represents the number of cars passing through a point on the track in the interval of 1 s. The potential difference (p.d.) corresponds to the amount of energy per car necessary for displacement of 1 m. Similarly to Ohm's law, each route is classified by its resistance, with the one with greater resistance being the most congested. The application shows the routes in increasing order, that is, from the route of least to greatest resistance.
As a test for the system, three possible routes are used for a trip from A to B, with the values of p.d. and current as shown in the table.

Route	p.d. $\left( \frac{\mathrm{J}}{\text{car} \cdot \mathrm{m}} \right)$	Current $\left( \frac{\text{car}}{\mathrm{s}} \right)$
1	510	4
2	608	4
3	575	3

In this test, the ordering of the routes indicated by the application will be:
(A) $1,2,3$.
(B) $1,3,2$.
(C) $2,1,3$.
(D) $3,1,2$.
(E) $3,2,1$.

Ethanol is a fuel produced from the fermentation of sucrose present in sugarcane juice. One of the factors that affects the production of this alcohol is the degree of sucrose deterioration, which begins after cutting due to the action of microorganisms. Five samples of different types of sugarcane were analyzed and each received an identification code. The table presents data on the concentration of sucrose and microorganisms present in these samples.

\cline{2-6} \multicolumn{1}{c|}{}	\multicolumn{5}{c|}{Sugarcane sample}
\cline{2-6} \multicolumn{1}{c|}{}	RB72	RB84	RB92	SP79	SP80
\begin{tabular}{ c } Initial sucrose
concentration $\left( \mathrm{g~L}^{-1} \right)$

& 13.0 & 18.0 & 16.0 & 14.0 & 17.0 \hline

Microorganism

concentration

$\left( \mathrm{mg~L}^{-1} \right)$

& 0.7 & 0.8 & 0.6 & 0.5 & 0.9 \hline \end{tabular}
It is intended to choose the type of sugarcane that will contain the highest sucrose content 10 hours after cutting and that, consequently, will produce the largest amount of ethanol by fermentation. Consider that there is a reduction of approximately 50\% of the sucrose concentration in this time for each $1.0 \mathrm{~mg~L}^{-1}$ of microorganisms present in the sugarcane.
Which type of sugarcane should be chosen?
(A) RB72
(B) RB84
(C) RB92
(D) SP79
(E) SP80

Tartaric acid is the main acid in wine and is directly related to its quality. In the evaluation of a white wine in production, an analyst neutralized an aliquot of $25.0 \mathrm{~mL}$ of the wine with NaOH at $0.10 \mathrm{~mol~L}^{-1}$, consuming a volume equal to $8.0 \mathrm{~mL}$ of this base. The reaction for this titration process is represented by the chemical equation:
Tartaric acid (molar mass: $150 \mathrm{~g~mol}^{-1}$) reacts with NaOH in a neutralization reaction.
The concentration of tartaric acid in the analyzed wine is closest to:
(A) $1.8 \mathrm{~g~L}^{-1}$
(B) $2.4 \mathrm{~g~L}^{-1}$
(C) $3.6 \mathrm{~g~L}^{-1}$
(D) $4.8 \mathrm{~g~L}^{-1}$
(E) $9.6 \mathrm{~g~L}^{-1}$

The manual of an electric shower informs that its three heating levels (warm, hot, and superhot) present the following variations in water temperature as a function of its flow rate:

\multirow{2}{*}{Flow rate $\left( \frac{\mathrm{L}}{\mathrm{min}} \right)$}	\multicolumn{3}{|c|}{$\Delta \mathrm{T} \left( {}^{\circ} \mathrm{C} \right)$}
\cline{2-4}	Warm	Hot	Superhot
3	10	20	30
6	5	10	15

A circuit breaker is used to protect this shower circuit against electrical overloads at any heating level. By standard, the circuit breaker is specified by the nominal current equal to the multiple of 5 A immediately higher than the maximum current of the circuit. Consider that the shower should be connected to 220 V and that all energy is dissipated through the shower's resistance and converted into thermal energy transferred to the water, which has a specific heat of $4.2 \frac{\mathrm{~J}}{\mathrm{~g~}^{\circ}\mathrm{C}}$ and density of $1000 \frac{\mathrm{~g}}{\mathrm{~L}}$. The circuit breaker suitable for protecting this shower is specified by:
(A) 60 A
(B) 30 A
(C) 20 A
(D) 10 A
(E) 5 A

A teacher throws a sphere vertically upward, which returns, after a few seconds, to the launch point. He then lists on a board all the possibilities for kinematic quantities.

