id
stringlengths 4
8
| image_url
stringlengths 77
81
| query
stringlengths 7
1.13k
| answer
stringlengths 1
99
| choice
stringlengths 4
553
| question_type
stringclasses 2
values |
|---|---|---|---|---|---|
func631 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/631.png | 2. As shown in the figure, in the Cartesian coordinate plane, the triangle △ABC is rotated 180° about a point to form △DEF (point A falls at point D, point B falls at point E, and point C falls at point F). What are the coordinates of the rotation center O?
A. (3, 3) B. (3, 2) C. (2, 3) D. (2, 2) | C | ['(3, 3)', '(3, 2)', '(2, 3)', '(2, 2)'] | multi_choice |
func634 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/634.png | As shown in the figure, in the rectangle OABC, vertices A and C are located on the x-axis and y-axis respectively. The graph of the inverse proportional function y = k/x passes through the intersection point D of the diagonals of rectangle OABC, intersects BC at point E, and intersects AB at point F. Given that the coordinates of point B are (4, 2), the ratio of the areas of △CED to △AFB is ( )
A. 2 B. 1.5 C. 1 D. 0.5 | C | ['2', '1.5', '1', '0.5'] | multi_choice |
func649 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/649.png | As shown in the figure, the flight height h (unit: m) of the ball and the flight time t (unit: s) follow the function relationship h = 20t - 5t². Which of the following explanations is correct?
A. When the flight height of the ball is 15m, the flight time is 1s
B. When the ball flies for 3s, the flight height is 15m, and it will continue to rise
C. It takes 4s for the ball to travel from takeoff to landing
D. The flight height of the ball can reach 25m | C | ['When the flight height of the ball is 15m, the flight time is 1s.', 'When the flight time is 3s, the flight height of the ball is 15m, and it continues to rise.', 'It takes 4s for the ball to fall to the ground from the highest point.', 'The flight height of the ball can reach 25m.'] | multi_choice |
func651 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/651.png | As shown in figure (i), in the square ABCD, point P starts from point A and moves uniformly along the path AB→BC, stopping at point C. A line PQ is drawn through point P such that PQ∥BD, and PQ intersects side AD (or side CD) at point Q. The function graph of the length of PQ (cm) as a function of the time x (seconds) for point P's motion is shown in figure (ii). What is the side length of the square ABCD? | B. 4 cm | ['2 cm', '4 cm', '4√2 cm', 'Cannot be determined'] | multi_choice |
func654 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/654.png | 1. After graduating from the Agricultural University, Xiao Wang returned to his hometown to start his own business, cultivating a new variety of mushrooms in a greenhouse. This type of mushroom grows fastest at 18℃ and the temperature control system is turned on only once per day. As shown in the figure, the function graph depicts the change of internal greenhouse temperature y (℃) from the moment the system is turned on, stabilizing the temperature, and then shutting off. For segment BC, the function is y = kx (k > 0). If the mushroom's ideal growing temperature is no lower than 12℃, for how long on that day was the mushroom in an optimal growing environment? ( ) | B | ['18 hours', '17.5 hours', '12 hours', '10 hours'] | multi_choice |
func657 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/657.png | As shown in the figure, in the rectangular coordinate system, circle ⊙P intersects the x-axis at points A and B, and the coordinates of point P are (3, -1), with AB = 2√3. If ⊙P is translated parallel to the y-axis such that it becomes tangent to the x-axis, the distance of translation is ( ). | D | ['1', '2', '3', '1 or 3'] | multi_choice |
func663 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/663.png | As shown in the figure, the coordinates of vertices A, B, and C of quadrilateral ABCD are (0, 2), (-4, -4), and (4, -4), respectively. What are the coordinates of vertex D? | D. (8, 2) | ['(-4, 1)', '(8, -2)', '(4, 1)', '(8, 2)'] | multi_choice |
func664 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/664.png | As shown in the figure, the graph of the inverse proportional function y = k/x intersects with the graph of the linear function y = ax + b at points A(2, m²) and B(m, -6). Then the solution set of the inequality k/x < ax + b is ( ). | A. -3 < x < 0 or x > 2 | ['-3 < x < 0 or x > 2', 'x < -3 or 0 < x < 2', '-2 < x < 0 or x > 2', '-3 < x < 0 or x > 3'] | multi_choice |
func675 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/675.png | As shown in the figure, the straight line y = ax + b and the straight line y = mx + n intersect at point P. Based on the graph analysis, the solution of the system of linear equations in two variables (ax - y + b = 0, mx - y + n = 0) is ( ). | C | ['{ x = -2, y = 4 }', '{ x = 2, y = -4 }', '{ x = 2, y = 4 }', '{ x = -2, y = -4 }'] | multi_choice |
func676 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/676.png | In the plane rectangular coordinate system, the graph of the linear function y = kx + b (where k and b are constants, and k ≠ 0) is as shown. Then, the solution to the equation kx + b = 5 with respect to x is ( ). | A. x = 3 | ['x = 3', 'x = 5', 'x = 0', 'x = b'] | multi_choice |
func686 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/686.png | As shown in the figure, in the rectangular coordinate system, the side OB of the right triangle Rt△AOB lies on the y-axis, ∠AOB = 90°, OB = √3, point C is on AB, BC/AB = 1/3, and ∠BOC = ∠A. If the hyperbola y = k/x passes through point C, then the value of k is ( )
A.√5 B.√3 C.1 D.2 | B | ['√5', '√3', '1', '2'] | multi_choice |
func704 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/704.png | As shown in the figure, point A lies on the hyperbola y = 1/x, and point B lies on the hyperbola y = 3/x. If quadrilateral ABCD is a rectangle, what is its area? | B. 2 | ['1', '2', '3', '4'] | multi_choice |
