exam stringclasses 4
values | exam_stage stringclasses 2
values | subject stringclasses 4
values | domain stringlengths 6 27 | subdomain stringlengths 8 31 ⌀ | context stringlengths 19 362 ⌀ | image_context float64 | image stringlengths 14 157 | question stringlengths 16 513 | options stringlengths 42 560 | answer stringlengths 27 114 |
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naep | standalone | maths | functions | domain_and_range | The complete graph of a function is shown in the $xy$ -plane. | null | images/87cd824f67a14e9c9987cdeabfa8207d_4_img.webp | Which of the following inequalities best represents the domain of the function shown? | {'A': '$-2 \\le x \\le 3$', 'B': '$-4 \\le x \\le 7$', 'C': '$-4 \\le y \\le 7$', 'D': '$-5 \\le x \\le 6$', 'E': '$-5 \\le y \\le 6$'} | {"label": "D", "text": "$-5 \\le x \\le 6$"} |
naep | standalone | maths | functions | domain_and_range | The complete graph of a function is shown in the $xy$ -plane. | null | images/87cd824f67a14e9c9987cdeabfa8207d_4_img.webp | Which of the following inequalities best represents the range of the function shown? | {'A': '$-4 \\le y \\le -2$', 'B': '$-4 \\le x \\le 7$', 'C': '$-4 \\le y \\le 7$', 'D': '$-5 \\le x \\le 6$', 'E': '$-5 \\le y \\le 6$'} | {"label": "C", "text": "$-4 \\le y \\le 7$"} |
naep | standalone | maths | geometry | polygon_interior_angles | All interior angles of the figure shown are congruent. | null | images/bb8c10c2b41d8155228e3246fb999df9_3_img.webp | What is the measure of the marked angle? | {'A': '$108^\\circ$', 'B': '$114^\\circ$', 'C': '$120^\\circ$', 'D': '$126^\\circ$', 'E': '$130^\\circ$'} | {"label": "A", "text": "$108^\\circ$"} |
naep | standalone | maths | geometry | geometric_measurement | Note: Figures not drawn to scale. | null | images/8a45382bc4a84beef792eb81d62a386c_3_img.webp | What is the value of $h$ in the figure? | {'A': '10', 'B': '25', 'C': '60', 'D': '120', 'E': '144'} | {"label": "D", "text": "120"} |
naep | standalone | maths | modeling | function_model_selection | Andy received an e-mail message. Andy sent the e-mail message to 3 people, who then each sent the e-mail message to 3 more people who had not already received the e-mail message. The table and graph show the first five stages and the number of people receiving the e-mail message at that stage. | null | images/d190c7f249f89e4512ed50d3b8002907_5_img.webp | Which of the following types of functions would best model these data? | {'A': 'Constant', 'B': 'Exponential', 'C': 'Linear', 'D': 'Quadratic', 'E': 'Trigonometric'} | {"label": "B", "text": "Exponential"} |
naep | standalone | maths | geometry | similar_triangles | Triangles $ABC$ and $DEF$ are similar. | null | images/5e55fc81a32a6015f28ba8addf401a6f_3_img.webp; images/5e55fc81a32a6015f28ba8addf401a6f_4_img.webp | What is the length of side $DE$ ? | {'A': '7', 'B': '14', 'C': '21', 'D': '28', 'E': '35'} | {"label": "A", "text": "7"} |
naep | standalone | maths | modeling | trend_extrapolation | The graph shows the number of homes built every 5th year by a construction company. | null | images/a4dea138f3918d4c1ed7318bfe71d501_4_img.webp | Based on the information given, which of the following is the best estimate of the number of homes that will be built in the 60th year of business, if the trend continues as shown? | {'A': '20', 'B': '30', 'C': '40', 'D': '45', 'E': '50'} | {"label": "B", "text": "30"} |
naep | standalone | maths | geometry | isosceles_triangles | In the figure, $\triangle ABC$ is isosceles, with $AB = BC$ . | null | images/0466b2c8500795936a4d92d23850597a_3_img.webp | What is the length of $\overline{DE}$ ? | {'A': '6 units', 'B': '12 units', 'C': '14 units', 'D': '18 units', 'E': '36 units'} | {"label": "D", "text": "18 units"} |
