id stringlengths 4 8 | image_url stringlengths 77 81 | query stringlengths 7 1.32k | answer stringlengths 1 148 | choice stringlengths 4 597 | question_type stringclasses 2 values |
|---|---|---|---|---|---|
func713 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/713.png | As shown in the figure, point A lies on the graph of the inverse proportional function y = k/x (k < 0, x > 0). Point B is the foot of the perpendicular from A to the x-axis. Point C lies on the positive semi-axis of the y-axis, and line segment BC is connected. Line AD is parallel to BC and intersects the y-axis at point D. If the area of quadrilateral ABCD is 0.5, what is the value of k? | C. -0.5 | ['1', '0.5', '-0.5', '-1'] | multi_choice |
func715 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/715.png | The graph of the linear function y = kx + b is shown in the diagram. What are the values of k and b, respectively? ( ) | B | ['k = 1, b = -2', 'k = -2, b = -4', 'k = 1/2, b = -2', 'k = -2, b = 4'] | multi_choice |
func716 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/716.png | As shown in the figure, identical rectangular paper sheets are arranged in a specific pattern in the Cartesian coordinate system. Given that B(2,4), the coordinates of point A are ( ). | B (5,5) | ['(4,5)', '(5,5)', '(5,6)', '(6,6)'] | multi_choice |
func718 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/718.png | The hyperbola L1: y=3/x (x>0) and the hyperbola L2: y=1/x (x>0) are shown in the figure. Let point P be on L1, PC is perpendicular to the x-axis at point C and intersects L2 at point A, PD is perpendicular to the y-axis at point D and intersects L2 at point B. What is the area of △AOB? ( ) | A | ['4/3', '5/3', '2', '3'] | multi_choice |
func719 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/719.png | A ship usually sails from point A to point B, stays at point B for a period of time, and then returns from point B to point A. The horizontal axis represents the sailing time (h), and the vertical axis represents the distance of the ship from point A (km). Which of the following statements is incorrect?
A. The average speed of the ship from point A to point B is 40 km/h
B. The ship stayed at point B for 3 hours
C. The average speed of the ship on the return journey from point B to point A is greater than its speed on the outward journey
D. The distance between points A and B is 300 km | C | ['The average speed of the ship from point A to point B is 40 km/h', 'The ship stayed at point B for 7.5 hours', 'The average speed of the ship from point B to point A is greater than the speed when going to point B', 'The distance between point A and point B is 300 km'] | multi_choice |
func72 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/72.png | As shown in the figure, point A is on the graph of the function y = k/x. From point A, draw AF perpendicular to the y-axis, with F as the foot of the perpendicular. The area of rectangle AEOF is 6. Then k = ________. | -6 | NULL | free_form |
func720 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/720.png | As shown in the figure, the line y = -x + b intersects the line y = 2x at point A with an x-coordinate of -1. What is the solution set for the inequality -y + b > 2x? | B | ['x < -2', 'x < -1', '-2 < x < -1', '-1 < x < 2'] | multi_choice |
func722 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/722.png | The atmosphere around the Earth blocks ultraviolet rays and cosmic rays from harming Earth's life while generating a certain atmospheric pressure. The atmospheric pressure varies with altitude. Observe the graph, which of the following statements is correct ( ). | D | ['The higher the altitude, the higher the atmospheric pressure.', 'When the altitude is 7 kilometers, the atmospheric pressure is about 60 kilopascals.', 'The curve in the graph is an image of an inverse proportional function.', 'The graph shows the relationship between atmospheric pressure and altitude.'] | multi_choice |
func724 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/724.png | As shown in the figure, the graph of the inverse proportional function y = k / x (k ≠ 0, x ≠ 0) passes through the midpoint D of the diagonal AC of rectangle OABC. If the area of rectangle OABC is 16, what is the value of k? | A | ['4', '-4', '-8', '8'] | multi_choice |
func725 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/725.png | As shown in the figure, in a coordinate plane, point A(2,3), point B(4,1). The following statements by two students are correct ( ). Linlin: When the coordinates of point C are (2,1), △ABC is a right triangle. Zhuangzhuang: When the coordinates of point C are (0,1), △ABC is a right triangle. | C. Both are correct | ['Only Linlin is correct', 'Only Zhuangzhuang is correct', 'Both are correct', 'Both are incorrect'] | multi_choice |
func726 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/726.png | As shown in the figure, the parabola y = ax² + bx + c intersects the x-axis at points A(-2, 0) and B(6, 0), and intersects the y-axis at point C. The following conclusions are given: ① b² - 4ac > 0; ② abc > 0; ③ When y > 0, -2 < x < 6; ④ a + b + c < 0. The number of correct statements is ( ). | B | ['4', '3', '2', '1'] | multi_choice |
