data_source stringclasses 1
value | prompt listlengths 1 1 | images images listlengths 1 1 | reward_model dict | extra_info dict |
|---|---|---|---|---|
scibench_multimodal | [
{
"content": "<image>The graph of a function $f$ is given. State the value of $f(1)$.",
"role": "user"
}
] | {
"ground_truth": "3",
"style": "rule"
} | {
"gt_answer": "3",
"id": "scibench_multimodal--0",
"mc_options": null,
"original_question": "<image>The graph of a function $f$ is given. State the value of $f(1)$."
} | |
scibench_multimodal | [
{
"content": "<image>The graph shows the power consumption for a day in September in San Francisco. $P$ is measured in megawatts; $t$ is measured in hours starting at midnight. What was the power consumption at 6 AM?",
"role": "user"
}
] | {
"ground_truth": "500 MW",
"style": "rule"
} | {
"gt_answer": "500 MW",
"id": "scibench_multimodal--1",
"mc_options": null,
"original_question": "<image>The graph shows the power consumption for a day in September in San Francisco. $P$ is measured in megawatts; $t$ is measured in hours starting at midnight. What was the power consumption at 6 AM?"
} | |
scibench_multimodal | [
{
"content": "<image>For the function $g$ whose graph is given, state the value of $\\lim _{t \\rightarrow 0^{+}} g(t)$.",
"role": "user"
}
] | {
"ground_truth": "-2",
"style": "rule"
} | {
"gt_answer": "-2",
"id": "scibench_multimodal--2",
"mc_options": null,
"original_question": "<image>For the function $g$ whose graph is given, state the value of $\\lim _{t \\rightarrow 0^{+}} g(t)$."
} | |
scibench_multimodal | [
{
"content": "<image>Figure 23-46a shows three plastic sheets that are large, parallel, and uniformly charged. Figure 23-46b gives the component of the net electric field along an $x$ axis through the sheets. The scale of the vertical axis is set by $E_s=6.0 \\times 10^5 \\mathrm{~N} / \\mathrm{C}$. What is the... | {
"ground_truth": "$-1.5$",
"style": "rule"
} | {
"gt_answer": "$-1.5$",
"id": "scibench_multimodal--3",
"mc_options": null,
"original_question": "<image>Figure 23-46a shows three plastic sheets that are large, parallel, and uniformly charged. Figure 23-46b gives the component of the net electric field along an $x$ axis through the sheets. The scale of the v... | |
scibench_multimodal | [
{
"content": "<image>In Fig. 21-25, the particles have charges $q_1=-q_2=100 \\mathrm{nC}$ and $q_3=-q_4=200 \\mathrm{nC}$, and distance $a=$ $5.0 \\mathrm{~cm}$. What is the $x$ component of the net electrostatic force on particle 3?",
"role": "user"
}
] | {
"ground_truth": "0.17 $\\mathrm{~N}$",
"style": "rule"
} | {
"gt_answer": "0.17 $\\mathrm{~N}$",
"id": "scibench_multimodal--4",
"mc_options": null,
"original_question": "<image>In Fig. 21-25, the particles have charges $q_1=-q_2=100 \\mathrm{nC}$ and $q_3=-q_4=200 \\mathrm{nC}$, and distance $a=$ $5.0 \\mathrm{~cm}$. What is the $x$ component of the net electrostatic... | |
scibench_multimodal | [
{
"content": "<image>Suppose you design an apparatus in which a uniformly charged disk of radius $R$ is to produce an electric field. The field magnitude is most important along the central perpendicular axis of the disk, at a point $P$ at distance $2.00 R$ from the disk (Fig. 22-57a). Cost analysis suggests th... | {
"ground_truth": "$28$ $\\%$",
"style": "rule"
} | {
"gt_answer": "$28$ $\\%$",
"id": "scibench_multimodal--5",
"mc_options": null,
"original_question": "<image>Suppose you design an apparatus in which a uniformly charged disk of radius $R$ is to produce an electric field. The field magnitude is most important along the central perpendicular axis of the disk, a... | |
scibench_multimodal | [
{
"content": "<image> The square surface shown in Fig. 23-30 measures $3.2 \\mathrm{~mm}$ on each side. It is immersed in a uniform electric field with magnitude $E=1800 \\mathrm{~N} / \\mathrm{C}$ and with field lines at an angle of $\\theta=35^{\\circ}$ with a normal to the surface, as shown. Take that normal... | {
"ground_truth": "$-0.015$ $\\mathrm{~N} \\cdot \\mathrm{m}^2 / \\mathrm{C}$",
"style": "rule"
} | {
"gt_answer": "$-0.015$ $\\mathrm{~N} \\cdot \\mathrm{m}^2 / \\mathrm{C}$",
"id": "scibench_multimodal--6",
"mc_options": null,
"original_question": "<image> The square surface shown in Fig. 23-30 measures $3.2 \\mathrm{~mm}$ on each side. It is immersed in a uniform electric field with magnitude $E=1800 \\mat... | |
scibench_multimodal | [
{
"content": "<image>In crystals of the salt cesium chloride, cesium ions $\\mathrm{Cs}^{+}$form the eight corners of a cube and a chlorine ion $\\mathrm{Cl}^{-}$is at the cube's center (Fig. 21-36). The edge length of the cube is $0.40 \\mathrm{~nm}$. The $\\mathrm{Cs}^{+}$ions are each deficient by one electr... | {
"ground_truth": "$0$",
"style": "rule"
} | {
"gt_answer": "$0$",
"id": "scibench_multimodal--7",
"mc_options": null,
"original_question": "<image>In crystals of the salt cesium chloride, cesium ions $\\mathrm{Cs}^{+}$form the eight corners of a cube and a chlorine ion $\\mathrm{Cl}^{-}$is at the cube's center (Fig. 21-36). The edge length of the cube is... | |
scibench_multimodal | [
{
"content": "<image>Find the y coordinate of the center of mass of a uniform wire that subtends an arc $\\theta$ if the radius of the circular arc is $a$, as shown in Figure 9-A.",
"role": "user"
}
] | {
"ground_truth": "0",
"style": "rule"
} | {
"gt_answer": "0",
"id": "scibench_multimodal--8",
"mc_options": null,
"original_question": "<image>Find the y coordinate of the center of mass of a uniform wire that subtends an arc $\\theta$ if the radius of the circular arc is $a$, as shown in Figure 9-A."
