id stringlengths 4 8 | image_url stringlengths 77 81 | query stringlengths 7 1.32k | answer stringlengths 1 148 | choice stringlengths 4 597 | question_type stringclasses 2 values |
|---|---|---|---|---|---|
func812 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/812.png | As shown in the figure, the graph of the function y1 = x + 3/2 intersects with the graph of the function y2 = -2x + 6 at point A(3/2, m). What is the range of x when y1 > y2? | A. x > 3/2 | ['\\(x \\geq \\frac{3}{2}\\)', '\\(x < \\frac{3}{2}\\)', '\\(0 < x \\leq \\frac{3}{2}\\)', '\\(-\\frac{3}{2} < x \\leq 0\\)'] | multi_choice |
func813 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/813.png | As shown in the figure, in the Cartesian coordinate system, the line AB passes through the origin O and intersects the hyperbolic function y = -8/x at points A and B. AC ⊥ x-axis at point C. The area of ΔABC is ( ). | C | ['4', '6', '8', '12'] | multi_choice |
func814 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/814.png | As shown in the figure, in the plane rectangular coordinate system, the coordinates of vertex A of square OABC are (1, -2). What are the coordinates of point C? | C | ['(1, 2)', '(2, 3)', '(2, 1)', '(2, -1)'] | multi_choice |
func815 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/815.png | As shown in the figure, given a quadratic function y = ax² + bx + c (a ≠ 0) whose graph intersects the x-axis at point (-1, 0), the y-axis intersection point B lies between (0, -2) and (0, -1) (excluding these two points), and the axis of symmetry is the straight line x = 1. Among the following conclusions: ① abc > 0; ② 4ac - b² < 0; ③ 1/4 < a < 3/2; ④ a < 0. The option containing all the correct conclusions is ( ). | B. ②③ | ['\\(\\alpha < 0\\)', '\\(\\beta < 0\\)', '\\(\\gamma < 0\\)', '\\(\\delta < 0\\)'] | multi_choice |
func816 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/816.png | A lever device is shown in the figure. One end of the lever is used to lift a bucket of water, and the resistance remains constant. While keeping the lever balanced, Xiao Li measured the corresponding force F by changing the length of the effort arm L. The data are shown in the table below. Based on the data pattern in the table, determine the approximate force required when the length of the effort arm L is 2.0m. | C | ['302N', '300N', '150N', '120N'] | multi_choice |
func817 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/817.png | 10. The graph of the quadratic function y = a(x−m)^2−k is shown in the figure below. Among the four options, the correct one is ( ). | A. m<0, k<0 | ['\\(m < 0, k < 0\\)', '\\(m > 0, k > 0\\)', '\\(m > 0, k < 0\\)', '\\(m < 0, k > 0\\)'] | multi_choice |
func818 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/818.png | As shown in the figure, it is known that the area of rectangle OABC is 50/3. Its diagonal OB intersects the hyperbola y = k/x at point D, and OB:OD = 5:3. What is the value of k? | B.6 | ['5', '6', '7', '8'] | multi_choice |
func819 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/819.png | As shown in the figure, a segment of a parabola y = -x^2 + 8x (0 <= x <= 8), denoted as C1, intersects the x-axis at points O and A1. C1 is rotated 180º around point A1 to obtain C2, which intersects the x-axis at point A2. C2 is then rotated 180º around point A2 to obtain C3, which intersects the x-axis at point A3, and so on. Continuing this way, a 'wave-like curve' is formed. If (2023, m) lies on this 'wave-like curve', then the value of m is ( ). | D | ['-8', '8', '-7', '7'] | multi_choice |
func82 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/82.png | As shown in the figure, for the quadratic function y = ax² + bx + c (a ≠ 0), part of its graph and one of its x-axis intersection points is (−3, 0), and the axis of symmetry is the line x = −1. What is the range of x where y < 0? | −3 < x < 1 | NULL | free_form |
func820 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/820.png | It is known that Xiaowei's home, the stadium, and the library are on the same straight line. One day, Xiaowei left home, first running to the stadium. After exercising at the stadium for a while, he rode a bike to the library. After reading at the library for a while, he rode his bike back home (the speed and travel time for the return trip were the same). As shown in the graph, the function depicts the relationship between Xiaowei's distance from home, y (km), and time from home, x (min). Based on the graph, the following four statements are made: ① The stadium is located between Xiaowei's home and the library. ② The distance between the stadium and the library is 6 km. ③ Xiaowei's biking speed is 0.2 km/min. ④ The value of 'a' is 117.5. Among these statements, the correct ones are ( ). | C | ['1', '2', '3', '4'] | multi_choice |
func821 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/821.png | As shown in the figure, the quadratic function y = ax² + 2x - 3 intersects the x-axis at (-3, 0). Which of the following statements is correct?
