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 |
|---|---|---|---|---|---|
func62 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/62.png | As shown in the figure, P is a point on the graph of the inverse proportional function y = 4/x, and A is a point on the positive half-axis of the x-axis. If OP = PA, what is the area of triangle POA? | 4 | NULL | free_form |
func620 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/620.png | 7. The rhombic structure is delicate, with its sectional views all in the shape of a regular hexagon. As shown in the figure, one of these regular hexagons is ABCDEF, placed in a rectangular coordinate system. Points B, C, and D are three vertices of the regular hexagon lying on the coordinate axes. If the side length of the regular hexagon is 2, the coordinates of point D are ( ). | C | ['(3, √3)', '(√3, 4)', '(4, √3)', '(3, 2√3)'] | multi_choice |
func621 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/621.png | Given a quadratic function y = ax^2 + bx + c with its graph shown, what is the situation regarding the roots of the quadratic equation ax^2 + bx + c - 3 = 0? | C. There are two distinct real roots | ['No real roots', 'Two equal real roots', 'Two unequal real roots', 'Cannot be determined'] | multi_choice |
func622 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/622.png | As shown in the figure, the right triangle △AOB has its right-angle vertex A on the x-axis. The graph of the inverse proportional function y=k/x (k>0, x>0) passes through the midpoint C of the hypotenuse OB and intersects the perpendicular side AB at point D. If the coordinates of vertex B are (6, 4), then the area of △BOD is ( ).
A. 4 B. 6 C. 9 D. 12 | C | ['4', '6', '9', '12'] | multi_choice |
func623 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/623.png | As shown in the figure, let points A and B be two arbitrary points on the graph of the function y = 4 / x, which are centrally symmetric to each other. The hypotenuse is AB, and the two right-angle sides of the right triangle △ABC are parallel to the x-axis and y-axis, respectively. The area of △ABC is ( ). | C. 8 | ['2', '4', '8', 'Changes with points A and B'] | multi_choice |
func624 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/624.png | As shown in the figure, the straight line y = -x + b intersects the graph of the inverse proportional function y = k / x at points A and B. The x-coordinates of points A and B are 1 and 4, respectively. What is the area of △OAB? | A | ['15/2', '15', '10', '5'] | multi_choice |
func625 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/625.png | As shown in the figure, a quadratic function y = ax^2 + bx + 3 has its graph intersecting the negative x-axis at point A(-1, 0), the positive x-axis at point B, and the y-axis at point C. The following conclusions are given: ① 2a + b = 0; ② x = -3 is a root of the equation 2x^2 + bx + 3 = 0; ③ The minimum perimeter of △ABC is 10 + 3√2. Among these, the correct conclusions are ( ). | A. ①③ | ['①', '②', '①③', '②③'] | multi_choice |
func626 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/626.png | Two students, A and B, ride their bicycles from their respective homes to school. The distance y (km) from B's house as a function of departure time x (min) is shown in the graph. How many minutes earlier does B arrive at school compared to A? | A | ['2', '4', '6', '8'] | multi_choice |
func627 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/627.png | Given that the parabola y = ax^2 + bx + c has the shape as shown in the figure, how many of the algebraic expressions abc, b^2 - 4ac, 2a + b, and 9a + 3b + c have positive values? ( ) | A | ['4', '3', '2', '1'] | multi_choice |
func628 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/628.png | As shown in the figure, the graph of the linear function y = ax + b is a straight line. The solution set of the inequality ax + b < 1 with respect to x is ( ). | B | ['x < 0', 'x > 0', 'x < 1', 'x < 2'] | multi_choice |
func629 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/629.png | As shown in the figure, the parabola y = ax^2 + bx + c (a ≠ 0) passes through the point (-1, 2) and intersects the x-axis at points (x1, 0) and (x2, 0), where 0 < x1 < 1 and -2 < x2 < -1. Among the conclusions: ① 4a - 2b + c < 0; ② 2a - b < 0; ③ b^2 + 8a > 4ac; ④ c < 0, how many of them are correct? | D | ['1', '2', '3', '4'] | multi_choice |
func63 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/63.png | As shown in the figure, the graphs of the quadratic function y₁ = ax² + bx + c (a ≠ 0) and the linear function y₂ = mx + n (m ≠ 0) are given. When y₁ < y₂, the range of x is ________. | -2 < x < 1 | NULL | free_form |
func630 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/630.png | As shown in the figure, in the coordinate plane system established on graph paper, Rt△ABC is rotated 180° counterclockwise around point C to obtain Rt△FEC. What are the coordinates of point F, corresponding to point A? ( ). | B | ['(-1, 0)', '(0, 1)', '(1, 2)', '(2, 1)'] | multi_choice |
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 |
func632 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/632.png | As shown in the figure, the parabola y=ax^2 intersects the line y=bx+c at two points A(-2,4) and B(1,1). What is the solution set of the equation ax^2=bx+c for x? | C | ['-2 < x < 1', '-2 ≤ x ≤ 1', 'x < -2 or x > 1', 'x ≤ -2 or x ≥ 1'] | multi_choice |