func710 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/710.png | As shown in the figure, point A lies on one branch of the hyperbolic function y = k/(x+0) (k≠0), point B lies on one branch of the hyperbolic function y = -k/2x (k≠0), and points C and D lie on the x-axis. If quadrilateral ABCD is a square with an area of 9, the value of the real number k is ( ). | C | ['6', '3', '-6', '-9'] | multi_choice |
func715 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/715.png | The graph of the linear function y = kx + b is shown in the diagram. What are the values of k and b, respectively? ( ) | B | ['k = 1, b = -2', 'k = -2, b = -4', 'k = 1/2, b = -2', 'k = -2, b = 4'] | multi_choice |
func722 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/722.png | The atmosphere around the Earth blocks ultraviolet rays and cosmic rays from harming Earth's life while generating a certain atmospheric pressure. The atmospheric pressure varies with altitude. Observe the graph, which of the following statements is correct ( ). | D | ['The higher the altitude, the higher the atmospheric pressure.', 'When the altitude is 7 kilometers, the atmospheric pressure is about 60 kilopascals.', 'The curve in the graph is an image of an inverse proportional function.', 'The graph shows the relationship between atmospheric pressure and altitude.'] | multi_choice |
func726 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/726.png | As shown in the figure, the parabola y = ax² + bx + c intersects the x-axis at points A(-2, 0) and B(6, 0), and intersects the y-axis at point C. The following conclusions are given: ① b² - 4ac > 0; ② abc > 0; ③ When y > 0, -2 < x < 6; ④ a + b + c < 0. The number of correct statements is ( ). | B | ['4', '3', '2', '1'] | multi_choice |
func728 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/728.png | The graphs of the linear functions v₁ = kx + b and v₂ = x + a are shown in the diagram. Based on the graphs, the following conclusions are drawn: ① When x < 3, v₁ = v₂; ② When x < 3, v₂ > 0; ③ When x > 3, v₁ < v₂. The number of correct conclusions is ( ). | C | ['0', '1', '2', '3'] | multi_choice |
func743 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/743.png | A pebble drops into the surface of a lake, forming ripples as shown in the diagram. In the relationship between the area S and the radius r, expressed as S=πr², which are the variables ( )? | A. S, r | ['S, r', 'S, π', 'π, r', 'S, 2'] | multi_choice |
func752 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/752.png | In the same plane rectangular coordinate system, the graphs of the linear functions y₁ = ax + b (a ≠ 0) and y₂ = mx + n (m ≠ 0) are shown in the figure. Which of the following conclusions is incorrect? ( ).
A. y₁ decreases as x increases
B. b < n
C. When x = 2, y₁ > y₂
D. The solution of the system of equations (ax - y = b, mx - y = n) is (x = 2, y = 3) | B | ['\\(y_1\\) decreases as \\(x\\) increases', '\\(b \\leq n\\)', 'When \\(x = 2b\\), \\(y_1 = y_2\\)', 'The solution to the system of equations \\(\\begin{cases} ax - y = b \\\\ mx - y = n \\end{cases}\\) is \\(\\begin{cases} x = 2 \\\\ y = 3 \\end{cases}\\)'] | multi_choice |
func757 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/757.png | As shown in the figure, a linear function y = ax + b and a reciprocal function y = k/x (x > 0) intersect at point A(2, 4) and point B(m, −2). Then the solution set for the inequality ax + b > k/x with respect to x is ( ) | A | ['-4 < x < 0 or x > 2', 'x < -2 or 0 < x < 4', 'x < -4 or 0 < x < 2', '-2 < x < 0 or x > 4'] | multi_choice |
func760 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/760.png | The graph of the linear function y = -2x + 2 is shown in the figure. When y > 0, the range of x is ( ). | D. x < 1 | ['x < 2', 'x > 2', 'x > 1', 'x < 1'] | multi_choice |
func763 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/763.png | The range of real number 'a' is shown in the figure. Then the quadrant in which point P(a+1, a+3) is located is ( ). | B | ['First quadrant', 'Second quadrant', 'Third quadrant', 'Fourth quadrant'] | multi_choice |
func776 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/776.png | As shown in the figure, the graph of the inverse proportional function y=2/x intersects with the graph of the proportional function y=kx at two points. If the distance from one of the intersection points to the coordinate axes is 2, then the distance between the two intersection points is ( ). | B. 2√5 | ['\\(\\sqrt{5}\\)', '\\(2\\sqrt{5}\\)', '\\(\\sqrt{3}\\)', '\\(2\\sqrt{3}\\)'] | multi_choice |
func777 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/777.png | Given the linear function y = kx + b (k ≠ 0) with the graph shown as in the figure, the solution set of the inequality k(x − 1) + b ≤ 6 is ( ). | C. x ≤ 3 | ['x ≤ 2', 'x ≥ 2', 'x ≤ 3', 'x ≥ 4'] | multi_choice |
func782 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/782.png | As shown in the figure, in the Cartesian coordinate system, point P is on the graph of the reciprocal function y=12/x (x>0). Draw PA perpendicular to the x-axis at point A, point B is the midpoint of OA, and connect PB. The area of △PAB is ( ) | C | ['6', '12', '3', '4'] | multi_choice |
func786 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/786.png | As shown in Figure 1, a small ball of mass m starts falling from a certain height and comes to rest upon impacting a vertically placed light spring (the initial length of the spring in its natural state is 12 cm). During the process from the ball first contacting the spring to the spring being compressed to its shortest length (ignoring air resistance, with the spring undergoing elastic deformation throughout), the relationship between the ball's velocity v (cm/s) and the compression length Δl (cm) is depicted in the graph shown in Figure 2. Based on the graph, which of the following statements is correct?
