id
stringlengths 4
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| image_url
stringlengths 77
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| query
stringlengths 7
1.32k
| answer
stringlengths 1
148
| choice
stringlengths 4
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| question_type
stringclasses 2
values |
|---|---|---|---|---|---|
func121
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/121.png
|
As shown in the figure, △AOB is in a rectangular coordinate plane, the coordinates of point B are (7,0), ∠AOB=45°, and tan∠ABO=4/3. If the graph of the inverse proportional function y=k/x (k≠0) passes through point A, what is the value of k?
|
16
|
NULL
|
free_form
|
func122
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/122.png
|
In the linear function y = ax + b, Xiao Hang wants to solve for the range of x when y > 0. Therefore, he plotted the graph of y with respect to x. The range of x when y > 0 is ______.
|
x < -1 or x > 0
|
NULL
|
free_form
|
func123
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/123.png
|
As shown in the figure, in the plane Cartesian coordinate system, the coordinates of point A are (2, 3). Taking point O as the center and the length of OA as the radius, an arc is drawn, intersecting the positive y-axis at point B. What are the coordinates of point B? __________
|
(0, √13)
|
NULL
|
free_form
|
func124
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/124.png
|
As shown in the figure, point A is on the graph of the inverse proportion function y = k / x (k ≠ 0, x < 0). A line through point A is drawn perpendicular to the x-axis at point B, and point C lies on the x-axis. If the area of △ABC equals 3, then k = ________.
|
-6
|
NULL
|
free_form
|
func125
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/125.png
|
“During the Tang Dynasty, virtuous citizens emerged, and Changan prospered.” The 'Chang'an Twelve Hours' themed street area in Xi'an New Flower District has become a popular destination for experiencing Tang Dynasty culture. On a weekend morning at 9:00 AM, social media influencer Zhang Bin drives with his family to the 'Chang'an Twelve Hours' themed street area. During the journey, the car stopped for refueling for 12 minutes. The relationship between the distance of Zhang Bin's car from his home (in kilometers) and time (in hours) is shown in the graph below:
① Zhang Bin's home is 120 kilometers away from the 'Chang'an Twelve Hours' themed street area.
② Zhang Bin's family spent 7.5 hours playing at the 'Chang'an Twelve Hours' themed street area.
③ The family returned home at exactly 5:20 PM.
④ The car's speed during refueling was 80 kilometers per hour. Which statement is correct? _______
|
③.
|
NULL
|
free_form
|
func126
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/126.png
|
As shown in the figure, in △AOB, ∠AOB coincides with the x-axis, and ∠AOB = 45°. Point C is located on side A, and BC = 3AC. If the inverse proportion function y = 2 / x (x > 0) passes through both points B and C, then the coordinates of point C are.
|
(12, 3/4)
|
NULL
|
free_form
|
func128
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/128.png
|
As shown in the figure, in the rectangular coordinate system, the coordinates of vertices A and C of quadrilateral ABCO are A(2,0) and C(-1,2), respectively. The graph of the inverse proportion function y=k/x (k≠0) passes through point B. Then the expression of the inverse proportion function is ______.
|
y = 2/x
|
NULL
|
free_form
|
func129
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/129.png
|
It is known that the linear functions y = ax + 2 and y = kx + b have graphs as shown in the figure, and the solution to the system of equations {y = ax + 2, y = 1} is A(2, 1). The coordinates of point B are (0, -1), and P is a moving point on the y-axis. If S_ΔABP = 4, then the coordinates of point P are ______.
|
(0, -5) or (0, 3)
|
NULL
|
free_form
|
func13
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/13.png
|
As shown in the figure, the line y=mx intersects the hyperbola y=k/x at points A and B. Through point A, draw AM perpendicular to the x-axis with its foot at point M, and connect BM. If the area of triangle SABM = 4, what is the value of k? ______
|
-4
|
NULL
|
free_form
|
func130
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/130.png
|
The graph illustrates the functional relationship between the fare (in yuan) of a ride-hailing platform and the distance travelled (in kilometers). Based on the information in the graph, when Xiao Ming uses the ride-hailing platform to travel from his home to the airport for a total fare of 64 yuan, the distance between his home and the airport is ______ km.