naep | standalone | maths | geometry | spatial_geometry_and_angles | Fold the card provided with this test book along line AC so that point D coincides with point E. Open the card so that segment BE is perpendicular to segment BD, as shown below, and keep the card in this position to answer the question. | null | images/6bf78fa3cdad9f2593f09b08a67faf6c_5_img.webp | The lengths of some of the line segments on the card are given below: (AC = 12) centimeters, (BE = 3) centimeters, (BD = 3) centimeters, (FG = 8) centimeters. What is the measure of $\angle EBF$ ? | {'A': '$30^\\circ$', 'B': '$45^\\circ$', 'C': '$60^\\circ$', 'D': '$90^\\circ$', 'E': '$135^\\circ$'} | {"label": "D", "text": "$90^\\circ$"} |
naep | standalone | maths | geometry | spatial_geometry_and_angles | Fold the card provided with this test book along line AC so that point D coincides with point E. Open the card so that segment BE is perpendicular to segment BD, as shown below, and keep the card in this position to answer the question. | null | images/cc0dca8281840fd5994b7203f4824470_5_img.webp | The lengths of some of the line segments on the card are given below: (AC = 12) centimeters, (BE = 3) centimeters, (BD = 3) centimeters, (FG = 8) centimeters. What is the measure of $\angle BED$ ? | {'A': '$30^\\circ$', 'B': '$45^\\circ$', 'C': '$60^\\circ$', 'D': '$90^\\circ$', 'E': '$180^\\circ$'} | {"label": "B", "text": "$45^\\circ$"} |
naep | standalone | maths | data_statistics_probability | scatterplots_and_bivariate_data | In the scatterplot below, each point represents the adult heights of a sister-brother pair. | null | images/60df119e73d4f448daab647914fa121a_5_img.webp | What is the brothers height that corresponds to the tallest sisters height? | {'A': '74 inches', 'B': '71 inches', 'C': '67 inches', 'D': '66 inches', 'E': '62 inches'} | {"label": "B", "text": "71 inches"} |
naep | standalone | science | physical_science | null | The graph shows the temperature of a sample of a liquid substance as it is heated at a constant rate. | null | images/f3b07fa89531bb81e6ebf22d9b39bfc3_4_img.webp | Which statement about the liquid is correct after 180 seconds? | {'A': 'The liquid is boiling.', 'B': 'The liquid has all evaporated.', 'C': 'The liquid has stopped absorbing thermal energy.', 'D': 'The molecules of the liquid have started to lose kinetic energy.'} | {"label": "A", "text": "The liquid is boiling."} |
naep | standalone | science | earth_environmental | null | The diagram shows a cross section of the top layers of Earth. | null | images/8a1960d401b7853e082ae5c0c19eb80f_4_img.webp | Which statement best explains why the tectonic plates that carry the continent and the island are moving away from each other as shown in the diagram? | {'A': 'Gravitational force between the Sun and Earth is breaking up the plates.', 'B': "Convection currents in Earth's mantle are pulling the plates in opposite directions.", 'C': "Magnetic material in Earth's mantle is pulling each plate into a subduction zone.", 'D': 'Water currents in the ocean are pushing the ocean... | {"label": "B", "text": "Convection currents in the Earth's mantle are pulling the plates in opposite directions."} |
naep | standalone | economics | The Market Economy | null | DIGITALCAMERAMARKET | null | images/a2c7acd309492f2f2ed29a761cfcfbcd3252164f6e72b12a70656701ef4fb576.jpg | According to the graph above, which of the following is the equilibrium price for digital cameras? | {'A': '$200', 'B': '$300', 'C': '$400', 'D': '$500'} | {"label": "C", "text": "$400"} |
sat | standalone | maths | Algebra | Elementary Algebra | Graph of a system of two linear equations on a coordinate plane. The axes range from -6 to 6. The first line passes through (0, 3) and (4, -5). The second line passes through (-2, 3) and (0, -2). The intersection point is (-2, 3). | null | images/9c6c03ce1bce7432c187b9482a6441a9_10_img.webp | What is the solution $(x, y)$ to the system? | {'A': '(4, -5)', 'B': '(0, 3)', 'C': '(0, -2)', 'D': '(-2, 3)'} | {"label": "D", "text": "(-2, 3)"} |
