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func1 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1.png | As shown, A is a point on the hyperbolic function y = k/x. If the area of △ABO is 2, then the value of k is ______. | 4 | NULL | free_form |
func1000 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1000.png | According to research, an increase in blood lactate concentration in the human body is an important reason for feeling fatigued after exercise. When the blood lactate concentration drops below 50mg/L, the athlete has essentially recovered from fatigue. Sports scientists have drawn a graph based on experimental data, which reflects the change in blood lactate concentration in athletes over time for different recovery methods. Which of the following statements is incorrect? | C | ['The lactic acid concentration first rises and then falls after exercise.', 'At t = 20 min, the average lactic acid concentration under both methods is about 150mg/L.', 'Using a static method to relax, the athlete can eliminate fatigue in about 30 minutes.', 'To quickly achieve the effect of eliminating fatigue, the athlete should relax using a slow exercise method.'] | multi_choice |
func1002 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1002.png | As shown in the figure, the line l1: y = x + 4 intersects with the line l2: y = mx + n at point A(-1, b). Then the solution to the system of equations { y - x = 4, y - mx = n } with respect to x and y is ( ). | C | ['\\( \\begin{cases} x = 3 \\\\ y = 1 \\end{cases} \\)', '\\( \\begin{cases} x = -1 \\\\ y = -3 \\end{cases} \\)', '\\( \\begin{cases} x = -1 \\\\ y = 3 \\end{cases} \\)', '\\( \\begin{cases} x = 3 \\\\ y = -1 \\end{cases} \\)'] | multi_choice |
func1006 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1006.png | As shown in the figure, the linear function y₁ = x + b and the linear function y₂ = kx + 4 intersect at point P(2, 3). What is the solution set for the inequality x + b > kx + 4 with respect to x? | C. x > 2 | ['x > -2', 'x > 0', 'x > 2', 'x > 3'] | multi_choice |
func1022 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1022.png | As shown in the figure, the graphs of the functions y = 2x and y = ax + 6 intersect at point P(m, 4). Then the solution set of the inequality 2x ≥ ax + 6 in terms of x is ( ). | A. x ≥ 2 | ['\\(x \\geq 2\\)', '\\(x \\leq 2\\)', '\\(x \\geq 4\\)', '\\(x \\leq 3\\)'] | multi_choice |
func1026 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1026.png | As shown in the figure, P is a point in the rectangular coordinate system. A perpendicular is drawn from point P to the x-axis and y-axis, with the foot M on the x-axis having a coordinate of 3 and the foot N on the y-axis having a coordinate of 4. What are the coordinates of point P? ( ) | D | ['(0, 3)', '(0, 4)', '(4, 3)', '(3, 4)'] | multi_choice |
func1029 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1029.png | As shown in the figure, M is the center of the regular hexagon EFGHPQ. In the rectangular coordinate system, if the coordinates of point M are (0, 0) and the coordinates of point E are (-1, 0), then the coordinates of point H are ( ). | C. (1, 0) | ['(-2, 0)', '(1, 1)', '(1, 0)', '(2, 0)'] | multi_choice |
func1030 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1030.png | Spring chill, on March 23, 2024, it rained in Qixian, and soon turned into sleet. Figure 1 shows the variation of temperature over time. What is the day's temperature difference (the difference between the highest and lowest temperatures)? | B. 12°C | ['16°C', '12°C', '8°C', '4°C'] | multi_choice |
func1032 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1032.png | As shown in the figure, in a plane rectangular coordinate system, two insects, A and B, start simultaneously from point O at the same speed and crawl at a uniform speed along paths L1 and L2 (indicated by bold lines) respectively, completing one round and returning to the origin. The time taken is t1 and t2 respectively. If point A(-4, 4) and point B(4, 4), what is the relationship between t1 and t2? ( ) | B | ['t1 < t2', 't1 = t2', 't1 > t2', 'Cannot be determined'] | multi_choice |
func1035 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1035.png | As shown in the figure, in the same Cartesian coordinate system, the graphs of the functions y₁ = 2x + a and y₂ = -x + 2 intersect at point A(m, 3). Then the solution set of the inequality y₁ < y₂ is ( ). | C | ['x > -1', 'x > -1', 'x < -1', 'x ≤ -1'] | multi_choice |
func1036 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1036.png | As shown in the figure, the linear function y₁ = kx + 4 and y₂ = x + b intersect at point P(1, 3). Observing this, the solution set of the inequality x + b ≥ kx + 4 with respect to x is ( ). | D. x ≥ 1 | ['x < 1', 'x < 1', 'x \\geq 3', 'x \\geq 1'] | multi_choice |
func1051 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1051.png | As shown in figure (a), a moving point P on the edge of rectangle ABCD starts from point B and travels uniformly in the direction B→C→D→A until it stops at point A. The moving speed of point P is 2 cm/s. Let the movement time of point P be t (s), and the area of △PAB be y (cm²). If the function graph related to this is as shown in figure (b), then the perimeter of rectangle ABCD is ( ). | B. 28 cm | ['14cm', '28cm', '36cm', '48cm'] | multi_choice |