A. The ball starts slowing down as soon as it contacts the spring.
B. The ball's velocity is maximum when the spring is compressed to its shortest length.
C. When the ball's velocity is maximum, the length of the spring is 2 cm.
D. When the ball reaches its lowest position, the length of the spring is 6 cm. | D | ['The small ball starts to accelerate as soon as it touches the spring.', 'When the spring is compressed to its shortest length, the speed of the small ball is the greatest.', 'When the speed of the small ball is the greatest, the compression length of the spring is 2 cm.', 'When the small ball falls to the lowest point, the compression length of the spring is 6 cm.'] | multi_choice |
func788 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/788.png | The graph of the linear function y = kx - 3 is shown below. Which of the following statements is correct? ( ) | B | ['k < 0', 'y increases as x increases', 'The graph passes through the origin', 'The graph passes through the first, second, and fourth quadrants'] | multi_choice |
func791 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/791.png | Xiao Ming and Xiao Zhang went on a weekend trip with their families by car. The relationship between their time (h) and the distance traveled (km) is shown in the graph below. Which of the following statements is incorrect?
A. The relationship between Xiao Ming's distance traveled and time is s=60t.
B. The relationship between Xiao Zhang's distance traveled and time is s=40t.
C. Xiao Ming's car travels faster.
D. Xiao Zhang's car travels faster. | D | ["The relationship between Xiaoming's driving distance and time is s = 60t", "The relationship between Xiaozhang's driving distance and time is s = 40t", "Xiaoming's driving speed is faster", "Xiaozhang's driving speed is faster"] | multi_choice |
func799 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/799.png | As shown in the figure, in the rectangular coordinate system, △OABC has its vertex O at the origin. Point E is a point on the diagonal AC. A line through point E, EF // BC, intersects AB at point F. OC = 2, ∠AOC = 45°, the coordinates of point O are (0,0), the x-coordinate of point E is 5. Calculate the length of EF ( ). | D | ['1', '2', '3', '√2'] | multi_choice |
func808 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/808.png | As shown in the figure, the line y = ax + b (a ≠ 0) passes through points A(0, 2) and B(3, 0). What is the solution set for the inequality ax + b > 0? | B. x < 3 | ['x > 3', 'x < 3', 'x > 2', 'x < 2'] | multi_choice |
func823 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/823.png | As shown in the figure, in ΔABC, ∠C=90°, AC=5, BC=10. Moving points M and N start at A and C, respectively, and move along AC and CB at a speed of 1 unit per second. The initial positions of points M and N are A and C, respectively. Let the moving time be t, and the motion equations of M and N are AC-t and CB-t, respectively. The distance between the two points is y, and the area of △MCN is S. The functional relationships satisfied by y and S are ( ).
A. Proportional function relationship, linear function relationship
B. Proportional function relationship, quadratic function relationship
C. Linear function relationship, proportional function relationship
D. Linear function relationship, quadratic function relationship | D | ['Proportional relationship, linear function relationship', 'Proportional relationship, quadratic function relationship', 'Quadratic function relationship, proportional relationship', 'Linear function relationship, quadratic function relationship'] | multi_choice |
func824 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/824.png | As shown in the figure, in the rectangular coordinate system, three vertices of the parallelogram ABCD have coordinates A(-1, -2), C(5, 2), and D(1, 1). What are the coordinates of vertex B? ( ) | C | ['(-1, 3)', '(4, -1)', '(3, -1)', '(3, -2)'] | multi_choice |
func828 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/828.png | Xiao Ming spent his spare time finding several pairs of myopia glasses with different diopters. He held the lenses directly facing sunlight and moved them up and down until the light spot on the ground became the smallest. He then measured the distance from the lens to the light spot, obtained a set of data, and used a computer to plot the graph of lens diopter x (diopter) versus the distance y (meters) between the lens and the light spot, as shown in the figure. Which of the following conclusions is correct? | C. The greater the lens diopter, the smaller the distance between the lens and the light spot. | ['The relationship between y and x is y = 1000 / x', 'When x = 0.1, y = 100', 'The larger the degree of the lens, the shorter the distance from the lens to the light spot', 'The distance from the lens to the light spot of a flat lens (with a degree of nearsightedness of 0) is 0 meters'] | multi_choice |
func831 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/831.png | In the same Cartesian coordinate system, the graphs of the linear functions y1 = kx + 2 and y2 = k'x + b (k < 0) are shown in the diagram. Which of the following statements is incorrect? ( )
A. y1 decreases as x increases
B. b > 3
C. When 0 < x1 < x2, -1 < k < -2
D. The solution to the system of equations x - 2y = -4 and kx - y = b is {x = 2, y = 3} | C | ['\\(y_2\\) decreases as \\(x\\) increases', '\\(b > 3\\)', 'When \\(0 < x_1 < x_2\\), \\(-1 < k < 2\\)', 'The solution of the system of equations \\(\\begin{cases} x - 2y = -4 \\\\ kx - y = b \\end{cases}\\) is \\(\\begin{cases} x = 2 \\\\ y = 3 \\end{cases}\\)'] | multi_choice |
func857 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/857.png | As shown in the figure, an equilateral triangle with a side length of 2 is folded consecutively along the positive direction of the x-axis 2019 times, resulting in points P1, P2, P3, ..., P2019. What are the coordinates of point P2019? | B (4037, √3) | ['(4036, √3)', '(4037, √3)', '(4036, √5)', '(4037, √5)'] | multi_choice |
func860 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/860.png | As shown in the figure, the line y = kx + b passes through the points A(2, 1) and B(-1, -2). What is the solution set of the inequality kx + b > -2? | A. x > -1 | ['x > -1', 'x < -1', 'x > 2', 'x < 2'] | multi_choice |
func863 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/863.png | As shown in Figure 1, in △ABC, AB = AC, and the moving point P starts from point C and moves along the broken line C→B→A at a speed of 2 cm/s, eventually reaching point A. The relationship between the length of BP (in cm) and the time t (in seconds) is shown in Figure 2. What is the perimeter of △ABC? | C | ['13 cm', '23 cm', '36 cm', '39 cm'] | multi_choice |
func867 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/867.png | If Xiaoying draws a graph showing the changes in wind force over 12 consecutive hours on August 16, 2023, in her city, which of the following statements is correct based on the graph? | C. The duration of wind force above level 5 is approximately 3.5 hours. | ["The wind force is the smallest at 8 o'clock.", "The maximum wind force is 5 levels from 8 o'clock to 12 o'clock.", 'The duration of wind force above level 5 is about 3.5 hours.', "The wind force continues to increase from 8 o'clock to 14 o'clock."] | multi_choice |
func868 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/868.png | As shown in the figure, the graph of the linear function y = kx + b passes through points A and B. What is the solution set for kx + b > 0? | D | ['x > 0', '-3 < x < 2', 'x > 2', 'x > -3'] | multi_choice |
func878 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/878.png | As shown in the figure, there are two points P and Q on the coordinate plane, and their coordinates are (5, a) and (b, 7), respectively. Based on the positions of points P and Q in the figure, the point (6 − b, a − 10) is located in which of the following options?