|
20
|
NULL
|
free_form
|
func131
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/131.png
|
As shown in the figure, the line y=2x+3 intersects the coordinate axes at points A and B, respectively. Point P lies on the line x=-1, and the area of △ABP is bisected by the y-axis. What are the coordinates of point P? ________.
|
(3/2, -3/2)
|
NULL
|
free_form
|
func132
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/132.png
|
The graph of the linear function y = ax + b is shown in the figure. Simplify the result of |a−b|+|b+1| as ________.
|
a+1
|
NULL
|
free_form
|
func133
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/133.png
|
As shown in the figure, △OAB lies in the first quadrant, with vertex A having coordinates (6, 3) and vertex B having an x-coordinate of 2. It is known that the hyperbolic function y = k/(x + l) passes through point B and intersects OA at point C. Connecting BC, if OC = 2AC, then the area of △OBC is ______.
|
6
|
NULL
|
free_form
|
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
|
func136
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/136.png
|
A school's eighth-grade students traveled to a labor base 2 kilometers away from the school to participate in tree planting activities. Some walked, while others rode bicycles. They traveled along the same route. As shown in the graph, l1 and l2 represent the distances (in kilometers) walked and cycled to the destination as functions of time x (in minutes). How many minutes does it take for the cyclists to catch up with the walkers?
|
15/2
|
NULL
|
free_form
|
func137
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/137.png
|
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 at point B, and the area of triangle ΔABC is 2. What is the value of k?
|
-4
|
NULL
|
free_form
|
func138
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/138.png
|
As shown in the figure, the line l1: y=2x+4 and the line l2: y=kx+b intersect at point P(1, m). Then the solution of the system of equations {y−2x=4, y−kx=b} is ________.
|
{x=1, y=6}
|
NULL
|
free_form
|
func139
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/139.png
|
As shown in the figure, a straight line passing through the origin intersects the hyperbolic function y = k/x at points A and B. Draw a perpendicular from point A to the x-axis at point C, and connect BC. If the area of △ABC is 2, the value of k is ______.
|
2
|
NULL
|
free_form
|
func14
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/14.png
|
3. Alongside a road are three villages, A, B, and C, arranged in sequence. Two people, Jia and Yi, start cycling simultaneously from Village A and Village B respectively, heading towards Village C. The functional relationship between the distance x (in km) between Jia and Yi and the cycling time t (in hours) is shown in the graph. Which of the following statements are correct: ① At the start, Yi is 4 km ahead of Jia; ② After t=1.25 hours, they meet; ③ Jia cycles 5π/6 km more per hour than Yi; ④ After meeting, Yi cycles for another 15 minutes or they are 2 km apart again. Which of these statements are correct? (Fill in the serial numbers).
|
②③④
|
NULL
|
free_form
|
func140
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/140.png
|
As shown in the figure, in a plane Cartesian coordinate system, the vertex A of rectangle OABC and the vertices of square ADEF are on the graph of the inverse proportional function y = -k/x (k ≠ 0, x < 0). Points A and D are on the x-axis, point C is on the y-axis, and the coordinates of point B are (-2, 4). What are the coordinates of point E?
|
(-4, 2)
|
NULL
|
free_form
|
func141
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/141.png
|
As shown in the figure, if the quadratic function y = ax² + bx + c (a ≠ 0) has its axis of symmetry at the line x = 1, intersects the x-axis at point C, and B(-1, 0) lies on the graph, which of the following conclusions are correct? ① abc > 0; ② the maximum value of the quadratic function is a + b + c; ③ a - b + c = 0; ④ ac < 0; ⑤ when y = 0, -1 ≤ x < 3.