func1061 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1061.png | The function y = kx + b (where k and b are constants, k ≠ 0) is graphed as shown. Which of the following statements is correct? ( )
A. When x = -2, y = 1
B. If the points (m, 1) and (1, n) lie on the line, then m > n
C. k < 0
D. If the graph of y = kx + b forms a triangle with the coordinate axes with an area of 2, then b = 2 | D | ['When x = -2, y = 1', 'If point (1, m) and point (1, n) are on the line, then m > n', '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'] | multi_choice |
func1062 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1062.png | As shown in the figure, the line y=kx intersects the hyperbolic curve y=m/x at points A and B. Given that the coordinates of point A are (4, 1), what is the solution set of the inequality kx ≥ m/x? | D | ['x > 4', '0 < x \\leq 4', 'x \\geq 4 or x \\leq -4', 'x > 4 or -4 \\leq x < 0'] | multi_choice |
func1066 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1066.png | As shown in the figure, in the rectangular coordinate system Oxy, point A(4,3) is given, and the angle between the line OA and the positive x-axis is α. What is the value of cosα? ( ) | C | ['3/5', '3/4', '4/5', '4/3'] | multi_choice |
func1082 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1082.png | If the linear function y = kx + b (k ≠ 0) has a graph as shown in the figure, which of the following statements is correct?
A. k > 0
B. b = 4
C. y increases as x increases
D. When x > 4, y < 0 | D | ['k > 0', 'b = 4', 'The slope increases with the increase of \\(b\\)', 'When \\(x > 4\\), \\(y < 0\\)'] | multi_choice |
func109 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/109.png | As shown in the figure, the relationship between temperature T (℃) of a certain area and the increase in altitude h (km) is provided. Observing the graph, it can be concluded that the ground temperature of the area is ______ ℃; when the altitude exceeds ______ km, the temperature will drop below 0℃. | 30, 5 | NULL | free_form |
func1091 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1091.png | On Saturday, Li Jian rode his bicycle from home to the botanical garden to play. After spending some time there, he headed back home. On his way back, he discovered a beautiful view near a homestay, stopped to take some photos, and then continued cycling home. Based on the graph showing the distance from and time away from home, which of the following statements is correct?
A. Li Jian's home is 10 kilometers away from the botanical garden.
B. He spent 1.5 hours playing in the botanical garden.
C. His average speed cycling back home from the homestay after taking photos was 10 km/h.
D. The homestay is 2 kilometers away from Li Jian's home. | C | ["The distance from Li Jian's home to the botanical garden is 10 km.", 'He played in the botanical garden for 1.5 hours.', 'The average speed of his return journey from the homestay is 10 km/h.', "The distance from the homestay to Li Jian's home is 2 km."] | multi_choice |
func1108 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1108.png | As shown in the figure, Xiao Ming and his father are playing on a seesaw. It is known that Xiao Ming's weight is 50kg, and the distance from the fulcrum of the seesaw is 1.2m. Let the father's weight be x kg, and the distance from the fulcrum of the seesaw be y m. To keep the seesaw balanced, the relationship between x and y should satisfy ( ). | C | ['y = 60x', 'y = x/60', 'y = 60/x', 'y = 50x'] | multi_choice |
func1119 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1119.png | 7. The combination of numbers and shapes is a commonly used method for solving mathematical problems. As shown in the figure, the line y=2x-1 intersects with the line y=-x+b at point P(2,m). Then, the solution set for the inequality 2x-b > -x+1 with respect to x is ( ). | B. x > 2 | ['x < 2', 'x > 2', 'x < 3', 'x > 3'] | multi_choice |
func112 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/112.png | As shown in the figure, the inverse proportion function y = k/x (k ≠ 0) has a point A, and the area of △AOB is 5. Then, the expression of this inverse proportion function is ________. | y = -10/x | NULL | free_form |
func1122 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1122.png | As shown in the figure, in the plane rectangular coordinate system, OP=√13. With point O as the center of a circle and the length of OP as the radius, the circle intersects the negative x-axis at point A. The x-coordinate of point A lies in ( )
A. Between 3 and 4
B. Between 4 and 5
C. Between -4 and -3
D. Between -5 and -4 | C | ['Between 3 and 4', 'Between 4 and 5', 'Between -4 and -3', 'Between -5 and -4'] | multi_choice |
func1128 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1128.png | As shown in Figure 1, in a right triangle △ABC, point P moves from point A to point B and then to point C before stopping. The velocity is 2 units/second, and the relationship between the length of BP and the time of motion (in seconds) is shown in Figure 2. What is the length of AC? | C. 17 | ['15√5/2', '√427', '17', '√5'] | multi_choice |