sat | standalone | maths | Algebra | Elementary Algebra | The scatterplot shows the relationship between two variables, $x$ and $y$. A line of best fit is also shown. | null | images/2e9b3426dd35315f9e873a289f77e662_9_img.webp | Which of the following equations best represents the line of best fit shown? | {'A': '$y = x + 3.4$', 'B': '$y = x - 3.4$', 'C': '$y = -x + 3.4$', 'D': '$y = -x - 3.4$'} | {"label": "A", "text": "$y = x + 3.4$"} |
sat | standalone | maths | Algebra | Elementary Algebra | The graph shows the linear relationship between $x$ and $y$. | null | images/2e9b3426dd35315f9e873a289f77e662_13_img.webp | Which table gives three values of $x$ and their corresponding values of $y$ for this relationship? | {'A': 'A table with values: (0, 0), (1, -7), (2, -9)', 'B': 'A table with values: (0, 0), (1, -3), (2, -1)', 'C': 'A table with values: (0, -5), (1, -7), (2, -9)', 'D': 'A table with values: (0, -5), (1, -3), (2, -1)'} | {"label": "C", "text": "A table with values: (0, -5), (1, -7), (2, -9)"} |
sat | standalone | maths | Algebra | Elementary Algebra | The graph shows the relationship between the number of shares of stock from Company A, $x$, and the number of shares of stock from Company B, $y$, that Simone can purchase. | null | images/ab7802307f393335c7a30a5e5a6d2e95_9_img.webp | Which equation could represent this relationship? | {'A': '$y = 8x + 12$', 'B': '$8x + 12y = 480$', 'C': '$y = 12x + 8$', 'D': '$12x + 8y = 480$'} | {"label": "B", "text": "$8x + 12y = 480$"} |
sat | standalone | maths | Statistics | Descriptive Statistics | Histograms showing frequency distributions for Data Set A and Data Set B. Both histograms have Frequency (Y-axis) ranging from 0 to 12, and Integer (X-axis) intervals from 10 to 60, with tick marks every 10 units. | null | images/eacad03400a69d473cc109518dad36cd_5_img.webp | What is the smallest possible difference between the mean of data set A and the mean of data set B? | {'A': '0', 'B': '1', 'C': '10', 'D': '23'} | {"label": "B", "text": "1"} |
dc | standalone | maths | algebra | functions | The function $g$ is defined by $g(x) = - 3x + 2$ . Which statements are true? Select all that apply. | null | images/13_0.jpg | Which statements are true? Select all that apply. | {"A": "$f(-2)$ is greater than $g(-2)$ .", "B": "$f(-1)$ is less than $g(-1)$ .", "C": "$f(0)$ is greater than $g(0)$ .", "D": "$f(1)$ is less than $g(1)$ .", "E": "$f(2)$ is greater than $g(2)$ ."} | {"labels": ["C", "E"], "texts": ["C. $f(0)$ is greater than $g(0)$ ., E. $f(2)$ is greater than $g(2)$ ."]} |
dc | standalone | maths | algebra | inequalities | Leah would like to earn at least $120 per month. She babysits for $5 per hour and works at an ice cream shop for $8 per hour. Leah cannot work more than a total of 20 hours per month. Let x represent the number of hours Leah babysits and let y represent the number of hours Leah works at the ice cream shop. | null | images/15_0.jpg | Which graph shows the set of points that represents the number of hours that Leah can work in order to earn at least $120 and not work more than 20 hours per month? | {"A": "Graph A", "B": "Graph B", "C": "Graph C", "D": "Graph D"} | {"label": "D", "text": "D"} |
dc | standalone | maths | algebra | functions | null | null | images/29_0.jpg | According to the graph, what is the approximate average rate of change in the radius of the circle as the area increases from 3 square feet to 7 square feet? | {"A": "0.125 foot per square foot", "B": "0.25 foot per square foot", "C": "0.5 foot per square foot", "D": "8 feet per square foot"} | {"label": "A", "text": "A. 0.125 foot per square foot"} |
bowl | final | physics | mechanics | kinematics | A mass moves along the x-axis following the position vs. time graph provided. | null | images/f35e7fd51a51a7df26adf7b048b28f44_4_img.webp | During what time interval(s) does the mass have an acceleration of $0 \frac{\text{m}}{\text{s}^2}$ ? Time is represented as $t$ . | {"A": "only from $0 \\text{ s} < t < 3 \\text{ s}$ ", "B": "only at $t = 5 \\text{ s}$ ", "C": "only from $7 \\text{ s} < t < 10 \\text{ s}$ ", "D": "only from $0 \\text{ s} < t < 3 \\text{ s}$ and $7 \\text{ s} < t < 10 \\text{ s}$ ", "E": "only from $0 \\text{ s} < t < 3 \\text{ s}$ , $t = 5 \\text{ s... | {"label": "D", "text": "only from $0 \\text{ s} < t < 3 \\text{ s}$ and $7 \\text{ s} < t < 10 \\text{ s}$ "} |