Kinematic quantity	Magnitude	Direction
\multirow{3}{*}{Velocity}	\multirow{2}{*}{$v \neq 0$}	Upward
\cline { 3 - 3 }		Downward
\cline { 2 - 3 }	$v = 0$	Undefined*
\multirow{3}{*}{Acceleration}	\multirow{2}{*}{$a \neq 0$}	Upward
\cline { 2 - 3 }		Downward
\cline { 2 - 3 }	$a = 0$	Undefined*

*Quantities with zero magnitude do not have a defined direction. He asks students to analyze the kinematic quantities at the instant when the sphere reaches maximum height, choosing a combination for the magnitudes and directions of velocity and acceleration. The choice that corresponds to the correct combination is
(A) $v = 0$ and $a \neq 0$ upward.
(B) $v \neq 0$ upward and $a = 0$.
(C) $v = 0$ and $a \neq 0$ downward.
(D) $v \neq 0$ upward and $a \neq 0$ upward.
(E) $v \neq 0$ downward and $a \neq 0$ downward.

A gym decides to gradually replace its weight training equipment. Now, users who use type 1 apparatus can also use type 2 apparatus, represented in the figure, to lift loads corresponding to masses $\mathbf{M}_{1}$ and $\mathbf{M}_{2}$, at constant velocity. In order for the exercise to be performed with the same force $\vec{F}$, users should be instructed about the relationship between the loads in the two types of apparatus, since fixed pulleys only change the direction of forces, while the movable pulley divides the forces.
In both apparatus, consider the cords inextensible, the masses of the pulleys and cords negligible, and that there is no energy dissipation.
For this gym, what should be the ratio $\frac{\mathbf{M}_{2}}{\mathbf{M}_{1}}$ informed to users?
(A) $\frac{1}{4}$
(B) $\frac{1}{2}$
(C) 1
(D) 2
(E) 4

In the comic strip by Mauricio de Sousa, the characters Cebolinha and Cascão play a game using two cans and a string. When they realize that sound can be transmitted through the string, they decide to change the length of the string to make it increasingly longer. All other conditions remained unchanged during the game.
In practice, as the length of the string increases, there is a reduction in which characteristic of the sound wave?
(A) Pitch.
(B) Period.
(C) Amplitude.
(D) Velocity.
(E) Wavelength.

Digital information - data - is recorded on optical discs, such as CDs and DVDs, in the form of microscopic cavities. The recording and optical reading of this information are performed by a laser (monochromatic light source). The smaller the dimensions of these cavities, the more data is stored in the same area of the disc. The limiting factor for reading data is light scattering by the diffraction effect, a phenomenon that occurs when light passes through an obstacle with dimensions on the order of its wavelength. This limitation motivated the development of lasers with emission at shorter wavelengths, making it possible to store and read data in increasingly smaller cavities. In which spectral region is the wavelength of the laser that optimizes data storage and reading on discs of the same area located?
(A) Violet.
(B) Blue.
(C) Green.
(D) Red.
(E) Infrared.

Bluetooth is a short-range wireless communication technology present in different consumer electronic devices. It allows different electronic devices to connect and exchange data with each other. In the bluetooth standard, called Class 2, the antennas transmit signals with power equal to $2.4 \mathrm{~mW}$ and allow two devices distanced up to 10 m to connect. Consider that these antennas behave as point sources that emit spherical electromagnetic waves and that signal intensity is calculated as power per unit area. Consider 3 as an approximate value for $\pi$. For the bluetooth signal to be detected by the antennas, the minimum value of its intensity, in $\frac{\mathrm{W}}{\mathrm{m}^{2}}$, is closest to
(A) $2.0 \times 10^{-6}$.
(B) $2.0 \times 10^{-5}$.
(C) $2.4 \times 10^{-5}$.
(D) $2.4 \times 10^{-3}$.
(E) $2.4 \times 10^{-1}$.