func1131 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1131.png | As shown in the figure, the graph of the inverse proportional function y = k/x passes through vertex B of the rectangle OABC. If the coordinates of point A are (-1, 0) and the coordinates of point C are (0, 2), what is the value of k? ( ) | D. -2 | ['2', '1', '-1', '-2'] | multi_choice |
func1141 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1141.png | As shown in the figure, a checkerpiece originally at point A on the board, represented as (1, 2), moves in the direction indicated by the arrow to point B. The correct representation of its path using ordered pairs is ( ). | D | ['(1, 2) → (4, 1) → (4, 5)', '(1, 2) → (1, 4) → (4, 5)', '(1, 2) → (4, 1) → (5, 4)', '(1, 2) → (1, 4) → (5, 4)'] | multi_choice |
func1150 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1150.png | As shown in the figure, in the Cartesian coordinate system, the line y = kx + b (k ≠ 0) intersects the line y = −2x + 1 at point A(m, 3). Which of the following statements is incorrect? ( )
A. k > 0, b > 0
B. The line y = −2x + 1 passes through the first, second, and fourth quadrants.
C. The solution to the system of equations y = kx + b and y = −2x + 1 with respect to x and y is
D. The solution set for the inequality kx + b > −2x + 1 with respect to x is x > 1. | D | ['k > 0, b > 0', 'The line passing through the first, second, and fourth quadrants is y = -2x + 1', 'The solution of the equation kx + b = y is y = -2x + 1', 'The solution set of the inequality kx + b > -2x + 1 is y = -2x + 1'] | multi_choice |
func1151 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1151.png | The process reflected below is: Li Hong walked from home to the Sports Center Square, exercised there for a while, then went to a noodle shop for noodles, and finally walked back home. Where x represents time and y represents Li Hong's distance from home. Based on the graph, which of the following four statements is incorrect ( ) | B. The distance between the Sports Center Square and the noodle shop is 4 kilometers | ['The average speed of Li Xiaohong walking home from the noodle shop is 3 km/h', 'The distance from the sports center to the noodle shop is 4 km', 'Li Xiaohong stayed at the sports center for 15 minutes', "The distance from the sports center to Li Xiaohong's home is 2.5 km"] | multi_choice |
func1152 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1152.png | As shown in the figure, points A, B, and C are all on the grid points of the graph paper. If the coordinates of point B are (1, 0) and the coordinates of point C are (1, 1), then the coordinates of point A are ( ). | B. (-1, 2) | ['(1, 2)', '(-1, 2)', '(-1, -2)', '(2, -1)'] | multi_choice |
func1160 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1160.png | As shown in the figure, the radar detector detects six targets A, B, C, D, E, and F. According to the specified method of representing targets, the positions of targets C and F are represented as C(7,120°) and F(6,210°), respectively. Using this method to represent the positions of targets A, B, D, and E, which one is incorrectly represented? ( ) | D | ['(6, 30°)', '(2, 90°)', '(5, 240°)', '(4, 60°)'] | multi_choice |
func1168 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1168.png | As shown in the figure, the function y1 = kx (k ≠ 0) intersects with y2 = 2x + b at point 4. Which of the following statements is correct? ( ) | D | ['k < 0', 'k > b', 'When \\(x > 0\\), \\(y_1 > y_2\\)', 'When \\(x < -\\frac{3}{2}\\), \\(y_1 > y_2\\)'] | multi_choice |
func1171 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1171.png | As shown in the figure, if the coordinates of point A are (1, 3) and the coordinates of point C are (-2, -1), then the coordinates of point B are ( ). | B. (-1, 2) | ['(1, 2)', '(-1, 2)', '(-1, -2)', '(1, -2)'] | multi_choice |
func1173 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1173.png | As shown in the figure, A and B are arbitrary points on the inverse proportion function y = (k/x) (k < 0). Vertical lines are drawn from points A and B to the y-axis, with their feet being C and D respectively. Connect OA and OB. Let the areas of △AOC and △BOD be S1 and S2 respectively. Then ( ) | B | ['S1 > S2', 'S1 = S2', 'S1 < S2', 'Cannot be determined'] | multi_choice |
func1174 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1174.png | Photosynthesis usually refers to the process where green plants (including algae) absorb light energy to synthesize organic compounds from carbon dioxide and water, while releasing oxygen. The entire process is influenced by various factors such as light intensity, carbon dioxide concentration, and temperature. Xiao Ming studied the relationship between the rate of oxygen release (mg/hour) of a green plant during photosynthesis and light intensity L (kilolux) (unit of light intensity). He designed an experimental setup as shown in Figure ① and plotted the relationship between oxygen release rate W (mg/hour) and light intensity L (kilolux) at 15°C and 25°C, as shown in Figure ②. Which of the following statements is correct? ( )