} | |
scibench_multimodal | [
{
"content": "<image>A common test for AIDS is called the ELISA (enzyme-linked immunosorbent assay) test. Among 1 million people who are given the ELISA test, we can expect results similar to those given in the following table.\r\nIf one of these 1 million people is selected randomly, find the following probabi... | {
"ground_truth": "$\\frac{5000}{1000000}$",
"style": "rule"
} | {
"gt_answer": "$\\frac{5000}{1000000}$",
"id": "scibench_multimodal--9",
"mc_options": null,
"original_question": "<image>A common test for AIDS is called the ELISA (enzyme-linked immunosorbent assay) test. Among 1 million people who are given the ELISA test, we can expect results similar to those given in the... | |
scibench_multimodal | [
{
"content": "<image>In Fig. 22-66, particle 1 (of charge $+1.00 \\mu \\mathrm{C}$ ), particle 2 (of charge $+1.00 \\mu \\mathrm{C})$, and particle 3 (of charge $Q$ ) form an equilateral triangle of edge length $a$. For what value of $Q$ (both sign and magnitude) does the net electric field produced by the part... | {
"ground_truth": "$1.00$ $\\mu \\mathrm{C}$",
"style": "rule"
} | {
"gt_answer": "$1.00$ $\\mu \\mathrm{C}$",
"id": "scibench_multimodal--10",
"mc_options": null,
"original_question": "<image>In Fig. 22-66, particle 1 (of charge $+1.00 \\mu \\mathrm{C}$ ), particle 2 (of charge $+1.00 \\mu \\mathrm{C})$, and particle 3 (of charge $Q$ ) form an equilateral triangle of edge len... | |
scibench_multimodal | [
{
"content": "<image>In Fig. 22-54, Figure 22-53 Problem 30. a nonconducting rod of length $L=$ $8.15 \\mathrm{~cm}$ has a charge $-q=-4.23 \\mathrm{fC}$ uniformly distributed along its length. What is the linear charge density of the rod? ",
"role": "user"
}
] | {
"ground_truth": "$-5.19$ $10^{-14} \\mathrm{C} / \\mathrm{m}$",
"style": "rule"
} | {
"gt_answer": "$-5.19$ $10^{-14} \\mathrm{C} / \\mathrm{m}$",
"id": "scibench_multimodal--11",
"mc_options": null,
"original_question": "<image>In Fig. 22-54, Figure 22-53 Problem 30. a nonconducting rod of length $L=$ $8.15 \\mathrm{~cm}$ has a charge $-q=-4.23 \\mathrm{fC}$ uniformly distributed along its le... | |
scibench_multimodal | [
{
"content": "<image>A bicycle pedal is pushed by a foot with a $60-\\mathrm{N}$ force as shown. The shaft of the pedal is $18 \\mathrm{~cm}$ long. Find the magnitude of the torque about $P$.\r\n",
"role": "user"
}
] | {
"ground_truth": "$10.8\\sin(80^{\\circ})$ $\\mathrm{N}\\cdot \\mathrm{m}$",
"style": "rule"
} | {
"gt_answer": "$10.8\\sin(80^{\\circ})$ $\\mathrm{N}\\cdot \\mathrm{m}$",
"id": "scibench_multimodal--12",
"mc_options": null,
"original_question": "<image>A bicycle pedal is pushed by a foot with a $60-\\mathrm{N}$ force as shown. The shaft of the pedal is $18 \\mathrm{~cm}$ long. Find the magnitude of the t... | |
scibench_multimodal | [
{
"content": "<image>For the function $g$ whose graph is given, state the value of $\\lim _{t \\rightarrow 2^{-}} g(t)$.",
"role": "user"
}
] | {
"ground_truth": "2",
"style": "rule"
} | {
"gt_answer": "2",
"id": "scibench_multimodal--13",
"mc_options": null,
"original_question": "<image>For the function $g$ whose graph is given, state the value of $\\lim _{t \\rightarrow 2^{-}} g(t)$."
} | |
scibench_multimodal | [
{
"content": "<image>$\\bullet \\bullet 17$ Two charged beads are on the plastic ring in Fig. 22-44a. Bead 2 , which is not shown, is fixed in place on the ring, which has radius $R=60.0 \\mathrm{~cm}$. Bead 1 , which is not fixed in place, is initially on the $x$ axis at angle $\\theta=0^{\\circ}$. It is then ... | {
"ground_truth": "$-90$ $^{\\circ}$",
"style": "rule"
} | {
"gt_answer": "$-90$ $^{\\circ}$",
"id": "scibench_multimodal--14",
"mc_options": null,
"original_question": "<image>$\\bullet \\bullet 17$ Two charged beads are on the plastic ring in Fig. 22-44a. Bead 2 , which is not shown, is fixed in place on the ring, which has radius $R=60.0 \\mathrm{~cm}$. Bead 1 , whi... | |
scibench_multimodal | [
{
"content": "<image>The cube in Fig. 23-31 has edge length $1.40 \\mathrm{~m}$ and is oriented as shown in a region of uniform electric field. Find the electric flux through the right face if the electric field, in newtons per coulomb, is given by $6.00 \\hat{\\mathrm{i}}$?",
"role": "user"
}
] | {
"ground_truth": "$0$",
"style": "rule"
} | {
"gt_answer": "$0$",
"id": "scibench_multimodal--15",
"mc_options": null,
"original_question": "<image>The cube in Fig. 23-31 has edge length $1.40 \\mathrm{~m}$ and is oriented as shown in a region of uniform electric field. Find the electric flux through the right face if the electric field, in newtons per c... | |
scibench_multimodal | [
{
"content": "<image>In Fig. 23-54, a solid sphere of radius $a=2.00 \\mathrm{~cm}$ is concentric with a spherical conducting shell of inner radius $b=2.00 a$ and outer radius $c=$ $2.40 a$. The sphere has a net uniform charge $q_1=+5.00 \\mathrm{fC}$; the shell has a net charge $q_2=-q_1$. What is the magnitud... | {
"ground_truth": "$0$",
"style": "rule"
} | {
"gt_answer": "$0$",
"id": "scibench_multimodal--16",
"mc_options": null,
"original_question": "<image>In Fig. 23-54, a solid sphere of radius $a=2.00 \\mathrm{~cm}$ is concentric with a spherical conducting shell of inner radius $b=2.00 a$ and outer radius $c=$ $2.40 a$. The sphere has a net uniform charge $q... | |
scibench_multimodal | [
{
"content": "<image>What is the y coordinate of the center of mass of the isosceles right triangle of uniform areal density shown in Figure 9-C?",
"role": "user"
}
] | {
"ground_truth": "$\\frac{1}{3 \\sqrt{2}}$ $a$",
"style": "rule"
} | {
"gt_answer": "$\\frac{1}{3 \\sqrt{2}}$ $a$",
"id": "scibench_multimodal--17",
"mc_options": null,
"original_question": "<image>What is the y coordinate of the center of mass of the isosceles right triangle of uniform areal density shown in Figure 9-C?"
} | |
scibench_multimodal | [
{
"content": "<image>Figure 22-52a shows a nonconducting rod with a uniformly distributed charge $+Q$. The rod forms a half-circle with radius $R$ and produces an electric field of magnitude $E_{\\mathrm{arc}}$ at its center of curvature $P$. If the arc is collapsed to a point at distance $R$ from $P$ (Fig. 22-... | {
"ground_truth": "$1.57$",
"style": "rule"
} | {
"gt_answer": "$1.57$",
"id": "scibench_multimodal--18",
"mc_options": null,
"original_question": "<image>Figure 22-52a shows a nonconducting rod with a uniformly distributed charge $+Q$. The rod forms a half-circle with radius $R$ and produces an electric field of magnitude $E_{\\mathrm{arc}}$ at its center o... | |
scibench_multimodal | [
{
"content": "<image>Two large parallel copper plates are $5.0 \\mathrm{~cm}$ apart and have a uniform electric field between them as depicted in Fig. 22-60. An electron is released from the negative plate at the same time that a proton is released from the positive plate. Neglect the force of the particles on ... | {
"ground_truth": "$27$ $\\mu \\mathrm{m}$",
"style": "rule"
} | {
"gt_answer": "$27$ $\\mu \\mathrm{m}$",
"id": "scibench_multimodal--19",
"mc_options": null,
"original_question": "<image>Two large parallel copper plates are $5.0 \\mathrm{~cm}$ apart and have a uniform electric field between them as depicted in Fig. 22-60. An electron is released from the negative plate at ... | |
scibench_multimodal | [
{
"content": "<image>Figure 22-40 shows a proton (p) on the central axis through a disk with a uniform charge density due to excess electrons. The disk is seen from an edge-on view. Three of those electrons are shown: electron $\\mathrm{e}_c$ at the disk center and electrons $\\mathrm{e}_s$ at opposite sides of... | {
"ground_truth": "$3.60$ $10^{-6} \\mathrm{~N} / \\mathrm{C}$",
"style": "rule"
} | {
"gt_answer": "$3.60$ $10^{-6} \\mathrm{~N} / \\mathrm{C}$",
"id": "scibench_multimodal--20",
"mc_options": null,
"original_question": "<image>Figure 22-40 shows a proton (p) on the central axis through a disk with a uniform charge density due to excess electrons. The disk is seen from an edge-on view. Three o... | |
scibench_multimodal | [
{
"content": "<image> In Fig. 22-64a, a particle of charge $+Q$ produces an electric field of magnitude $E_{\\text {part }}$ at point $P$, at distance $R$ from the particle. In Fig. 22-64b, that same amount of charge is spread uniformly along a circular arc that has radius $R$ and subtends an angle $\\theta$. T... | {
"ground_truth": "$217$ $^{\\circ}$",
"style": "rule"
} | {
"gt_answer": "$217$ $^{\\circ}$",
"id": "scibench_multimodal--21",
"mc_options": null,
"original_question": "<image> In Fig. 22-64a, a particle of charge $+Q$ produces an electric field of magnitude $E_{\\text {part }}$ at point $P$, at distance $R$ from the particle. In Fig. 22-64b, that same amount of charg... | |
scibench_multimodal | [
{
"content": "<image>In Fig. 22-42, the three particles are fixed in place and have charges $q_1=q_2=$ $+e$ and $q_3=+2 e$. Distance $a=6.00 \\mu \\mathrm{m}$. What is the magnitude of the net electric field at point $P$ due to the particles?",
"role": "user"
}
] | {
"ground_truth": "$160$ $\\mathrm{~N} / \\mathrm{C}$",
"style": "rule"
} | {
"gt_answer": "$160$ $\\mathrm{~N} / \\mathrm{C}$",
"id": "scibench_multimodal--22",
"mc_options": null,
"original_question": "<image>In Fig. 22-42, the three particles are fixed in place and have charges $q_1=q_2=$ $+e$ and $q_3=+2 e$. Distance $a=6.00 \\mu \\mathrm{m}$. What is the magnitude of the net elec... | |
scibench_multimodal | [
{
"content": "<image>In Fig. 21-38, particle 1 of charge $+4 e$ is above a floor by distance $d_1=2.00 \\mathrm{~mm}$ and particle 2 of charge $+6 e$ is on the floor, at distance $d_2=6.00 \\mathrm{~mm}$ horizontally from particle 1 . What is the $x$ component of the electrostatic force on particle 2 due to par... | {
"ground_truth": "$1.31$ $10^{-22} \\mathrm{~N}$",
"style": "rule"
} | {
"gt_answer": "$1.31$ $10^{-22} \\mathrm{~N}$",
"id": "scibench_multimodal--23",
"mc_options": null,
"original_question": "<image>In Fig. 21-38, particle 1 of charge $+4 e$ is above a floor by distance $d_1=2.00 \\mathrm{~mm}$ and particle 2 of charge $+6 e$ is on the floor, at distance $d_2=6.00 \\mathrm{~mm}... | |
scibench_multimodal | [
{
"content": "<image>For the function $g$ whose graph is given, state the value of $\\lim _{t \\rightarrow 2} g(t)$.",
"role": "user"
}
] | {
"ground_truth": "0",
"style": "rule"
} | {
"gt_answer": "0",
"id": "scibench_multimodal--24",
"mc_options": null,
"original_question": "<image>For the function $g$ whose graph is given, state the value of $\\lim _{t \\rightarrow 2} g(t)$."