func633 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/633.png | In the rectangular coordinate system xOy, the parabola y=ax²+bx+c is shown in the figure. What is the case of the roots of the equation ax²+bx+c=2? ( ) | B | ['There are two equal real roots', 'There are two unequal real roots', 'There are real roots', 'There are no real roots'] | 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 |
func635 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/635.png | As shown in the figure, the ball initially starts at (3, 0) and moves in the direction indicated. The trajectory of the ball is shown in the diagram. If the ball initially starts at (1, 0) and is hit in the same original direction, the position of the ball when it first hits the edge of the table is (0, 1). What is the position of the ball when it hits the edge of the table for the 2023rd time? | A | ['(0, 1)', '(5, 4)', '(7, 0)', '(8, 1)'] | multi_choice |
func636 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/636.png | As shown in the figure, given that the graphs of the functions y=2x and y=-x+b intersect at point P(1,a), the solution for the system of equations (2x-y=0, x+y=b) is ( ). | A | ['\\( \\begin{cases} x = 1 \\\\ y = 2 \\end{cases} \\)', '\\( \\begin{cases} x = 2 \\\\ y = 1 \\end{cases} \\)', '\\( \\begin{cases} x = 1 \\\\ y = -2 \\end{cases} \\)', '\\( \\begin{cases} x = -2 \\\\ y = 1 \\end{cases} \\)'] | multi_choice |
func637 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/637.png | In a sealed container there are four types of gases: A, B, C, and D. As shown in the figure, the four points respectively describe the density ρ (kg/m³) and volume V (m³) of these four gases. Among them, the points describing gases B and D fall exactly on the graph of an inverse proportional function. Which of these four gases has the smallest mass? | A. A | ['A', 'B', 'C', 'D'] | multi_choice |
func638 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/638.png | There is a resistor R and a light bulb L. The relationship between the voltage U (unit: V) across them and the current I (unit: A) through them is shown in the graph. Based on the graph, which of the following statements is incorrect?
A. When the current through the light bulb L is 0.3A, the voltage across it is 1V
B. When the voltage across the resistor R is 4V, the current through it is 0.4A
C. When the current through both the resistor R and the light bulb L is 0.6A, the voltage across the resistor R is twice that of the voltage across the light bulb L
D. When the voltage across the resistor R and the light bulb L is the same (not 0), the current through the light bulb L is always smaller than the current through the resistor R | D | ['When the current passing through the light bulb is 0.3A, the voltage across it is 3V.', 'When the voltage across the resistor R is 4V, the current passing through it is 0.4A.', 'When the current passing through the resistor R and the light bulb L is 0.6A, the voltage across the resistor R is twice that of the light bulb L.', 'When the voltage across the resistor R and the light bulb L is the same (not 0), the current passing through the light bulb is smaller than that through the resistor R.'] | multi_choice |
func639 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/639.png | As shown in the figure, point A lies on the hyperbola y = k/x, AB is perpendicular to the x-axis at point B, and the area of △AOB is 2. What is the value of k? | A | ['-4', '-2', '2', '4'] | multi_choice |
func64 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/64.png | As shown in the figure, in the rectangular coordinate plane, the endpoints of line segment AB have coordinates A(1, 2) and B(5, 2) respectively. When the parabola y = -x² + 2mx - m² + 2m (where m is a constant) intersects line segment AB, what is the range of values for m? | 1 ≤ m ≤ 9 | NULL | free_form |
func640 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/640.png | Given the quadratic function y = ax^2 + 2ax - 3, part of its graph is shown in the figure. From the graph, it can be seen that the roots of the quadratic equation ax^2 + 2ax - 3 = 0 are x1 = 1.3 and x2 = ( ). | D. -3.3 | ['-1.3', '-2.3', '-0.3', '-3.3'] | multi_choice |
func641 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/641.png | As shown in the figure, in the right triangle △ABC, ∠C = 90°, AB = 5, BC = 3, point A is on the positive half of the y-axis, point C is in the first quadrant, and AC ∥ x-axis. Point B is below point C. The hyperbolic function y = k/x passing through point B intersects AC at point D. If AD = 1, the value of k is ( )
A. 1
B. 2
C. 3
D. 4 | D | ['1', '2', '3', '4'] | multi_choice |
func642 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/642.png | As shown in the figure, the graph of a linear function y1 = kx + b passes through point A(2,0) and intersects the graph of the proportional function y2 = 2x at point B. The solution set for the inequality 0 < kx + b < 2x is ( )
A. x > 0
B. x > 1
C. 0 < x < 1
D. 1 < x < 2 | D | ['x > 0', 'x > 1', '0 < x < 1', '1 < x < 2'] | multi_choice |
func643 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/643.png | As shown in the figure, the upper base of the trapezoid is 8, the lower base is x, the height is 10, and the area of the trapezoid is y. Which of the following statements is incorrect?