bowl | final | physics | mechanics | circular_motion_gravitation | A $2000 \text{ kg}$ car moves over a hill at a constant speed of $12.0 \frac{\text{m}}{\text{s}}$ . At the very top of the hill, the shape of the road can be approximated as a circle with radius $25 \text{ m}$ , as indicated in the figure. | null | images/f35e7fd51a51a7df26adf7b048b28f44_7_img.webp | Which one of the following choices best represents the magnitude of the upward force exerted by the road on the car? | {"A": " $20000 \\text{ N}$ ", "B": " $8000 \\text{ N}$ ", "C": " $12000 \\text{ N}$ ", "D": " $2000 \\text{ N}$ ", "E": " $0 \\text{ N}$ "} | {"label": "B", "text": " $8000 \\text{ N}$ "} |
bowl | final | physics | mechanics | dynamics | Two blocks X and Y are in contact on a frictionless horizontal surface. A constant 35 N force is applied to the right onto block X. | null | images/d98bf7e51c320d151c0bd990eb530297_14_img.webp | What is the magnitude of the force that block Y exerts onto block X? | {"A": "35 N", "B": "28 N", "C": "25 N", "D": "14 N", "E": "10 N"} | {"label": "C", "text": "25 N"} |
bowl | final | physics | mechanics | work_energy_power | A box slides with uniform acceleration up an incline. The box has an initial speed of $9.0 \frac{\text{m}}{\text{s}}$ and rises vertically $2.60 \text{ m}$ before coming to rest. If the angle of the incline is $30^\circ$ , | null | images/4be22b6d0a1f3bc5893246f8eef539ed_5_img.webp | what is the coefficient of kinetic friction between the box and the incline? | {"A": "0.298", "B": "0.322", "C": "0.372", "D": "0.483", "E": "0.557"} | {"label": "B", "text": "0.322"} |
bowl | final | physics | mechanics | circular_motion_gravitation | A $4.00 \text{ kg}$ mass is in uniform circular motion as shown in the figure. The string to which the mass is attached has a length of $L = 3.00 \text{ m}$ and forms an angle of $\theta = 50.0^\circ$ with the vertical. | null | images/4be22b6d0a1f3bc5893246f8eef539ed_8_img.webp | What is the speed of the mass? | {"A": " $5.23 \\frac{\\text{m}}{\\text{s}}$ ", "B": " $5.54 \\frac{\\text{m}}{\\text{s}}$ ", "C": " $5.98 \\frac{\\text{m}}{\\text{s}}$ ", "D": " $6.62 \\frac{\\text{m}}{\\text{s}}$ ", "E": " $6.90 \\frac{\\text{m}}{\\text{s}}$ "} | {"label": "A", "text": " $5.23 \\frac{\\text{m}}{\\text{s}}$ "} |
bowl | final | physics | mechanics | momentum_collisions | A $2.0 \text{ kg}$ mass moves at $10.0 \frac{\text{m}}{\text{s}}$ when it has a collision in space. The mass's speed was unchanged, but the direction of its velocity was altered by $80^\circ$ . If the collision lasted $0.25 \text{ s}$ , | null | images/4be22b6d0a1f3bc5893246f8eef539ed_11_img.webp | what was the magnitude of the average force exerted on the mass? | {"A": " $200 \\text{ N}$ ", "B": " $100 \\text{ N}$ ", "C": " $103 \\text{ N}$ ", "D": " $50 \\text{ N}$ ", "E": " $25 \\text{ N}$ "} | {"label": "C", "text": " $103 \\text{ N}$ "} |
bowl | final | physics | mechanics | kinematics | Two cars, $P$ and $Q$ , each start from rest at the origin and will move along the $x$ -axis. The acceleration vs. time graph for each car is shown. | null | images/d2537c1c5e7ff2f06e8580bbabb9ac71_5_img.webp | Which one of the following choices correctly identifies the relationship for both the speeds ( $v_P$ and $v_Q$ ) and the positions ( $x_P$ and $x_Q$ ) of the cars at time $T$ ? | {"A": " $v_P = v_Q$ and $x_P > x_Q$ ", "B": " $v_P > v_Q$ and $x_P > x_Q$ ", "C": " $v_P = v_Q$ and $x_P = x_Q$ ", "D": " $v_P < v_Q$ and $x_P < x_Q$ ", "E": " $v_P = v_Q$ and $x_P < x_Q$ "} | {"label": "A", "text": " $v_P = v_Q$ and $x_P > x_Q$ "} |