} | |
scibench_multimodal | [
{
"content": "<image>A cross-section of an airplane wing is shown. Measurements of the thickness of the wing, in centimeters, at 20-centimeter intervals are 5.8, 20.3, 26.7, 29.0, 27.6, 27.3, 23.8, 20.5, 15.1, 8.7, and 2.8. Use the Midpoint Rule to estimate the area of the wing's cross-section.",
"role": "u... | {
"ground_truth": "4232 $\\mathrm{cm}^2$",
"style": "rule"
} | {
"gt_answer": "4232 $\\mathrm{cm}^2$",
"id": "scibench_multimodal--25",
"mc_options": null,
"original_question": "<image>A cross-section of an airplane wing is shown. Measurements of the thickness of the wing, in centimeters, at 20-centimeter intervals are 5.8, 20.3, 26.7, 29.0, 27.6, 27.3, 23.8, 20.5, 15.1, ... | |
scibench_multimodal | [
{
"content": "<image> In Fig. 21-32, particles 1 and 2 of charge $q_1=q_2=+3.20 \\times 10^{-19} \\mathrm{C}$ are on a $y$ axis at distance $d=17.0 \\mathrm{~cm}$ from the origin. Particle 3 of charge $q_3=+6.40 \\times 10^{-19} \\mathrm{C}$ is moved gradually along the $x$ axis from $x=0$ to $x=$ $+5.0 \\mathr... | {
"ground_truth": "$0$",
"style": "rule"
} | {
"gt_answer": "$0$",
"id": "scibench_multimodal--26",
"mc_options": null,
"original_question": "<image> In Fig. 21-32, particles 1 and 2 of charge $q_1=q_2=+3.20 \\times 10^{-19} \\mathrm{C}$ are on a $y$ axis at distance $d=17.0 \\mathrm{~cm}$ from the origin. Particle 3 of charge $q_3=+6.40 \\times 10^{-19} ... | |
scibench_multimodal | [
{
"content": "<image>Figure 22-45 shows an electric dipole. What is the direction (relative to the positive direction of the $x$ axis) of the dipole's electric field at point $P$, located at distance $r \\gg d$ ?",
"role": "user"
}
] | {
"ground_truth": "$-90$ $^{\\circ}$",
"style": "rule"
} | {
"gt_answer": "$-90$ $^{\\circ}$",
"id": "scibench_multimodal--27",
"mc_options": null,
"original_question": "<image>Figure 22-45 shows an electric dipole. What is the direction (relative to the positive direction of the $x$ axis) of the dipole's electric field at point $P$, located at distance $r \\gg d$ ?"
} | |
scibench_multimodal | [
{
"content": "<image>B.A. Bovenzi and G.A. Pearse, Jr. (J. Chem. Soc. Dalton Trans., 2793 (1997)) synthesized coordination compounds of the tridentate ligand pyridine-2,6-diamidoxime $\\left(7, \\mathrm{C}_7 \\mathrm{H}_9 \\mathrm{~N}_5 \\mathrm{O}_2\\right)$. The compound which they isolated from the reaction ... | {
"ground_truth": "4",
"style": "rule"
} | {
"gt_answer": "4",
"id": "scibench_multimodal--28",
"mc_options": null,
"original_question": "<image>B.A. Bovenzi and G.A. Pearse, Jr. (J. Chem. Soc. Dalton Trans., 2793 (1997)) synthesized coordination compounds of the tridentate ligand pyridine-2,6-diamidoxime $\\left(7, \\mathrm{C}_7 \\mathrm{H}_9 \\mathrm{... | |
scibench_multimodal | [
{
"content": "<image>This problem is quite challenging in setting up but takes only a few lines of algebra to solve. We deal with not only uniformly circular motion but also a ramp. However, we will not need a tilted coordinate system as with other ramps. Instead we can take a freeze-frame of the motion and wor... | {
"ground_truth": "12 $^{\\circ}$",
"style": "rule"
} | {
"gt_answer": "12 $^{\\circ}$",
"id": "scibench_multimodal--29",
"mc_options": null,
"original_question": "<image>This problem is quite challenging in setting up but takes only a few lines of algebra to solve. We deal with not only uniformly circular motion but also a ramp. However, we will not need a tilted ... | |
scibench_multimodal | [
{
"content": "<image>Figure shows a water-slide ride in which a glider is shot by a spring along a water-drenched (frictionless) track that takes the glider from a horizontal section down to ground level. As the glider then moves along ground-level track, it is gradually brought to rest by friction. The total m... | {
"ground_truth": "69.3 m",
"style": "rule"
} | {
"gt_answer": "69.3 m",
"id": "scibench_multimodal--30",
"mc_options": null,
"original_question": "<image>Figure shows a water-slide ride in which a glider is shot by a spring along a water-drenched (frictionless) track that takes the glider from a horizontal section down to ground level. As the glider then m... | |
scibench_multimodal | [
{
"content": "<image>A uniform ball, of mass $M=6.00 \\mathrm{~kg}$ and radius $R$, rolls smoothly from rest down a ramp at angle $\\theta=30.0^{\\circ}$ (Figure).\r\nThe ball descends a vertical height $h=1.20 \\mathrm{~m}$ to reach the bottom of the ramp. What is its speed at the bottom?",
"role": "user"
... | {
"ground_truth": "4.10 m/s",
"style": "rule"
} | {
"gt_answer": "4.10 m/s",
"id": "scibench_multimodal--31",
"mc_options": null,
"original_question": "<image>A uniform ball, of mass $M=6.00 \\mathrm{~kg}$ and radius $R$, rolls smoothly from rest down a ramp at angle $\\theta=30.0^{\\circ}$ (Figure).\r\nThe ball descends a vertical height $h=1.20 \\mathrm{~m}... | |
scibench_multimodal | [
{
"content": "<image>The main lesson of this sample problem is this: It is perfectly all right to choose an easy path instead of a hard path. Figure shows a $2.0 \\mathrm{~kg}$ block of slippery cheese that slides along a frictionless track from point $a$ to point $b$. The cheese travels through a total distanc... | {
"ground_truth": "15.7 J",
"style": "rule"
} | {
"gt_answer": "15.7 J",
"id": "scibench_multimodal--32",
"mc_options": null,
"original_question": "<image>The main lesson of this sample problem is this: It is perfectly all right to choose an easy path instead of a hard path. Figure shows a $2.0 \\mathrm{~kg}$ block of slippery cheese that slides along a fri... | |
scibench_multimodal | [
{
"content": "<image>In Figure, a cockroach with mass $m$ rides on a disk of mass $6.00 \\mathrm{~m}$ and radius $R$. The disk rotates like a merry-go-round around its central axis at angular speed $\\omega_i=1.50 \\mathrm{rad} / \\mathrm{s}$. The cockroach is initially at radius $r=0.800 R$, but then it crawls... | {
"ground_truth": "1.37 rad/s",
"style": "rule"
} | {
"gt_answer": "1.37 rad/s",
"id": "scibench_multimodal--33",
"mc_options": null,
"original_question": "<image>In Figure, a cockroach with mass $m$ rides on a disk of mass $6.00 \\mathrm{~m}$ and radius $R$. The disk rotates like a merry-go-round around its central axis at angular speed $\\omega_i=1.50 \\mathr... | |
scibench_multimodal | [
{
"content": "<image>This sample problem involves a tilted applied force, which requires that we work with components to find a frictional force. The main challenge is to sort out all the components. Figure shows a force of magnitude $F=$ $12.0 \\mathrm{~N}$ applied to an $8.00 \\mathrm{~kg}$ block at a downwar... | {
"ground_truth": "10.39 N",
"style": "rule"
} | {
"gt_answer": "10.39 N",
"id": "scibench_multimodal--34",
"mc_options": null,
"original_question": "<image>This sample problem involves a tilted applied force, which requires that we work with components to find a frictional force. The main challenge is to sort out all the components. Figure shows a force of ... | |
scibench_multimodal | [
{
"content": "<image>For the function $g$ whose graph is given, state the value of $g(2)$.",
"role": "user"
}
] | {
"ground_truth": "1",
"style": "rule"
} | {
"gt_answer": "1",
"id": "scibench_multimodal--35",
"mc_options": null,
"original_question": "<image>For the function $g$ whose graph is given, state the value of $g(2)$."