func727 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/727.png | As shown in the figure, the relationship between the resistance (R(Ω)) and temperature (T(℃)) of two materials is displayed. Which of the following statements is incorrect? ( ) | B | ['When T = a, the resistances of the two materials are equal.', 'The resistances of both materials decrease with increasing temperature.', 'When the temperature is lower than a °C, the resistance of the semiconductor is greater than that of the thermistor.', 'When the resistance of the thermistor exceeds b, the temperature is higher than c °C.'] | multi_choice |
func728 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/728.png | The graphs of the linear functions v₁ = kx + b and v₂ = x + a are shown in the diagram. Based on the graphs, the following conclusions are drawn: ① When x < 3, v₁ = v₂; ② When x < 3, v₂ > 0; ③ When x > 3, v₁ < v₂. The number of correct conclusions is ( ). | C | ['0', '1', '2', '3'] | multi_choice |
func729 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/729.png | As shown in the figure, use direction and distance to describe the position of the library relative to Xiaoyi's home. Which of the following options is correct ( ). | D. North 35° East, 3km | ['North-east 55°, 3km', 'North-east 45°, 3km', 'North-west 35°, 3km', 'North-east 35°, 3km'] | multi_choice |
func73 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/73.png | A courier company works with two warehouses during the time period 9:30 AM to 10:30 AM. During this period, warehouse A is used for collecting parcels, and warehouse B is used for delivering parcels. The number of parcels V (units) in warehouses A and B is a function of time x (minutes), as shown in the graph. Starting from 9:30 AM, after how many minutes will the number of parcels in the two warehouses be the same? | 20 | NULL | free_form |
func730 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/730.png | As shown in the figure, the ordered pair of real numbers corresponding to W is (2,4). There is an English word with letters corresponding sequentially to the ordered pairs of real numbers in the figure: (1,2), (1,3), (2,3), (5,1). What is this English word? | C | ['BERO', 'HOLD', 'HOPE', 'HERO'] | multi_choice |
func731 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/731.png | As shown in the figure, given point A(-1,0) and point B(2,3), if the parabola y=ax^2-x+2 (where a is a constant and a≠0) has two distinct intersection points with line segment AB, then the range of values for a is ( ). | B. -3/4 ≤ a < 1 | ['a < -1 or 2 < a ≤ 3', 'a ≤ -3/4 or 3/4 ≤ a < 1', '-3/4 < a ≤ 3/4', '3/4 < a < 1'] | multi_choice |
func732 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/732.png | As shown in the figure, in the same plane Cartesian coordinate system, the graphs of the linear functions y=k₁x+b₁ and y=k₂x+b₂ are the straight lines l₁ and l₂ respectively. Which of the following conclusions is incorrect? | B | ['\\(k_1 \\cdot k_2 < 0\\)', '\\(k_1 - k_2 > 0\\)', '\\(b_1 + b_2 > 0\\)', '\\(b_1 \\cdot b_2 > 0\\)'] | multi_choice |
func733 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/733.png | Given a linear function y = kx + b (k ≠ 0) with its graph shown in the diagram, the graph of y = bx - k will definitely not pass through ( ). | A | ['First quadrant', 'Second quadrant', 'Third quadrant', 'Fourth quadrant'] | multi_choice |
func734 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/734.png | As shown in the figure, in the Cartesian coordinate system, A(1,1), B(−1,1), C(−1,−2), D(1,−2), a non-elastic fine thread with a length of 2024 units (ignoring the thread's thickness) is fixed at point A, and it wraps around the edges of the quadrilateral ABCD following the sequence A→B→C→D→A… repetitively. What are the coordinates of the other end of the thread? | A | ['(−1,−1)', '(−1,0)', '(−1,−2)', '(0,1)'] | multi_choice |
func735 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/735.png | As shown in the figure, the graph of the inverse proportional function y=k/x (k≠0, and k is a constant) intersects with the straight line y=ax (a≠0, and a is a constant) at points A(-2,3) and B. What are the coordinates of point B? | D | ['(-3, 2)', '(-3, -2)', '(-2, -3)', '(2, -3)'] | multi_choice |
func736 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/736.png | Given that the quadratic function y=ax^2+bx+c has its graph as shown in the figure, which quadrant will the graph of the linear function y=(a-b)x+c-a definitely not pass through? ( ). | B | ['First quadrant', 'Second quadrant', 'Third quadrant', 'Fourth quadrant'] | multi_choice |
func738 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/738.png | Lettuce is a highly nutritious vegetable. The practice group observed and recorded the growth process of lettuce. The figure below represents the function graph of lettuce growth height y (cm) and observation time x (days). What is the maximum height of lettuce growth? ( ) | B. 32cm | ['25cm', '32cm', '35cm', '40cm'] | multi_choice |
func739 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/739.png | As shown in the figure, a linear function y = kx + b (k ≠ 0) intersects the line y = x + 2 at point M(m, 4). Then the solution set of the linear inequality kx - 2 < x - 1 with respect to x is ( ) | C. x > 2 | ['x > 4', 'x < 4', 'x ≥ 2', 'x < 2'] | multi_choice |