A. When L = 7, the oxygen release rate of the green plant at 25°C is higher than that at 15°C.
B. When L = 8, after 3 hours of photosynthesis at 25°C, the green plant releases 30 mg more oxygen.
C. When L = 10, the light intensity required for photosynthesis of the green plant at 15°C is 10 kilolux.
D. The higher the light intensity, the faster the oxygen release rate of the green plant. | A | ['At 7 hours, the oxygen release rate of green plants at 25°C is higher than that at 15°C.', 'At 8 hours, the oxygen release rate of green plants at 25°C is 30 mg/hour higher than that at 15°C.', 'At 10 hours, the light intensity required for green plants at 15°C is 1 thousand lux higher than that at 25°C.', 'As light intensity increases, the oxygen release rate of green plants decreases.'] | multi_choice |
func1179 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1179.png | As shown in Figure ①, in the rectangle MNPQ, point R starts from point N and moves along the path N→P→Q→M to the endpoint M. Let the distance traveled by point R be x, and the area of △MNR be y. If the graph of y as a function of x is as shown in Figure ②, which of the following statements is incorrect? ( ) | B | ['When y = 6, x = 10', 'When y = 5, x = 2', 'The maximum value of y is 10', 'The perimeter of rectangle MNPO is 18'] | multi_choice |
func1191 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1191.png | The following three problems all involve two variables: ① A water tank contains l m³ of water. When a water inlet is opened, water flows in at a speed of m³/h. After x hours, the water tank contains v m³ of water. ② A telecom company's monthly phone charges are as follows: a base rental fee of 12 yuan per phone per month, plus a call charge of 0.2 yuan/min. If the call time for a month is x minutes, the total cost is y yuan. ③ A piece of wire with a length of 1 is used to form a rectangle, where the area of the rectangle is y, and one side length is x. Among these, the functional relationship between the variables x and y can be represented by the graph shown in the figure ( ). | A | ['① ②', '② ③', '① ③', '① ② ③'] | multi_choice |
func1198 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1198.png | As shown in the figure, the quadratic function y = ax² + bx + c (where a, b, and c are constants, and a ≠ 0) has its graph intersecting the x-axis at points A(-3, 0) and B(1, 0). The following conclusions are provided:
① a < b < 0;
② If the points (-2, y₁) and (0.5, y₂) both lie on the parabola, then y₁ > y₂;
③ 9a - 3b + c = 0;
④ 4a + 2b + c > 0.
How many of the above are correct?
A. 1
B. 2
C. 3
D. 4 | C | ['1', '2', '3', '4'] | multi_choice |
func1199 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1199.png | As shown in the figure, two wooden strips are fixed together at one end with a bolt, allowing them to rotate freely. During the movement, the quantity that remains constant is ( )
A. The measure of ∠BAC
B. The length of AB
C. The length of BC
D. The area of △ABC | B | ['The measure of ∠BAC', 'The length of AB', 'The length of BC', 'The area of △ABC'] | multi_choice |
func1203 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1203.png | Teacher Liu went to a gas station to refuel. As shown in the picture, this is the display screen of the fuel pump he used at a certain moment. Which one of the following is the constant ( )? | B. Unit price | ['Amount', 'Unit Price', 'Quantity', 'Amount and Quantity'] | multi_choice |
func1204 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/1204.png | Henan is China's granary, and the moisture content of grain is an important indicator for evaluating grain quality. Grain moisture detection plays a very important role in the purchase, transportation, and storage of grain. The internal circuit of the resistance-based grain moisture meter is shown in Figure A. When grain is placed on the moisture-sensitive resistor R1, the resistance value of R1 changes, and its resistance varies with the grain moisture content as shown in Figure B. Based on the figures, which of the following statements is incorrect?