} | |
scibench_multimodal | [
{
"content": "<image>Comet Halley orbits the Sun with a period of 76 years and, in 1986, had a distance of closest approach to the Sun, its perihelion distance $R_p$, of $8.9 \\times 10^{10} \\mathrm{~m}$. Table shows that this is between the orbits of Mercury and Venus. What is the eccentricity $e$ of the orbi... | {
"ground_truth": "0.97",
"style": "rule"
} | {
"gt_answer": "0.97",
"id": "scibench_multimodal--36",
"mc_options": null,
"original_question": "<image>Comet Halley orbits the Sun with a period of 76 years and, in 1986, had a distance of closest approach to the Sun, its perihelion distance $R_p$, of $8.9 \\times 10^{10} \\mathrm{~m}$. Table shows that this ... | |
scibench_multimodal | [
{
"content": "<image>Let\r\n$$\r\n\\mathbf{F}(x, y, z)=\\left(3 x^2 y z-3 y\\right) \\mathbf{i}+\\left(x^3 z-3 x\\right) \\mathbf{j}+\\left(x^3 y+2 z\\right) \\mathbf{k}\r\n$$\r\nEvaluate $\\int_C \\mathbf{F} \\cdot d r$, where $C$ is the curve with initial point $(0,0,2)$ and terminal point $(0,3,0)$ shown in ... | {
"ground_truth": "-4",
"style": "rule"
} | {
"gt_answer": "-4",
"id": "scibench_multimodal--37",
"mc_options": null,
"original_question": "<image>Let\r\n$$\r\n\\mathbf{F}(x, y, z)=\\left(3 x^2 y z-3 y\\right) \\mathbf{i}+\\left(x^3 z-3 x\\right) \\mathbf{j}+\\left(x^3 y+2 z\\right) \\mathbf{k}\r\n$$\r\nEvaluate $\\int_C \\mathbf{F} \\cdot d r$, where $C... | |
scibench_multimodal | [
{
"content": "<image>Here is an example of a common technique in physics. We have a demonstration that cannot be worked out as a whole (we don't have a workable equation for it). So, we break it up into steps that can be worked separately (we have equations for them).\r\n\r\nThe ballistic pendulum was used to m... | {
"ground_truth": "630 m/s",
"style": "rule"
} | {
"gt_answer": "630 m/s",
"id": "scibench_multimodal--38",
"mc_options": null,
"original_question": "<image>Here is an example of a common technique in physics. We have a demonstration that cannot be worked out as a whole (we don't have a workable equation for it). So, we break it up into steps that can be wor... | |
scibench_multimodal | [
{
"content": "<image>In Fig. 4-20a, a plane moves due east while the pilot points the plane somewhat south of east, toward a steady wind that blows to the northeast. The plane has velocity $\\vec{v}_{P W}$ relative to the wind, with an airspeed (speed relative to the wind) of $215 \\mathrm{~km} / \\mathrm{h}$, ... | {
"ground_truth": "228 km/h",
"style": "rule"
} | {
"gt_answer": "228 km/h",
"id": "scibench_multimodal--39",
"mc_options": null,
"original_question": "<image>In Fig. 4-20a, a plane moves due east while the pilot points the plane somewhat south of east, toward a steady wind that blows to the northeast. The plane has velocity $\\vec{v}_{P W}$ relative to the wi... | |
scibench_multimodal | [
{
"content": "<image>Some of the funniest videos on the web involve motorists sliding uncontrollably on icy roads. Here let's compare the typical stopping distances for a car sliding to a stop from an initial speed of $10.0 \\mathrm{~m} / \\mathrm{s}$ on a dry horizontal road, an icy horizontal road, and (every... | {
"ground_truth": "8.50 m",
"style": "rule"
} | {
"gt_answer": "8.50 m",
"id": "scibench_multimodal--40",
"mc_options": null,
"original_question": "<image>Some of the funniest videos on the web involve motorists sliding uncontrollably on icy roads. Here let's compare the typical stopping distances for a car sliding to a stop from an initial speed of $10.0 \... | |
scibench_multimodal | [
{
"content": "<image>Figure shows an overhead view of two particles moving at constant momentum along horizontal paths. Particle 1, with momentum magnitude $p_1=5.0 \\mathrm{~kg} \\cdot \\mathrm{m} / \\mathrm{s}$, has position vector $\\vec{r}_1$ and will pass $2.0 \\mathrm{~m}$ from point $O$. Particle 2 , wit... | {
"ground_truth": "2.0 $\\mathrm{kg} \\cdot \\mathrm{m}^2 / \\mathrm{s}$",
"style": "rule"
} | {
"gt_answer": "2.0 $\\mathrm{kg} \\cdot \\mathrm{m}^2 / \\mathrm{s}$",
"id": "scibench_multimodal--41",
"mc_options": null,
"original_question": "<image>Figure shows an overhead view of two particles moving at constant momentum along horizontal paths. Particle 1, with momentum magnitude $p_1=5.0 \\mathrm{~kg}... | |
scibench_multimodal | [
{
"content": "<image>A spaceship of mass $m=4.50 \\times 10^3 \\mathrm{~kg}$ is in a circular Earth orbit of radius $r=8.00 \\times 10^6 \\mathrm{~m}$ and period $T_0=118.6 \\mathrm{~min}=$ $7.119 \\times 10^3 \\mathrm{~s}$ when a thruster is fired in the forward direction to decrease the speed to $96.0 \\%$ of... | {
"ground_truth": "6.356 $10^3 s$",
"style": "rule"
} | {
"gt_answer": "6.356 $10^3 s$",
"id": "scibench_multimodal--42",
"mc_options": null,
"original_question": "<image>A spaceship of mass $m=4.50 \\times 10^3 \\mathrm{~kg}$ is in a circular Earth orbit of radius $r=8.00 \\times 10^6 \\mathrm{~m}$ and period $T_0=118.6 \\mathrm{~min}=$ $7.119 \\times 10^3 \\mathr... | |
scibench_multimodal | [
{
"content": "<image>\"Whiplash injury\" commonly occurs in a rear-end collision where a front car is hit from behind by a second car. In the 1970s, researchers concluded that the injury was due to the occupant's head being whipped back over the top of the seat as the car was slammed forward. As a result of thi... | {
"ground_truth": "2.0 m/s",
"style": "rule"
} | {
"gt_answer": "2.0 m/s",
"id": "scibench_multimodal--43",
"mc_options": null,
"original_question": "<image>\"Whiplash injury\" commonly occurs in a rear-end collision where a front car is hit from behind by a second car. In the 1970s, researchers concluded that the injury was due to the occupant's head being ... | |
scibench_multimodal | [
{
"content": "<image>Phenylalanine (Phe, 5) is a naturally occurring amino acid. What is the energy of interaction between its phenyl group and the electric dipole moment of a neighbouring peptide group? Take the distance between the groups as $4.0 \\mathrm{~nm}$ and treat the phenyl group as a benzene molecule... | {
"ground_truth": "-4.3 $10^{-28} \\mathrm{~J}$",
"style": "rule"
} | {
"gt_answer": "-4.3 $10^{-28} \\mathrm{~J}$",
"id": "scibench_multimodal--44",
"mc_options": null,
"original_question": "<image>Phenylalanine (Phe, 5) is a naturally occurring amino acid. What is the energy of interaction between its phenyl group and the electric dipole moment of a neighbouring peptide group? ... | |
scibench_multimodal | [
{
"content": "<image>Figure shows a safe (mass $M=430 \\mathrm{~kg}$ ) hanging by a rope (negligible mass) from a boom $(a=1.9 \\mathrm{~m}$ and $b=$ $2.5 \\mathrm{~m})$ that consists of a uniform hinged beam $(m=85 \\mathrm{~kg})$ and horizontal cable (negligible mass).\r\nWhat is the tension $T_c$ in the cabl... | {