func74 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/74.png | Given that the area of rectangle ABCD is 20, and taking the intersection of its diagonals as the origin to establish the rectangular coordinate plane shown in the figure, such that the sides of rectangle ABCD are parallel or perpendicular to the coordinate axes. If the hyperbolic function y=k(x≠0) passes through vertex A of the rectangle, then the value of k is ________. | -5 | NULL | free_form |
func740 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/740.png | As shown in the figure, in the rectangular coordinate system, the parallelogram OABC has its side OA on the positive x-axis, and the coordinates of points A and C are (2, 0) and (1, 2) respectively. Point B is in the first quadrant. The line y = -2x + 2m is shifted m (m > 0) units to the right along the x-axis. If the shifted line intersects side AB, what is the range of m? | D | ['4 ≤ m ≤ 8', '0 < m < 4', '2 < m ≤ 8', '2 ≤ m ≤ 4'] | multi_choice |
func741 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/741.png | Have you ever played Gomoku? The rules of the game state that as long as five pieces of the same color form a straight line first, they win. As shown in the figure, this is a game between two players. If the position of white piece ① is (1, -1) and the position of black piece ② is (2, 0), now it's black's turn. Player A believes that placing a black piece at position (2, 4) would result in a win, while Player B believes placing a black piece at position (7, -1) would result in a win. What do you think?
A. A is correct, B is wrong
B. A is wrong, B is correct
C. Both are correct
D. Neither is correct | C | ['A is right, B is wrong', 'A is wrong, B is right', 'Both are right', 'Both are wrong'] | multi_choice |
func742 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/742.png | As shown in the figure, the parabola of the quadratic function y = ax² + bx + c intersects the y-axis at point A(0, 2), and its axis of symmetry is the line x = 1/2. Then the solution set for the inequality ax² + bx + c ≤ 2 is ( ). | D | ['x \\leq 0', 'x \\leq -1 or x \\geq 2', '0 \\leq x \\leq 1', 'x \\leq 0 or x \\geq 1'] | multi_choice |
func743 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/743.png | A pebble drops into the surface of a lake, forming ripples as shown in the diagram. In the relationship between the area S and the radius r, expressed as S=πr², which are the variables ( )? | A. S, r | ['S, r', 'S, π', 'π, r', 'S, 2'] | multi_choice |
func744 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/744.png | As shown in the figure, if the input value of x is −6, then the output value of y is ( ). | C | ['-5', '-7', '7', '5'] | multi_choice |
func745 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/745.png | As shown in the figure, the parabola y = ax^2 + bx + c (a ≠ 0) passes through the point (-1, 0). Among the following four conclusions: ①a > 0; ②2a + b < 0; ③4a + 2b + c > 0; ④The quadratic equation ax^2 + bx + c = 0 has two distinct real roots. Which of the following sequences contains all the correct conclusions? ( ). | D | ['①②', '②③', '③④', '②③④'] | multi_choice |
func746 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/746.png | As shown in the figure, the side length of square ABCD is 3, the coordinates of point A are (2, 1), and AB is parallel to the x-axis. What are the coordinates of point C? | D | ['(1, 3)', '(1, 4)', '(-1, 3)', '(-1, 4)'] | multi_choice |
func748 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/748.png | As shown in the figure, a linear function y1 = kx + b (k ≠ 0) and a reciprocal function y2 = m/x (m ≠ 0) intersect at points A(1, 2) and B(-2, a). What is the solution to the inequality kx + b − m/x < 0? ( ) | B. x < −2 or 0 < x < 1 | ['x < -2', 'x < -2 or 0 < x < 1', '-2 < x < 0 or x > 1', 'x < 1'] | multi_choice |
func749 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/749.png | It is known that the voltage of a storage battery is constant. When using the storage battery, the current I (unit: A) and the resistance R (unit: Ω) have an inverse proportional relationship. The graph of this relationship is shown. When the resistance is 3Ω, what is the current? | C | ['4A', '9A', '12A', '36A'] | multi_choice |
func75 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/75.png | As shown in the figure, point A is a point on the hyperbolic function graph y = k/x. Draw AC perpendicular to the x-axis at point A, with C as the foot of the perpendicular. Point B is a point on the y-axis. Connect AB and BC. If the area of △ABC is 6, then the value of k is ______. | -12 | NULL | free_form |
func750 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/750.png | As shown in Figure 1, in rectangle ABCD, a moving point P starts from point B and moves along the edges of the rectangle in the order B→C→D→A. Let the distance traveled by point P be x, and the area of △ABP be y. Viewing y as a function of x, the graph of the function is shown in Figure 2. What is the area of △ABC? | A | ['10', '16', '18', '20'] | multi_choice |
func752 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/752.png | In the same plane rectangular coordinate system, the graphs of the linear functions y₁ = ax + b (a ≠ 0) and y₂ = mx + n (m ≠ 0) are shown in the figure. Which of the following conclusions is incorrect? ( ).