A. When the moisture content is 0, the resistance value of R1 is 40Ω.
B. The resistance value of R1 decreases as the grain moisture content increases.
C. The maximum grain moisture content that this device can detect is 12.5%.
D. The relationship between the moisture-sensitive resistor R1 and the grain moisture content is an inverse proportional relationship. | D | ['When the moisture content is 0, the resistance of R1 is 40Ω.', 'The resistance of R1 decreases with the increase of the moisture content of the grain.', 'The maximum moisture content of the grain measured by this device is 12.5%.', 'The moisture-sensitive resistor R1 is inversely proportional to the moisture content of the grain.'] | multi_choice |
func134 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/134.png | As shown in the figure, part of the parabola y = ax^2 + bx + c has its axis of symmetry as the line x = 1. If one intersection point of the parabola and the x-axis is A(-1, 0), then based on the graph, the solution set of the inequality ax^2 + bx + c < 0 is __________. | -1 < x < 3 | NULL | free_form |
func135 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/135.png | As shown in the figure, P is a point on the graph of the inverse proportional function y = k/x in the second quadrant, and the area of rectangle PEOF is 2. What is the value of k? __________ | -2 | NULL | free_form |
func151 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/151.png | As shown in the figure, the line y = ax + b and the line y = kx + m intersect the x-axis at points A(-4, 0) and B(2, 0) respectively. What is the solution set for the inequality system (ax + b > 0, kx + m > 0)? | -4 < x < 2 | NULL | free_form |
func152 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/152.png | As shown in the figure, the line y = kx + b does not pass through the third quadrant. If points M(x₁, y₁) and N(x₂, y₂) lie on this line, and y₁ > y₂, what is the relationship between the sizes of x₁ and x₂? | x₁ < x₂ | NULL | free_form |
func156 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/156.png | In a certain circuit, the voltage of the power supply is constant, and the current I (A) is inversely proportional to the resistance R (Ω). The graph shows the relationship between the current and the resistance R in this circuit. Then, the function expression in terms of R is __________. | I = 6 / R (R > 0) | NULL | free_form |
func164 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/164.png | The volume V (unit: m³) of a certain gas with a mass of m (unit: kg) is inversely proportional to its density ρ (unit: kg/m³) (V = m / ρ). The graph is shown in the figure. What is the value of m? | 8 | NULL | free_form |
func168 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/168.png | As shown in the figure, in the plane rectangular coordinate system, given points A(-1, 0) and B(1, 3), the line segment AB is translated to form line segment CD. If the coordinates of point C, corresponding to point A, are (1, -2), what are the coordinates of point D, corresponding to point B? | (3, 1) | NULL | free_form |
func170 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/170.png | It is known that the voltage of the storage battery is constant. When using the storage battery, the current I (unit: A) and the resistance R (unit: Ω) are inversely proportional according to the relationship I = k/R (k ≠ 0). Its graph is shown as above. What is the value of k? | 36 | NULL | free_form |
func177 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/177.png | As shown in the figure, in a Cartesian coordinate system, point A is on the graph of the inverse proportion function y = k/x (where k is a constant, x > 0). A perpendicular is drawn from point A to the x-axis, and the foot of the perpendicular is B. Connect points O and A. If the area of △OAB is 5, then k = ______. | 10 | NULL | free_form |
func178 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/178.png | On the grid paper shown in the figure, establish an appropriate plane Cartesian coordinate system. If the coordinates of point B are (0,1) and those of point C are (-1,2), then the coordinates of point A are ______________. | (-2, 0) | 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 the x-axis, and lines M A and N A are connected, then S_AMN equals ________. | 4 | 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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
func327 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/327.png | As shown in the figure, place the chessboard in a Cartesian coordinate system. The position of White Chess 2 is (-5, -2), and the position of White Chess 1 is (-4, -5). What are the coordinates of Black Chess 3? __________. | (-2, -3) | NULL | free_form |
func333 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/333.png | In a plane rectangular coordinate system, the graphs of the linear functions y₁ = kx (k is a constant, k ≠ 0) and y₂ = mx + n (m is a constant, m ≠ 0) are shown as in the figure. Then the solution set of the inequality (k − m)x ≥ n with respect to x is ______. | x ≤ −3 | NULL | free_form |