"ground_truth": "6093 N",
"style": "rule"
} | {
"gt_answer": "6093 N",
"id": "scibench_multimodal--45",
"mc_options": null,
"original_question": "<image>Figure shows a safe (mass $M=430 \\mathrm{~kg}$ ) hanging by a rope (negligible mass) from a boom $(a=1.9 \\mathrm{~m}$ and $b=$ $2.5 \\mathrm{~m})$ that consists of a uniform hinged beam $(m=85 \\mathrm{... | |
scibench_multimodal | [
{
"content": "<image>For the function $g$ whose graph is given, state the value of $\\lim _{t \\rightarrow 4} g(t)$.",
"role": "user"
}
] | {
"ground_truth": "3",
"style": "rule"
} | {
"gt_answer": "3",
"id": "scibench_multimodal--46",
"mc_options": null,
"original_question": "<image>For the function $g$ whose graph is given, state the value of $\\lim _{t \\rightarrow 4} g(t)$."
} | |
scibench_multimodal | [
{
"content": "<image>One of the most dramatic videos on the web (but entirely fictitious) supposedly shows a man sliding along a long water slide and then being launched into the air to land in a water pool. Let's attach some reasonable numbers to such a flight to calculate the velocity with which the man would... | {
"ground_truth": "10.44 m/s",
"style": "rule"
} | {
"gt_answer": "10.44 m/s",
"id": "scibench_multimodal--47",
"mc_options": null,
"original_question": "<image>One of the most dramatic videos on the web (but entirely fictitious) supposedly shows a man sliding along a long water slide and then being launched into the air to land in a water pool. Let's attach s... | |
scibench_multimodal | [
{
"content": "<image>Figure shows a uniform disk, with mass $M=2.5 \\mathrm{~kg}$ and radius $R=20 \\mathrm{~cm}$, mounted on a fixed horizontal axle. A block with mass $m=1.2 \\mathrm{~kg}$ hangs from a massless cord that is wrapped around the rim of the disk. Find the tension in the cord. The cord does not sl... | {
"ground_truth": "6.0 N",
"style": "rule"
} | {
"gt_answer": "6.0 N",
"id": "scibench_multimodal--48",
"mc_options": null,
"original_question": "<image>Figure shows a uniform disk, with mass $M=2.5 \\mathrm{~kg}$ and radius $R=20 \\mathrm{~cm}$, mounted on a fixed horizontal axle. A block with mass $m=1.2 \\mathrm{~kg}$ hangs from a massless cord that is ... | |
scibench_multimodal | [
{
"content": "<image>In Figure, suppose that Barbara's velocity relative to Alex is a constant $v_{B A}=52 \\mathrm{~km} / \\mathrm{h}$ and car $P$ is moving in the negative direction of the $x$ axis.\r\n(a) If Alex measures a constant $v_{P A}=-78 \\mathrm{~km} / \\mathrm{h}$ for car $P$, what velocity $v_{P B... | {
"ground_truth": "-130 km/h",
"style": "rule"
} | {
"gt_answer": "-130 km/h",
"id": "scibench_multimodal--49",
"mc_options": null,
"original_question": "<image>In Figure, suppose that Barbara's velocity relative to Alex is a constant $v_{B A}=52 \\mathrm{~km} / \\mathrm{h}$ and car $P$ is moving in the negative direction of the $x$ axis.\r\n(a) If Alex measur... | |
scibench_multimodal | [
{
"content": "<image>Figure is an overhead view of the path taken by a race car driver as his car collides with the racetrack wall. Just before the collision, he is traveling at speed $v_i=70 \\mathrm{~m} / \\mathrm{s}$ along a straight line at $30^{\\circ}$ from the wall. Just after the collision, he is travel... | {
"ground_truth": "2.583 $10^5$ N",
"style": "rule"
} | {
"gt_answer": "2.583 $10^5$ N",
"id": "scibench_multimodal--50",
"mc_options": null,
"original_question": "<image>Figure is an overhead view of the path taken by a race car driver as his car collides with the racetrack wall. Just before the collision, he is traveling at speed $v_i=70 \\mathrm{~m} / \\mathrm{s... | |
scibench_multimodal | [
{
"content": "<image>A raindrop with radius $R=1.5 \\mathrm{~mm}$ falls from a cloud that is at height $h=1200 \\mathrm{~m}$ above the ground. The drag coefficient $C$ for the drop is 0.60 . Assume that the drop is spherical throughout its fall. The density of water $\\rho_w$ is $1000 \\mathrm{~kg} / \\mathrm{m... | {
"ground_truth": "7.4 m/s",
"style": "rule"
} | {
"gt_answer": "7.4 m/s",
"id": "scibench_multimodal--51",
"mc_options": null,
"original_question": "<image>A raindrop with radius $R=1.5 \\mathrm{~mm}$ falls from a cloud that is at height $h=1200 \\mathrm{~m}$ above the ground. The drag coefficient $C$ for the drop is 0.60 . Assume that the drop is spherical... | |
scibench_multimodal | [
{
"content": "<image>A modern race car is designed so that the passing air pushes down on it, allowing the car to travel much faster through a flat turn in a Grand Prix without friction failing. This downward push is called negative lift. Can a race car have so much negative lift that it could be driven upside ... | {
"ground_truth": "663.7 N",
"style": "rule"
} | {
"gt_answer": "663.7 N",
"id": "scibench_multimodal--52",
"mc_options": null,
"original_question": "<image>A modern race car is designed so that the passing air pushes down on it, allowing the car to travel much faster through a flat turn in a Grand Prix without friction failing. This downward push is called ... | |
scibench_multimodal | [
{
"content": "<image>When a spring does work on an object, we cannot find the work by simply multiplying the spring force by the object's displacement. The reason is that there is no one value for the force-it changes. However, we can split the displacement up into an infinite number of tiny parts and then appr... | {
"ground_truth": "1.2 $10^{-2}$ m",
"style": "rule"
} | {
"gt_answer": "1.2 $10^{-2}$ m",
"id": "scibench_multimodal--53",
"mc_options": null,
"original_question": "<image>When a spring does work on an object, we cannot find the work by simply multiplying the spring force by the object's displacement. The reason is that there is no one value for the force-it change... | |
scibench_multimodal | [
{
"content": "<image>The magnitude of the acceleration vector a is $10 \\mathrm{~cm} / \\mathrm{s}^2$. Use the figure to estimate the tangential components of $\\mathbf{a}$.\r\n",
"role": "user"
}
] | {
"ground_truth": "4.5 $\\mathrm{cm}/\\mathrm{s^2}$",
"style": "rule"
} | {
"gt_answer": "4.5 $\\mathrm{cm}/\\mathrm{s^2}$",
"id": "scibench_multimodal--54",
"mc_options": null,
"original_question": "<image>The magnitude of the acceleration vector a is $10 \\mathrm{~cm} / \\mathrm{s}^2$. Use the figure to estimate the tangential components of $\\mathbf{a}$.\r\n"
} | |
scibench_multimodal | [
{
"content": "<image>Figure shows an arrangement of three particles, particle 1 of mass $m_1=6.0 \\mathrm{~kg}$ and particles 2 and 3 of mass $m_2=$ $m_3=4.0 \\mathrm{~kg}$, and distance $a=2.0 \\mathrm{~cm}$. What is the net gravitational force $\\vec{F}_{1, \\text { net }}$ on particle 1 due to the other part... | {
"ground_truth": "4.1 $10^{-6} \\mathrm{~N}$",
"style": "rule"
} | {
"gt_answer": "4.1 $10^{-6} \\mathrm{~N}$",