A. y₁ decreases as x increases
B. b < n
C. When x = 2, y₁ > y₂
D. The solution of the system of equations (ax - y = b, mx - y = n) is (x = 2, y = 3) | B | ['\\(y_1\\) decreases as \\(x\\) increases', '\\(b \\leq n\\)', 'When \\(x = 2b\\), \\(y_1 = y_2\\)', 'The solution to the system of equations \\(\\begin{cases} ax - y = b \\\\ mx - y = n \\end{cases}\\) is \\(\\begin{cases} x = 2 \\\\ y = 3 \\end{cases}\\)'] | multi_choice |
func753 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/753.png | 1. As shown in the figure, during a middle school endurance test competition, the function relationship between the distance (meters) S and time (seconds) t for two students, A and B, is represented by the broken line OABC and the line segment OD, respectively. Which of the following statements is correct? ( ) | C. During the competition (excluding the start and end points), the two students meet twice. | ['Student A reaches the endpoint after student B.', "Student B's speed increases with time.", 'During the race (excluding the start and end points), students A and B meet twice.', "During the race, student A's initial speed is faster than student B's."] | multi_choice |
func754 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/754.png | As shown in the figure, in a Cartesian coordinate system, a moving point starts from the origin O and moves 1 unit at a time in the direction indicated by the arrows, successively obtaining the points P1(0,1), P2(1,1), P3(1,0), P4(1,-1), P5(2,-1), P6(2,0)... What are the coordinates of point P2024? | B. (675, 1) | ['(675, -1)', '(675, 1)', '(337, -1)', '(337, 1)'] | multi_choice |
func755 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/755.png | As shown in the figure, △OABC has its vertex O at the origin of the coordinate system, with A on the positive half of the x-axis. The hyperbolic function y = k/x passes through point C, where k > 0, and △OABC's area passes through point B. If OC = AC, then the value of k is ( ). | A. 3 | ['3', '4', '5', '6'] | multi_choice |
func756 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/756.png | As shown in the figure, point A lies on the graph of the inverse proportional function y = 2/x (x < 0), and point B lies on the graph of the inverse proportional function y = -4/x (x > 0). Line segment AB intersects the y-axis at point C, and AB is parallel to the x-axis. Point D is on the positive half of the x-axis. Connecting AD and BD, the area of △ABD is ( ). | B. 3 | ['2', '3', '4', '6'] | multi_choice |
func757 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/757.png | As shown in the figure, a linear function y = ax + b and a reciprocal function y = k/x (x > 0) intersect at point A(2, 4) and point B(m, −2). Then the solution set for the inequality ax + b > k/x with respect to x is ( ) | A | ['-4 < x < 0 or x > 2', 'x < -2 or 0 < x < 4', 'x < -4 or 0 < x < 2', '-2 < x < 0 or x > 4'] | multi_choice |
func758 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/758.png | As shown in the figure, in a rectangular coordinate system, the vertices of triangle ABC are A(0, a), B(-1, b), C(2, c), BC passes through the origin O, and CD ⊥ AB with the foot of perpendicular at point D, and AB·CD = 12. What is the value of a? | B. 4 | ['3', '4', '8', '12'] | multi_choice |
func759 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/759.png | As shown in the figure, in the plane rectangular coordinate system (Oxy), △OABC has vertex C located on the positive half of the x-axis. If the coordinates of A are (3,4), and OA=OC, what are the coordinates of B? | B. (8,4) | ['(5, 4)', '(8, 4)', '(5, 3)', '(8, 3)'] | multi_choice |
func76 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/76.png | As shown in the figure, it is a partial graph of the function y = -1/2x + 5.
(1) The value range of the independent variable x is ________;
(2) When x is ________, the minimum value of y is ________. | 0 <= x <= 5 5 2.5 | NULL | free_form |
func760 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/760.png | The graph of the linear function y = -2x + 2 is shown in the figure. When y > 0, the range of x is ( ). | D. x < 1 | ['x < 2', 'x > 2', 'x > 1', 'x < 1'] | multi_choice |
func761 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/761.png | As shown in the figure, in rectangle COED, the coordinates of point D are (1,3). What is the length of CE? | C. √10 | ['3', '2√2', '√10', '4'] | multi_choice |
func762 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/762.png | As shown in the diagram, an elastic ball starts from P(0,1) and moves in the indicated direction. Each time the ball hits the side of the square OABC, it rebounds, and the reflection angle is equal to the incident angle. When the ball hits the side of the square for the first time, it is at P1(2,0). When the ball hits the square for the second time, it is at P2. When the ball hits the square for the nth time, it is at Pn. What are the coordinates of point P2024?
