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
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func227 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/227.png | A and B are 60 km apart. Two individuals, A and B, start cycling simultaneously from points A and B, respectively, towards each other at a constant speed. B rests for 0.5 hours during the journey before continuing at the original speed. The relationship between the distance (km) from point A and the time (hours) is sho... | 2.1 | NULL | free_form |
func229 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/229.png | The graph of the linear function y = kx + b and y = -2x + 4 is shown in the figure. What is the solution set for the inequality kx + b ≥ -2x + 4? | x ≥ 1/2 | NULL | free_form |
func230 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/230.png | In the same coordinate system, as shown in the figure, the graphs of the linear functions y = k1x, y = k2x, y = k3x, y = k4x are represented by l1, l2, l3, and l4 respectively. The relationship of the magnitudes of k1, k2, k3, and k4 is __________________. | k3 > k4 > k1 > k2 | NULL | free_form |
func231 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/231.png | As shown in the figure, in the plane Cartesian coordinate system, E is the midpoint of BC. Given A(0,4), B(-2,0), C(8,0), and D(4,4), point P is a moving point on line segment BC. When the length of BP is ______, the quadrilateral with vertices at P, A, D, and E is a parallelogram. | 1 or 9 | NULL | free_form |
func232 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/232.png | As shown in the figure, given the inverse proportional function y = k / x (k is a constant, k ≠ 0) passes through point A. Draw AB perpendicular to the x-axis at point A, with the foot of the perpendicular at B. If the area of △AOB is 4, then k = | -8 | NULL | free_form |
func233 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/233.png | As shown in the figure, P is a point on the graph of the parabola y = x^2 − 3x − 4 in the fourth quadrant. Draw perpendicular lines from point P to the x-axis and y-axis, with foot points A and B, respectively. What is the maximum perimeter of the quadrilateral OAPB? ________. | 16 | NULL | free_form |
func234 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/234.png | It is known that the inverse proportional function y = -6 / x (x < 0), y = 2 / x (x > 0) has its graph shown in the figure. From any point P on the positive half of the x-axis, draw a line parallel to the x-axis, intersecting the graphs of these two functions at points M and N respectively. If point A is any point on t... | 4 | NULL | free_form |
func235 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/235.png | As shown in the figure, in the plane Cartesian coordinate system, the coordinates of points A and B are (-2, 0) and (0, 3), respectively. Taking point A as the center of the circle and AB as the radius, draw an arc intersecting the positive x-axis at point C. What are the coordinates of point C? | (√13 − 2, 0) | NULL | free_form |
func236 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/236.png | As shown in the figure, a rectangular vegetable garden ABCD is to be enclosed. One side AD is a wall, and the length of AD cannot exceed 26 meters. The other three sides AB, BC, and CD are surrounded by a fence, with the total length of these three sides being 40 meters. The following conclusions are given: ① The lengt... | ③② | NULL | free_form |
func237 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/237.png | As shown in the figure, in the rectangle OABC and the square CDEF, point A lies on the positive half of the y-axis, points C and F are both on the positive half of the x-axis, and point D is on side BC, where BC = 2CD, and AB = 1. If points B and E lie on the same rectangular hyperbola, then the expression for this rec... | y = 2/x | NULL | free_form |
func238 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/238.png | As shown in the figure, in a Cartesian coordinate system, the rectangle OABC has two sides OA and OC lying on the x-axis and y-axis, respectively, and OA = 4, OC = 3. If rectangle OABC is rotated counterclockwise around point O such that point A lands exactly on point A1 on the BC side, what are the coordinates of poin... | (√7, 3) | NULL | free_form |
func239 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/239.png | As shown in the figure, the equation of line AB is y1 = k1x + b1, and the equation of line AC is y2 = k2x + b2. They intersect the x-axis at points B and C, respectively, and the x-coordinates of points B, A, and C are -2, -1, and 2. The range of x values that satisfy y1 > y2 > 0 is ______. | -1 < x < 2 | NULL | free_form |
func24 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/24.png | The graph of the quadratic function y = ax^2 + bx + c is shown. When the function value y < 0, what is the range of the independent variable x? | -1 < x < 3 | NULL | free_form |