A transportation safety team from a company evaluates the behavior of tensions that appear in two ropes, 1 and 2, used to secure a load of mass $\mathbf{M}=200 \mathrm{~kg}$ on the truck bed, as shown in the illustration. When the truck starts from rest, its acceleration is constant and equal to $3 \mathrm{~m}/\mathrm{s}^{2}$ and, when it is braked abruptly, its braking is constant and equal to $5 \mathrm{~m}/\mathrm{s}^{2}$. In both situations, the load is on the verge of movement, and the direction of the truck's movement is indicated in the figure. The coefficient of static friction between the box and the truck bed floor is equal to 0.2. Consider the acceleration due to gravity equal to $10 \mathrm{~m}/\mathrm{s}^{2}$, the initial tensions in the ropes equal to zero, and both ropes ideal.
In the situations of acceleration and braking of the truck, the tensions in ropes 1 and 2, in newtons, will be
(A) acceleration: $T_{1}=0$ and $T_{2}=200$; braking: $T_{1}=600$ and $T_{2}=0$.
(B) acceleration: $T_{1}=0$ and $T_{2}=200$; braking: $T_{1}=1400$ and $T_{2}=0$.
(C) acceleration: $T_{1}=0$ and $T_{2}=600$; braking: $T_{1}=600$ and $T_{2}=0$.
(D) acceleration: $T_{1}=560$ and $T_{2}=0$; braking: $T_{1}=0$ and $T_{2}=960$.
(E) acceleration: $T_{1}=640$ and $T_{2}=0$; braking: $T_{1}=0$ and $T_{2}=1040$.

Cosmic rays are sources of ionizing radiation potentially dangerous to the human organism. To quantify the dose of radiation received, the sievert (Sv) is used, defined as the unit of energy received per unit of mass. Exposure to radiation from cosmic rays increases with altitude, which can represent a problem for aircraft crews. Recently, accurate measurements of ionizing radiation doses were performed for flights between Rio de Janeiro and Rome. The results have indicated that the average radiation dose received during the cruise phase (which generally represents 80\% of the total flight time) of this intercontinental route is $2 \mu\mathrm{Sv}/\mathrm{h}$. International civil aviation standards limit to 1000 hours per year the working time for crews operating on intercontinental flights. Consider that the ionizing radiation dose for a chest radiograph is estimated at $0.2 \mathrm{mSv}$.
How many chest radiographs does the dose of ionizing radiation to which a crew member operating on the Rio de Janeiro-Rome route is exposed over one year correspond to?
(A) 8
(B) 10
(C) 80
(D) [options cut off in source]

The volume of a sphere with radius $r = 3$ cm is:
(A) $12\pi$ cm$^3$
(B) $24\pi$ cm$^3$
(C) $36\pi$ cm$^3$
(D) $48\pi$ cm$^3$
(E) $72\pi$ cm$^3$

A cone has base radius 3 cm and height 4 cm. What is the lateral surface area, in square centimeters, of this cone?
(A) $9\pi$
(B) $12\pi$
(C) $15\pi$
(D) $18\pi$
(E) $21\pi$

A regular hexagon has side length 4 cm. What is its area, in square centimeters?
(A) $24\sqrt{3}$
(B) $32\sqrt{3}$
(C) $36\sqrt{3}$
(D) $40\sqrt{3}$
(E) $48\sqrt{3}$

A trapezoid has parallel sides of length 6 cm and 10 cm, and height 4 cm. What is its area, in square centimeters?
(A) 24
(B) 28
(C) 32
(D) 36
(E) 40

The pentagonal gyroelongated cupola is a Johnson polyhedron, whose faces are regular polygons, but which is not a Platonic polyhedron, Archimedean polyhedron, prism, or antiprism.
The figures present this polyhedron in two positions and one of its nets.
How many vertices does this polyhedron have?
(A) 21
(B) 25
(C) 55
(D) 80
(E) 110

An ecological brick factory with 3 employees, each working 6 hours daily, produces 720 units per day. To meet the growing demand for this type of brick, this factory now has 5 employees, each working 9 hours per day, thus increasing its production capacity. All employees produce an equal quantity of bricks each hour, regardless of whether they work 6 or 9 hours daily.
The number of bricks manufactured daily after the increase in production capacity is
(A) 800.
(B) 1080.
(C) 1200.
(D) 1800.
(E) 2520.

To monitor the flow of visitors to its building, a company established an identification code for visits. According to the established rule, each visitor will be identified with a sequential 7-digit numerical code, determined, from left to right, as follows:

• the first digit indicates the floor to which the visitor is going, which is a number from 1 to 4;
• the next two digits correspond to the number of the company sector to which the visitor is destined. This number ranges from 01 to 20;
• the following three digits correspond to the number of the company employee with whom the visitor will meet. This number ranges from 001 to 135;
• the last digit indicates whether the visitor arrived at the company in the morning, digit 0, or in the afternoon, digit 1.