bowl | final | physics | mechanics | rotational_motion | A solid cylinder rolls without slipping on a rough inclined plane. | null | images/d2537c1c5e7ff2f06e8580bbabb9ac71_7_img.webp | Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinder as it rolls up the incline? | {"A": "static friction up the incline", "B": "static friction down the incline", "C": "kinetic friction up the incline", "D": "kinetic friction down the incline", "E": "no friction"} | {"label": "A", "text": "static friction up the incline"} |
bowl | final | physics | electricity_magnetism | magnetic_fields | Two long wires are fixed in space so that the conventional current in the left wire ( $2 A$ ) comes out of the plane of the page and the conventional current in the right wire ( $3 A$ ) goes into the plane of the page. | null | images/7c8c14edf77a81260ce4b88e13121629_2_img.webp | In which Region(s) is there a place on the $x$ -axis (aside from infinity) at which the magnetic field is equal to zero from these currents? | {"A": "Only in Region I", "B": "In both Regions I and II", "C": "Only in Region II", "D": "In both Regions I and III", "E": "In both Regions II and III"} | {"label": "A", "text": "Only in Region I"} |
bowl | final | physics | mechanics | momentum_collisions | A $9.20 m$ long uniform plank rests on a frictionless ice pond. A $52 kg$ box rests on the plank's left end while a $71 kg$ person stands at the plank's right end. After the person walks to the left on the plank and stands at the same location as the box, the plank has slid $3.84 m$ to the right relative to the... | null | images/7c8c14edf77a81260ce4b88e13121629_4_img.webp | Which one of the following choices best represents the mass of the plank? | {"A": " $123 kg$ ", "B": " $61.5 kg$ ", "C": " $47.1 kg$ ", "D": " $36.5 kg$ ", "E": " $31.2 kg$ "} | {"label": "C", "text": " $47.1 kg$ "} |
bowl | final | physics | electricity_magnetism | electromagnetic_induction | A metal bar is moving to the left across a set of frictionless conducting rails as seen in the figure. Throughout the region between the rails, there is a uniform magnetic field directed into the plane of the page. The resistors labeled X and Y are identical. | null | images/7c8c14edf77a81260ce4b88e13121629_6_img.webp | Which one of the following choices correctly indicates the direction of the conventional current in the resistors and the relation between the magnitude of the currents through each resistor at the instant shown? | {"A": "Current through X: Up the plane of the page; Current through Y: Up the plane of the page; $I_X > I_Y$", "B": "Current through X: Up the plane of the page; Current through Y: Up the plane of the page; $I_X = I_Y$", "C": "Current through X: Up the plane of the page; Current through Y: Down the plane of the page; $... | {"label": "B", "text": "Up the plane of the page and Up the plane of the page and $I_X = I_Y$ "} |
bowl | final | physics | mechanics | circular_motion_gravitation | A small $2.0 \text{ kg}$ block rests at the bottom of a bucket. The bucket is spun in a vertical circle of radius $L$ by a rope. When the bucket reaches the highest point in its motion, it moves just fast enough for the block to remain in place in the bucket. When the bucket is at an angle $\theta = 30^\circ$ fro... | null | images/08fc1517af692c13332a6da067c46497_8_img.webp | what is the magnitude of the normal force (perpendicular to the surface) provided by the bucket onto the block? Note that the direction of the gravitational field is indicated in the diagram by $\vec{g}$ and that the block does not touch any sides of the bucket aside from the bottom of it. | {"A": " $8.0 \\text{ N}$ ", "B": " $10.0 \\text{ N}$ ", "C": " $15.4 \\text{ N}$ ", "D": " $18.7 \\text{ N}$ ", "E": " $37.3 \\text{ N}$ "} | {"label": "A", "text": " $8.0 \\text{ N}$ "} |
bowl | final | physics | mechanics | dynamics | A small object of mass $M$ is released from rest at the top of a frictionless incline. The incline has a mass $M$ and makes an angle $\theta$ with the horizontal. The incline remains at rest on a table as the small object slides. | null | images/08fc1517af692c13332a6da067c46497_21_img.webp | During the slide, what is the magnitude of the normal force from the table on the incline? | {"A": " $2Mg(1 - \\tan \\theta)$ ", "B": " $2Mg(1 - \\sin \\theta)$ ", "C": " $2Mg$ ", "D": " $Mg(2 - \\sin^2 \\theta)$ ", "E": " $Mg(2 - \\sin \\theta)$ "} | {"label": "D", "text": " $Mg(2 - \\sin^2 \\theta)$ "} |