A. (4,1)
B. (4,3)
C. (2,4)
D. (1,4) | A | ['(4,1)', '(4,3)', '(2,4)', '(1,4)'] | multi_choice |
func763 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/763.png | The range of real number 'a' is shown in the figure. Then the quadrant in which point P(a+1, a+3) is located is ( ). | B | ['First quadrant', 'Second quadrant', 'Third quadrant', 'Fourth quadrant'] | multi_choice |
func764 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/764.png | As shown in the diagram, there are 4 steps, each with a height of 1 and a width of 2. The top points of each step are called turning points, denoted as Tm (where m is an integer from 1 to 7). The function y = k / x (x > 0) is represented as curve L. When curve L passes through the maximum number of turning points simultaneously, the value of k is ( ). | B | ['6', '8', '12', '16'] | multi_choice |
func765 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/765.png | As shown in the figure, in the Cartesian coordinate plane, the vertex B of the equilateral triangle OAB has coordinates (2,0), and point A is in the first quadrant. The triangle △OAB is translated along the direction of line OA to the position of △OAB′, and at this time, the x-coordinate of point A′ is 3. What are the coordinates of point B′? | C. (4, 2√3) | ['(3, 3)', '(3, 3√3)', '(4, 2√3)', '(4, 3√3)'] | multi_choice |
func766 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/766.png | On a construction site, along one side near the wall, an 81-meter-long iron fence was used to enclose three connected rectangular warehouses. The total area of the warehouses is y square meters. To facilitate access, a 1-meter-wide gap is left between each warehouse as a passage, and a 1-meter-wide gap is left on the side parallel to the wall as a small door. Let 4B = x meters, then the functional relationship for x is ( ). | D | ['y = x(81 - 4x)', 'y = x(78 - 2x)', 'y = x(84 - 2x)', 'y = x(84 - 4x)'] | multi_choice |
func767 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/767.png | As shown in the figure, in a plane rectangular coordinate system, given A1(2,4), A2(4,4), A3(6,0), A4(8,−4), A5(10,−4), A6(12,0), … following this pattern, the coordinates of point A2024 are ( ). | A | ['(4048, 4)', '(4050, 4)', '(4050, -4)', '(4048, -4)'] | multi_choice |
func768 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/768.png | As shown in the graph, the functions y = 2x and y = ax + 4 intersect at point A(m, 3). The solution set of the inequality 2x ≥ ax + 4 is ( ). | A. x ≥ 3/2 | ['x ≥ 3/2', 'x ≤ 3', 'x ≤ 3/2', 'x ≥ 3'] | multi_choice |
func769 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/769.png | The quadratic function y = ax² + bx + c has a graph as shown in the figure. Then, the graph of the quadratic function y = bx² + ax must not pass through ( ). | B. Second quadrant | ['First quadrant', 'Second quadrant', 'Third quadrant', 'Fourth quadrant'] | multi_choice |
func77 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/77.png | As shown in the figure, this is the parabolic arch bridge and its schematic diagram in the cultural ecological park of a certain city. The function expression of the parabola is y = -1/40x² + 10. To beautify the night scene of the arch bridge, a night light strip EF is planned to be installed 6m away from (AB) on the arch bridge. The length of the night light strip EF is _______ m. | 8√10 | NULL | free_form |
func770 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/770.png | 9. If there are two linear functions y1 = kx + b and y2 = -kx + a, the following conclusions are: ① k < 0; ② a > 0; ③ b > 0; ④ the solution to the equation kx + b = -kx + a is x = 3. How many of these are incorrect? ( ). | A. 1 | ['1', '2', '3', '4'] | multi_choice |
func771 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/771.png | A car moves uniformly through a certain section of the road, and the required time t (hours) and speed v (km/h) satisfy the function relationship: t = k / v, and its graph is a curve shown as a segment, with endpoints A(40, 1) and B(m, 0.5). If the travel time must not be less than 0.5 hours, the maximum speed the car can achieve on this section of the road is ( ). | A. 80 km/h | ['80 km/h', '60 km/h', '40 km/h', '20 km/h'] | multi_choice |
func772 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/772.png | Xiao Ming investigates the density of four substances: A, B, C, and D. He plots the measurement results into the graph as shown. Which of the four substances has the highest density? ( ) | A | ['A', 'B', 'C', 'D'] | multi_choice |
func773 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/773.png | As shown in the figure, points A and B are on the hyperbola y = k / x (x > 0). Connect OA and OB. From point A, draw OC 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 3, and the coordinates of point B are (m, 2), then the value of m is ( ). | B. 6 | ['3', '6', '9', '\\(\\frac{3}{2}\\)'] | multi_choice |