"id": "scibench_multimodal--55",
"mc_options": null,
"original_question": "<image>Figure shows an arrangement of three particles, particle 1 of mass $m_1=6.0 \\mathrm{~kg}$ and particles 2 and 3 of mass $m_2=$ $m_3=4.0 \\mathrm{~kg}$, and distance $a=2.0 \\mathrm{~c... | |
scibench_multimodal | [
{
"content": "<image>In Figure, a rescue plane flies at $198 \\mathrm{~km} / \\mathrm{h}(=55.0 \\mathrm{~m} / \\mathrm{s})$ and constant height $h=500 \\mathrm{~m}$ toward a point directly over a victim, where a rescue capsule is to land.\r\nWhat should be the angle $\\phi$ of the pilot's line of sight to the v... | {
"ground_truth": "48.0 $^{\\circ}$",
"style": "rule"
} | {
"gt_answer": "48.0 $^{\\circ}$",
"id": "scibench_multimodal--56",
"mc_options": null,
"original_question": "<image>In Figure, a rescue plane flies at $198 \\mathrm{~km} / \\mathrm{h}(=55.0 \\mathrm{~m} / \\mathrm{s})$ and constant height $h=500 \\mathrm{~m}$ toward a point directly over a victim, where a res... | |
scibench_multimodal | [
{
"content": "<image>Use the given graph of $f$ to find the largest number $\\delta$ such that if $\\quad|x-1|<\\delta \\quad$ then $\\quad|f(x)-1|<0.2$.",
"role": "user"
}
] | {
"ground_truth": "0.1",
"style": "rule"
} | {
"gt_answer": "0.1",
"id": "scibench_multimodal--57",
"mc_options": null,
"original_question": "<image>Use the given graph of $f$ to find the largest number $\\delta$ such that if $\\quad|x-1|<\\delta \\quad$ then $\\quad|f(x)-1|<0.2$."
} | |
scibench_multimodal | [
{
"content": "<image>Figure shows a block $S$ (the sliding block) with mass $M=3.3 \\mathrm{~kg}$. The block is free to move along a horizontal frictionless surface and connected, by a cord that wraps over a frictionless pulley, to a second block $H$ (the hanging block), with mass $m=2.1 \\mathrm{~kg}$. The cor... | {
"ground_truth": "13 N",
"style": "rule"
} | {
"gt_answer": "13 N",
"id": "scibench_multimodal--58",
"mc_options": null,
"original_question": "<image>Figure shows a block $S$ (the sliding block) with mass $M=3.3 \\mathrm{~kg}$. The block is free to move along a horizontal frictionless surface and connected, by a cord that wraps over a frictionless pulley... | |
scibench_multimodal | [
{
"content": "<image>For the function $f$ whose graph is given, state $\\lim _{x \\rightarrow \\infty} f(x)$.",
"role": "user"
}
] | {
"ground_truth": "-2",
"style": "rule"
} | {
"gt_answer": "-2",
"id": "scibench_multimodal--59",
"mc_options": null,
"original_question": "<image>For the function $f$ whose graph is given, state $\\lim _{x \\rightarrow \\infty} f(x)$."
} | |
scibench_multimodal | [
{
"content": "<image>For the function $f$ whose graph is given, state $\\lim _{x \\rightarrow-\\infty} f(x)$.",
"role": "user"
}
] | {
"ground_truth": "2",
"style": "rule"
} | {
"gt_answer": "2",
"id": "scibench_multimodal--60",
"mc_options": null,
"original_question": "<image>For the function $f$ whose graph is given, state $\\lim _{x \\rightarrow-\\infty} f(x)$."
} | |
scibench_multimodal | [
{
"content": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Find the average rate of cell phone growth from 2002 to 2006.",
"role": "user"
}
] | {
"ground_truth": "23 million/year",
"style": "rule"
} | {
"gt_answer": "23 million/year",
"id": "scibench_multimodal--61",
"mc_options": null,
"original_question": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Find the average rate of cell phone growth from 2002 to 2006."
} | |
scibench_multimodal | [
{
"content": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Find the average rate of cell phone growth from 2002 to 2004.",
"role": "user"
}
] | {
"ground_truth": "20.5 million/year",
"style": "rule"
} | {
"gt_answer": "20.5 million/year",
"id": "scibench_multimodal--62",
"mc_options": null,
"original_question": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Find the average rate of cell phone growth from 2002 to 2004."
} | |
scibench_multimodal | [
{
"content": "<image>Use the given graphs of $f$ and $g$ to evaluate $f(g(2))$.",
"role": "user"
}
] | {
"ground_truth": "4",
"style": "rule"
} | {
"gt_answer": "4",
"id": "scibench_multimodal--63",
"mc_options": null,
"original_question": "<image>Use the given graphs of $f$ and $g$ to evaluate $f(g(2))$."
} | |
scibench_multimodal | [
{
"content": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Find the average rate of cell phone growth from 2000 to 2002.",
"role": "user"
}
] | {
"ground_truth": "16 million/year",
"style": "rule"
} | {
"gt_answer": "16 million/year",
"id": "scibench_multimodal--64",
"mc_options": null,
"original_question": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Find the average rate of cell phone growth from 2000 to 2002."
} | |
scibench_multimodal | [
{
"content": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Estimate the instantaneous rate of growth in 2002 by taking the average of two average rates of change with units.",
"role": "user"
}
] | {
"ground_truth": "18.25 million/year",
"style": "rule"
} | {
"gt_answer": "18.25 million/year",
"id": "scibench_multimodal--65",
"mc_options": null,
"original_question": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Estimate the instantaneous rate of growth in 2002 by taking the average of t... | |
scibench_multimodal | [
{
"content": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Estimate the instantaneous rate of growth in 2002 by measuring the slope of a tangent.",
"role": "user"
}
] | {
"ground_truth": "17 million/year",
"style": "rule"
} | {
"gt_answer": "17 million/year",
"id": "scibench_multimodal--66",
"mc_options": null,
"original_question": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Estimate the instantaneous rate of growth in 2002 by measuring the slope of a t... | |
scibench_multimodal | [
{
"content": "<image>Let $T(t)$ be the temperature (in ${ }^{\\circ} \\mathrm{F}$ ) in Phoenix $t$ hours after midnight on September 10, 2008. The table shows values of this function recorded every two hours. Estimate the value of $T^{\\prime}(8)$.",
"role": "user"
}
] | {
"ground_truth": "3.75 $^{\\circ} \\mathrm{F} / \\mathrm{h}$",
"style": "rule"
} | {
"gt_answer": "3.75 $^{\\circ} \\mathrm{F} / \\mathrm{h}$",
"id": "scibench_multimodal--67",
"mc_options": null,
"original_question": "<image>Let $T(t)$ be the temperature (in ${ }^{\\circ} \\mathrm{F}$ ) in Phoenix $t$ hours after midnight on September 10, 2008. The table shows values of this function record... | |
scibench_multimodal | [
{
"content": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow 2^{+}} f(x)$.",
"role": "user"
}
] | {
"ground_truth": "3",
"style": "rule"
} | {
"gt_answer": "3",
"id": "scibench_multimodal--68",
"mc_options": null,
"original_question": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow 2^{+}} f(x)$."