A. a < 0
B. The vertex is at (-1, -3)
C. The axis of symmetry is the line x = -1
D. When x < -3, y increases as x increases | C | ['a < 0', 'The vertex coordinates are \\((-1, -3)\\)', 'The axis of symmetry is the line \\(x = -1\\)', 'When \\(x < -3\\), the value of \\(y\\) increases as \\(x\\) decreases'] | multi_choice |
func822 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/822.png | The line y=2x+1 is shown in the figure. Passing through the point P(2,1), a line parallel to it is drawn as y=kx+b. What are the values of k and b? ( ) | B. k=2, b=-3 | ['k = 2, b = 3', 'k = 2, b = -3', 'k = 2, b = -1', 'k = -2, b = -3'] | 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 |
func826 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/826.png | Team A and Team B are each digging two sections of canals simultaneously. The relationship between the canal length y (m) and the excavation time x (h) is shown in the graph. Which of the following statements are definitely correct?
① When Team A has excavated 20m, it took them 2h;
② In the first 2 hours, Team A excavated 10m more than Team B;
③ Between 2h and 6h, Team B excavates 5 meters per hour;
④ After 4 hours, the total canal lengths excavated by both teams are equal.
A. 1 correct B. 2 correct C. 3 correct D. 4 correct | D | ['Team A dug 20 meters in 2 hours.', 'At the start of digging, Team A dug 10 meters more than Team B.', 'Team B dug 5 meters per hour from the 2nd hour to the 6th hour.', 'After 4 hours of digging, the lengths of the river sections dug by Team A and Team B are equal.'] | multi_choice |
func827 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/827.png | As shown in the figure, in the plane rectangular coordinate system, point A(2,3), point B(-3,-2), and point C(4,-3), what is the area of triangle ABC? | B | ['19', '20', '21', '21.5'] | 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 |
func83 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/83.png | As shown in the figure, in the rectangular coordinate system, point P(2,2) is a light source. The coordinates of the two ends of the wooden rod AB are (0,1) and (3,1), respectively. What is the projection length of the wooden rod AB on the x-axis __________. | 6 | NULL | free_form |
func830 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/830.png | As shown in the figure, point A is on the graph of the function y=4/x (x<0), point B is on the graph of the function y=-6/x (x>0). AB intersects the y-axis at point C, and D is a point on the x-axis. Lines AD, BD, and CD are connected. If AB is parallel to the x-axis, then the area ratio of △ACD to △BCD is ( ). | B | ['\\(\\frac{2}{5}\\)', '\\(\\frac{2}{3}\\)', '\\(\\frac{3}{2}\\)', '\\(\\frac{4}{9}\\)'] | 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 |
func832 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/832.png | As shown in figure (a), A and B are two fixed points on circle O, and ∠AOB = 90°. A moving point P starts from point B and moves counterclockwise at a constant speed to point A. The motion time is t (s), and the length of line segment AP is v (cm). Figure (b) represents the graph of the relationship between v and t, where the x-intercept of the graph is marked as m. What is the value of m ( )? | B | ['8', '6', '4√2', '14/3'] | 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 |
func834 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/834.png | As shown in the figure, given point A(1,3) and B(4,1), the line segment AB is rotated counterclockwise around point M to A1B1, where point A1 corresponds to A, and point B1 corresponds to B. What are the coordinates of point M? ( ) | C | ['(-1, -2)', '(1, 0)', '(-1, 1)', '(1, -3)'] | multi_choice |