A. First quadrant B. Second quadrant C. Third quadrant D. Fourth quadrant | D | ['First quadrant', 'Second quadrant', 'Third quadrant', 'Fourth quadrant'] | multi_choice |
func879 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/879.png | As shown in the figure, the vertices of △ABC are A(0,2), B(2,-2), and C(1,-2). Move point C one unit to the right and then two units up to get C₁, and similarly move point C one unit to the right and then two units up again to get C₂. Let the area of △ABC be S, the area of △ABC₁ be S₁, and the area of △ABC₂ be S₂. The size relationship between S, S₁, and S₂ is ( ). | C. S = S₁ = S₂ | ['S < S1 < S2', 'S < S < S2', 'S = S1 = S2', 'Cannot be determined'] | multi_choice |
func884 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/884.png | As shown in the figure, it depicts the driving speed of a car (km/h) and time (minutes). The correct number of statements among the following is ( ):
(1) The car drives for 40 minutes.
(2) AB represents the car traveling at a constant speed.
(3) At the 30th minute, the car's speed is 80 km/h.
(4) At the 40th minute, the car stops.
A. 1 B. 2 C. 3 D. 4 | D | ['1', '2', '3', '4'] | multi_choice |
func887 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/887.png | As shown in the diagram, in the plane rectangular coordinate system, point O(0, 0) and point A(3, 5) are given. Taking point O as the center and OA as the radius, a circle is drawn that intersects the positive x-axis at point B. The x-coordinate of point B lies within the range ( ). | C | ['Between 3 and 4', 'Between 4 and 5', 'Between 5 and 6', 'Between 6 and 7'] | multi_choice |
func889 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/889.png | It is known that the voltage of a certain battery is a constant value. When using this battery, the current (unit: A) and the resistance R (unit: Ω) have an inverse proportional relationship. Its graph is shown in the figure. Which of the following statements is correct? ( )
A. When the resistance is 6Ω, the current is 2A
B. The current decreases as the resistance R increases
C. When the resistance is greater than 8Ω, the current is greater than 6A
D. The point (-8, -6) lies on the graph | B | ['When the resistance is 6Ω, the current is 2A', 'The current decreases as the resistance increases', 'When the resistance is greater than 8Ω, the current is greater than 6A', 'The point (-8, -6) is on the graph'] | multi_choice |
func892 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/892.png | As shown in the figure, a moving point P moves in the direction indicated by the arrow in the coordinate plane. For the 1st move, it moves from the origin to the point (-1, 1); for the 2nd move, it continues to the point (-2, 0); for the 3rd move, it continues to the point (-3, 2); ... Following this pattern of movement, what will be the coordinates of point P after the 2024th move? | B | ['(2024, 0)', '(-2024, 0)', '(-2024, 1)', '(-2024, 2)'] | multi_choice |
func894 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/894.png | The graph of the linear function y = kx + b is shown in the figure. The solution set of the inequality kx + b < 0 is ( ). | D | ['x > 3', 'x ≤ 3', 'x ≥ 3', 'x < 3'] | multi_choice |
func897 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/897.png | As shown in the figure, in a Cartesian coordinate plane, a moving point P starts from the origin O, shifts horizontally 1 unit to the left, then shifts vertically 1 unit downward to reach point P1(-1, -1); then shifts horizontally 2 units to the right, and vertically 2 units upward to reach point P2(1, 1); then shifts horizontally 3 units to the left and vertically 3 units downward to reach point P3(-2, -2); then shifts horizontally 4 units to the right and vertically 4 units upward to reach point P4... Continuing this pattern, the coordinates of point P2025 are ( ). | C | ['(-1012, -1013)', '(-2025, -2025)', '(-1013, -1013)', '(-2024, -2024)'] | multi_choice |
func9 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/9.png | As shown in the figure, it is known that the graph of the quadratic function y1=ax²+bx+c and the linear function y2=kx+m intersect at point A(-5, -3) and point B(3, 4). Then the solutions to the equation ax²+bx+c=kx+m in terms of x are ________. | x1=-5, x2=3 | NULL | free_form |
func900 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/900.png | As shown in the figure, point P moves in the direction indicated by the arrow in the plane rectangular coordinate system. On the 1st move, it moves from the origin to point (1,1). On the 2nd move, it continues to point (2,0). On the 3rd move, it continues to point (3,2), and so on. Following this motion pattern, what will the coordinates of point P be after the 2024th move? | B | ['(2024, 1)', '(2024, 0)', '(2024, 2)', '(2025, 0)'] | multi_choice |
func901 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/901.png | As shown in the figure, the graph of the linear function y = kx + b intersects the y-axis at point A(0, 3) and intersects the x-axis at point B(4, 0). What is the expression for this function? | B. y = −3/4x + 3 | ['y = -\\frac{4}{3}x + 3', 'y = -\\frac{3}{4}x + 3', 'y = -\\frac{4}{3}x + 4', 'y = -\\frac{3}{4}x + 4'] | multi_choice |
func903 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/903.png | As shown in the figure, in a plane Cartesian coordinate system, there are four points: A, B, C, and D. If there is a line passing through the point (-4, 3) and perpendicular to the x-axis, which of the following points will the line also pass through? ( )
A. Point A B. Point B C. Point C D. Point D | A | ['Point A', 'Point B', 'Point C', 'Point D'] | multi_choice |
func904 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/904.png | As shown in the diagram, there is one paper cup and six paper cups stacked together. Xiaohong explores the relationship between the total height of stacked paper cups and the number of cups. She stacks 50 identical paper cups together. What is the approximate total height of these 50 paper cups? ( ) | C | ['50cm', '56cm', '57cm', '58cm'] | multi_choice |