|
②⑤
|
NULL
|
free_form
|
func142
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/142.png
|
With the continuous development of China's economy and urbanization, the functionality of urban roads has been continuously improved. The complex urban road network requires an increasing number of depressed interchange bridges. Depressed interchange bridges set the intersecting main road at the ground level or elevated, while the main road is set at the underground level or underground roadway. Depressed interchange bridges are characterized by dangerous spans and lower costs compared to tunnel interchanges. This makes the bridge deck of the depressed interchange more complex in terrain. How to establish a rectangular coordinate system with the lowest point of the bridge deck as the origin and the horizontal line passing through the origin as the x-axis? It is known that the span of the main bridge deck is AB=100m, and the distance from the lowest point O of the main bridge deck to AB is 10m. Since the main road bridge deck of the depressed interchange is lower than the surrounding ground and has a steep longitudinal slope, waterlogging tends to occur on the deck. During a torrential rain, there is water accumulation on the bridge deck with a depth of 0.3m. If a common sedan driver can safely drive through this depressed interchange, the length of the waterlogged span CD must not exceed ______ meters.
|
10√3
|
NULL
|
free_form
|
func143
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/143.png
|
As shown in the figure, in the Cartesian coordinate plane, it is known that the graphs of the functions y = kx + b (k ≠ 0) and y = m/x (m ≠ 0) intersect at points A(-2, 3) and B(3, -2). Then the solution set of the inequality kx + b > m/x is ______.
|
x < -2 or 0 < x < 3
|
NULL
|
free_form
|
func144
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/144.png
|
As shown in the figure, given square ABCD with vertices A(1,3), B(1,1), C(3,1), and D(3,3), it is stipulated that 'the square ABCD is first reflected with respect to the x-axis, then translated 1 unit to the left' as a single transformation. After undergoing such transformation 2015 times consecutively, the coordinates of the intersection point M of the diagonals of the square become ____________.
|
(-2013, -2)
|
NULL
|
free_form
|
func145
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/145.png
|
Xiao Lin, while conducting an experiment to explore the relationship between electric power and resistance, recorded the data shown in the table below. Please analyze the data in the table and summarize the relationship between electric power P and resistance R as: ______.
|
P = 36 / R
|
NULL
|
free_form
|
func146
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/146.png
|
As shown in the figure, point M is on the graph of the inverse proportional function y = -k/x (x < 0). A perpendicular line MN is drawn from point M to the x-axis at point N, and point P lies on the y-axis. If the area of △MNP is 3, then k = _______.
|
-6
|
NULL
|
free_form
|
func148
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/148.png
|
As shown in the figure, A and B are points on the inverse proportional 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 D is the midpoint of AC and the area of △AOD is 2, with the coordinates of point B being (m, 3), then the value of m is ______.
|
8 / 3
|
NULL
|
free_form
|
func149
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/149.png
|
As shown in the figure, point A is a moving point on the graph of the inverse proportional function y1 = k/x (k≠0, x>0). Through point A, lines parallel to the x-axis and y-axis are drawn, intersecting the graph of the inverse proportional function y2 = 4/x (x>0) at points B and C. Connecting OB and OC, if the area of quadrilateral OBAC is 6, then k=________.
|
10
|
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
|
func153
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/153.png
|
As shown in the figure, in the rectangular coordinate system Ox, point P(1,0) is the center of circle P. The circle intersects the x-axis at points A(-1,0) and B, and intersects the y-axis at points C and D. Point M is on arc CBD (not coinciding with C or D). Then, tan∠CMD = ______________.
|
√3
|
NULL
|
free_form
|
func154
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/154.png
|
As shown in the figure, the coordinates of point A are (0,6). If △OAB is translated horizontally along the x-axis to become △O′A′B′, and the corresponding point A′ of point A lies on the line y=2x-1, then the distance between point B and its corresponding point is ______.
|
7/2
|
NULL
|
free_form
|
func155
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/155.png
|
As shown in Figure 1, there is a parabolic arch bridge in the Lotus Hill Scenic Area. A plane rectangular coordinate system is established as shown in Figure 2, and the equation of the parabola is y = -1/36 x². When the water level is normal, the width of the water surface AB is 36m. When the water level rises by 5m, the width of the water surface CD is ________.