func835 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/835.png | As shown in the figure, in the rectangular coordinate system Oxy, the hypotenuse of the right triangles Rt△OA1C1, Rt△OA2C2, …, lies on the coordinate axes, with ∠A1OA2 = 30°, ∠A2OA3 = 30°, …, and ∠An-1OAn = 30°. If the coordinates of point O are (3, 0), and OA1 = OC2, OA2 = OC3, OA3 = OC4, …, then according to this pattern, the y-coordinate of point A2024 is ( ). | D | ['3', '\\( \\frac{3\\sqrt{3}}{2} \\)^{2023}', '\\( \\frac{-8\\sqrt{3}}{3} \\)', '\\( -3 \\times \\left( \\frac{2\\sqrt{3}}{3} \\right)^{2023} \\)'] | multi_choice |
func836 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/836.png | As shown in the figure, a linear function y = ax + b and an inverse proportional function y = k / x intersect at points A and B. What is the solution set for the inequality ax + b > k / x? | B | ['x < 3', '-3 < x < 0 or x > 1', 'x < -3 or x > 1', '-3 < x < 1'] | multi_choice |
func837 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/837.png | It is known that the voltage of the battery U (unit: V) is a constant value. When using the battery, the current I (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 incorrect?
A. When I = 10 A, R = 4 Ω
B. The voltage of the battery is 40 V
C. When R = 8 Ω, I = 5 A
D. The expression of the function is I = 40 / R (R > 0) | A | ['When I = 10 A, R = 4 Ω', 'The voltage of the battery is 40 V', 'When R = 8 Ω, I = 5 A', 'The expression of the function is I = 40 / R (R > 0)'] | multi_choice |
func838 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/838.png | The distance between locations A and B is 540 km. A fast train travels at a constant speed from location A to location B, and a slow train travels at a constant speed from location B to location A. Both trains start at the same time, and the function Sx (km), which represents the distance between the two trains, is given in relation to the travel time t (hours) of the fast train, as shown in the figure. What is the speed of the slow train? | D | ['100km/h', '120km/h', '80km/h', '60km/h'] | multi_choice |
func839 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/839.png | As shown in the figure, the graph of a linear function y = kx + b passes through the points (2, 0) and (0, -4). When y > 0, the range of x is ( ). | A. x > 2 | ['x > 2', 'x < 2', 'x > -4', 'x < -4'] | multi_choice |
func84 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/84.png | As shown in the figure, in the rhombus OABC, side OB lies on the x-axis, point A(8,4), and tan∠COB=3. If the graph of the inverse proportion function y=k/(x) (k≠0) passes through point C, what is the value of k? ________. | 12 | NULL | free_form |
func841 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/841.png | As shown in the figure, the line y=√3x−3 intersects the coordinate axes at points A and B. What are the coordinates of point C? | A. (−3√3, 0) | ['(-3√3, 0)', '(-6, 0)', '(-2√3, 0)', '(-√3, 0)'] | multi_choice |
func842 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/842.png | As shown in the figure, in the plane Cartesian coordinate system, draw an arc with O as the center and an appropriate radius, intersecting the x-axis at point M and the y-axis at point N. Then take points M and N as centers, respectively, and draw arcs with radii greater than 1/2 MN. The two arcs intersect at point P in the second quadrant. If the coordinates of point P are (a-1, b+1), then the quantitative relationship between a and b is ( ). | A | ['a + b = 0', 'a - b = 2', 'a + b = 1', 'a - b = 0'] | multi_choice |
func843 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/843.png | As shown in the figure, the coordinates of the intersection point of lines l₁ and l₂ can be considered as the solution to which of the following systems of equations _______ _______ ( ). | A | ['y = x + 1\ny = 2x - 1', 'y = x + 1\ny = 2x + 1', 'y = x - 1\ny = 2x - 1', 'y = x - 1\ny = 2x + 1'] | multi_choice |