func912 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/912.png | A biology interest group observes the growth of a certain plant and obtains the function graph showing the height of the plant (y, in cm) in relation to the observation time x (in days), as depicted in the diagram. Based on this, calculate the minimum number of days required for the plant's height to exceed 10 cm ( ). | C | ['16 days', '32 days', '40 days', '60 days'] | multi_choice |
func913 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/913.png | As shown in the figure, given that the line v1 = k1x + b1 passes through point A(-3,2), the line v2 = k2x + b2 passing through point A also intersects at point B(-5,0). What is the solution set for the inequality 0 < k2x + b2 < k1x + b1? ( ) | B. −5 < x < −3 | ['x < -3', '-5 < x < -3', '-5 < x < 0', 'x < 0'] | multi_choice |
func916 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/916.png | As shown in the figure, in a Cartesian coordinate plane, a moving point P starts from the origin O, moves horizontally to the right by 1 unit, and then vertically upward by 1 unit, reaching point P1(1, 1). Then it moves horizontally to the left by 2 units, and vertically downward by 2 units, reaching point P2(-1, -1). Next, it moves horizontally to the right by 3 units, and vertically upward by 3 units, reaching point P3(2, 2). Then it moves horizontally to the left by 4 units, and vertically downward by 4 units, reaching point P4(-2, -2). Following this pattern, what are the coordinates of point P2024? | B | ['(1012, 1012)', '(-1012, -1012)', '(1013, 1013)', '(-1013, -1013)'] | multi_choice |
func92 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/92.png | In the recently concluded school sports meet, A and B had a race. Initially, A was 4 meters ahead of B. Both started running at the same time, with A's speed being 4 meters per second and B's speed being 6 meters per second. As shown in the graph, the distance (s) of both runners is represented as a function of running time (t). The coordinates of the intersection point P of the two graphs are ________. | (2, 12) | NULL | free_form |
func926 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/926.png | As shown in the figure, the parabola y = ax^2 + bx + c (a ≠ 0) has its axis of symmetry at the line x = 1 and one of its intersection points with the x-axis is (-1, 0). Part of the graph is shown in the figure. Which of the following statements is incorrect? A. b^2 - 4ac < b^2 B. The equation ax^2 + bx + c = 0 has two roots: x = 1 and x = 3 C. When x ∈ R, y increases as x increases D. b = 2a | C | ['The discriminant \\(4ac < b^2\\)', 'The two roots of the quadratic equation \\(ax^2 + bx + c = 0\\) are \\(x = -1, x = 3\\)', 'The vertex of the parabola is \\((1, -4a)\\)', 'When \\(x > 1\\), \\(y\\) increases with \\(x\\)'] | multi_choice |
func928 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/928.png | As shown in the figure, in rectangle ABCD, A(-4, 1), B(0, 1), and C(0, 3), what are the coordinates of point D? | C. (-4, 3) | ['(-3, 3)', '(-2, 3)', '(-4, 3)', '(4, 3)'] | multi_choice |
func932 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/932.png | Based on the knowledge of physics, under constant pressure, the pressure p (Pa) exerted on an object is an inverse proportional function of its force-bearing area S (m²). The graph of the function is shown. When S = 0.25 m², the pressure p exerted on the object is ( ). | B | ['100', '400', '1000', '2500'] | multi_choice |
func939 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/939.png | In a certain city, typhoons often occur during summer, causing significant inconvenience for people's travel. Xiao Ming observed the wind force changes over 12 consecutive hours on August 16 and plotted a graph showing the variations in wind force over time (as shown in the figure). Which of the following statements is correct? ( ) A. The wind force is minimal at 8:00. B. From 8:00 to 12:00, the maximum wind force is 7 levels. C. From 8:00 to 14:00, the wind force continuously increases. D. From 15:00 to 20:00, the wind force continuously decreases. | D | ["The wind force is the smallest at 8 o'clock.", "The wind force is the largest at 7 levels from 8 o'clock to 12 o'clock.", "The wind force increases continuously from 8 o'clock to 14 o'clock.", "The wind force decreases continuously from 15 o'clock to 20 o'clock."] | multi_choice |
func946 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/946.png | As shown in the diagram, the graphs of functions v1 = -2x and v2 = ax + 3 intersect at point A(m, 2). Then the solution set for the inequality -2x > ax + 3 is ( ). | C. x < -1 | ['x > -1', '-1 < x < 0', 'x < -1', '-3 < x < -1'] | multi_choice |
func951 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/951.png | As shown in the figure, the graphs of the linear functions y1 = kx + 4 and y2 = x + b intersect at point P(1,3). What is the solution set of the inequality x + b ≤ kx + 4 with respect to x? | D. x ≤ 1 | ['x ≥ 3', 'x ≤ 3', 'x ≥ 1', 'x ≤ 1'] | multi_choice |
func962 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/962.png | As shown in the diagram, which illustrates the height changes of a boy and a girl from elementary school to high school, which of the following statements about their height growth rate is incorrect? | D | ["The boy's growth rate is fastest at the age of 12.", "The boy's height growth rate can reach 7 cm/year.", "The girl's growth rate is faster than the boy's at the age of 10.", "The girl's height growth rate can reach 7 cm/year."] | multi_choice |
func964 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/964.png | As shown in the figure, the graphs of the functions y = -2x and y = kx + 4 intersect at point A(m, 4). Then the solution set of the inequality kx + 4 + 2x ≥ 0 with respect to x is ( ). | C. x ≥ -2 | ['x ≥ 4', 'x ≤ 4', 'x ≥ -2', 'x ≤ -2'] | multi_choice |