|
24m
|
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
|
func158
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/158.png
|
The car radar senses and identifies the surrounding environment of the vehicle by emitting high-frequency electromagnetic waves, receiving the reflected signals from the target, and performing post-processing. According to the knowledge of physics, when the speed of the electromagnetic wave is constant, the wavelength λ (mm) is an inverse proportional function of the frequency f (GHz), and its function graph is shown in the figure. When λ = 8 mm, what is the frequency of this electromagnetic wave in GHz?
|
30
|
NULL
|
free_form
|
func159
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/159.png
|
In the Cartesian coordinate system xOy, the graphs of the linear functions y = kx and y = mx + n are shown as in the diagram. Then the solution set of the linear inequality (k−m)x < n is ______.
|
x < 1
|
NULL
|
free_form
|
func160
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/160.png
|
As shown in the figure, in the plane Cartesian coordinate system, the intersection point of the diagonals of quadrilateral ABCD is the origin O, point B is in the first quadrant, and both point B(m, 2m) and point D are on the graph of the inverse proportional function y = 2/x. Then the coordinates of point D are ________.
|
(-1, -2)
|
NULL
|
free_form
|
func161
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/161.png
|
As shown in the figure, the graphs of the functions y = -3x and y = kx + b intersect at point A(-2, m). Then the solution set of the inequality -3x > kx + b with respect to x is __________.
|
x < -2
|
NULL
|
free_form
|
func162
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/162.png
|
As shown in the figure, this is a formation of a bomber squadron. If the coordinates of two bombers are C(3, -1) and A(-1, 1), then the coordinates of bomber B are _____.
|
(-1, -3)
|
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
|
func165
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/165.png
|
As shown in the figure, points A and B lie on the hyperbolic functions y = k/x (k ≠ 0) and y = -k/x (k ≠ 0) in the first quadrant respectively.
(1) If points P(x₁, y₁) and Q(x₂, y₂) lie on the hyperbolic function y = k/x, and x₁y₂ - x₂y₁ = 2, then y₁/x₁ - y₂/x₂ = ________;
(2) Perpendiculars are constructed through points A and B to the y-axis, and the area enclosed by these perpendiculars and the coordinate axes is 12, then k = ________.
|
18
|
NULL
|
free_form
|
func166
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/166.png
|
As shown in the figure, each section of a chain is 3.6 cm long, and the diameter of the overlapping circle where two chain sections connect is 1.2 cm. Based on this connection method, the total length of x chain sections is y cm. The relationship between y and x is ______.
|
y = 2.4x + 1.2
|
NULL
|
free_form
|
func167
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/167.png
|
As shown in the figure, points A and B are on the hyperbola y = k/x. Perpendiculars from the y-axis intersect at points D and C, while perpendiculars from the x-axis intersect at points F, with BE intersecting at point G. The area of quadrilateral OEGD is 2, and OE/OC = 2/5. Then k = ______.
|
5
|
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
|
func169
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/169.png
|
As shown in the figure, in a rectangular coordinate system, points A and B are on the graph of the inverse proportional function y = k/x. AC ⊥ x-axis at point C, BD ⊥ y-axis at point D, AC = 2√3, BD = 4, and OB = 8. What is the value of k?
|
12√7
|
NULL
|
free_form
|
func17
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/17.png
|
As shown in the figure, the graph of the linear function y = ax intersects the line y = bx + c at the point (1, 2). Then, the solution set of the inequality ax ≤ bx + c is ______.
|
x ≤ 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
|
func173
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/173.png
|
A courier truck and a cargo truck of a logistics company set off from location A at the same time, traveling at their respective constant speeds. After the courier truck arrives at location B, it unloads and reloads goods, spending a total of 45 minutes, then immediately returns along the same route at another constant speed until it meets the cargo truck. Given that the speed of the cargo truck is 60 km/h, the graph below shows the relationship between the distance y (in kilometers) between the two vehicles and the travel time x (in hours) for the cargo truck. Based on the graph, the following conclusions are presented: ① The speed of the courier truck from location A to location B is 100 km/h; ② The distance between locations A and B is 120 km; ③ The coordinates of point A on the graph are (15/4, 75); ④ The speed of the courier truck when returning from location B is 90 km/h. Which of the above conclusions are correct? (Provide your answer by listing the serial numbers)
|
③④
|
NULL
|
free_form
|
func174
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/174.png
|
As shown in the figure, given points A(2,3) and B(3,4), one branch of the hyperbolic function y = k / x intersects the line segment AB. Write down an integer value of k that satisfies the condition: ________.