func844 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/844.png | As shown in the figure, the coordinates of points A, B, and C of parallelogram ABCD are (0, 2), (-4, -4), and (4, -4), respectively. Then the coordinates of point D are ( ). | D | ['(-8, 2)', '(4, 2)', '(8, 4)', '(8, 2)'] | multi_choice |
func845 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/845.png | As shown in the figure, point A lies on the graph of the inverse proportional function y = 12/x, point B lies on the graph of the inverse proportional function y = 4/x, AB is parallel to the y-axis, and intersects the x-axis at point C. Connect OA, take the midpoint D of OA, and connect BD. Then the area of △ADB (shaded region) is ( ). | D | ['16', '8', '4', '2'] | multi_choice |
func846 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/846.png | As shown in the figure, quadrilateral OABC is a parallelogram. In the rectangular coordinate system, point A is (-1, 2), OC = 5, and the coordinates of point B are ( ). | C | ['(2, 4)', '(2, -4)', '(4, 2)', '(4, -2)'] | multi_choice |
func847 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/847.png | As shown in the figure, given the point P(6,3), draw PM ⊥ x-axis at point M and PN ⊥ y-axis at point N through point P. The graph of the inverse proportion function y = k/x intersects PM at point A and intersects PN at point B. If the area of the quadrilateral OAPB is 12, what is the value of k? ( ) | A | ['6', '-6', '12', '-1'] | multi_choice |
func848 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/848.png | The graphs of the line l1: y = k1x + b1 and the line l2: y = k2x + b2 are shown in the same plane rectangular coordinate system. The solution set of the inequality k1x + b1 > k2x + b2 with respect to x is ( ). | D. x > -1 | ['x < -3', 'x < -1', 'x > -3', 'x > -1'] | multi_choice |
func849 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/849.png | As shown in the figure, the two rays in the figure respectively represent the linear function graphs of the movement of student A and student B. In the figure, s (unit: meters) and t (unit: seconds) represent the distance traveled and time respectively. It is known that A's speed is faster than B's. The following statements are given: ① A gave B a 12-meter head start; ② the ray AB represents the functional relationship between the distance and time for both individuals; ③ A's speed is 1.5 meters/second faster than B's; ④ after 8 seconds, A surpassed B. Which of the statements are correct ( ) | C | ['1', '2', '3', '4'] | multi_choice |
func85 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/85.png | As shown in the figure, point A is on the graph of the inverse proportional function y = k/x (x < 0). AB is perpendicular to the x-axis at point B. Point C is on the x-axis, and CO = OB. The area of △ABC is 5. What is the value of k? | -5 | NULL | free_form |
func850 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/850.png | As shown in the figure, in rectangle ABCD, a moving point P starts from point B and moves along BC, CD, and DA to stop at point A. Let the distance moved by point P be x, and the area of ΔABP be y. If the graph of the function y in terms of x is as shown in Figure (2), what is the area of rectangle ABCD? | A | ['15', '16', '20', '36'] | multi_choice |
func851 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/851.png | As shown in Figure 1, point P starts from vertex B of △ABC and moves uniformly along B→C→A to point A. Figure 2 shows the relationship between the length y of segment BP and time x during point P's movement. The curved part represents a parabolic graph, and point M is the lowest point. What is the area of △ABC? | C. 12 | ['6', '9', '12', '15'] | multi_choice |
func852 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/852.png | As shown in the figure, given A1(2,4), A2(4,4), A3(6,0), A4(8,-4), A5(10,-4), A6(12,0), ..., following this pattern, the coordinates of point A2024 are ( ). | D | ['(4046, -4)', '(4046, 4)', '(4048, 0)', '(4048, 4)'] | multi_choice |