A. The relationship between the trapezoid area y and the lower base length x is y = 5x + 40
B. When y = 40, x = 0, and this represents the area of a triangle
C. When x increases by 1, y increases by 5
D. When x changes from 15 to 8, y changes from 105 to 80 | D | ['The relationship between the area of the trapezoid y and the length of the lower base x is y = 5x + 40.', 'When y = 40, x = 0, at this time it represents the area of a triangle.', 'When x increases by 1, y increases by 10.', 'When x changes from 15 to 8, the value of y changes from 105 to 80.'] | multi_choice |
func644 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/644.png | As shown in the figure, in the rectangular coordinate system, suppose a particle M starts at P0 (1,0), moves upward by 1 unit to P1, then moves leftward by 2 units to P2, then moves rightward by 4 units to P3, then moves upward by 5 units to P4, and so on. Based on this pattern, what are the coordinates of P2023? ( ) | D | ['(-1011, 1011)', '(-505, 506)', '(505, 505)', '(-1011, -1012)'] | multi_choice |
func645 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/645.png | As shown in the figure, if a Cartesian coordinate system is established on the chessboard such that the 'Shuai' chess piece is located at the point (2,0) and the 'Pao' chess piece is located at the point (-1,3), then after moving the 'Ma' chess piece upward by two units, it will be located at the point ( ). | C | ['(4,2)', '(4,1)', '(4,4)', '(6,2)'] | multi_choice |
func646 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/646.png | As shown in the figure, A is a point on the y-axis in the rectangular coordinate system xOy with coordinates (0, −5). Now, a circle is drawn with point A as the center and 13 as the radius. The circle intersects the negative x-axis at point B. What are the coordinates of point B? | B | ['(-6, 0)', '(-12, 0)', '(-9, 0)', '(-5, 0)'] | multi_choice |
func647 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/647.png | As shown in Figure 1, in quadrilateral ABCD, AD ∥ BC, line l ∥ AB. When line l starts translating rightward along ray BC from point B, it intersects with the sides of quadrilateral ABCD at points E and F. Suppose the translation distance of line l is x, and the length of segment EF is y, with the functional relationship between y and x shown in Figure 2. Among the following conclusions: ① The length of BC is 5; ② The length of AB is √3; ③ When 4 ≤ x ≤ 8, the area of △BEF remains unchanged. How many of these statements are correct? | B | ['0', '1', '2', '3'] | multi_choice |
func648 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/648.png | As shown in the figure, it is known that the area of the square ABCD is 4, and its two vertices B and D lie on the graph of the inverse proportional function y = k/x (k > 0, x > 0). If the coordinates of point D are (b, a), what is the value of a - b? | B. 2 | ['3', '2', '-3', '-2'] | 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 |
func65 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/65.png | As shown in the figure, it is a parabolic arch bridge. When the arch top is 2m above the water surface, the water surface width is 4m. What is the increase in water surface width when the water level drops by 1m? | (2√6 − 4)m | NULL | free_form |
func650 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/650.png | The graph of the quadratic function y = ax^2 + bx + c (a ≠ 0) is shown in the figure below. Its axis of symmetry is the line x = -1, and it intersects the x-axis at the points (x1, 0) and (x2, 0), where x1 < x2 < 1. The following conclusions are given: ① b^2 - 4ac > 0; ② a + b + c > 0; ③ -3 < x1 < -2; ④ x2 < 1; ⑤ 3a + c < 0. Which of the following conclusions are correct? _______. | C | ['①②⑤', '①③⑤', '①③④', '①④⑤'] | 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 |
func652 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/652.png | Given that the quadratic function y = ax^2 + bx + c has a graph as shown, which quadrant does the point P(b, c) belong to? | C | ['First Quadrant', 'Second Quadrant', 'Third Quadrant', 'Fourth Quadrant'] | multi_choice |
func653 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/653.png | Xiaoming departs from home at 8 a.m. to go to the outskirts for flower viewing. The distance he travels (in kilometers) changes with time (in hours) as shown in the figure. Which of the following statements is incorrect?