A visitor arrived at the company at 10 o'clock in the morning to meet with the employee identified by the number 109, who works in sector 08 of the company, located on the $2^{\underline{\text{nd}}}$ floor.
The identification code of this visitor is
(A) 0109082.
(B) 0281090.
(C) 1010982.
(D) 2081090.
(E) 2810910.

In athletics, a major challenge in the 100-meter sprint is completing it in a time below the reference mark of 10.00 seconds. Several athletes have already achieved this feat. In 2009, Jamaican Usain Bolt set the men's world record for this event, with a time of 9.58 seconds.
What is the difference, in seconds, between the reference mark and the mark established by Usain Bolt in 2009?
(A) 0.02
(B) 0.42
(C) 0.52
(D) 1.02
(E) 1.42

The remote control of a toy car comes equipped with a screen that automatically adjusts the scale used in displaying each displacement. The screen displays the image of the displacement, the scale used in generating this image, and the length of this displacement, in centimeters, in accordance with the scale used. The figures represent the remote control screen displaying data from five displacements made by this toy car.
The option that indicates the displacement of greatest length performed by the toy car is
(A) I.
(B) II.
(C) III.
(D) IV.
(E) V.

An artist, who usually makes drawings with sand on the beach, asked a beachgoer to make a small drawing, which would serve as a sketch for a large work of art to be made in the sand. This drawing is represented in the figure.
After completion, the work of art obtained maintained the same proportions as the drawing made by the beachgoer, with the measurements indicated in the figure being enlarged to 30 m.
At what scale does this drawing represent the work of art?
(A) 1 : 1.5
(B) 1 : 2.25
(C) 1 : 10
(D) 1 : 100
(E) 1 : 150

The owner of an ice cream shop stores ice cream in containers of $20{,}000\,\mathrm{cm}^3$. He serves the ice cream in cups, in portions of 250 mL.
The number of cups he can serve from a full container of ice cream is
(A) 5.
(B) 8.
(C) 50.
(D) 80.
(E) 800.

The gray squares in the figure represent the city blocks in a part of the neighborhood where João and his friend live. The small square (A), painted in black and located in the upper left corner of a larger square, indicates the house of João's friend. João also lives in a corner house, but at the northeast end of a city block. To reach his friend's house, upon leaving home, João must walk through the block where he lives in the west direction, turn right, walk through three blocks in the north direction, and turn left. His friend's house is in the second block to the west.
The city block where João's house is located is represented by the square with the letter
(A) P.
(B) Q.
(C) R.
(D) S.
(E) T.

In a city, a tunnel will be built that crosses a mountain to facilitate the transit of automobiles and bicycles. Two projects were developed and the schemes with the front views of these projects are presented in the figure.
Project 1 has two tunnels, one exclusive for bicycles and the other for automobiles. Project 2 has a single tunnel, with spaces reserved for exclusive transit of bicycles and automobiles. In both projects, the tunnels have the shape of a straight semicylinder of the same length, with two-way routes for both types of vehicles, separated by walls.
The project to be approved will be the one that presents the smallest cross-sectional area, as it will imply a smaller volume of material removed from the mountain.
Consider 3 as an approximation for $\pi$ and disregard the thicknesses of the walls.
The project to be approved is
(A) 1, as it presents a cross-sectional area measuring $67.5\,\mathrm{m}^2$.
(B) 2, as it presents a cross-sectional area measuring $121.5\,\mathrm{m}^2$.
(C) 1, as it presents a cross-sectional area measuring $135\,\mathrm{m}^2$.
(D) 2, as it presents a cross-sectional area measuring $243\,\mathrm{m}^2$.
(E) either one of the two, as they present cross-sectional areas with equal measurements.

The final of a football championship was disputed in 2 regular periods, of 45 minutes each, without added time, with an extension of 30 minutes, also without added time. A player entered at the beginning of the second period, with equipment to measure the distance traveled during his participation in the game. At the end of the second regular period, this player had traveled $4.5\,\mathrm{km}$. He maintained in the extension the same average speed that he had maintained in the second regular period.
The distance traveled by this player during his participation in the match, in kilometers, was
(A) 4.5.
(B) 6.0.
(C) 7.5.
(D) 9.0.
(E) 12.0.