func854 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/854.png | As shown in the figure, the line l1: y = kx + b and the line l2: y = mx + n intersect at point P(1, 3). What is the solution set of the linear inequality kx + b ≤ mx + n? | C. x ≤ 1 | ['x ≥ 3', 'x ≥ 1', 'x ≤ 1', 'x ≤ 3'] | 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 |
func856 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/856.png | As shown in the figure, A is a point on the hyperbolic function y = k/x. Draw AB perpendicular to the x-axis intersecting at point B, and point P lies on the y-axis. The area of △ABP is 2. What is the value of k? | D | ['2', '4', '-2', '-4'] | 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 |
func858 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/858.png | As shown in the figure, in a rectangular coordinate system, A(1,1), B(-1,1), C(-1,-2), D(1,-2), an electronic ant starts from point A and follows the path A→D→C→B→A→… moving 1 unit length per second. Where will the ant be located at the 2024th second? | D | ['(1, 0)', '(1, -2)', '(1, -1)', '(0, -2)'] | multi_choice |
func859 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/859.png | Given OA = √2, OB = 2, △AOB is folded along a certain line CD as shown in the figure. Point C intersects the x-axis at point C, and intersects AB at point D. What are the coordinates of point C?
A. (0.4, 0) B. (0.5, 0) C. (0.6, 0) D. (0.7, 0) | B | ['(0.4, 0)', '(0.5, 0)', '(0.6, 0)', '(0.7, 0)'] | multi_choice |
func86 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/86.png | As shown in the figure, for the linear function y = -1/2x + m - 4, the range of m is ________. | m < 4 | NULL | free_form |
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 |
func861 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/861.png | 8. As shown in the figure, P and Q are points on the inverse proportional functions y = k1 / x and y = k2 / x, respectively. The coordinates of point P are (-3/2, -2). Perpendiculars PM and QN are drawn from points P and Q to the x-axis at points M and N, respectively. If the area of the quadrilateral PMNQ is 2, what is the value of k2? | D. −1 | ['5', '-5', '1', '-1'] | multi_choice |
func862 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/862.png | As shown in the diagram, in a rectangular coordinate system, AB∥EG∥x-axis, BC∥DE∥HG∥AP∥y-axis, points D, C, P, H lie on the x-axis, A(1, 2), B(-1, 2), D(-3, 0), E(-3, -2), G(3, -2). A non-elastic string (length 2024 units, negligible thickness) is fixed at point A, and it is wound around the convex edges of the figure in the sequence A-B-C-D-E-F-G-H-P-A. The question asks for the coordinates of the point where the free end of the string will be located. | C. (-1, 0) | ['(1, 2)', '(-1, 2)', '(-1, 0)', '(1, 0)'] | 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 |
func865 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/865.png | As shown in the figure, it is the flight formation of a bomber squadron. Given that the coordinates of bombers B and C are (-2, -3) and (2, -1) respectively, what are the coordinates of bomber A ( )? | A | ['(-2, 1)', '(2, 1)', '(-2, 3)', '(-3, 2)'] | multi_choice |
func866 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/866.png | The following four scenarios describe the relationship between two variables:
(1) The relationship between the height of a basketball thrown by a basketball player and time.
(2) Xiaohua buys the same unit of exercise books in a bookstore. The relationship between the cost paid and the quantity of exercise books.
(3) Mr. Li takes a taxi to work. The relationship between the taxi fare he pays and the travel distance.
(4) On the weekend, Xiaoliang travels from home to the gym, plays basketball for a while, and then returns home. The relationship between Xiaoliang's distance from home and time. Use graphs to represent the above relationships between variables systematically.