bowl | final | physics | mechanics | rotational_motion | A long uniform rod, pivoted at one end affixed to the ground, is in static equilibrium. A horizontal rope acts 75% of the way up the rod while a vertical rope acts at the far end. The magnitude of each rope's force is the same as the gravitational force acting on the rod. | null | images/9947ca5d7d665eba4cea275a2a92e2b4_5_img.webp | What is the value of the angle $\theta$ in the figure? | {"A": " $30^\\circ$ ", "B": " $45^\\circ$ ", "C": " $33.7^\\circ$ ", "D": " $60^\\circ$ ", "E": " $90^\\circ$ "} | {"label": "C", "text": " $33.7^\\circ$ "} |
bowl | final | physics | electricity_magnetism | electric_fields | A semi-circle has radius $R$ , total charge $Q$ , and a charge per unit length given as $\lambda = \lambda_0 \cos \theta$ with $\theta$ defined in the figure and $\lambda_0$ a positive constant. | null | images/9947ca5d7d665eba4cea275a2a92e2b4_7_img.webp | Which one of the following choices gives the electric field strength at the point labeled $P$ ? | {"A": " $\\frac{\\lambda_0}{2\\pi\\epsilon_0 R}$ ", "B": " $\\frac{\\lambda_0}{\\pi\\epsilon_0 R}$ ", "C": " $\\frac{\\lambda_0}{2\\epsilon_0 R}$ ", "D": " $\\frac{\\lambda_0}{\\epsilon_0 R}$ ", "E": " $\\frac{\\lambda_0}{2\\pi\\epsilon_0 R}$ directed downward"} | {"label": "E", "text": " $\\frac{\\lambda_0}{2\\pi\\epsilon_0 R}$ directed downward"} |
bowl | final | physics | electricity_magnetism | circuits | Once the circuit shown reaches equilibrium, | null | images/ad538ef8cd4ece4a634014620e69dd22_4_img.webp | what is the magnitude of the potential difference across the capacitor? | {"A": " $0 \\xi$ ", "B": " $\\frac{1}{9} \\xi$ ", "C": " $\\frac{2}{9} \\xi$ ", "D": " $\\frac{5}{9} \\xi$ ", "E": " $\\frac{2}{3} \\xi$ "} | {"label": "D", "text": " $\\frac{5}{9} \\xi$ "} |
bowl | final | physics | mechanics | circular_motion_gravitation | In the binary star system shown, the two stars follow circular orbits about the system's center of mass. The stars are separated by a distance $D$ that is large compared to their size and are subject only to their mutual gravitational attraction. The orbital period of the star of mass $M$ is $T$ . | null | images/ad538ef8cd4ece4a634014620e69dd22_7_img.webp | Which one of the following choices represents the total mass of the binary star system? | {"A": " $\\frac{\\pi^2 D^3}{5GT^2}$ ", "B": " $\\frac{4\\pi^2 D^3}{5GT^2}$ ", "C": " $\\frac{4\\pi^2 D^3}{GT^2}$ ", "D": " $\\frac{16\\pi^2 D^3}{5GT^2}$ ", "E": " $\\frac{25\\pi^2 D^3}{4GT^2}$ "} | {"label": "C", "text": " $\\frac{4\\pi^2 D^3}{GT^2}$ "} |
bowl | final | physics | thermal_physics | thermodynamics | A monatomic ideal gas undergoes the reversible cyclic process (ABCA) shown in the PV diagram. Process $A \to B$ is adiabatic. | null | images/ad538ef8cd4ece4a634014620e69dd22_12_img.webp | What is the efficiency of this engine? | {"A": "0.15", "B": "0.22", "C": "0.33", "D": "0.47", "E": "0.67"} | {"label": "B", "text": "0.22"} |
bowl | final | physics | mechanics | dynamics | Three blocks ( $m_1=1$ kg, $m_2=2$ kg, $m_3=3$ kg) connected by cords are pulled by a constant force, $F$ , of 18 N on a frictionless horizontal table. $T_2$ is the tension in the rope between $m_2$ and $m_3$ . | null | images/489976adf336856c6381d9d53050b626_10_img.webp | What is $T_2$ ? | {"A": "3 N", "B": "6 N", "C": "9 N", "D": "12 N", "E": "15 N"} | {"label": "C", "text": "9 N"} |