|
8
|
NULL
|
free_form
|
func175
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/175.png
|
As shown in the figure, given the straight line y = -1/2x + b and the straight line y = -1/2x + b' intersect at point M(a, 2), the solution set of the inequality y = -1/2x + b ＞ y = -1/2x + b' is ______.
|
x < 2
|
NULL
|
free_form
|
func176
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/176.png
|
Teacher Feng's home, the school where he works, and a restaurant are on the same straight line in the north-south direction. One day, after leaving work, Teacher Feng walked north to the restaurant, had a meal for 1 hour, and then rode a bicycle back to his home. During this process, the function graph showing the distance (km) between Teacher Feng and the school as a function of the time elapsed (minutes) after work is shown in the figure. Which of the following statements are correct: ① Teacher Feng's walking speed is 0.06 km/min; ② Teacher Feng's home is 1.2 km due north of the school; ③ The average speed of riding from the restaurant to home is 0.13 km/min. The correct statement numbers are ________.
|
①②③
|
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
|
func179
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/179.png
|
As shown in the figure, the straight line y = -x + 2 intersects with y = ax + b (a ≠ 0 and a, b are constants) at the point (3, -1). Therefore, the solution set of the inequality -x + 2 > ax + b is ______.
|
x < 3
|
NULL
|
free_form
|
func18
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/18.png
|
7. The Quanshui Bridge (as shown in picture ①) was first built during the late Tang Dynasty. It has a delicate design and is the oldest bridge remaining in Shandong Province. The middle arch of the bridge roughly resembles a parabola. A Cartesian coordinate system is established with the highest point of the middle arch as the origin (as shown in picture ②). It is known that the distance between points A and B is 6 meters, and their distance to the x-axis is 3 meters. When the water surface EF is 4 meters above the x-axis, the width of the water surface EF is ______ meters.
|
4√3
|
NULL
|
free_form
|
func180
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/180.png
|
As shown in the figure, in the plane Cartesian coordinate system, there are several integer points arranged in order as indicated by the '→' direction in the figure, such as (1,0), (2,0), (2,1), (3,2), (3,1), (3,0). If (1,0) is the first point, then the coordinates of the 64th point are ________.
|
(11,2)
|
NULL
|
free_form
|
func181
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/181.png
|
As shown in the figure, in the rectangular coordinate plane, the rhombus OABC has its diagonal OB lying on the x-axis, and vertex A is on the graph of the reciprocal function y = k/x (k≠0, x>0). If the area of the rhombus OABC is 8√3, what is the value of k? ______
|
4√3
|
NULL
|
free_form
|
func182
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/182.png
|
As shown in the figure, it is known that the coordinates of point O are (1,3). The sequence of letters of an English word corresponds to the coordinates on the graph, which are (3,1), (1,2), (2,2), (7,2), and (1,1). Please write this English word or its Chinese translation as ______.
|
CHINA (or 中国)
|
NULL
|
free_form
|
func183
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/183.png
|
7. As shown in the figure, in a rectangular coordinate system, points A and B are both located on the graph of the inverse proportional function y = 6 / x. Line segment AB passes through the origin O, and AC ⊥ y-axis at point C. Then the area of △ABC is ______.
|
6
|
NULL
|
free_form
|
func184
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/184.png
|
As shown in the figure, point A is a point on the graph of an inverse proportional function. A perpendicular is drawn from point A to the x-axis, meeting it at point B, and point C is a point on the y-axis. Lines AC and BC are connected. If the area of △ABC is 2, then the expression for the inverse proportional function is ________.
|
y = -4/x
|
NULL
|
free_form
|
func185
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/185.png
|
As shown in the figure, in the plane Cartesian coordinate system, point A is on the negative half-axis of the x-axis, point B is in the second quadrant, and the graph of the inverse proportional function y = k / x (x < 0) passes through the vertex B of △OAB and the midpoint C of side AB. If k = -4, then the area of △OAB is equal to _______.