func340 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/340.png | If it is a set of regular patterns composed of equilateral triangles with equal side lengths, the first pattern has 4 triangles, the second pattern has 7 triangles, the third pattern has 10 triangles, and this pattern continues. If the nth pattern contains y triangles, what is the relationship between y and n? | y = 3n + 1 | NULL | free_form |
func345 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/345.png | 8. Straight line l₁: y = k₁x + b₁ and straight line l₂: y = k₂x + b₂ are shown in the graph in the same plane rectangular coordinate system. Then the solution set of the inequality k₁x + b₁ > k₂x + b₂ with respect to x is ______. | x < -1 | NULL | free_form |
func35 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/35.png | As shown in the figure, in the Cartesian coordinate plane, the graphs of the functions y = mx + n and y = kx + b intersect at the point P(-2, 1). Therefore, the solution to the system of equations {y = mx + n, y = kx + b = 0} is ________. | x = -2, y = 1 | NULL | free_form |
func36 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/36.png | As shown in the figure, the parabola y = -x² + bx + c intersects the y-axis at the point (0,5), and the axis of symmetry is the line x = -2. If y ≥ 5, then the range of x is ______. | -4 ≤ x ≤ 0 | NULL | free_form |
func373 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/373.png | As shown in the figure, the inverse proportional function y = k / x (k ≠ 0) passes through point A and point B, then m = ______. | 2 | NULL | free_form |
func374 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/374.png | As shown in the figure, in △ABC, point P moves from point A towards point C. During this movement, let x represent the length of line segment AP, y represent the area of △ABP, and the distance from point B to line AC is 6. What is the relationship between y and x? __________ | y = 3x | NULL | free_form |
func377 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/377.png | As shown in the figure, in the plane Cartesian coordinate system, the line segment OA connecting point A(4, 3) and the origin O forms an angle α with the positive x-axis. What is the value of sinα? | 3/5 | NULL | free_form |
func398 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/398.png | As shown in the figure, the line y=2x intersects the line y=kx+b (k≠±1) at point M(1,2). Then the solution set of the inequality 2x > kx + b is ______. | x > 1 | NULL | free_form |
func42 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/42.png | The graphs of the inverse proportional functions y = k1/x, y = k2/x, y = k3/x are shown in the same coordinate system. What is the relationship of the sizes of k1, k2, and k3? | k1 < k2 < k3 | NULL | free_form |
func43 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/43.png | As shown in the figure, P(12,a) lies on the hyperbolic function y=60/x. PH is perpendicular to the x-axis at point H. Find the value of sin∠POH ________. | 5/13 | NULL | free_form |
func441 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/441.png | As shown in the figure, in the plane rectangular coordinate system, based on this pattern of exploration, point A₁(1, 2), A₂(2, 0), A₃(3, -2), A₄(4, 0)... Based on this pattern, determine the coordinates of point A₂₀₂₄ ______. | (2024, 0) | NULL | free_form |
func45 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/45.png | In ancient times, Emperor Qianlong once passed by Lugou Bridge in autumn and composed a poem: "Half an axis retains the reflection of three autumns, a streak divides the waves brighter than a mirror," and inscribed the phrase "Lugou Morning Moon" on a stele at the bridgehead. The main arch of Lugou Bridge can be approximated as a parabola. If the span OA of the arch over the water surface is about 22 meters and a plane rectangular coordinate system is built as shown in the diagram, the equation of the parabola representing the main bridge arch is y = -13/121(x-11)^2 + k. Then the distance between the highest point P of the main arch and its reflection P' in the water is ___ meters. | 26 | NULL | free_form |
func451 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/451.png | As shown in the figure, the straight line l passes through point P and intersects the graphs of the inverse proportional functions y₁ = k₁ / x (x > 0) and y₂ = k₂ / x (x > 0) at points A and B, respectively. Connecting OA and OB, it is known that the area of △AOB is 6. Then, k₁ - k₂ = _______. | 12 | NULL | free_form |
func452 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/452.png | As shown in the figure, points A and B are respectively on the graphs of the inverse proportional functions y=2k/(x+1) and y=k/x. Vertical lines are drawn from points A and B to the x-axis and y-axis, forming a shaded region with an area of 5. What is the value of k? ______. | 4 | NULL | free_form |
func455 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/455.png | As shown in the figure, a moving point P moves in the direction indicated by the arrows. The first time, it moves from the origin to the point (2,2). The second time, it moves to the point (4,0). The third time, it moves to the point (6,4), and so on, following this pattern. What will be the coordinates of the point after the 2024th move? | (4048, 0) | NULL | free_form |