A. In this process, the independent variable is time, and the dependent variable is distance.
B. Xiaoming took a half-hour break during the trip.
C. From 8 a.m. to 10 a.m., Xiaoming traveled approximately 9 kilometers.
D. Xiaoming's average speed from the time he resumed travel until reaching the destination was approximately 1.25 km/h. | D | ['During this process, the independent variable is time, and the dependent variable is distance.', 'Xiaoming rested for half an hour on the way.', 'From 8 am to 10 am, Xiaoming traveled a distance of 9 kilometers.', 'The average speed from the time Xiaoming rested until he reached his destination is approximately 1.25 kilometers per hour.'] | 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 |
func655 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/655.png | 4. The graph of the quadratic function y = (x + m)^2 + n is shown. The graph of the linear function y = mx + n passes through which quadrants?
A. First, Second, and Third quadrants
B. First, Second, and Fourth quadrants
C. First, Third, and Fourth quadrants
D. Second, Third, and Fourth quadrants | D | ['First, Second, and Third quadrants', 'First, Second, and Fourth quadrants', 'First, Third, and Fourth quadrants', 'Second, Third, and Fourth quadrants'] | multi_choice |
func656 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/656.png | The graph of the inverse proportional function y = k / x (k ≠ 0) is shown in the figure. AB // y-axis, and if the area of △ABC is 3, then the value of k is ( ). | C | ['-3', '-\\frac{3}{2}', '-6', '-9'] | 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 |
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 |
func659 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/659.png | 7. As shown in the figure, 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, meeting at point B, and point C lies on the y-axis. Connect AC and BC. If the area of △ABC is 3, then the value of k is ( ). | B. -6 | ['3', '-6', '6', '-3'] | multi_choice |
func66 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/66.png | As shown in the diagram, the graph of the direct proportional function y = kx (k is a constant, k ≠ 0) intersects with the graph of the linear function y = -x + 6 at point P. The y-coordinate of point P is 4. The solution set of the inequality -x + 6 > kx is ______. | x < 2 | NULL | free_form |
func660 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/660.png | As shown in the diagram, given the functions y = ax + b and y = kx, the intersection point P of their graphs can be determined. Based on the graphs, the solution to the system of linear equations in x and y is ( ). | C | ['(x = 3, y = -1)', '(x = -3, y = -1)', '(x = -3, y = 1)', '(x = 3, y = 1)'] | multi_choice |
func661 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/661.png | As shown in the figure, light enters water from air, and the light paths before and after entering the water are illustrated. If coordinate axes are established as shown in the figure, and the equations of the lines for the light before and after entering the water are y1 = k1x and y2 = k2x respectively, then which of the following relationships between k1 and k2 is correct? ( ) | C. |k1| > |k2| | ['|k1| < k2, k2 < 0', 'k1 < 0, k2 > 0', '|k1| < |k2|', '|k1| > |k2|'] | multi_choice |
func662 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/662.png | △ABC is located in the plane rectangular coordinate system as shown in the figure. △ABC is first translated 2 units to the right to get △A1B1C1, and then △A1B1C1 is rotated 180° about point O to get △A2B2C2. What are the coordinates of point C2? | B (-1, -2) | ['(1, 2)', '(-1, -2)', '(-2, -1)', '(1, -2)'] | 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 |
func666 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/666.png | The physics interest group designed an electrical circuit while studying electricity in the laboratory, and the circuit diagram is shown in Figure 1. Through testing, it was found that the current I (A) changes with resistance R (Ω), and based on the data, points were plotted, connected, and a functional graph (Figure 2) was drawn. If the minimum resistance of the circuit is 1Ω, then the circuit can carry ( ) | A. The maximum current is 36A | ['The maximum current is 36A', 'The maximum current is 27A', 'The minimum current is 36A', 'The minimum current is 27A'] | multi_choice |
func667 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/667.png | As shown in the figure, in a Cartesian coordinate plane, the graph of the function y = -k₁ / x (x ≠ 0) intersects the graph of the function y = k₂x (x ≠ 0) at points A and B. From point A, draw AC perpendicular to the x-axis at point C, and connect BC. If the area of △ABC (S_△ABC) = 8, then the value of k₁ is ( ). | B | ['-6', '-8', '-10', '8'] | multi_choice |
func668 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/668.png | A certain balloon is filled with a fixed mass of gas. When the temperature remains constant, the pressure p (kPa) of the gas inside the balloon is inversely proportional to the volume V (m³) of the gas (as shown in the figure). Which of the following statements is correct? ( )