func775 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/775.png | As shown in Figure 1, point P starts from vertex A of the isosceles right triangle ABC, moves along a straight line to a point inside the triangle, and then moves along a straight line to point D, the midpoint of side AC. Let the distance traveled by point P be x, and the area of △PBC be y. Figure 2 shows the relationship between y and x as point P moves. What is the length of BC? ( ) | B | ['1', '2', '√2', '2√2'] | multi_choice |
func776 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/776.png | As shown in the figure, the graph of the inverse proportional function y=2/x intersects with the graph of the proportional function y=kx at two points. If the distance from one of the intersection points to the coordinate axes is 2, then the distance between the two intersection points is ( ). | B. 2√5 | ['\\(\\sqrt{5}\\)', '\\(2\\sqrt{5}\\)', '\\(\\sqrt{3}\\)', '\\(2\\sqrt{3}\\)'] | multi_choice |
func777 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/777.png | Given the linear function y = kx + b (k ≠ 0) with the graph shown as in the figure, the solution set of the inequality k(x − 1) + b ≤ 6 is ( ). | C. x ≤ 3 | ['x ≤ 2', 'x ≥ 2', 'x ≤ 3', 'x ≥ 4'] | multi_choice |
func778 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/778.png | Building tunnels can shorten road lengths and bring great convenience to people's lives. The cross-section of a tunnel is usually circular or parabolic. As shown in the figure, the cross-section of a certain tunnel is parabolic. The clear width of the tunnel AB is 11m, and the clear height OC is 5m. If a Cartesian coordinate system is established with point O as the origin and the line where OC lies as the y-axis, the corresponding equation of the parabola would be ( ). | B | ['y = -\\frac{10}{121}x^2 + 5', 'y = -\\frac{20}{121}x^2 + 5', 'y = -\\frac{10}{11}x^2 + 5', 'y = -\\frac{20}{11}x^2 + 5'] | multi_choice |
func779 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/779.png | The hyperbola C₁: y=4/x (x>0) and C₂: y=2/x (x>0) are shown in the figure. Let point P be on C₁, PC ⊥ x-axis at point C, intersecting C₂ at point A, and PD ⊥ y-axis at point D, intersecting C₂ at point B. What is the area of quadrilateral PAOB? ( ) | B | ['1', '2', '3', '4'] | multi_choice |
func78 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/78.png | 7. Under the condition of constant temperature, by repeatedly reducing and increasing the pressure on the piston at the top of the cylinder, the pressure p (kPa) exerted by the gas on the cylinder wall is inversely proportional to the volume V (mL) of the gas inside the cylinder. The graph of the function p with respect to V is shown. If the pressure is reduced from 100 kPa to 75 kPa, the gas volume increases by _______ mL. | 20 | NULL | free_form |
func780 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/780.png | As shown in the figure, point A lies on the graph of the inverse proportion function y = k / x. A perpendicular AC is drawn from point A to the x-axis with foot C. Point B is located on the x-axis, and lines AB and BC are connected. If the area of △ABC is 6, what is the value of k? ( ) | D | ['6', '-6', '12', '-12'] | multi_choice |
func781 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/781.png | The following problem involves two variables: ② Draining water from the tank at a uniform rate until it is empty, the remaining water in the tank has a relationship with the draining time x; ③ Using a rope of fixed length to form a rectangle, the area of the rectangle has a relationship with one side length x. Among them, the functional relationship between variable y and variable x can be represented by the graph shown ( ). | B | ['①', '②', '①, ②', 'Neither ① nor ②'] | multi_choice |
func782 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/782.png | As shown in the figure, in the Cartesian coordinate system, point P is on the graph of the reciprocal function y=12/x (x>0). Draw PA perpendicular to the x-axis at point A, point B is the midpoint of OA, and connect PB. The area of △PAB is ( ) | C | ['6', '12', '3', '4'] | multi_choice |
func784 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/784.png | Aunt Zhang is planning to build a rectangular vegetable garden. One side of the garden uses a sufficiently long wall, with a 1-meter wide door in the middle of the wall. The total length of the other three sides fenced with wire is exactly 25 meters. The garden to be enclosed is a rectangle ABCD as shown in the figure. Let the length of side BC be x meters, and the length of side AB be y meters. What is the relation between y and x? ( ) | B | ['y = 25 - 1/2x', 'y = 13 - 1/2x', 'y = 25 - x', 'y = 26 - 2x'] | multi_choice |
func785 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/785.png | Given the quadratic function y = ax^2 + bx + c (a ≠ 0), whose graph is shown below, which of the following statements is incorrect?