The correct arrangement is:
A. (1), (2), (3), (4)
B. (1), (3), (2), (4)
C. (4), (2), (3), (1)
D. (3), (2), (4), (1) | D | ['(1) → (2), (2) → (3), (3) → (4), (4) → (1)', '(1) → (3), (2) → (4), (3) → (1), (4) → (2)', '(1) → (4), (2) → (1), (3) → (2), (4) → (3)', '(1) → (1), (2) → (2), (3) → (3), (4) → (4)'] | 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 |
func869 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/869.png | As shown in the figure, in the Cartesian coordinate system, point A lies on the graph of the inverse proportional function y = k / x. A perpendicular is drawn from point A to the x-axis, with the foot of the perpendicular being point B. Connect points O and A. If the area of △OAB is 2, then k = ( ). | D | ['-2', '-4', '2', '4'] | multi_choice |
func87 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/87.png | As shown in the figure, in the square grid of x-y coordinates, the endpoints of line segment a are on the grid points. Line segment a is rotated about point P to obtain line segment b, and the endpoints of line segment b are also on the grid points. If the side length of each small square is 1, then the coordinates of point P are ______. | (2, 2) or (2, 3) | NULL | free_form |
func870 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/870.png | The square ABCD is positioned in a Cartesian coordinate plane as shown in the figure, and its side length is 4. The coordinates of point D are ( ). | A. (-4, 4) | ['(-4, 4)', '(-4, -4)', '(4, 4)', '(-4, -4)'] | multi_choice |
func871 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/871.png | As shown in the figure, in the Cartesian coordinate system, the coordinates of three vertices A, C, and D of quadrilateral ABCD are (-1, 2), (2, -1), and (3, 2), respectively. What are the coordinates of vertex B? | D | ['(-3, -2)', '(-2, -2)', '(-3, -1)', '(-2, -1)'] | multi_choice |
func872 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/872.png | 8. The distances (s) and times (t) of four students, A, B, C, and D, are shown in the figure. The two students with the same average speed are ( ). | D | ['A and D', 'A and B', 'C and D', 'B and C'] | multi_choice |
func873 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/873.png | As shown in the figure, this is a chess endgame. If the coordinates of the pieces 'cannon' and 'rook' are represented as (1, 2) and (-2, 0) respectively, then the coordinates of the piece 'knight' are ( ). | C | ['(-3,3)', '(-3,2)', '(4,2)', '(3,2)'] | multi_choice |
func874 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/874.png | As shown in the figure, in the Cartesian coordinate system, three vertices of the parallelogram ABCD have the coordinates A(-1, -2), D(1, 1), and C(5, 2). What are the coordinates of vertex B? | C | ['(-1, 3)', '(4, -1)', '(3, -1)', '(3, -2)'] | multi_choice |
func875 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/875.png | Which of the following relationships between two variables is correct? ( )
① The circumference of a circle C is a function of its radius r;
② In the expression y = √x, y is a function of x;
③ In the table below, n is a function of m;
④ In the graph, the curve shows that y is a function of x. | C | ['①③', '②④', '①②③', '①②③④'] | multi_choice |
func876 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/876.png | A quadrilateral is unstable. In the plane Cartesian coordinate system as shown in the figure, the side AB of rectangle ABCD is fixed on the x-axis, where A(-2, 0) and B(4, 0). By pushing the rectangle, it becomes a parallelogram ABCD'. The point D is moved to the corresponding point D', which lies on the y-axis. If AD = 4, what are the coordinates of the corresponding point C', point C'? | B | ['(6, 4)', '(6, 2√3)', '(4, 2√3)', '(5, 3√2)'] | multi_choice |
func877 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/877.png | As shown in the figure, in a plane Cartesian coordinate system, point C is on the OA side of △AOB, with AC:OC = 1:2. A line passing through C, CD // OB, intersects AB at point D. The y-coordinates of points C and D are 1 and 3 respectively. What is the y-coordinate of point B ( )? | C | ['4', '5', '6', '7'] | 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 |