A. The pressure of the gas inside the balloon increases as the volume of the gas increases.
B. The functional expression for the gas pressure p in terms of the volume V is p = 180/V (V > 0).
C. When the gas volume is 1m³, its pressure is 90kPa.
D. When the gas pressure is greater than 150kPa, the gas volume should not be less than 0.8m³. | C | ['The pressure of the gas inside the balloon increases as the volume of the gas increases.', 'The functional relationship between the pressure p and the volume V of the gas inside the balloon is p=180/V (V>0).', 'When the volume of the gas is 1 m³, its pressure is 90 kPa.', 'When the pressure of the gas is greater than 150 kPa, the balloon will explode, so the volume of the gas should not be less than 0.8 m³.'] | multi_choice |
func669 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/669.png | As shown in the figure, the parabola y = ax² + bx + c (a ≠ 0) intersects the x-axis at point (3, 0) and has its axis of symmetry on the line x = 1.
① ac < 0;
② a < 0;
③ When x > 2, the value of y increases as x increases;
④ The quadratic equation ax² + bx + c = 0 has two distinct real roots. Which of the conclusions above are correct? ( ) | C. ①③④ | ['①②③', '①②③④', '①③④', '②③④'] | multi_choice |
func67 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/67.png | As shown in the figure, it is the graphs of the inverse proportional functions y=3/5x and y=-5/2x above the x-axis. Point C is a point on the positive x-axis. A line passing through point C, parallel to the x-axis, intersects these two graphs at points A and B, respectively. If point P moves along the x-axis, the area of △ABP equals ________. | 4 | NULL | free_form |
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 |
func671 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/671.png | In the same rectangular coordinate system, the functions y = kx - k and y = -k / |x| (k ≠ 0) have approximate graphs as ( ) | B. ② or ③ | ['① or ④', '② or ③', '① or ③', '② or ④'] | multi_choice |
func672 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/672.png | The graph of the function y = kx + b is shown in the figure below. Which of the following statements is correct?
A. When x = -2, y = 1
B. k < 0
C. If the triangle formed by the graph of y = kx + b and the coordinate axes has an area of 2, then b = 2
D. If the points (-1, m) and (1, n) lie on the line, then m > n. | C | ['When x = -2, y = 1', 'k < 0', 'If the area of the triangle formed by the graph of y = kx + b and the coordinate axes is 2, then b = 2', 'If point (l, m) and point (l, n) are on the line, then m > n'] | multi_choice |
func673 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/673.png | As shown in the figure, point A is on the hyperbolic function y = k/x. A perpendicular is drawn from point A to the x-axis, with the foot of the perpendicular at point B. Point C is on the y-axis, and the area of △ABC is 2. What is the value of k? | C. -4 | ['-2', '2', '-4', '4'] | multi_choice |
func674 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/674.png | As shown in the figure, the coordinates of the intersection of lines l₁ and l₂ can be considered 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 |
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 |
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 |
func678 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/678.png | As shown in the figure, in the rectangular coordinate system, point A has coordinates (3√3, √3), point B is on the positive x-axis with OB=4. The line y=√3x+√3 is translated rightwards along the x-axis to form △CDE. If point D happens to lie on this line, what are the coordinates of point D? | A. (7, 0) | ['(7, 0)', '\\((4\\sqrt{3}, 0)\\)', '(6, 0)', '\\(\\left(\\frac{5\\sqrt{3}}{2}, 0\\right)\\)'] | multi_choice |
func679 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/679.png | Xiaoying went to a fruit store to buy oranges. The image shows the data on the display screen of the electronic scale used for weighing the oranges. Among them, the variables are ( ). | D. Amount and quantity | ['Amount', 'Quantity', 'Unit price', 'Amount and quantity'] | multi_choice |
func680 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/680.png | As shown in the figure, the line l1: y = 2x + b and the line l2: y = mx + 4 intersect at point P(1,3). Then, the solution set of the linear inequality 2x + b > mx + 4 is ( ). | B. x > 1 | ['x < 1', 'x > 1', 'x < 3', 'x > 3'] | multi_choice |