bowl | final | physics | mechanics | work_energy_power | A spring with spring constant $k = 20 \text{ kN/m}$ , is used to stop a 50 kg box that is sliding on a horizontal surface. The spring is initially in its equilibrium state. At position A, shown in the top diagram, the box has a speed of 3.0 m/s. The compression of the spring when the box is instantaneously at rest (po... | null | images/9a46f24143eba7ec125a9ec8356436fa_2_img.webp; images/9a46f24143eba7ec125a9ec8356436fa_3_img.webp | Determine the coefficient of kinetic friction between the box and the surface. | {"A": "0.125", "B": "0.230", "C": "0.245", "D": "0.280", "E": "0.315"} | {"label": "D", "text": "0.280"} |
bowl | final | physics | optics | geometric_optics | A combination of two thin convex lenses is placed as shown at right. An object is placed 5 cm in front of $L_1$ which has a focal length of 10 cm. $L_2$ is 10 cm behind $L_1$ and has a focal length of 12 cm. | null | images/231736673388485f65696f89f08b2a44_8_img.webp | How far from $L_2$ is the final image for this lens combination? | {"A": "8 cm", "B": "15 cm", "C": "22 cm", "D": "24 cm", "E": "30 cm"} | {"label": "D", "text": "24 cm"} |
bowl | final | physics | electricity_magnetism | capacitors | In the circuit shown below, the voltage source, switch, capacitor and connecting wires have no resistance. Let $\Delta V_R$ and $\Delta V_C$ represent the potential differences across the resistor and the capacitor, respectively. The capacitor is initially uncharged. | null | images/4c63fcc1104c65e90b87b92af5bc3ff2_15_img.webp | Which of the following choices correctly compares these potential differences immediately after the switch is closed and after the circuit has reached steady state. | {"A": "Switch Closed: $\\Delta V_R = \\Delta V_C$; Steady State: $\\Delta V_R = \\Delta V_C$", "B": "Switch Closed: $\\Delta V_R > \\Delta V_C$; Steady State: $\\Delta V_R = \\Delta V_C$", "C": "Switch Closed: $\\Delta V_R = \\Delta V_C$; Steady State: $\\Delta V_R < \\Delta V_C$", "D": "Switch Closed: $\\Delta V_R > \... | {"label": "D", "text": "Switch Closed: $\\Delta V_R > \\Delta V_C$; Steady State: $\\Delta V_R < \\Delta V_C$"} |
bowl | final | physics | optics | geometric_optics | A triangular glass prism ( $n = 1.6$ ) is immersed in a liquid ( $n = 1.1$ ) as shown. A laser light is incident as shown on face $AB$ making an angle of $20^\circ$ with the normal ( $N$ ). | null | images/aa9dceb3380664e56c9f65f2401583bb_9_img.webp | Calculate the angle that the ray emerging from $AC$ makes with the ground when it leaves $AC$ and strikes the ground. | {"A": "$28.1^\\circ$", "B": "$30.3^\\circ$", "C": "$33.8^\\circ$", "D": "$36.1^\\circ$", "E": "$18.9^\\circ$"} | {"label": "B", "text": "$30.3^\\circ$"} |
bowl | final | physics | electricity_magnetism | electric_fields | Each of the two curved rods shown in the picture form one-quarter of a circle with a radius $R$ . Both rods carry a uniformly-distributed electric charge $+Q$ . | null | images/483ee9626be126c96ae8f54fa2988ed8_2_img.webp | Which of the following choices correctly expresses the net electric field and net electric potential at the origin? Assume $V \to 0$ as $r \to \infty$ . | {"A": "Electric Field: zero; Electric Potential: zero", "B": "Electric Field: zero; Electric Potential: $\\frac{2kQ}{R}$", "C": "Electric Field: $\\frac{2kQ}{R^2}$; Electric Potential: zero", "D": "Electric Field: $\\frac{\\sqrt{2}kQ}{R^2}$; Electric Potential: $\\frac{2kQ}{R}$", "E": "Electric Field: $\\frac{2kQ}{R^2}... | {"label": "B", "text": "Electric Field: zero; Electric Potential: $\\frac{2kQ}{R}$"} |
bowl | final | physics | electricity_magnetism | circuits | The diagram below shows combinations X, Y, and Z of three identical resistors. | null | images/483ee9626be126c96ae8f54fa2988ed8_11_img.webp; images/483ee9626be126c96ae8f54fa2988ed8_13_img.webp; images/483ee9626be126c96ae8f54fa2988ed8_15_img.webp | What is the correct order of the total resistance of the combinations going from lowest resistance to highest resistance? | {"A": "Y, X, Z", "B": "Z, X, Y", "C": "X, Y, Z", "D": "Z, Y, X", "E": "Y, Z, X"} | {"label": "B", "text": "Z, X, Y"} |