} | |
scibench_multimodal | [
{
"content": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow-3^{+}} f(x)$.",
"role": "user"
}
] | {
"ground_truth": "0",
"style": "rule"
} | {
"gt_answer": "0",
"id": "scibench_multimodal--69",
"mc_options": null,
"original_question": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow-3^{+}} f(x)$."
} | |
scibench_multimodal | [
{
"content": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow 4} f(x)$.",
"role": "user"
}
] | {
"ground_truth": "2",
"style": "rule"
} | {
"gt_answer": "2",
"id": "scibench_multimodal--70",
"mc_options": null,
"original_question": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow 4} f(x)$."
} | |
scibench_multimodal | [
{
"content": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow \\infty} f(x)$.",
"role": "user"
}
] | {
"ground_truth": "4",
"style": "rule"
} | {
"gt_answer": "4",
"id": "scibench_multimodal--71",
"mc_options": null,
"original_question": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow \\infty} f(x)$."
} | |
scibench_multimodal | [
{
"content": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow-\\infty} f(x)$.",
"role": "user"
}
] | {
"ground_truth": "-1",
"style": "rule"
} | {
"gt_answer": "-1",
"id": "scibench_multimodal--72",
"mc_options": null,
"original_question": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow-\\infty} f(x)$."
} | |
scibench_multimodal | [
{
"content": "<image>If $f$ and $g$ are the functions whose graphs are shown, let $u(x)=f(x) g(x)$ and $v(x)=f(x) / g(x)$. Find $u^{\\prime}(1)$.",
"role": "user"
}
] | {
"ground_truth": "0",
"style": "rule"
} | {
"gt_answer": "0",
"id": "scibench_multimodal--73",
"mc_options": null,
"original_question": "<image>If $f$ and $g$ are the functions whose graphs are shown, let $u(x)=f(x) g(x)$ and $v(x)=f(x) / g(x)$. Find $u^{\\prime}(1)$."
} | |
scibench_multimodal | [
{
"content": "<image>Find the value of $C$ in the exponential function $f(x)=C a^x$ whose graph is given.",
"role": "user"
}
] | {
"ground_truth": "3",
"style": "rule"
} | {
"gt_answer": "3",
"id": "scibench_multimodal--74",
"mc_options": null,
"original_question": "<image>Find the value of $C$ in the exponential function $f(x)=C a^x$ whose graph is given."
} | |
scibench_multimodal | [
{
"content": "<image>If $f$ and $g$ are the functions whose graphs are shown, let $u(x)=f(x) g(x)$ and $v(x)=f(x) / g(x)$. Find $v^{\\prime}(5)$.",
"role": "user"
}
] | {
"ground_truth": "$ -\\frac{2}{3}$",
"style": "rule"
} | {
"gt_answer": "$ -\\frac{2}{3}$",
"id": "scibench_multimodal--75",
"mc_options": null,
"original_question": "<image>If $f$ and $g$ are the functions whose graphs are shown, let $u(x)=f(x) g(x)$ and $v(x)=f(x) / g(x)$. Find $v^{\\prime}(5)$."
} | |
scibench_multimodal | [
{
"content": "<image>If $f$ and $g$ are the functions whose graphs are shown, let $u(x)=f(g(x)), v(x)=g(f(x))$, and $w(x)=g(g(x))$. Find the derivative, $u^{\\prime}(1)$.",
"role": "user"
}
] | {
"ground_truth": "$\\frac{3}{4}$",
"style": "rule"
} | {
"gt_answer": "$\\frac{3}{4}$",
"id": "scibench_multimodal--76",
"mc_options": null,
"original_question": "<image>If $f$ and $g$ are the functions whose graphs are shown, let $u(x)=f(g(x)), v(x)=g(f(x))$, and $w(x)=g(g(x))$. Find the derivative, $u^{\\prime}(1)$."
} | |
scibench_multimodal | [
{
"content": "<image>If $f$ and $g$ are the functions whose graphs are shown, let $u(x)=f(g(x)), v(x)=g(f(x))$, and $w(x)=g(g(x))$. Find the derivative, $w^{\\prime}(1)$.",
"role": "user"
}
] | {
"ground_truth": "-2",
"style": "rule"
} | {
"gt_answer": "-2",
"id": "scibench_multimodal--77",
"mc_options": null,
"original_question": "<image>If $f$ and $g$ are the functions whose graphs are shown, let $u(x)=f(g(x)), v(x)=g(f(x))$, and $w(x)=g(g(x))$. Find the derivative, $w^{\\prime}(1)$."
} | |
scibench_multimodal | [
{
"content": "<image>If $g(x)=\\sqrt{f(x)}$, where the graph of $f$ is shown, evaluate $g^{\\prime}(3)$.",
"role": "user"
}
] | {
"ground_truth": "$-\\frac{1}{6} \\sqrt{2}$",
"style": "rule"
} | {
"gt_answer": "$-\\frac{1}{6} \\sqrt{2}$",
"id": "scibench_multimodal--78",
"mc_options": null,
"original_question": "<image>If $g(x)=\\sqrt{f(x)}$, where the graph of $f$ is shown, evaluate $g^{\\prime}(3)$."
} | |
scibench_multimodal | [
{
"content": "<image>The table gives the population of the world in the 20th century. Estimate the rate of population growth in 1920 and in 1980 by averaging the slopes of two secant lines.",
"role": "user"
}
] | {
"ground_truth": "16 million/year",
"style": "rule"
} | {
"gt_answer": "16 million/year",
"id": "scibench_multimodal--79",
"mc_options": null,
"original_question": "<image>The table gives the population of the world in the 20th century. Estimate the rate of population growth in 1920 and in 1980 by averaging the slopes of two secant lines."
} | |
scibench_multimodal | [
{
"content": "<image>The table gives the population of the world in the 20th century. Estimate the rate of growth in 1985.",
"role": "user"
}
] | {
"ground_truth": "81.62 million/year",
"style": "rule"
} | {
"gt_answer": "81.62 million/year",
"id": "scibench_multimodal--80",
"mc_options": null,
"original_question": "<image>The table gives the population of the world in the 20th century. Estimate the rate of growth in 1985."
} | |
scibench_multimodal | [
{
"content": "<image>The table gives estimates of the world population, in millions, from 1750 to 2000. Use the exponential model and the population figures for 1750 and 1800 to predict the world population in 1900.",
"role": "user"
}
] | {
"ground_truth": "1508 million",
"style": "rule"
} | {
"gt_answer": "1508 million",
"id": "scibench_multimodal--81",
"mc_options": null,
"original_question": "<image>The table gives estimates of the world population, in millions, from 1750 to 2000. Use the exponential model and the population figures for 1750 and 1800 to predict the world population in 1900."
} | |
scibench_multimodal | [
{
"content": "<image>The table gives estimates of the world population, in millions, from 1750 to 2000. Use the exponential model and the population figures for 1850 and 1900 to predict the world population in 1950. ",
"role": "user"
}
] | {
"ground_truth": "2161 million",
"style": "rule"
} | {
"gt_answer": "2161 million",
"id": "scibench_multimodal--82",
"mc_options": null,
"original_question": "<image>The table gives estimates of the world population, in millions, from 1750 to 2000. Use the exponential model and the population figures for 1850 and 1900 to predict the world population in 1950. "
} | |
scibench_multimodal | [
{
"content": "<image>The table gives estimates of the world population, in millions, from 1750 to 2000. Use the exponential model and the population figures for 1900 and 1950 to predict the world population in 2000. ",
"role": "user"
}
] | {
"ground_truth": "3972 million",
"style": "rule"
} | {
"gt_answer": "3972 million",
"id": "scibench_multimodal--83",
"mc_options": null,
"original_question": "<image>The table gives estimates of the world population, in millions, from 1750 to 2000. Use the exponential model and the population figures for 1900 and 1950 to predict the world population in 2000. "
} | |
scibench_multimodal | [
{
"content": "<image>Suppose that the only information we have about a function $f$ is that $f(1)=5$ and the graph of its derivative is as shown. Use a linear approximation to estimate $f(0.9)$.",
"role": "user"
}
] | {
"ground_truth": "4.8",
"style": "rule"
} | {
"gt_answer": "4.8",
"id": "scibench_multimodal--84",
"mc_options": null,
"original_question": "<image>Suppose that the only information we have about a function $f$ is that $f(1)=5$ and the graph of its derivative is as shown. Use a linear approximation to estimate $f(0.9)$."