func461 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/461.png | As shown in the figure, the graph of the inverse proportional function y = k/x (x > 0) passes through point A(2,1). If x > 2, what is the range of values for y________. | 0 < y < 1 | NULL | free_form |
func462 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/462.png | As shown in the figure, the graph of the linear function y = -x + b intersects with y = x + 2 at the point M(2,4). Then the solution set of the linear inequality -x + b > x + 2 with respect to x is ____________. | x < 2 | NULL | free_form |
func469 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/469.png | As shown in the figure, rectangle OABC and square ADEF have their vertices A and D on the positive x-axis, vertex C on the positive y-axis, vertex F on edge AB, and vertices B and E on the graph of the inverse proportional function y = k/(x > 0). If the coordinates of point B are (8, 6), what are the coordinates of point E? | (12, 4) | NULL | free_form |
func472 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/472.png | As shown in the figure, point A is on the graph of the inverse proportional function y = k/x (x > 0). A perpendicular line is drawn from point A to the y-axis, intersecting the y-axis at point B. If point C lies on the x-axis and the area of △ABC is 1, then the value of k is ______. | 2 | NULL | free_form |
func481 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/481.png | As shown in the figure, given that the graphs of the functions y1 = x + b and y2 = ax + 3 intersect at point P, the solution set for the inequality ax + 3 < x + b is ________. | x > 1 | NULL | free_form |
func488 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/488.png | As shown in the figure, the vertex A of a square ABCD with a side length of 4 is located on the positive x-axis. The reciprocal function y=k/x (k≠0) passes through the origin O and the midpoint E of side BC in the first quadrant. What is the value of k? ________. | 16 | NULL | free_form |
func494 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/494.png | As shown in the figure, the vertices A, B, C of the parallelogram ▭ABCD have coordinates (0,2), (-1,-1), and (2,-1), respectively. What are the coordinates of vertex D? ________. | (3,2) | NULL | free_form |
func5 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/5.png | As shown in the figure, the straight line y = ax + c intersects the straight line y = mx + n at point A(-4, 0). What is the solution set of the inequality ax + c > mx + n with respect to x? | x > -4 | NULL | free_form |
func502 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/502.png | As shown in the figure: Given that the coordinates of point A are (-2√3, 2), and the diagonals of rhombus ABCD intersect at the origin O, the coordinates of point C are ________. | (2√3, -2) | NULL | free_form |
func504 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/504.png | As shown in the figure, the straight line y = x + m intersects the straight line y = -1/2x - n at point A. Then the solution set of the inequality x + m ≥ -1/2x - n regarding x is ____________. | x ≥ -4 | NULL | free_form |
func517 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/517.png | As shown in the figure, fishing boat A and port B are 19 nautical miles apart. We use the ordered pair (39° south of west, 19 nautical miles) to describe the position of fishing boat A relative to port B. Then the position of port B relative to fishing boat A can be described as _____. | (39° north of east, 19 nautical miles) | NULL | free_form |
func534 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/534.png | As shown in the figure, in the plane Cartesian coordinate system, the graph of the quadratic function y = ax^2 + bx + c intersects the x-axis at one point (-3, 0), and its axis of symmetry is the line x = -1. Then, the coordinate of the other intersection point of the graph with the x-axis is ________. | (1, 0) | NULL | free_form |
func540 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/540.png | As shown in the figure, in a rectangular coordinate plane, the coordinates of point P are (-4, 3). What is the length of OP? | 5 | NULL | free_form |
func542 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/542.png | As shown in the figure, the line y = -x + b intersects the line y = kx + 6 at point P(2,4). Then the solution set of the inequality kx + 6 < x + b with respect to x is ______. | x > 2 | NULL | free_form |
func558 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/558.png | As shown in the figure, in the Cartesian coordinate plane, the isosceles right triangle OAA1 has its right angle side OA lying on the x-axis, and the coordinates of point A1 are (1,1). Using point A1 as the vertex of the right angle and OA1 as one of the right-angle sides, another isosceles right triangle OA1A2 is constructed. Then, using point A2 as the vertex of the right angle and OA2 as one of the right-angle sides, another isosceles right triangle OA2A3 is constructed, and so on. According to this pattern, what are the coordinates of point A2024 ( )? | D | ['(2^1011, -2^1011)', '(2^1011, 0)', '(2^1012, -2^1012)', '(2^1012, 0)'] | multi_choice |