func240 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/240.png | Given the quadratic function y = -x^2 + x + 6 and the linear function y = -2x + m, the graph of the quadratic function above the x-axis is reflected downward across the x-axis, while the rest of the graph remains unchanged, resulting in a new function (as shown in the diagram). When the line y = -2x + m intersects this... | -25/4 < m < -4 | NULL | free_form |
func241 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/241.png | The graph of the quadratic function y = x² - x - 2 is shown in the figure. Then the range of x when the function value y ≥ 0 is __. | x ≤ -1 or x ≥ 2 | NULL | free_form |
func242 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/242.png | As shown in the figure, given points M(1,3) and N(3,3), one branch of the hyperbolic function y=k/x (k≠0) intersects the line segment MN. How many integer values of k satisfy this condition? | 7 | NULL | free_form |
func243 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/243.png | As shown in the figure, A and B are points on the hyperbolic function y = k / x (x > 0). Connect OA and OB. Through point A, draw AC perpendicular to the x-axis at point C, intersecting OB at point D. If AD : DC = 2 : 3, the area of △AOD is 2, and the coordinates of point B are (m, 2), then the value of m is ______. | 5 | NULL | free_form |
func244 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/244.png | As shown in the figure, the line y = kx + b passes through the point (-1, 2). The solution set of the inequality (k + 2)x + b > 0 with respect to x is ________. | x > -1 | NULL | free_form |
func245 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/245.png | The quadratic function y = ax^2 + bx has a graph as shown. If the quadratic equation ax^2 + bx = m in terms of x has real roots, the value of m could be _________ (provide one possible value). | -2 (the answer is not unique) | NULL | free_form |
func246 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/246.png | Ice and snow sports are becoming increasingly popular. In a freestyle skiing big air training session, an athlete slides off a jump 2m high, and their trajectory follows a parabolic path. Let their horizontal distance from the edge of the platform be x m, and their vertical height from the horizontal plane at the base ... | 6 | NULL | free_form |
func247 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/247.png | As shown in the figure, given that the line y₁ = x + m and y₂ = kx - 1 intersect at point P(-3, 2), what is the solution set for the inequality x + m < kx - 1 with respect to x? | x < -3 | NULL | free_form |
func248 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/248.png | It is known that the graph of the linear function y = kx + b is shown in the figure. When y > -4, the range of x is __________. | x > 0 | NULL | free_form |
func249 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/249.png | As shown in the figure, point P(3a, a) is an intersection point of the hyperbolic function graph y = k/x (k > 0) with O. The area of the shaded region in the figure is 10π. Then, k = ______. | 12 | NULL | free_form |
func25 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/25.png | As shown in the figure, point A lies on the graph of the inverse proportional function y = k/x in the first quadrant, point B is on the positive half-axis of the x-axis, OA = AB, and the area of △AOB is 3. What is the value of k? | 3 | NULL | free_form |
func250 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/250.png | As shown in the figure, let points A and B lie on the hyperbolic function y = k/x (x > 0). From point A, draw AC perpendicular to the x-axis at point C, and from point B, draw BD perpendicular to the y-axis at point D. Draw BE perpendicular to the x-axis at point E, and connect AD. Given that AC = 1, BE = 1, and the ar... | 1/4 | NULL | free_form |
func251 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/251.png | As shown in the figure, in the Cartesian coordinate plane, O is the origin, A(4, 4.8), B(10, 0). Connect AO and AB. Points C and D are respectively on line segments AB and OB. The triangle △CDB is folded along the line containing CD such that the corresponding point D' of D falls on line segment AO, and BD' = OB'. What... | (40/13, 30/13) | NULL | free_form |
func252 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/252.png | As shown in the figure, the hypotenuse AB of the right triangle △AOB intersects the x-axis at point B, and AC = BC. The graph of the inverse proportional function y = k / (x < 0) passes through point A. If B(3, 1) and the area of △AOC is 7.5, then the value of k is ______. | -27 | NULL | free_form |
func253 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/253.png | As shown in the figure, the equation y = k/x represents the hyperbolic curve above the x-axis. The area of parallelogram OABC is 5. If point A lies on the x-axis, point B lies on the curve y = k1/x, and point C lies on the curve y = k2/x, what is the value of k2 - k1? | -5/2 | NULL | free_form |
