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]

A map uses a scale of 1:50,000. On the map, the distance between two cities is 8 cm. What is the real distance between the two cities, in kilometers?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10

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) $21\pi$

The equation of the line passing through the points $(0, 3)$ and $(2, 7)$ is:
(A) $y = x + 3$
(B) $y = 2x + 3$
(C) $y = 3x + 1$
(D) $y = 2x + 1$
(E) $y = x + 5$

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 a computer game, a cube is initially positioned as indicated in the figure.
Each displacement made by this cube always occurs in one of the directions defined by the three coordinate axes. When moving from the initial position, this cube moved 3 units closer to the $yz$ plane, moved 5 units away from the $xz$ plane, and moved 4 units closer to the $xy$ plane.
The figure that presents the orthogonal projections of this cube onto the three coordinate planes, after performing the described movements, is
(A), (B), (C), (D), or (E) as indicated in the figures.

A person intends to install a natural gas vehicle (NGV) kit in his car. At the store he chose to make the purchase and installation of this kit, there were five models of cylinders for gas storage, whose capacities, in cubic meters, were, respectively: $10, 14, 17, 21$, and 25. The price of the cylinder is proportional to its capacity. This car will travel 30 km daily, 7 days a week, and the NGV consumption is $1\,\mathrm{m}^3$ for every 13 km traveled. The person will choose the cylinder model with the lowest price and that guarantees only one refueling per week.
Under these conditions, what will be the capacity, in cubic meters, of the cylinder chosen by this person?
(A) 10
(B) 14
(C) 17
(D) 21
(E) 25

In a school cafeteria, there are five foods sold in packages with different quantities of servings.
The nutritional information contained on the labels of these products is indicated in the images.
A student always chooses the food with the lowest total amount of sodium per package.
Which of these products should be chosen by the student?
(A) Potato chips.
(B) Salted sticks.
(C) Multigrain biscuit.
(D) Polvilho biscuit.
(E) Water and salt biscuit.

A factory used a 3D printer to produce the prototype of a part. The prototype has the shape of a convex polyhedron, obtained by the juxtaposition of two distinct solids, one with the shape of a regular hexagonal prism and the other with the shape of a straight hexagonal pyramid frustum. The larger base of the pyramid frustum coincides with one of the bases of the prism.
After printing the prototype, it was sent to the customization sector for painting its surface. The criterion defined for painting considers that congruent faces must be painted with the same color, and non-congruent faces must have different colors. What is the quantity of colors used to paint the prototype?
(A) 9
(B) 8
(C) 6
(D) 4
(E) 3

Research in the area of neurobiology confirms that meditative practice is responsible for considerably reducing respiratory frequency for advanced practitioners, who, after initiating meditation, have their respiratory frequencies reduced until they stabilize at a lower level. The graph presents the relationship of respiratory frequency, in breaths per minute (rpm), in relation to time, in minutes, of an advanced practitioner, in which $(\mathrm{f}_1)$ represents the frequency at instant $\mathrm{t}_1$, when meditative practice begins; and $(\mathrm{f}_2)$, the frequency at instant $t_2$, from which it stabilizes during meditation.
From the instant $\mathrm{t}_1$, when the meditative practice begins, the behavior of respiratory frequency, in relation to time,
(A) remains constant.
(B) is directly proportional to time.
(C) is inversely proportional to time.
(D) decreases until the instant $\mathrm{t}_2$, after which it becomes constant.
(E) decreases proportionally to time, both between $\mathrm{t}_1$ and $\mathrm{t}_2$ and after $t_2$.

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

Around a circular lagoon, whose radius measures 1 km, there is a bicycle path. Due to frequent bicycle thefts, the city council plans to allocate police officers in strategic positions to patrol this bicycle path, in order to make it fully protected. A point on the bicycle path is considered protected if there is at least one police officer at most 200 m away from that point, positioned on the bicycle path. The figure illustrates a point $P$ on the bicycle path, which will be protected if there is at least one police officer positioned on the dark gray region.
Disregard the width of the bicycle path and use 3 as an approximation for $\pi$.
Under these conditions, the minimum number of police officers to be allocated along this bicycle path to make it protected is
(A) 4.
(B) 8.
(C) 15.
(D) 30.
(E) 60.

In a laboratory, a container holds 10 liters of a solution composed only of substances $\mathrm{S}_1$ and $\mathrm{S}_2$. Of this solution, 99.95\% is $\mathrm{S}_1$. An amount of $\mathrm{S}_1$ will be removed from this solution, maintaining the initial amount of $\mathrm{S}_2$, so that 99.90\% of the new solution is $S_1$.
What is the amount of $\mathrm{S}_1$, in liters, that will be removed?
(A) 0.0050
(B) 0.0100
(C) 0.5000
(D) 4.9775
(E) 5.0000

A fuel distributor owns tanker trucks with a capacity of 30,000 liters each. In any transport carried out by these trucks, the same volume of fuel is discarded because it contains many impurities. This discarded volume is independent of the quantity transported.
A gas station ordered 10,000 liters of gasoline from this distributor, which sent 10,200 liters, considering the volume discarded in transport. Nevertheless, the amount of gasoline delivered to the gas station was 9,900 liters.
In a new order, this gas station requested that exactly double the volume of gasoline ordered in the previous order be delivered.
Using the same truck from the previous delivery, what is the minimum volume of gasoline, in liters, that the distributor should send to guarantee delivery of the ordered quantity in this new order?
(A) 20,100
(B) 20,200
(C) 20,300
(D) 20,400
(E) 20,600