func575 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/575.png | As shown in the figure, it depicts the flight formation of a bomber squadron. It is known 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, 1)', '(-2, 3)', '(-3, 2)'] | multi_choice |
func584 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/584.png | As shown in Figure 1, this is a parabolic arch bridge in a park. According to Figure 2, a plane rectangular coordinate system is established, and the function y = -1/25x^2 is obtained. At normal water level, the width of the water surface AB is 30 meters. When the water level rises by 7 meters, the width of the water surface CD is ( ). | D. 10√2 meters | ['5 meters', '5√2 meters', '10 meters', '10√2 meters'] | multi_choice |
func595 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/595.png | As shown in the figure, the graph of the linear function y = ax + b and the hyperbolic function y = k/x (k > 0) intersect at points A(1,2) and B(m,-1). Then the solution set of ax + b > k/x is ( ). | C | ['\\(-2 < x < 0\\) or \\(0 < x < 1\\)', '\\(-1 < x < 0\\) or \\(0 < x < 2\\)', '\\(-2 < x < 0\\) or \\(x > 1\\)', '\\(-1 < x < 0\\) or \\(x > 2\\)'] | multi_choice |
func598 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/598.png | As shown in the figure, a linear function y = kx + b intersects y = -2x + 1 at point P(1,3). Which of the following statements is incorrect ( ). | D | ['k > 0', 'b > 0', 'The solution to the equation kx + b = -1 is x = -1', 'The solution set of the inequality kx + b < -2x + 1 is x < 3'] | multi_choice |
func601 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/601.png | As shown in the figure, the graphs of the functions y = kx + b (k ≠ 0) and y = mx + n (m ≠ 0) are displayed. What are the coordinates of the point corresponding to the solution of the system of equations y = kx + b and y = mx + n, with respect to its symmetric point about the y-axis? | B | ['(-2, 3)', '(2, 3)', '(2, -3)', '(-2, -3)'] | multi_choice |
func602 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/602.png | As shown in the figure, the graph of the linear function y = x + m intersects the x-axis at the point (-3, 0). What is the solution to the inequality x + m > 0? | A | ['x > -3', 'x < -3', 'x > 3', 'x < 3'] | multi_choice |
func604 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/604.png | As shown in the figure, in the Cartesian coordinate system, the coordinates of point A are (0,3). △OAB is translated rightward along the x-axis to form △O′A′B′. If the corresponding point A′ lies on the line y=3/4x, then the distance between point B and its corresponding point B′ is ( ). | D | ['4/3', '4√3', '3', '4'] | multi_choice |
func608 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/608.png | As shown in the figure, if the graph of the linear function y = kx + b (k≠0) intersects the x-axis at point (3, 0), then the solution set of the inequality k(x+5) + b > 0 with respect to x is ( ). | B. x > -2 | ['x < -2', 'x > -2', 'x < 8', 'x > 8'] | multi_choice |
func612 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/612.png | Driving under the influence (DUI) is defined as having a blood alcohol content of 200 micrograms or more per milliliter. A research institute experimentally determined the relationship between the blood alcohol concentration y (micrograms/milliliter) and drinking time x (hours) after consuming a certain brand of 38-degree liquor, as shown in the graph (when 4 ≤ x ≤ 10, y and x are inversely proportional). Which of the following statements is incorrect?
A. Within the first 4 hours of drinking, the longer the drinking time, the higher the blood alcohol concentration.
B. When x = 8, the blood alcohol concentration is 320.
C. When x = 6, the blood alcohol concentration is 100.
D. For drinking times between 4 hours and 10 hours, the duration of blood alcohol concentration above the legal limit is less than 1 hour. | D | ['If the driver drinks within 4 hours, the longer the drinking time, the higher the blood alcohol concentration.', 'When x = 8 hours, the blood alcohol concentration is 320 micrograms per liter.', 'When x = 9 hours, the blood alcohol concentration is 1600/9 micrograms per liter.', 'The blood alcohol concentration will remain above 200 micrograms per liter for 7 hours after drinking.'] | multi_choice |
func616 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/616.png | In an exploratory lesson, the teacher posed a question: 'Using the graphs of a quadratic function and a linear function, find the approximate roots of the quadratic equation 2x² = x + 2.' Xiao Hua used a computer to draw the graphs shown below. By observation, it can be seen that the two approximate roots of the equation, x1 and x2, satisfy -1 < x1 < 0 and 1 < x2 < 2. The mathematical idea reflected in Xiao Hua's method is ( ). | C | ['Rationalization', 'Classification discussion', 'Graphical combination', 'From special to general'] | multi_choice |
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