bowl | final | physics | mechanics | work_energy_power | null | null | images/1_0.jpg | A force, $F$ , could be applied to a cart in a variety of directions as shown at right. Which of the applications of $F$ would result in no work being done? | {"A": "A", "B": "B", "C": "C", "D": "D", "E": "All of them result in work being done."} | {"label": "C", "text": "C"} |
bowl | final | physics | mechanics | kinematics | null | null | images/1_1.jpg | The figure to the right shows the position-time graph of an object traveling in a straight line, starting out moving to the right (the positive $x$ -direction). At which points is the object moving to the left? | {"A": "B and F", "B": "E and F", "C": "A, B, and C", "D": "C, D, and E", "E": "None of the above"} | {"label": "D", "text": "C, D, and E"} |
bowl | final | physics | mechanics | kinematics | null | null | images/5_0.jpg | At $\mathrm{t = 0}$ , Ball 1 is rolling up a ramp and Ball 2 is released from the top of the same ramp. The balls don't collide. Which velocity vs. time graph at right best represents the motion of the two balls? | {"A": "A ", "B": "B ", "C": "C ", "D": "D ", "E": "Both A & D "} | {"label": "A", "text": "A "} |
bowl | final | physics | electricity_magnetism | forces_on_charges | null | null | images/5_1.jpg | Two balloons are charged identically and uniformly by rubbing them with wool. One is placed on a scale which is then tared. No charge is transferred to the scale. The other is then placed above it separated by $30\mathrm{cm}$ . The scale reads 0.32 grams. What is the closest estimate for the charge on each balloon? | {"A": "$200\\mathrm{C}$ ", "B": "$200\\mathrm{mC}$ ", "C": "$200\\mu \\mathrm{C}$ ", "D": "$200\\mathrm{nC}$ ", "E": "$200\\mathrm{pC}$ "} | {"label": "D", "text": "$200\\mathrm{nC}$ "} |
bowl | final | physics | circular_motion_gravitation | uniform_circular_motion | null | null | images/6_0.jpg | An amusement park ride called "The Rotor" has people standing in a vertical cylinder, in this case 6 m in diameter, which rotates and presses them against the wall with sufficient force that the floor can then drop without them sliding down the wall. Shown here is the magnitude of accelerometer data from a device carri... | {"A": "0", "B": "$10 \\mathrm{m / s}^{2}$", "C": "$20 \\mathrm{m / s}^{2}$", "D": "$26 \\mathrm{m / s}^{2}$", "E": "$28 \\mathrm{m / s}^{2}$"} | {"label": "D", "text": "$26 \\mathrm{m / s}^{2}$"} |
bowl | final | physics | mechanics | simple_harmonic_motion | null | null | images/7_0__bowl_physics_2021__98f8d6d3ed.jpg | Two identical uniform sticks have small holes drilled in them. The sticks are marked with equally spaced lines as shown. Each stick is suspended from a pin through the hole and is free to rotate about the pin. Both sticks are displaced a small angle from the vertical and released. What is the ratio of the period of pen... | {"A": "1:1", "B": "2:3", "C": "4:3", "D": "10:9", "E": "16:9"} | {"label": "A", "text": "1:1"} |
bowl | final | physics | electricity_magnetism | circuits | null | null | images/9_0.jpg | What is the voltage drop across $\mathrm{R}_3$ ? | {"A": "0.250 V", "B": "0.500 V", "C": "1.00 V", "D": "2.00 V", "E": "3.00 V"} | {"label": "D", "text": "2.00 V"} |
bowl | final | physics | electricity_magnetism | circuits | null | null | images/9_0.jpg | What is the current in $\mathrm{R}_3$ ? | {"A": "0.125 A", "B": "0.250 A", "C": "0.500 A", "D": "0.750 A", "E": "1.00 A"} | {"label": "A", "text": "0.125 A"} |
bowl | final | physics | electromagnetic_induction | faradays_law | null | null | images/10_0.jpg | In the 1990s, the space shuttle flew two separate tethered satellite experiments. One purpose was to generate power via the induced voltage in a $20\mathrm{km}$ long tether moving perpendicular to the Earth's 0.5 Gauss magnetic field lines at roughly $8\mathrm{km / s}$ What is the theoretical voltage across the tether ... | {"A": "10 Volts", "B": "100 Volts", "C": "1,000 Volts", "D": "10,000 Volts", "E": "100,000 Volts"} | {"label": "D", "text": "10,000 Volts"} |
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