|
6
|
NULL
|
free_form
|
func186
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/186.png
|
As shown in the figure, point O is the origin of the plane Cartesian coordinate system. The vertex C of the parallelogram ABCO lies on the graph of the reciprocal function y = k / x. If point A(5,0) and point B(4,2), then the value of k is ______.
|
-2
|
NULL
|
free_form
|
func187
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/187.png
|
A school is planning to promote labor courses by constructing a vegetable base on campus. The base is planned to be adjacent to a wall on one side, with a total area of 28㎡. It is enclosed by a fence and divided into four equal rectangular vegetable plots, each with one side length x (in meters) and the other side length y (in meters) (as shown in the diagram). Based on the problem setup, derive the functional relationship of y with respect to x __________________. (There is no need to specify the domain of the variable).
|
y = 7/x
|
NULL
|
free_form
|
func189
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/189.png
|
Xiaoming uses the password table shown in the figure to play a game of guessing words by sound. For example, 'Dong - Dong' represents (1,1), which is O, and 'Dong - Dong Dong' represents (1,2), which is W. When hearing 'Dong - Dong, Dong Dong Dong - Dong, Dong Dong Dong Dong - Dong,' the word represented is ______.
|
CAT
|
NULL
|
free_form
|
func19
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/19.png
|
As shown in the figure, the graph of the linear function y = 2x + 1 intersects with the graph of y = kx + b at point 4. Then the solution of the system of equations (2x - y = -1, kx - y = -b) is ______.
|
x = 1, y = 3
|
NULL
|
free_form
|
func190
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/190.png
|
As shown in the figure, point B lies on the graph of the inverse proportion function y=4/x (x>0), point C lies on the graph of the inverse proportion function y=6/x (x>0), and BC∥y-axis. AB⊥BC, with B as the foot of the perpendicular, intersects the x-axis at point A. Then, the area of △ABC is _______.
|
5
|
NULL
|
free_form
|
func192
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/192.png
|
As shown in the graph, it represents the relationship between taxi fare and travel distance in a certain city, which is composed of line segments AB, BC, and ray CD. If Xiaoming pays 14 yuan for a 5km taxi ride, how much should Mr. Zhang pay if his taxi ride is 11km? ______ yuan.
|
27
|
NULL
|
free_form
|
func193
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/193.png
|
As shown in the figure, if the quadrilateral ABCD is a parallelogram, then the coordinates of point D are __________.
|
(-1, -4)
|
NULL
|
free_form
|
func194
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/194.png
|
The graphs of the linear functions y₁ = mx + n and y₂ = kx + a are shown as in the diagram. The solution set of mx - kx > a - n is ________.
|
x < 2
|
NULL
|
free_form
|
func195
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/195.png
|
As shown in the figure, point A is on the inverse proportional function y=1/x (x<0). A perpendicular line is drawn from point A to the x-axis, intersecting the x-axis at point B, and intersecting another inverse proportional function y=1/x (x<0) at point C. Points P and O are two moving points on the y-axis. Connecting PAB, PBO, and OBC. If k1=-k2=1, then the value of \frac{S_{PAB}}{S_{PBO}} is ______.
|
-8
|
NULL
|
free_form
|
func196
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/196.png
|
As shown in the figure, given the linear function y = mx - 1 (m ≠ 0) and y = -2x - n intersecting at point P(1, 2), the solution to the system of linear equations { mx - y = 1, 2x + y = n } is ________.
|
x = 1, y = 2
|
NULL
|
free_form
|
func197
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/197.png
|
As shown in the figure, given point A(1, 3) and point B(3, 3), find a possible value for k in the directly proportional function y = kx (k ≠ 0). (Provide one possible value only)
|
2 (the answer is not unique)
|
NULL
|
free_form
|
func198
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/198.png
|
As shown in the figure, the graphs of 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
|
func199
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/199.png
|
As shown in the figure, points A and B are on the graph of the inverse proportional function y=k/x. Given that k=6 and the shaded area S=2, what is the value of the unshaded area S1+S2? ______
|
8
|
NULL
|
free_form
|
func20
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/20.png
|
As shown in the figure, in the plane rectangular coordinate system, the coordinates of point A are (0, 2), and point B (2, 0) is a point in the first quadrant. If ∠BAC = 90°, the relationship between y and x is ______.