A. The graph is symmetric about the line x = 1.
B. The minimum value of the function y = ax^2 + bx + c (a ≠ 0) is −4.
C. When x < 1, y increases as x increases.
D. −1 and 3 are the two roots of the equation ax^2 + bx + c = 0 (a ≠ 0). | C | ['The graph is symmetric about the line \\(x = 1\\).', 'The minimum value of the function \\(y = ax^2 + bx + c \\ (a \\neq 0)\\) is -4.', 'When \\(x < 1\\), \\(y\\) increases as \\(x\\) increases.', 'The equation \\(x^2 + bx + c = 0 \\ (a \\neq 0)\\) has two roots, 1 and 3.'] | multi_choice |
func786 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/786.png | As shown in Figure 1, a small ball of mass m starts falling from a certain height and comes to rest upon impacting a vertically placed light spring (the initial length of the spring in its natural state is 12 cm). During the process from the ball first contacting the spring to the spring being compressed to its shortest length (ignoring air resistance, with the spring undergoing elastic deformation throughout), the relationship between the ball's velocity v (cm/s) and the compression length Δl (cm) is depicted in the graph shown in Figure 2. Based on the graph, which of the following statements is correct?
A. The ball starts slowing down as soon as it contacts the spring.
B. The ball's velocity is maximum when the spring is compressed to its shortest length.
C. When the ball's velocity is maximum, the length of the spring is 2 cm.
D. When the ball reaches its lowest position, the length of the spring is 6 cm. | D | ['The small ball starts to accelerate as soon as it touches the spring.', 'When the spring is compressed to its shortest length, the speed of the small ball is the greatest.', 'When the speed of the small ball is the greatest, the compression length of the spring is 2 cm.', 'When the small ball falls to the lowest point, the compression length of the spring is 6 cm.'] | multi_choice |
func787 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/787.png | 1. The figure shows the graphs of the functions y = x² - 1, y = x² + 6x + 8, y = x² - 6x + 8, y = x² - 12x + 35 in the same Cartesian coordinate system. Which graph is most likely the graph of y = x² - 6x + 8? ( ) | C | ['①', '②', '③', '④'] | multi_choice |
func788 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/788.png | The graph of the linear function y = kx - 3 is shown below. Which of the following statements is correct? ( ) | B | ['k < 0', 'y increases as x increases', 'The graph passes through the origin', 'The graph passes through the first, second, and fourth quadrants'] | multi_choice |
func789 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/789.png | As shown in the figure, the parabola y = ax^2 + bx + c (a ≠ 0) intersects the x-axis at points A (-4, 0) and B, and intersects the y-axis at point C. The following conclusions are provided: ①abc > 0; ②2a − b = 0; ③4a + c < 2b; ④Point (x1, y1) lies on the parabola, and when x1 = −1, x1 + x2 = −1. How many of these statements are correct? ( )
A. 1 B. 2 C. 3 D. 4 | B | ['1', '2', '3', '4'] | multi_choice |
func79 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/79.png | The graph of the linear function y = (k−1)x + k is shown in the figure. Simplify |k−1| + √(k^2−4k+4). The result is ________. | 1 | NULL | free_form |
func790 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/790.png | The quadratic function y=ax²+hx+c (a≠0) has its graph as shown in the figure below. The following conclusions are given: ① a+b+c<0; ② c>3b; ③ x₁²+x₂²=2x₁x₂+hx₂, and x₁+x₂=2. Then a+b+c+4ac, which of the following is correct? ( ) | D | ['①③', '②③', '②', '①③④'] | multi_choice |
func791 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/791.png | Xiao Ming and Xiao Zhang went on a weekend trip with their families by car. The relationship between their time (h) and the distance traveled (km) is shown in the graph below. Which of the following statements is incorrect?