func255 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/255.png | As shown in the figure, in the rectangular coordinate system, it is known that line l1 and line l2 intersect at point C(0,1), and the angle between them is 90°. Line l1 intersects the negative x-axis at point A, and line l2 intersects the positive x-axis at point B(2,0). What are the coordinates of point A? | (-1/2, 0) | NULL | free_form |
func256 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/256.png | As shown in the figure, in the plane Cartesian coordinate system, the straight line AB intersects the hyperbolic function y = k/x (x > 0) at points A and B, intersects the x-axis at point C(3, 0), and intersects the y-axis at point D(0, 2). If AD = AB = BC, then k = ______. | 4/3 | NULL | free_form |
func257 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/257.png | As shown in the figure, point A is on the negative half of the x-axis, point C is on the positive half of the y-axis, and the quadrilateral OABC is a rectangle. Point D is the midpoint of AB. The graph of the inverse proportion function y = -k/x (x < 0) passes through point D and intersects BC at point E. Connect DE. I... | -4 | NULL | free_form |
func258 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/258.png | As shown in the diagram, a moving point P starts from point B and travels along the edges of the figure (adjacent edges are perpendicular) at a speed of 2 cm per second, following the path B→C→D→E→F→A. The corresponding area (cm²) of △ABP and the graph of the motion time t (s) of point P are shown in the second diagram... | 3 or 14 | NULL | free_form |
func259 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/259.png | As shown in the figure, A(2√2, 0), AB = 3√2. Taking point A as the center of the circle and the length of AB as the radius, an arc intersects the negative x-axis at point C. The coordinates of point C are ______. | (-√2, 0) | NULL | free_form |
func26 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/26.png | As shown in the graph of the quadratic function y = ax² + bx + c, the following information is given: ①c > 0; ②a < 0; ③a − b + c > 0; ④b² > 4ac; ⑤2a − 2b − 2h. Which of these are correct (fill in the sequence numbers). | ③④⑤ | NULL | free_form |
func260 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/260.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 point A. If the coordinates of point A are (1, 2), then the solution set for the inequality k₁x > k₂/x with respect to x is ______. | −1 < x < 0 or x > 1 | NULL | free_form |
func261 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/261.png | As shown in the figure, in the isosceles triangle △ABO, the side OA lies on the negative half of the x-axis, point B is in the second quadrant, and the area of △ABO is 6. The hyperbolic function y=k/x passes through point B. What is the value of k? | -6 | NULL | free_form |
func262 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/262.png | In a Cartesian coordinate system, a moving point follows the direction as shown in the diagram: (0, 0) → (1, 1) → (2, 2) → (2, 3) → (3, 3) → (4, 4) → ..., and so on. According to this pattern, with (0, 0) being the 1st point, find the coordinates of the 78th point. | (520, 521) | NULL | free_form |
func263 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/263.png | As shown in the figure, the graph of the direct proportional function y = -3x intersects with the linear function y = kx + b (k > 0) at the point (m, -6). The solution set of the inequality kx + b < -3x with respect to x is ________. | x < 2 | NULL | free_form |
func264 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/264.png | As shown in the figure, the graph of the linear function y = kx + b intersects the x-axis and y-axis at points A(2, 0) and B(0, -1.5), respectively. What is the range of the independent variable x when y < 0? | x < 2 | NULL | free_form |
func265 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/265.png | A straightedge with a 45° angle and a triangle board are placed as shown in the diagram on the Cartesian coordinate plane, where A(-2, 0) and B(0, 1). What is the equation of the line BC? | y = -1/3x + 1 | NULL | free_form |
func266 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/266.png | As shown in the figure, the graph of the linear function y = kx + b passes through the points (-1,0) and (0,-2). The solution set for the inequality kx + b < 0 is ______. | x < -1 | NULL | free_form |
func267 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/267.png | As shown in the figure, given the line l: y = √3x, passing through point M(2, 0), draw a perpendicular to the axis intersecting line l at point N. From point N, draw a perpendicular to line l intersecting the x-axis at point M1; from point M1, draw a perpendicular to line l intersecting line l at point N1; from point N... | (2^4n, 0) | NULL | free_form |
func268 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/268.png | A and B both ride bicycles at a constant speed, departing from location A towards location B. The relationship between their distance from A, v (in km), and the riding time, t (in hours), is shown in the graph. When t = 2, how far apart are A and B (in km)? | 5 | NULL | free_form |