|
y = x + 2
|
NULL
|
free_form
|
func201
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/201.png
|
As shown in the figure, placing the 'QQ' smiling face on the Cartesian coordinate system, it is known that the coordinates of the left eye A are (-2, 3) and the coordinates of the right eye B are (0, 3). After shifting the 'QQ' smiling face 3 units to the right, the coordinates of the mouth C are ________.
|
(2, 1)
|
NULL
|
free_form
|
func202
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/202.png
|
As shown in the diagram, in the rectangular coordinate system, O is the origin, □ABOD is a parallelogram where vertex B lies on the graph of the inverse proportional function y = k/x (x > 0), vertex A lies on the graph of y = k/x (x < 0), and vertex D is on the negative x-axis. If the area of □ABOD is 6, then the value of k is ______.
|
4
|
NULL
|
free_form
|
func203
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/203.png
|
As shown in the figure, △ABC is an equilateral triangle with AB=4 and AB⊥x-axis at point B. The hyperbolic function y=k/x (k≠0) passes through points A and C. Find the value of k.
|
-8√3
|
NULL
|
free_form
|
func204
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/204.png
|
Given two squares ① and ② are placed in the same coordinate system as shown in the figure. They each have a vertex A and B, respectively, located on the graph of the inverse proportional function y=4/x (x>0). The area of square ① is 4, so the side length of square ② is _________________.
|
1+sqrt(5)
|
NULL
|
free_form
|
func205
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/205.png
|
As shown in the figure, point A is on the hyperbola y=1/x, point B is on the hyperbola y=3/(2x), and AB is perpendicular to the y-axis. What is the area of △ABO?
|
1
|
NULL
|
free_form
|
func206
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/206.png
|
5. In the Cartesian coordinate system, the graph of the linear function y = kx + b (k, b are constants, k ≠ 0) is shown in the figure. Then the solution set of the inequality kx + b > 0 with respect to x is ________, and the solution set of the inequality kx + b < n with respect to x is ________.
|
x > -1, x < -3
|
NULL
|
free_form
|
func207
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/207.png
|
As shown in the flowchart, if the output value y is 1, then the input value x is ________.
|
− or 1
|
NULL
|
free_form
|
func209
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/209.png
|
The graph below reflects the following process: Xiaolan runs from home to the sports park, exercises there for a while, then walks to the stationery store to buy a notebook, and finally strolls back home. In the graph, time t (minutes) is plotted, and s represents the distance (kilometers) Xiaolan is from home. How much time in total did Xiaolan spend exercising in the sports park and buying the notebook in the stationery store? ________ minutes.
|
50
|
NULL
|
free_form
|
func21
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/21.png
|
As shown in the figure, the line y=2x-1 intersects the line y=kx+b (k≠0) at point P(2, 3). Based on the graph, the solution set of the inequality 2x-1 > kx+b with respect to x is ________.
|
x>2
|
NULL
|
free_form
|
func210
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/210.png
|
As shown in the figure, the line y = 1/2x + 1 intersects the x-axis at point A and the y-axis at point B. △AOC and △BOC are homothetic figures with point A as the center of similarity, and the similarity ratio is 1:2. The coordinates of the corresponding point B' of point B are ______.
|
(2,2) or (-6,-2)
|
NULL
|
free_form
|
func211
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/211.png
|
The graph of the linear function y = kx + b (k ≠ 0) is shown in the figure. When y > 0, the range of x is ______.
|
x < 3
|
NULL
|
free_form
|
func212
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/212.png
|
10. As shown in the figure, in the Cartesian coordinate system, OA1B1C1 is a square with a side length of 2, and two sides lie on the coordinate axes. Using its diagonal OB1 as a side, another square OB1B2C2 is constructed. Similarly, using OB2, the diagonal of square OB1B2C2, as a side, another square OB2B3C3 is constructed. This process continues. What are the coordinates of vertex B2024 of square OB2023B2024C2024?