func967 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/967.png | As shown in the figure, the vertices O, A, and C of □OABC have coordinates (0, 0), (3, 0), and (1, 2), respectively. What are the coordinates of vertex B? | A. (4, 2) | ['(4,2)', '(2,4)', '(4,3)', '(3,4)'] | multi_choice |
func970 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/970.png | In the rectangular coordinate plane, the graph of the linear function y=2x-5 is shown as in the figure. Which of the following statements is incorrect? ( )
A. When x > 0, y > -5
B. The solution to the equation 2x-5=0 is x=5/2
C. When y < 0, x < -5
D. The solution set for the inequality 2x-5 > 0 is x > 5/2 | C | ['When \\(x > 0\\), \\(y > -5\\)', 'The solution to the equation \\(2x - 5 = 0\\) is \\(x = \\frac{5}{2}\\)', 'When \\(y < 0\\), \\(x < -5\\)', 'The solution set to the inequality \\(2x - 5 > 0\\) is \\(x > \\frac{5}{2}\\)'] | multi_choice |
func974 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/974.png | As shown in the figure, P is any point on the curve of the function y = 4/x in the first quadrant. The point P' is the symmetric point of P about the origin. Through P, draw P'A parallel to the y-axis; through P', draw P'A parallel to the x-axis. P'A and P'A intersect at point A. Then the area of △PAP' is ( )
A. Changes with the position of point P
B. Equals 8
C. Equals 4
D. Equals 6 | B | ['Changes with the position of point P', 'Equals 8', 'Equals 4', 'Equals 6'] | multi_choice |
func988 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/988.png | The square OBCD is shown in the rectangular coordinate system as illustrated. Point O(0, 0) and point D(0, 6), then the coordinates of point C are ( ). | D | ['(6, 3)', '(3, 6)', '(0, 6)', '(6, 6)'] | multi_choice |
func989 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/989.png | As shown in the figure, in the rectangle ABCD, side AB lies on the positive x-axis, and side CD is in the first quadrant. AB=3, BC=4. When point D lies on the graph of the reciprocal function y=k/x (x>0), the midpoint E of BC is also exactly on the graph of y=k/x (x>0). What is the value of k? ( ) | D | ['6', '8', '10', '12'] | multi_choice |
func1013 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1013.png | As shown in the figure, the graph of the linear function y = x + 2 intersects with the graph of the linear function y = kx + b (where k and b are constants, and k ≠ 0) at the point P(m, 4). Then the solution to the system of equations {y = x + 2, y = kx + b} with respect to x and y is ( ). | C | ['{ x = 2, y = 0 }', '{ x = 0, y = 4 }', '{ x = 2, y = 4 }', '{ x = 4, y = 2 }'] | multi_choice |
func118 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/118.png | If the coordinates of a point are (-1, 3), then the position of this point in the Cartesian coordinate system shown in the figure is point ______. | N | NULL | free_form |
func579 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/579.png | A farmer wants to use a fence to enclose a rectangular chicken farm, as shown in the figure, with one side of the chicken farm against the wall. If the total length of the fence is 20m, let the side of the rectangle against the wall be xm, and the area be ym². When x changes within a certain range, y changes accordingly. The functional relationship between y and x is ( ). | D | ['y = 20x', 'y = 20 - 2x', 'y = 20/x', 'y = x(20 - 2x)'] | multi_choice |
func670 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/670.png | As shown in the figure, quadrilateral ABCD is a rhombus, and the coordinates of points A and B are (-2√3, 2) and (-1, -√3) respectively. The diagonals intersect at point O. What are the coordinates of point C? | B | ['(−2√3, −2)', '(2√3, −2)', '(1, −√3)', '(−1, √3)'] | multi_choice |
func677 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/677.png | If in the same rectangular coordinate system, the graphs of the functions y₁=2x and y₂=2/x are observed, the solution set of the inequality 2x > 2/x is ( ) | D | ['-1 < x < 1', 'x < -1 or x > 1', 'x < -1 or 0 < x < 1', '-1 < x < 0 or x > 1'] | multi_choice |
func7 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/7.png | As shown in the figure, the x-coordinate of the intersection point of the graphs of the functions y=kx and y=6−x is 2. What is the value of k? | 2 | NULL | free_form |
func720 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/720.png | As shown in the figure, the line y = -x + b intersects the line y = 2x at point A with an x-coordinate of -1. What is the solution set for the inequality -y + b > 2x? | B | ['x < -2', 'x < -1', '-2 < x < -1', '-1 < x < 2'] | multi_choice |
func855 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/855.png | As shown in the figure, the graph of the linear function y = kx + 3 (k ≠ 0) intersects the graph of the direct proportion function y = mx (m ≠ 0) at point P. It is known that the x-coordinate of point P is 1. Then the solution set of the inequality kx - mx > -3 with respect to x is ( ). | A | ['x < 1', '1 < x < 2', '2 < x < 3', 'x > 3'] | multi_choice |
func893 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/893.png | As shown in the figure, a certain community has three ancient pine trees S1, S2, and S3. To strengthen the protection of these ancient pine trees, the gardening department represents the positions of two of them with coordinates: S1(-2,3), S2(1,4). The position of the third ancient pine tree S3 is represented by the coordinates ( ). | C. (-1,1) | ['(-2, 1)', '(2, 1)', '(-1, 1)', '(1, 1)'] | multi_choice |