func88 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/88.png | As shown in the figure, at point P(3, 4), draw PC ⊥ x-axis with C as the foot, and PD ⊥ y-axis with D as the foot. PC and PD intersect with the graph of the inverse proportional function y = 6/x (x > 0) at points A and B, respectively. What is the area of the shaded region? ________. | 6 | NULL | free_form |
func880 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/880.png | 8. Point A is on the hyperbola. A line through point A is drawn perpendicular to the x-axis at point B, forming △AOB on the graph with an area of 3. What is the equation of this inverse proportional function ( )? | B. y = -6 / x | ['y = \\frac{6}{x}', 'y = -\\frac{6}{x}', 'y = \\frac{3}{x}', 'y = -\\frac{3}{x}'] | multi_choice |
func881 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/881.png | Given that a+b>0 and ab>0, in the rectangular coordinate system shown in the figure, the possible coordinates of the point covered by the hand are ( ). | D | ['(a, b)', '(-a, b)', '(-a, -b)', '(a, -b)'] | multi_choice |
func882 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/882.png | 8. As shown in diagram ①, in △ABC, ∠ACB=90°, point P starts from point A and moves uniformly along the edges of triangle ABC at a speed of 1 unit/second. Let the distance traveled by point P be x. Diagram ② represents the function graph of the length of segment PC changing with x. Which of the following judgments is correct? ( ) | C | ['a. 6', 'b. \\( \\frac{50}{13} \\)', 'c. \\( \\frac{144}{13} \\)', 'd. 15'] | multi_choice |
func883 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/883.png | As shown in Figure 1, in rectangle ABCD, point E is the midpoint of AB. A moving point P starts from point A and moves uniformly along the polyline AD−DC, stopping when it reaches point C. Segment AP and PE are connected, and let AP be x and PE be y. The graph of y as a function of x is shown in Figure 2. What is the maximum value of AP? ( ) | A. 5 | ['5', '√21', '4', '√17'] | 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 |
func885 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/885.png | In the Cartesian coordinate plane xOy, the graph of the direct proportional function y = kx and the linear function y = ax + 3 are shown in the figure below. The solution set for the system of linear inequalities (ax + 3 > 0, kx > ax + 3) with respect to x is ( ). | D. 1 < x < 3 | ['x < 0', 'x > 1', '0 < x < 1', '1 < x < 3'] | 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 |
func888 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/888.png | As shown in the diagram, the scale has a fixed hanging hook at point A, a hanging pan at point B, and point C serves as the measuring point. When the pan is empty and the hook is lifted, the weight sits at point C, and the lever remains balanced. After placing x grams of items on the pan and adjusting the position of the weight so that the distance between the weight's hanging position and the hook is y millimeters, the lever again becomes balanced. The corresponding values of x and y are measured as shown in the table: From the data in the table, the functional relationship between y and x is ( ) A. y = 2x + 8 B. y = x + 9 C. y = –x + 11 D. y = –2x + 12 | A | ['y = 2x + 8', 'y = x + 9', 'y = -x + 11', 'y = -2x + 12'] | 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 |
func89 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/89.png | As shown in the figure, the graph of the direct variation function y1 = -3x intersects the graph of the inverse variation function y2 = k/x at points A and B. Point C lies on the negative half-axis of the x-axis, with AC = AO, and the area of △ACO is 12. Find the value of k. | -12 | NULL | free_form |
func890 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/890.png | In the same plane rectangular coordinate system, the graph of line l1: y = ax + b and line l2: y = mx + n is shown in the figure. From the graph, it is known that the solution set of the inequality ax + b < mx + n < 0 is ( ). | A | ['-4 < x < -3', '-3 < x < -1', 'x < -3', 'x < -1'] | multi_choice |
func891 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/891.png | We call the sequence 1, 1, 2, 3, 5, 8, 13, 21,… the Fibonacci sequence. To further study, we take each number in this sequence as the radius to draw 90° arcs P1P2, P2P3, P3P4,… resulting in a Fibonacci spiral. Then, successively connect P1P2, P2P3, P3P4,… to obtain a spiral broken line (as shown in the figure). Given that point P1(0, 1), P2(-1, 0), P3(0, -1), what are the coordinates of point P8 on this broken line? | B. (-6, -25) | ['(-6, 24)', '(-6, 25)', '(-5, 24)', '(-5, 25)'] | 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 |