func681 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/681.png | As shown in the figure, the hyperbolic function y = k/x intersects with y = 5/0 at point P(2,1). What is the area of the shaded region in the figure? ( ) | C | ['\\( \\frac{3}{4} \\pi \\)', '\\( \\pi \\)', '\\( \\frac{5}{4} \\pi \\)', '\\( \\frac{3}{2} \\pi \\)'] | multi_choice |
func682 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/682.png | The graphs of the inverse proportional functions y1 = 7/x and y2 = 5/x in the first quadrant are shown in the figure. P is a point on the curve y1. A perpendicular line from point P intersects the x-axis at point A and intersects the curve y2 at point B. What is the area of △OBP? | A | ['1', '2', '3', '4'] | multi_choice |
func683 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/683.png | As shown in the figure, this is the graph of the quadratic function y = ax^2 + bx + c. Simplify the result of |a - b + c| + |a + b| ( ). | A | ['-2a - c', 'c - 2b', '2a + c', '2a - b + c'] | multi_choice |
func684 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/684.png | As shown in the figure, in the plane Cartesian coordinate system, the center of the regular hexagon ABCDEF with a side length of 2 coincides with the origin O. AB is parallel to the x-axis and intersects the x-axis at point P. If △OAP is rotated clockwise about point O, with each rotation being 90°, what will the coordinates of point A be after the 2024th rotation? | D | ['(√3, -1)', '(-1, -√3)', '(-√3, 1)', '(1, √3)'] | multi_choice |
func685 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/685.png | As shown in the figure, in a plane Cartesian coordinate system, the line y=kx (k≠0) intersects the line y=ax+b (a≠0) at point P. Then the solution of the system of equations {kx-y=0, ax-y+b=0} in terms of x and y is ( ). | A | ['\\( x = 1, \\\\ y = 2 \\)', '\\( x = 2, \\\\ y = 1 \\)', '\\( x = -1, \\\\ y = 2 \\)', '\\( x = 1, \\\\ y = -2 \\)'] | 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 |
func687 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/687.png | As shown in the figure, the line y = kx + b (k ≠ 0) intersects with the graph of y = x − 6 at point A(m, −4). Then the solution set of the inequality kx + b < x − 6 with respect to x is ( ). | C. x > 2 | ['x > -4', 'x < -4', 'x > 2', 'x < 2'] | multi_choice |
func688 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/688.png | As shown in the figure, in the plane Cartesian coordinate system, the triangle OAB is transformed into triangle OA1B1 for the first time, the triangle OA1B1 is transformed into triangle OA2B2 for the second time, the triangle OA2B2 is transformed into triangle OA3B3 for the third time… Given that A1(4,13), A2(4,3), A3(4,3), B(2,0), B1(4,0), B2(8,0), B3(16,0), observe the changes in the vertices of the triangle before and after each transformation. According to this pattern of transformation, the coordinates of point An are ( ). | A | ['(2^4, 3)', '(2^1, 3)', '(2^1+1, 0)', '(2^1, 0)'] | multi_choice |
func689 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/689.png | As shown in the figure, the graph of the quadratic function y = ax² - x + a² is given. The value of a is ( )
A. a = -1 B. a = 1/2 C. a = 1 D. a = 1 or a = -1 | C | ['a = -1', 'a = \\(\\frac{1}{2}\\)', 'a = 1', 'a = 1 or a = -1'] | multi_choice |
func69 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/69.png | 4. Two engineering teams, A and B, are simultaneously excavating a segment of a high-speed rail tunnel. Each team maintains a constant daily excavation rate. After working together for a period, Team B stopped due to equipment maintenance, and Team A completed the remainder of the task alone. The relationship between the total length excavated by both teams, y (in meters), and the working time of Team A, x (in days), is shown in the graph. How much longer is the total length excavated by Team A compared to Team B, in meters? | 60 | NULL | free_form |
func690 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/690.png | As shown in the figure, among the points M, N, P, and Q, the graph of the linear function y = kx - 2 (k > 0) is least likely to pass through which point ( ). | B. N | ['M', 'N', 'P', 'Q'] | multi_choice |
func691 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/691.png | As shown in the figure, a linear function y = kx + b (k, b are constants, k ≠ 0) intersects a proportional function y = mx (m is a constant, m ≠ 0) at point M(1, 2). The following judgments are incorrect ( ):