func269 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/269.png | As shown in the diagram, a rectangular vegetable garden ABCD is enclosed using a 60-meter-long fence, with one side adjacent to a wall (the wall's length is unlimited). Let the length of the fence AB parallel to the wall be x meters, and the area of the vegetable garden be y m². Write the relationship between y and x _... | y = -1/2x² + 30x | NULL | free_form |
func27 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/27.png | As shown in the figure, the vertex of the parabola y = x² - 4x + 2 is A, and it intersects the y-axis at point B. What is the equation of line AB? ______ | y = -2x + 2 | NULL | free_form |
func270 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/270.png | As shown in the figure, the straight line l parallel to the x-axis intersects the graphs of the functions y=6/x (x>0) and y=2/x (x>0) at points A and B, respectively. Connecting AO and BO, the area of △ABO is _______. | 2 | NULL | free_form |
func271 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/271.png | The water dispenser in the classroom automatically heats when powered on. During heating, the water temperature rises by 10°C per minute, stopping at 100°C. Afterward, the temperature begins to drop, and at this stage, the water temperature y (in °C) is inversely proportional to time t (in minutes). When the water temp... | 12 | NULL | free_form |
func272 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/272.png | As shown in the figure, in the rectangular coordinate system xOy, there are three points A(0, 1), B(4, 1), C(5, 6). What is sin∠BAC? ______. | √2/2 | NULL | free_form |
func273 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/273.png | As shown in the figure, in the Cartesian coordinate plane xOy, the quadrilateral ABCD is a rhombus, ∠ABC=120°, and the coordinates of point B are (0, -3). What are the coordinates of point A?______. | (-3√3, 0) | NULL | free_form |
func274 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/274.png | As shown in the figure, it is a part of the graph of the inverse proportional function y = k + 3 / x (k is a constant and k ≠ -3, x < 0). What could be the value of k? (Write only one) | -5 (not unique) | NULL | free_form |
func275 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/275.png | As shown in the figure, it is known that the graphs of a directly proportional function and a linear function y2=1/2x+b intersect at point P. Below are four statements: ①a<0; ②b<0; ③When x>0, y1>y2; ④When x=-2, y1=y2. Which of these statements are correct? (Only fill in the serial numbers) | ①④ | NULL | free_form |
func276 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/276.png | Given the function y=|x²-4| with a graph roughly as shown in the figure, for the equation |x²-4|=m (where m is a real number), if the equation has exactly 3 distinct real roots, what is the value of m? | 4 | NULL | free_form |
func277 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/277.png | As shown in Figure ①, in the right triangle △ABC, ∠B = 90°, a moving point P starts at point A and moves along the broken line A—B—C at a speed of 2 units per second (stopping at point C). The function graph of the length of BP changing with the time t (in seconds) is shown in Figure ②. What is the length of BC? | 8 | NULL | free_form |
func278 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/278.png | As shown in the figure, the graphs of the linear function y = kx + b and the reciprocal function y = m/x intersect at points A(1,6) and B(n,-2). Then the solution of the equation kx + b = m/x is ____________. | 1 or -3 | NULL | free_form |
func279 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/279.png | Jialu conducts an electric experiment with a sliding rheostat in a dynamic circuit. The power supply voltage remains constant, and the relationship between current I (A) and resistance R (Ω) is shown in the diagram.
(1) The power supply voltage is ______ V;
(2) The sliding rheostat is labeled as '20Ω 2A,' where '20Ω' i... | 3; 1.5 | NULL | free_form |
func28 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/28.png | As shown in the figure, a radar detector measures the results. If the position of target A in the figure is recorded as (2, 90°), the position of target B is (3, 30°), and there is a target C at position (4, x°), where the distance between target C and target B is 5, then the value of x is______. | 120 or 300 | NULL | free_form |
func280 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/280.png | As shown in the figure, in the rectangular coordinate plane, the quadrilateral OABC is a rhombus. If the coordinates of point A are (8, 15), what is the perimeter of the rhombus__________? | 68 | NULL | free_form |
func281 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/281.png | As shown in the figure, D is a point on the graph of the inverse proportional function y=1/k (k>0) in the first quadrant. Connect O and extend to point B, such that BD=OD. From point D, draw a perpendicular BA to point A, which intersects the graph of the inverse proportional function y=1/k (k>0) at point C.