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 |
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 |
func895 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/895.png | As shown in Figure 1, in rectangle ABCD, point P starts at point B and moves in the direction of B→C→D→A until it stops at point A. Let x represent the distance traveled by point P, and y represent the area of △ABP. If the graph of the function y in relation to x is shown in Figure 2, what is the area of rectangle ABCD? | B. 20 | ['10', '20', '30', '36'] | multi_choice |
func896 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/896.png | As shown in the figure, in the same plane rectangular coordinate system, the graphs of the functions y = kx and y = -k/x (k ≠ 0) overlap at ( ). | C | ['① ②', '① ③', '② ④', '③ ④'] | 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 |
func898 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/898.png | As shown in the figure, Xiao Ming places four cards with the words 'Knowledge,' 'Expansion,' 'Broadening,' and 'Development' into a Cartesian coordinate system. The possible coordinates of the point obscured by the card labeled 'Expansion' are ( ). | C | ['(-5, -3)', '(-5, 3)', '(5, -3)', '(5, 3)'] | multi_choice |
func899 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/899.png | As shown in the figure, in the plane Cartesian coordinate system, a farmer starts from the origin and moves according to the direction indicated by the arrows in the figure. The farmer starts at the origin and moves to point M1(1, 1) during the 1st movement, then moves to point M2(2, 0) during the 2nd movement, then moves to point M3(3, -2) during the 3rd movement, and then moves to point M4(4, 0) during the 4th movement, and so on. According to this movement pattern, what are the coordinates of point M2024? | C | ['(2023, 0)', '(2023, 1)', '(2024, 0)', '(2024, -2)'] | 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 |
func90 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/90.png | As shown in the figure, point P(−3, 4). A line PC is drawn passing through P and parallel to the y-axis, and a line PB is drawn parallel to the x-axis, intersecting the hyperbola y=−k/x (k<0) at points C and B, respectively. Lines OB and OC are connected. If the area of △PEOF is 8, then k= | −4 | 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 |
func902 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/902.png | As shown in the figure, line AB intersects the x-axis at point C and intersects the graph of the inverse proportional function y = k/x at points A and B. From point B, draw BD perpendicular to the y-axis, with the foot of the perpendicular being point D. Connect CD. What is the value of the area of △S_ABCD ( ). | A | ['4', '5', '6', '8'] | 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 |
func905 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/905.png | The quadratic function y=2(x+m)^2+n is shown in the graph. The linear function y=nx+m passes through which regions ( )? | D. The second, third, and fourth quadrants | ['First, Second, Third quadrants', 'First, Second, Fourth quadrants', 'First, Third, Fourth quadrants', 'Second, Third, Fourth quadrants'] | multi_choice |
func906 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/906.png | As shown in the figure, if the intersection of 5th Avenue and 2nd Street at point A is represented by the ordered pair (5,2), then the ordered pair used to represent point B in the figure is ( ). | B. (2,3) | ['(2,1)', '(2,3)', '(3,1)', '(3,2)'] | multi_choice |
func907 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/907.png | As shown in the figure, in the plane rectangular coordinate system, there are several integer points arranged in the "→" direction as shown in the diagram, such as (1, 0), (2, 0), (2, 1), (3, 2), (3, 1), (3, 0), ... Based on this pattern, the coordinates of the 90th point are ( ). | B. (13, 1) | ['(13, 0)', '(13, 1)', '(13, 2)', '(13, 3)'] | multi_choice |
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