A. The solution to the equation mx = kx + b with respect to y is x = 1
B. The solution set for the inequality mx < kx + b with respect to y is x > 1
C. When k < 0, the value of the function y = kx + b is greater than the value of the function y = mx
D. The solution to the system of equations y = mx and y = kx + b with respect to x, y is x = 1 | B | ['The solution of the equation \\(mx = kx + b\\) is \\(m = 1\\)', 'The solution set of the inequality \\(mx > kx + b\\) is \\(m > 1\\)', 'When \\(x < 0\\), the value of the function \\(y = mx\\) is greater than the value of the function \\(y = kx + b\\)', 'The solution of the equation group \\(\\begin{cases} y = mx \\\\ y = kx + b \\end{cases}\\) is \\(x = 1, y = 2\\)'] | multi_choice |
func692 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/692.png | As shown in the figure, A and B are two points on the parabola y=-x², and the line segment AB is perpendicular to the y-axis. If AB=6, then the coordinates of point A are ( ). | D. (-3, 9) | ['(3, 3)', '(3, 9)', '(-3, 3)', '(-3, 9)'] | multi_choice |
func693 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/693.png | 5. In the same plane Cartesian coordinate system, the graph of the parabola y1 = ax^2 + bx and the line y2 = 2x is shown in the figure. What is the solution set of the inequality ax^2 + bx > 2x? ( ) | B | ['x < 0', '0 < x < 2', 'x ≥ 2', 'x < 0 or x > 2'] | multi_choice |
func694 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/694.png | There is an arch bridge whose cross-section is parabolic in shape. The maximum height of the bridge is 16m, and the span is 40m. The diagram (as shown) is placed in a rectangular coordinate system. What is the equation of the parabola? ( ) | B | ['y = \\frac{1}{25}x^2 + \\frac{5}{8}x', 'y = -\\frac{1}{25}x^2 + \\frac{5}{8}x', 'y = -\\frac{5}{8}x^2 - \\frac{1}{25}x', 'y = \\frac{1}{25}x^2 + \\frac{5}{8}x + 16'] | multi_choice |
func695 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/695.png | As shown in the figure, if a 10m long iron wire is used with the help of wall AB to form a right triangle △ECD with the hypotenuse ED, what is the maximum area of △ECD? ( ) | D | ['5.5m²', '7.5m²', '10.5m²', '12.5m²'] | multi_choice |
func696 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/696.png | Paper cutting is one of the oldest folk arts in ancient China, which contains the transformation of shapes. As shown in the figure, it is a butterfly paper cutting that contains axial symmetry transformation. Point A and point B are symmetric, and point C and point D are symmetric. Placing it in a Cartesian coordinate system, the coordinates of points A, B, and C are (2, 0), (0.5, 4), and (0, 4) respectively. What are the coordinates of point D? | B | ['(3.5, 4)', '(5.5, 4)', '(5, 4)', '(6, 4)'] | multi_choice |
func697 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/697.png | A ship travels from Port A to Port B, 160 km away, at a speed of 20 km/h. Two hours later, a speedboat also departs from Port A to Port B at a speed of 40 km/h. The graphs of the distance traveled by the ship (s₁ in km) and the distance traveled by the speedboat (s₂ in km) with respect to time (h in hours) are shown. Which of the following statements is incorrect? | B. 5 hours ago, s₁ < s₂ | ['4 hours before, s1 < s2', '5 hours before, s1 < s2', '4 hours later, s1 < s2', '5 hours later, s1 < s2'] | multi_choice |
func698 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/698.png | As shown in the figure, △ABC is placed in a rectangular coordinate plane. Points B and C are on the x-axis, and point A is on the y-axis. It is known that AC = BC, AB = 5, and the coordinates of point A are (0, 3). What are the coordinates of point C? | A | ['(-7/8, 0)', '(-4/5, 0)', '(-1, 0)', '(-2, 0)'] | multi_choice |
func699 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/699.png | As shown in the figure, △ABC is folded along the x-axis and then rotated 180° about the origin to form △A'B'C'. What are the coordinates of point B' corresponding to point B? | A | ['(3, 1)', '(2, 1)', '(-3, -1)', '(-1, -3)'] | 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 |
func70 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/70.png | As shown in the figure, in △AOB, AO=2. △AOB is rotated around point O to position △ABO′, where A is the midpoint of OB, and B′ lies on the hyperbolic function y=k/x. What is the value of k? ______. | 4√3 | NULL | free_form |