(1) If ∠AO... | √3 | NULL | free_form |
func283 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/283.png | Place 5 identical squares in a Cartesian coordinate plane. If the coordinates of vertices M and N are (-3, 2) and (9, 2) respectively, then the coordinates of vertex A are ________. | (13, -6) | NULL | free_form |
func284 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/284.png | As shown in the figure, in a rectangular coordinate system, point A lies on the graph of the inverse proportional function y = k/x (x > 0), B and C are two points on the positive half of the x-axis, AB = AC, OB = BC. If the area of △ABC is 4, the value of k is ______. | 12 | NULL | free_form |
func285 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/285.png | As shown in the figure, in the plane Cartesian coordinate system, the coordinates of points A, B, and C are (1,1), (4,1), and (2,3) respectively. If the line y = x + b intersects ΔABC, the range of b is ______. | −3 ≤ b ≤ 1 | NULL | free_form |
func286 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/286.png | As shown in the figure, a chain consists of several uniform iron rings fully stretched to the maximum extent. Each iron ring is 4 cm long and 0.5 cm thick, and the rings are in a state of maximum stretch. Let the length of the chain with n rings be y cm. Write the relationship between y and n: ________. | y = 3n + 1 | NULL | free_form |
func287 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/287.png | As shown in the figure, given A1(1,0), A2(1,-1), A3(-1,-1), A4(-1,1), A5(2,0), ..., find the coordinates of point A2024. | (-506,506) | NULL | free_form |
func288 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/288.png | As shown in the figure, in the coordinate plane oxy, the line y = kx + b intersects with y = mx + n at point M(2,4). Which of the following conclusions are correct? (Fill in the number). ① The solution to the system of equations y = kx + b and y = mx + n with respect to y is x = 2; ② The solution set of the two inequal... | ③④ | NULL | free_form |
func29 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/29.png | As shown in the figure, a square grid is placed in a certain plane Cartesian coordinate system. The coordinates of point B are (-1, -2). What are the coordinates of point C? | (2, 1) | NULL | free_form |
func290 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/290.png | As shown in the figure, in a Cartesian coordinate plane, circle ⊙A is tangent to the x-axis at point B. Draw the diameter BC. The graph of the function y = 20/x (x > 0) passes through point C. Point D is any point on the y-axis. Then the area of △ACD is ________. | 5 | NULL | free_form |
func291 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/291.png | As shown in the figure, the line y = -2x + 2 intersects with the line y = kx + b (where k, b are constants and k ≠ 0) at point A(m, 4). Then the solution set of the inequality -2x + 2 < kx + b is ______. | x > -1 | NULL | free_form |
func292 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/292.png | In the rectangular coordinate system xOy, point A(-2,3), point B(-1,0), point D(2,3), and point C lies on the x-axis. If CD = AB, what are the coordinates of point C? | (1,0) or (3,0) | NULL | free_form |
func293 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/293.png | As shown in the figure, the coordinates of three vertices of □ABCD are A(4, -2), B(5, 2), C(2, 2). What are the coordinates of the fourth vertex D? | (1, -2) | NULL | free_form |
func294 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/294.png | As shown in the figure, the 'heart' pattern is composed of part of the graph of the function y = −x^2 + 10 and its symmetric graph about the line y = −x. Point A is any point on the 'heart' pattern above the line y = −x, and point B is its symmetric point. When AB = √2, the coordinates of point B are __________. | (-2, 2) or (1, 5) | NULL | free_form |
func295 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/295.png | As shown in the figure, given that the straight line y = kx (k ≠ 0) intersects the hyperbola y = 2/x at two points A(m, 1) and B, the solution set of the inequality y > kx is ____________. | x < -2 or 0 < x < 2 | NULL | free_form |
func296 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/296.png | In the coordinate grid shown in the figure, write an integer coordinate where its distances to the two coordinate axes are equal: ________. | (1,1) (the answer is not unique) | NULL | free_form |
func297 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/297.png | As shown in the figure, in △OAB, the coordinates of vertices A and B are (2, 4) and (6, 0), respectively. When △OAB is translated horizontally along the x-axis to form △CDE:
(1) If CB = 3, then the length of OE is ________;
(2) Connect AD. Under the condition in (1), the area of quadrilateral OADE is ________. | (1) 21/2