func1045 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1045.png | PTC is a new type of semiconductor ceramic material with a temperature set as needed, called the 'Curie point temperature.' Below this temperature, its resistance decreases as the temperature increases, and above this temperature, its resistance increases as the temperature increases. PTC materials are widely used in heating components that possess dual functionalities of heating and temperature control. Figure 1 shows a household electric mosquito repellent device, whose heating section uses PTC heating materials. The relationship between resistance (R/kΩ) and temperature (T/°C) for this material is shown in Figure 2. Which of the following statements is NOT correct? ( ) | D | ['According to Figure 2, the Curie point temperature of the PTC material is 30°C.', 'When T = 80°C, the resistance value of the PTC heating element is 14kΩ.', 'When R = 10kΩ, T = 60°C.', 'The resistance value of the heating part increases with the increase in temperature.'] | multi_choice |
func1157 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1157.png | As shown in the figure, when a ball is hit at a certain angle to the ground at a specific speed, its trajectory is a parabola. Ignoring air resistance, the ball lands after 4 seconds. The function relationship between the ball's flight height h (in meters) and the flight time t (in seconds) is given by h = -5t² + 20t (where a is a constant, a ≠ 0). The following conclusions are made: ① The value of a is -5; ② The maximum height the ball can reach is 21 m; ③ There are two moments during the flight when the ball's height reaches exactly 15 m. The correct number of these conclusions is ( ) A. 0 B. 1 C. 2 D. 3 | C | ['The value of a is -5;', "The maximum height of the ball's flight can reach 1m;", 'The height of the ball reaches 15m at two different times during the flight.'] | multi_choice |
func1192 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1192.png | As shown in Figure 1, in △ABC, a moving point P starts at point A and moves along the path AB → BC → CA uniformly until it returns to point A and stops. Let the length of segment P be h, and the height of △ABC, CG = 7√3/2. Figure 2 roughly shows the relationship between h and time, where point F is the lowest point on curve DE. The coordinates of point F are ( ). | D. (12, 4√3) | ['(12, 4\\(\\sqrt{3}\\))', '(4, 4\\(\\sqrt{3}\\))', '(13, 2\\(\\sqrt{3}\\))', '(12, 4\\(\\sqrt{3}\\))'] | multi_choice |
func413 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/413.png | The growth of infants aged 1-6 months is rapid. If the birth weight of an infant is 3300g, the relationship between their weight y (g) and age x (months) can be approximately expressed as y = 3300 + 700x. When x is 3, the corresponding value of y is ________. | 5400 | NULL | free_form |
func552 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/552.png | As shown in the figure, P(12, a) is on the graph of the inverse proportion function y = 60/x. PH ⊥ x-axis at point H, then sin∠POH = ( ) | B. 5/13 | ['5/12', '5/13', '12/5', '12/13'] | multi_choice |
func566 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/566.png | In the rectangular coordinate system, the graph of the linear function y = kx + b is shown in the figure. What are the ranges of k and b? | C | ['k > 0, b > 0', 'k > 0, b < 0', 'k < 0, b > 0', 'k < 0, b < 0'] | multi_choice |
func658 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/658.png | As shown in the figure, given the straight line y = -3x + h (h is a constant) intersects the parabola y = -1/2x² + bx + c (b, c, h are constants) at points A and D, and intersects the coordinate axes at points B and C, where the x-coordinates of points A, B, C, and D are -1/2, 0, 2, and 3 respectively, then the solution of the inequality is ( ). | B | ['-1 < x < 2', '-\\frac{1}{2} < x < 3', '0 < x < 2', '0 < x < 3'] | multi_choice |
func707 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/707.png | The graph of the quadratic function y = a(x + m)^2 - n is shown in the diagram. Then the graph of the linear function y = mx + n passes through which of the following quadrants?
A. First, Second, and Third Quadrants
B. First, Second, and Fourth Quadrants
C. Second, Third, and Fourth Quadrants
D. First, Third, and Fourth Quadrants | B | ['First, Second, Third quadrants', 'First, Second, Fourth quadrants', 'Second, Third, Fourth quadrants', 'First, Third, Fourth quadrants'] | multi_choice |
func713 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/713.png | As shown in the figure, point A lies on the graph of the inverse proportional function y = k/x (k < 0, x > 0). Point B is the foot of the perpendicular from A to the x-axis. Point C lies on the positive semi-axis of the y-axis, and line segment BC is connected. Line AD is parallel to BC and intersects the y-axis at point D. If the area of quadrilateral ABCD is 0.5, what is the value of k? | C. -0.5 | ['1', '0.5', '-0.5', '-1'] | multi_choice |
func833 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/833.png | During this holiday, Xiaoxing's family drove to the Xibaipo scenic spot. The graph shows the relationship between the distance y (km) and the time x (h). Which of the following statements is correct?
A. The distance from Xiaoxing's home to the Xibaipo scenic spot is 50 km
B. Xiaoxing's average speed during the first hour from home was 25 km/h
C. Xiaoxing was 125 km away from home after 2 hours of departure
D. The total time used by Xiaoxing's family to travel from home to Xibaipo scenic spot is 3 hours | D | ["The distance from Xiaoxing's home to the scenic spot in the west is 50 km.", "The average speed of Xiaoxing's car in the first hour is 25 km/h.", "The distance from Xiaoxing's home to the scenic spot in the west is 125 km.", "The total time from Xiaoxing's home to the scenic spot in the west is 3 hours."] | multi_choice |
func922 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/922.png | As shown in the figure, it is a temperature variation chart of a certain day in Beijing. Based on the graph, which of the following statements is correct ( ).