func700 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/700.png | As shown in the figure, it represents the functional relationship between the number of remaining copies and the working time when Xiao Ming is photocopying materials. Based on the information provided in the figure, please determine Xiao Ming's photocopying situation at the 20th minute ( ). | B. Just finished printing | ['Unable to finish copying', 'Just finished copying', 'Finished copying one minute early', 'Finished copying half a minute early'] | multi_choice |
func702 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/702.png | As shown in Figure ①, point E lies on side AD of rectangle ABCD. Point P starts from point B and moves along the broken line B→E→D until it stops at point D. Point Q starts from point B and moves along BC until it stops at point C. Both move at a speed of 1 cm/s. Initially, points P and Q start moving simultaneously. Let the travel time be x (seconds) and the area of ΔBPQ be y (cm²). If the relationship between y and x is as shown in Figure ②, what is the area of rectangle ABCD? | C | ['96 cm²', '84 cm²', '72 cm²', '56 cm²'] | 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 |
func705 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/705.png | As shown in the figure, △ABC is transformed into △A'B'C' through a certain transformation. If the coordinates of point P on △ABC are (a, b), then the coordinates of its corresponding point P' are ( ) | C | ['(a - 3, b)', '(a + 3, b)', '(3 - a, -b)', '(a - 3, -b)'] | multi_choice |
func706 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/706.png | As shown in the figure, in a rectangular coordinate plane, given that the side AD of parallelogram □ABCD is parallel to the x-axis, and A(-1/2,2), B(5/2,1). If the hyperbolic function y = k/x passes exactly through points C and D in the first quadrant, what is the value of k?
A. 5 B. 6 C. 7 D. 8 | B | ['5', '6', '7', '8'] | 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 |
func708 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/708.png | It is known that Xiaoming's house, the library, and the school are on the same straight line. One day, Xiaoming cycled from home to school, stopping at the library first to pick up some study materials before heading to school. If the distance from Xiaoming’s home is represented by y, and the departure time by x, the relationship between y and x is shown in the graph. Which of the following conclusions is correct ( )? | D | ['Xiaoming stayed at the library for 10 minutes', "The distance from Xiaoming's home to school is 1000 meters", 'It took Xiaoming 25 minutes to get from the library to school', 'The speed from the library to the school is 110 meters/minute'] | multi_choice |
func709 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/709.png | As shown in the figure, the graph of the direct proportion function y = k1x intersects with the graph of the inverse proportion function y = k2/x at points A and B. The x-coordinate of point A is 2. When k1 > k2 > 0, what is the range of x values? | A | ['-2 < x < 0 or x > 2', 'x < -2 or 0 < x < 2', 'x < -2 or x > 2', '-2 < x < 0 or 0 < x < 2'] | multi_choice |
func71 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/71.png | As shown in the figure, the graph of the direct proportion function y = k₁x and the inverse proportion function y = k₂/x intersect at points A(1, m) and B. When k₁ ≤ k₂, what is the range of x values? ______ | −1 ≤ x < 0 or x ≥ 1 | NULL | free_form |
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 |
func711 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/711.png | 8. The graph of the linear function y = (k−3)x+4 is shown in the figure below. What is the range of k? ( ) | B. k<3 | ['\\(k > 3\\)', '\\(k < 3\\)', '\\(k > 4\\)', '\\(k < 4\\)'] | multi_choice |
func712 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/712.png | 5. Which of the following graphs closely represent the scenarios described below? The correct order is ( ). ① Emergency braking of a car (relationship between speed and time); ② Growth in a person's height over time (relationship between height and age); ③ A high jumper crossing the bar (relationship between height and time); ④ A flag being raised by a crane (relationship between height and time). A. abcd B. dabc C. abca D. cabd | C | ['dbca', 'dabc', 'abca', 'cabd'] | multi_choice |
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