(2) 30 | NULL | free_form |
func299 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/299.png | As shown in the figure, the graphs of the functions y = kx + b and y = mx intersect at point P. Then the solution to the two-variable linear equation system { y = kx + b, y = mx } concerning x and y is ________. | { x = 2, y = 1 } | NULL | free_form |
func3 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/3.png | As shown in the figure, the parabola y = x² is translated to obtain parabola m, which passes through point A(-2, 0) and the origin. Its vertex is P, and its axis of symmetry intersects the parabola y = -x² at point O. What is the area of the shaded region in the figure? | 1 | NULL | free_form |
func30 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/30.png | As shown in the figure, it is known that the graphs of the linear functions y = ax - 3 and y = bx + 12 intersect at point P(5, 7). Then the solution set for the inequality ax - 3 < bx + 12 is _______. | x < 5 | NULL | free_form |
func300 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/300.png | As shown in the diagram, in a plane Cartesian coordinate system, a moving point starts from the origin O and moves continuously in the upward and rightward directions, moving one unit at a time. Points A1(0, 1), A2(1, 1), A3(1, 0), A4(2, 0) ... are obtained as a result. What are the coordinates of point A42001 (n is a ... | (1000, 1) | NULL | free_form |
func301 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/301.png | To reasonably schedule commute and school time, a school investigation team surveyed the time spent commuting to and from school in one day among grade 9 students. In this survey, 20 students from grade 9 were randomly selected. The time spent commuting to school was used as the horizontal coordinate and the time spent... | 280 | NULL | free_form |
func302 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/302.png | As shown in the figure, the graph of the linear function y = kx + b passes through the point (1, -3). When y < -3, the range of values for x is ______. | x > 1 | NULL | free_form |
func303 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/303.png | Under the condition of constant temperature, the pressure P (kPa) produced by a gas is inversely proportional to the volume V (mL) of the gas. The graph shows the function of the pressure P of a certain gas after compression with respect to the volume V of the gas. If the pressure decreases from 100 kPa to 80 kPa, then... | 15 | NULL | free_form |
func305 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/305.png | As shown in the figure, the functions y = -2x and y = kx + 4 intersect at point A(m, 3). Then the solution set of the inequality kx + 4 + 2x ≤ 0 is ________. | x ≤ -1.5 | NULL | free_form |
func306 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/306.png | As shown in Figure 1, in rectangle ABCD, moving point P starts at point B and moves along BC, CD, and DA until it stops at point A. Let the path of point P be x, and the area of △ABP be y. If the function graph of y with respect to x is as shown in Figure 2, the length of the diagonal of the rectangle is ________. | √41 | NULL | free_form |
func307 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/307.png | As shown in the figure, the linear function y = kx + b passes through points A(5, 0) and B(0, -2). Then, the solution set of the inequality kx + b < 0 with respect to x is ________. | x < 5. | NULL | free_form |
func308 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/308.png | As shown in the figure, the straight lines y = kx + b and y = mx + n intersect the x-axis at points A(-1/2, 0) and B(2, 0), respectively. Then the solution set of the inequality system {kx + b < 0, mx + n < 0} is ______. | -1/2 < x < 2 | NULL | free_form |
func309 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/309.png | As shown in the figure, in the 2D Cartesian coordinate system, the quadrilateral AOCD is a parallelogram. The coordinates of A are (1,2), O is (0,0), and C is (3,0). What are the coordinates of point D? | (4,2) | NULL | free_form |
func31 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/31.png | The hyperbola y=4/x intersects the straight line y=kx at points A and B. Passing through point B, draw BC perpendicular to the x-axis at point C, and connect AC. Then, the area of △AOC is ________. | 2 | NULL | free_form |
func310 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/310.png | As shown in the figure, in a Cartesian coordinate system, the line y=4/3x+4 intersects the axes at points A and B, respectively. From point O, draw OC perpendicular to AB, intersecting AB at point C. What is the length of OC? ______. | 12/5 | NULL | free_form |