|
(2^1012, 0)
|
NULL
|
free_form
|
func213
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/213.png
|
As shown in the diagram, in the rectangular coordinate plane xOy, quadrilateral ABCD is a parallelogram, AB = 10, ∠DAB = 45°, point D is on the y-axis, and OD = 4. Then the coordinates of point B are __________.
|
(6, 0)
|
NULL
|
free_form
|
func214
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/214.png
|
As shown in the figure, given that △ABC is an isosceles right triangle, OA=4, OB=2, and the hyperbola y=-x passes through point C, k=______.
|
9
|
NULL
|
free_form
|
func215
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/215.png
|
As shown in the figure, the line y = kx (k ≠ 0) intersects y = 2/3 x + 4 at point A in the second quadrant. The line y = 2/3 x + 4 intersects the x-axis and y-axis at points B and C, respectively. If S_ABO : S_NACO = 12, then the solution of the equation is ________.
|
x = -4, y = 4/3
|
NULL
|
free_form
|
func216
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/216.png
|
As shown in the figure, P is a point in the first quadrant on the graph of the linear function y = -2x + 4. If the hyperbolic function y = k/x (k ≠ 0) passes through point P, then the range of k is ______.
|
0 < k ≤ 2
|
NULL
|
free_form
|
func217
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/217.png
|
In parallelogram ABCD, point P starts from point B and moves clockwise along BC and CD at a uniform speed towards endpoint D. Let the distance traveled by point P be x, and the area enclosed by line segments AP, AD, and the edges of the parallelogram be y. The graph roughly shows the functional relationship between y and x. What is the height of side AD?
|
4
|
NULL
|
free_form
|
func218
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/218.png
|
Xiao Hua designs a circuit scheme to measure air humidity for the school's vegetable greenhouse at the labor practice base. It is known that in this scheme, the voltage is constant, and the current (unit: A) is inversely proportional to the resistance R (unit: Ω). Its graph is as shown. When the resistance is 12Ω, the current is ________.
|
2A
|
NULL
|
free_form
|
func219
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/219.png
|
As shown in the figure, in the plane Cartesian coordinate system, the functions y = 1/x (x > 0) and y = x - 1 intersect at point P(a, b). What is the value of the algebraic expression 1/a - 1/b?
|
-1
|
NULL
|
free_form
|
func22
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/22.png
|
As shown in the figure, the graph of the direct proportion function y1 = kx and the inverse proportion function y2 = k/x intersect at points A(2,3) and B. If y1 > y2, then the range of x is ________________.
|
x > 2 or −2 < x < 0
|
NULL
|
free_form
|
func221
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/221.png
|
As shown in the figure, point A is a point on the graph of the inverse proportional function y = k/x (x < 0). A perpendicular AB is drawn from point A to the x-axis, with B as the foot of the perpendicular. Point C is a point on the y-axis, and lines AC and BC are connected. If the area of △ABC is 4, then the value of k is ________.
|
-8
|
NULL
|
free_form
|
func222
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/222.png
|
As shown in the figure, □ABCD is in a rectangular coordinate system. A(-2,0), B(4,0), C(3,5). What are the coordinates of point D?
|
(-3,5)
|
NULL
|
free_form
|
func223
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/223.png
|
As shown in the figure, A and B are points on the graph of the inverse proportion function y=8/x (x>0). The x-coordinates of points A and B are 1 and 4, respectively. Point C is a point on the negative half of the x-axis and its x-coordinate is one of the roots of the equation x² - x - 6 = 0. What is the area of △ABC?
|
21
|
NULL
|
free_form
|
func224
|
/home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/224.png
|
As shown in the figure, A and B are points on the hyperbola y=12/x. Through point A, draw AC⊥y-axis with foot C. AC intersects OB at point D. If D is the midpoint of OB, then the area of △ABD is ______.
|
9/2
|
NULL
|
free_form
|
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