A. The lowest temperature of the day is 0°C
B. Starting from 6 a.m., the temperature gradually rises, reaching the highest temperature of the day, close to 40°C, at 3 p.m.
C. There are two time points during the day when the temperature is 10°C
D. The duration of temperatures below 20°C exceeds 12 hours | D | ['The lowest temperature of the day is 0°C.', 'The temperature starts to rise gradually from 6 AM and reaches the highest temperature of the day close to 40°C at 1 PM.', 'There are two points in time when the temperature is 10°C.', 'The temperature stays below 20°C for more than 12 hours in the day.'] | multi_choice |
func965 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/965.png | As shown in the figure, in △AOB, OA=OB=8, the coordinates of point C are (0,2), and point P is a moving point on OB. Connect CP, and rotate CP counterclockwise by 90° around point C to obtain line segment CD, making point D fall on AB. What are the coordinates of point D? | D. (2,6) | ['(2, 4)', '(6, 2)', '(2, 5)', '(2, 6)'] | multi_choice |
func980 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/980.png | As shown in the figure, in the Cartesian coordinate plane, △ABO has vertices A, B, and O with coordinates (1,0), (0,1), and (0,0) respectively. Points P1, P2, P3, … have adjacent points symmetric concerning one of the vertices of △ABO. For instance, P1 and P2 are symmetric about point A; P2 and P3 are symmetric about point B; P3 and P4 are symmetric about point O; P4 and P5 are symmetric about point A; P5 and P6 are symmetric about point B; P6 and P7 are symmetric about point O, and this cycle continues. Given that the coordinates of P1 are (1,1), find the coordinates of P2024. | B | ['(1,1)', '(1,-1)', '(-1,3)', '(1,-3)'] | multi_choice |
func1023 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1023.png | As shown in Figure ①, in rectangle ABCD, point P starts from point B and moves uniformly along the path B-C-D-A, stopping at point A. The speed of point P is 2 cm/s. Let the movement time of point P be x (s), and the area of △PAB be y (cm²). If the function graph regarding x is shown in Figure ②, what is the area of rectangle ABCD? | A. 48 cm² | ['48 cm²', '32 cm²', '84 cm²', '36 cm²'] | multi_choice |
func1134 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1134.png | As shown in the figure, the edge length of the cube is x cm, and its surface area is y cm². What is the functional relationship between y and x? ( ) | D | ['y = x³', 'y = 6x³', 'y = x²', 'y = 6x²'] | multi_choice |
func129 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/129.png | It is known that the linear functions y = ax + 2 and y = kx + b have graphs as shown in the figure, and the solution to the system of equations {y = ax + 2, y = 1} is A(2, 1). The coordinates of point B are (0, -1), and P is a moving point on the y-axis. If S_ΔABP = 4, then the coordinates of point P are ______. | (0, -5) or (0, 3) | NULL | free_form |
func179 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/179.png | As shown in the figure, the straight line y = -x + 2 intersects with y = ax + b (a ≠ 0 and a, b are constants) at the point (3, -1). Therefore, the solution set of the inequality -x + 2 > ax + b is ______. | x < 3 | NULL | free_form |
func307 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/307.png | As shown in the figure, the linear function y = kx + b passes through points A(5, 0) and B(0, -2). Then, the solution set of the inequality kx + b < 0 with respect to x is ________. | x < 5. | NULL | free_form |
func4 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/4.png | As shown in the figure, point A lies on the graph of the inverse proportional function y = k/x. A vertical line segment is drawn from point A to the x-axis, and another to the y-axis. If the shaded area is 6, what is the value of k? | 6 | NULL | free_form |
func422 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/422.png | As shown in the figure, it is known that the linear function y = k₁x + b and the reciprocal function y = k₂ / x intersect at point A(1/2, 8) and point B(4, m) in the first quadrant. Through point A, a line AP is drawn perpendicular to the x-axis at point P, and through point B, a line BQ is drawn perpendicular to the x-axis at point Q. If the area of ΔAOP is denoted as S₁ and the area of ΔBOQ is denoted as S₂, then S₁ __ S₂ (fill in '＞', '＜', or '='). | = | NULL | free_form |
func572 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/572.png | 10. As shown in the figure, in the rectangular coordinate system, point O has coordinates (0,2). Using OA as a side, construct an equilateral triangle △OAA1 on the right. From point A1, draw a perpendicular line to the x-axis, with the foot of the perpendicular being O1. Using O1A1 as a side, construct an equilateral triangle △O1A1A2 on the right. Then, from point A2, draw a perpendicular line to the x-axis, with the foot of the perpendicular being O2. Continuing this process, construct equilateral triangles △O2A2A3, and so on. Following this pattern, what is the y-coordinate of point A2024? | A | ['(\\frac{1}{2}, 1)^{2023}', '(\\frac{1}{2}, 1)^{2024}', '(\\frac{\\sqrt{3}}{2}, 1)^{2023}', '(\\frac{\\sqrt{3}}{2}, 1)^{2024}'] | multi_choice |
func605 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/605.png | As shown in the figure, the quadratic function y = ax^2 + bx + c (a ≠ 0, a, b, and c are constants, and x is a part of the graph of the function) has an axis of symmetry at the line x = −1, passes through the point (1, 0), and the x-axis intercept is between the points (0, −2) and (0, −3). Among the given options, the correct one is ( ). | D | ['\\(b^2 < 4ac\\)', '\\(2ab = 0\\)', '\\(a - 3b + c > 0\\)', '\\(\\frac{4}{3} < b < 2\\)'] | multi_choice |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.