func311 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/311.png | As shown in the figure, the intersection of the two lines l1: y = 2x + b and l2: y = x - 2 is (5, 3). Then, the solution set of the inequality 2x + b > x - 2 with respect to x is ________. | x > 5. | NULL | free_form |
func312 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/312.png | As shown in the figure, point A is on the graph of the inverse proportional function y = k * (x > 0). Through point A, draw AB perpendicular to the y-axis. Point C is on the positive half of the y-axis. If the area of △ABC is 3, then the value of k is ________. | -6 | NULL | free_form |
func313 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/313.png | As shown in the figure, it is known that the graph of the function y = ax + b intersects the graph of the function y = kx - 3 at point P(4, -6). Then the solution set of the inequality ax + b ≤ kx - 3 is __________. | x ≤ 4 | NULL | free_form |
func314 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/314.png | As shown in the figure, P is a point on the graph of the inverse proportional function y = k/x (k ≠ 0, x > 0). A perpendicular is drawn from point P to the x-axis at point A, and point B is the reflection of point A about the x-axis. Connect PB. If the area of △PAB is 16, the value of k is ________. | 16 | NULL | free_form |
func315 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/315.png | As shown in the figure, it is known that parallelogram OABC is translated to the right to obtain parallelogram OA′B′C′. Point A′ happens to be the midpoint of AB, where point A has coordinates (√3, 2) and point B has coordinates (3√3, 2). What are the coordinates of point A′? _______ | (2√3, 2) | NULL | free_form |
func316 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/316.png | As shown in the figure, in the rectangular coordinate system, the coordinates of point A are (-1, 0), point B is on the positive half-axis of the y-axis. Taking point B as the center and the length of BA as the radius, an arc intersects the positive half-axis of the x-axis at point C. What are the coordinates of point ... | (1,0) | NULL | free_form |
func317 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/317.png | As shown in the figure, during an activity, Class A located at point A intends to travel 5 km to point B to meet with Class B. Describe the position of Class B relative to Class A in terms of direction and distance. | 5 km in the direction of 40° west of south. | NULL | free_form |
func318 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/318.png | As shown in the figure, in a rectangular coordinate system, quadrilateral ABCD is a square with A(1, 1), B(-1, 1), C(-1, -1), and D(1, -1). The curve A4A1, A1A2, A2A3... is called the 'involute of the square,' where the centers of arcs A4A1, A1A2, A2A3... are points B, C, D, and A in sequence, repeating cyclically. Wha... | (4049, -1) | NULL | free_form |
func32 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/32.png | As shown in the figure, in the Cartesian coordinate system, point A lies on the graph of the function y = -(k/x) (x < 0). A perpendicular is drawn from point A to the x-axis, intersecting the y-axis at point B. Point C lies on the x-axis. If the value of k is -8, then the area of △ABC is ________. | 4 | NULL | free_form |
func322 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/322.png | As shown in the figure, O is the origin of the coordinates. In the parallelogram OABC, the coordinates of vertex A are (-3, 4), vertex C lies on the negative half of the x-axis, and the graph of the inverse proportional function y = k/x passes through vertex B in the second quadrant. If the area of parallelogram OABC i... | -28 | NULL | free_form |
func323 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/323.png | As shown in the figure, the height AD of triangle ABC is 4, BC = 8, point E is on the side BC, and AE is connected. If the length of BE is x, and the area of triangle ACE is y, then the relationship between y and x is __________________. | y = 16 - 2x | NULL | free_form |
func324 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/324.png | In the figure, the graphs of the inverse proportional function y = k / x and the linear function y = ax + b are shown. The coordinates of the intersection points A(2, 3) and B(m, −2) are given. Directly write the inequality solution for ax + b > k / x: __________. | x > 2 or −3 < x < 0 | NULL | free_form |
func325 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/325.png | In the rectangular coordinate plane xOy, the graphs of the linear functions y1 = kx + b and y2 = x + m are shown as in the figure. If the x-coordinate of their intersection is 2, which of the following statements are correct? ① The acute angle between the line y2 = x + m and the x-axis is 45°; ② k + b > 0; ③ The soluti... | ①②④ | NULL | free_form |
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