} | |
scibench_multimodal | [
{
"content": "<image>Let $f$ be the function whose graph is given. Estimate the value of $f(2)$.",
"role": "user"
}
] | {
"ground_truth": "2.7",
"style": "rule"
} | {
"gt_answer": "2.7",
"id": "scibench_multimodal--85",
"mc_options": null,
"original_question": "<image>Let $f$ be the function whose graph is given. Estimate the value of $f(2)$."
} | |
scibench_multimodal | [
{
"content": "<image>Use the graph to state the absolute and local maximum",
"role": "user"
}
] | {
"ground_truth": "5",
"style": "rule"
} | {
"gt_answer": "5",
"id": "scibench_multimodal--86",
"mc_options": null,
"original_question": "<image>Use the graph to state the absolute and local maximum"
} | |
scibench_multimodal | [
{
"content": "<image>Use the graph of $f$ to estimate smallest value of $c$ that satisfy the conclusion of the Mean Value Theorem for the interval $[0,8]$.",
"role": "user"
}
] | {
"ground_truth": "0.3",
"style": "rule"
} | {
"gt_answer": "0.3",
"id": "scibench_multimodal--87",
"mc_options": null,
"original_question": "<image>Use the graph of $f$ to estimate smallest value of $c$ that satisfy the conclusion of the Mean Value Theorem for the interval $[0,8]$."
} | |
scibench_multimodal | [
{
"content": "<image>Use the graphs of $f$ and $g$ and their tangent lines at $(2,0)$ to find $\\lim _{x \\rightarrow 2} \\frac{f(x)}{g(x)}$.",
"role": "user"
}
] | {
"ground_truth": "$\\frac{9}{4}$",
"style": "rule"
} | {
"gt_answer": "$\\frac{9}{4}$",
"id": "scibench_multimodal--88",
"mc_options": null,
"original_question": "<image>Use the graphs of $f$ and $g$ and their tangent lines at $(2,0)$ to find $\\lim _{x \\rightarrow 2} \\frac{f(x)}{g(x)}$."
} | |
scibench_multimodal | [
{
"content": "<image>A point $P$ needs to be located somewhere on the line $A D$ so that the total length $L$ of cables linking $P$ to the points $A, B$, and $C$ is minimized (see the figure). By expressing $L$ as a function of $x=|A P|$ and using the graphs of $L$ and $d L / d x$, estimate the minimum value of... | {
"ground_truth": "9.35",
"style": "rule"
} | {
"gt_answer": "9.35",
"id": "scibench_multimodal--89",
"mc_options": null,
"original_question": "<image>A point $P$ needs to be located somewhere on the line $A D$ so that the total length $L$ of cables linking $P$ to the points $A, B$, and $C$ is minimized (see the figure). By expressing $L$ as a function of ... | |
scibench_multimodal | [
{
"content": "<image>The upper right-hand corner of a piece of paper, $12 \\mathrm{in}$. by 8 in., as in the figure, is folded over to the bottom edge. What value of $x$ will to minimize $y$ ?",
"role": "user"
}
] | {
"ground_truth": "6 in",
"style": "rule"
} | {
"gt_answer": "6 in",
"id": "scibench_multimodal--90",
"mc_options": null,
"original_question": "<image>The upper right-hand corner of a piece of paper, $12 \\mathrm{in}$. by 8 in., as in the figure, is folded over to the bottom edge. What value of $x$ will to minimize $y$ ?"
} | |
scibench_multimodal | [
{
"content": "<image> Where should the point $P$ be chosen on the line segment $A B$ so as to maximize the angle $\\theta$ ?",
"role": "user"
}
] | {
"ground_truth": "$5-2 \\sqrt{5}$",
"style": "rule"
} | {
"gt_answer": "$5-2 \\sqrt{5}$",
"id": "scibench_multimodal--91",
"mc_options": null,
"original_question": "<image> Where should the point $P$ be chosen on the line segment $A B$ so as to maximize the angle $\\theta$ ?"
} | |
scibench_multimodal | [
{
"content": "<image>A light is to be placed atop a pole of height $h$ feet to illuminate a busy traffic circle, which has a radius of $40 \\mathrm{ft}$. The intensity of illumination $I$ at any point $P$ on the circle is directly proportional to the cosine of the angle $\\theta$ (see the figure) and inversely ... | {
"ground_truth": "28 ft",
"style": "rule"
} | {
"gt_answer": "28 ft",
"id": "scibench_multimodal--92",
"mc_options": null,
"original_question": "<image>A light is to be placed atop a pole of height $h$ feet to illuminate a busy traffic circle, which has a radius of $40 \\mathrm{ft}$. The intensity of illumination $I$ at any point $P$ on the circle is direc... | |
scibench_multimodal | [
{
"content": "<image>The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower estimate for the distance that she traveled during these three seconds.",
"role": "user"
}
] | {
"ground_truth": "34.7",
"style": "rule"
} | {
"gt_answer": "34.7",
"id": "scibench_multimodal--93",
"mc_options": null,
"original_question": "<image>The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower estimate for the distance that she traveled during thes... | |
scibench_multimodal | [
{
"content": "<image>The velocity graph of a braking car is shown. Use it to estimate the distance traveled by the car while the brakes are applied.",
"role": "user"
}
] | {
"ground_truth": "155 ft",
"style": "rule"
} | {
"gt_answer": "155 ft",
"id": "scibench_multimodal--94",
"mc_options": null,
"original_question": "<image>The velocity graph of a braking car is shown. Use it to estimate the distance traveled by the car while the brakes are applied."
} | |
scibench_multimodal | [
{
"content": "<image>The graph of a function $f$ is given. Estimate $\\int_0^{10} f(x) d x$ using five subintervals with right endpoints.",
"role": "user"
}
] | {
"ground_truth": "6",
"style": "rule"
} | {
"gt_answer": "6",
"id": "scibench_multimodal--95",
"mc_options": null,
"original_question": "<image>The graph of a function $f$ is given. Estimate $\\int_0^{10} f(x) d x$ using five subintervals with right endpoints."
} | |
scibench_multimodal | [
{
"content": "<image>For the function $f$ whose graph is given, state the value of $\\lim _{x \\rightarrow 1} f(x)$.",
"role": "user"
}
] | {
"ground_truth": "2",
"style": "rule"
} | {
"gt_answer": "2",
"id": "scibench_multimodal--96",
"mc_options": null,
"original_question": "<image>For the function $f$ whose graph is given, state the value of $\\lim _{x \\rightarrow 1} f(x)$."
} | |
scibench_multimodal | [
{
"content": "<image>The graph of a function $f$ is given. Estimate $\\int_0^{10} f(x) d x$ using five subintervals with left endpoints.",
"role": "user"
}
] | {
"ground_truth": "4",
"style": "rule"
} | {
"gt_answer": "4",
"id": "scibench_multimodal--97",
"mc_options": null,
"original_question": "<image>The graph of a function $f$ is given. Estimate $\\int_0^{10} f(x) d x$ using five subintervals with left endpoints."
} | |
scibench_multimodal | [
{
"content": "<image>The graph of a function $f$ is given. Estimate $\\int_0^{10} f(x) d x$ using five subintervals with midpoints.",
"role": "user"
}
] | {
"ground_truth": "2",
"style": "rule"
} | {
"gt_answer": "2",
"id": "scibench_multimodal--98",
"mc_options": null,
"original_question": "<image>The graph of a function $f$ is given. Estimate $\\int_0^{10} f(x) d x$ using five subintervals with midpoints."
} | |
scibench_multimodal | [
{
"content": "<image>A table of values of an increasing function $f$ is shown. Use the table to find lower estimates for $\\int_{10}^{30} f(x) d x$.",
"role": "user"
}
] | {
"ground_truth": "-64",
"style": "rule"
} | {
"gt_answer": "-64",
"id": "scibench_multimodal--99",
"mc_options": null,
"original_question": "<image>A table of values of an increasing function $f$ is shown. Use the table to find lower estimates for $\\int_{10}^{30} f(x) d x$."
} |
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