A. The relationship between Xiao Ming's distance traveled and time is s=60t.
B. The relationship between Xiao Zhang's distance traveled and time is s=40t.
C. Xiao Ming's car travels faster.
D. Xiao Zhang's car travels faster. | D | ["The relationship between Xiaoming's driving distance and time is s = 60t", "The relationship between Xiaozhang's driving distance and time is s = 40t", "Xiaoming's driving speed is faster", "Xiaozhang's driving speed is faster"] | multi_choice |
func792 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/792.png | A large truck travels from City A to City B, during which the quantity of goods changes. The relationship between its path and time is illustrated in the graph. Which of the following statements is correct? ( ) | D | ['The speed of the truck at 20 hours is greater than the speed at 8 hours.', 'The truck cannot reach city B at 40 hours.', 'The quantity of goods at 12 hours is greater than the quantity of goods at 5 hours.', 'The quantity of goods at 12 hours is less than the quantity of goods at 5 hours.'] | multi_choice |
func793 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/793.png | As shown in the figure, during a badminton match, the trajectory of a shuttlecock can be regarded as part of the parabola y=1/4x^2+3/4x+1 (the horizontal ground is the x-axis, unit: m). The following conclusions are given: ① The distance between the point of release O and point B is 1m; ② The highest point the shuttlecock reaches is 25/16m; ③ The farthest horizontal distance the shuttlecock travels is 3m. How many of these conclusions are correct? ( ). | C. 2 | ['0', '1', '2', '3'] | multi_choice |
func794 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/794.png | The great ancient Greek philosopher, mathematician, and physicist Archimedes once said: 'Give me a fulcrum, and I can move the earth!' This famous quote reveals the meaning and value of the 'lever principle.' The 'lever principle' has widespread applications in production and daily life. For example, Xiao Ming uses a crowbar to move a large stone, which utilizes the 'lever principle.' Given that the relationship between the resistance force F₁ (N) and resistance arm L₁ (m) is shown in the figure, if Xiao Ming's applied force F₂ does not exceed 150N, then the driving arm L₂ (unit: m) must satisfy: A. 0 < L₂ ≤ 4 B. L₂ < 4 C. L₂ > 4 D. L₂ ≥ 4 | D | ['0 < L2 ≤ 4', 'L2 < 4', 'L2 > 4', 'L2 ≥ 4'] | multi_choice |
func795 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/795.png | As shown in the figure, given the upward-opening parabola y = ax² + bx + c intersects the x-axis at point (-1, 0), and its axis of symmetry is the line x = 1, which of the following conclusions is correct? ( ) | D. 4 values | ['1', '2', '3', '4'] | multi_choice |
func796 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/796.png | As shown in the figure, the line v1 = kx + b passes through points A and B, and the line v2 = 2x passes through point A. Then the solution set for the inequality 2x < kx + b < 0 is ( ). | B | ['x < -2', '-2 < x < -1', '-2 < x < 0', '-1 < x < 0'] | multi_choice |
func798 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/798.png | As shown in the figure, point A is on the graph of y = mx/n (x > 0). From point A, draw AB perpendicular to the x-axis with the foot of the perpendicular at B, and draw AC perpendicular to the y-axis with the foot of the perpendicular at C, intersecting the graph of y = n/m * x (x > 0) at point E. Connect OE. If AE = 3 × CE, and the area of quadrilateral OBAE is 7, then the correct values of m and n are ( ). | D | ['m = 6, n = 4', 'm = 4, n = 1', 'm = 12, n = 3', 'm = 8, n = 2'] | multi_choice |
func799 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/799.png | As shown in the figure, in the rectangular coordinate system, △OABC has its vertex O at the origin. Point E is a point on the diagonal AC. A line through point E, EF // BC, intersects AB at point F. OC = 2, ∠AOC = 45°, the coordinates of point O are (0,0), the x-coordinate of point E is 5. Calculate the length of EF ( ). | D | ['1', '2', '3', '√2'] | multi_choice |
func8 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/8.png | As shown in the figure, the straight line y = ax - 1 and the straight line y = kx intersect at point P. If the solution of the linear equation system {kx - y = 0, ax - y = b} is x, y, then x + y = ______. | 3 | NULL | free_form |
func80 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/80.png | As shown in the diagram, in the Cartesian coordinate system, the line l: y = -2x + 4 intersects the x-axis at point A and the y-axis at point B. Line l passes through the vertex B of △OAB and divides the area of △OAB into two parts in the ratio 1:3. What is the equation of line l? ________. | y = -1/2x + 1 or y = -3/2x + 3 | NULL | free_form |
func800 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/800.png | As shown in Figure 1, in the right triangle △ABC, ∠C = 90°, ∠B = 30°. Point P starts moving from point A towards point B and stops at point B. A line PQ perpendicular to AB is drawn through point P, intersecting the perpendicular sides AC (or BC) at point Q. Let the distance traveled by point P be x, and the area of △APQ be y. The functional relationship between y and x is shown in Figure 2. When x = 5, the area of △APQ is ( ). | C. 5/2√3 | ['\\( \\frac{3}{2} \\sqrt{3} \\)', '\\( 2 \\sqrt{3} \\)', '\\( \\frac{5}{2} \\sqrt{3} \\)', '\\( 4 \\sqrt{3} \\)'] | multi_choice |
func801 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/801.png | As shown in Figure 1, in △ABC, CA = CB, and line l passes through point A and is perpendicular to AB. The line is moved to the right at a uniform speed of 1 cm/s, stopping when it reaches point B. Line l intersects side AB at point M and intersects side AC (or BC) at point N. Let the time the line moves be t (seconds), and the area of △AMN be y (cm²). If the graph of y as a function of t is shown in Figure 2, then the perimeter of △ABC is ( ). | C | ['16 cm', '17 cm', '18 cm', '20 cm'] | multi_choice |
func802 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/802.png | During the 'May Day' holiday, a math teacher's family went on a self-driving trip to a place 170 kilometers away from home. Below is the graph of the function showing the distance y (kilometers) from home with respect to the driving time x (hours). How many kilometers are they from their destination after driving for 2.2 hours? ( ) | B. 24 | ['12', '24', '146', '164'] | multi_choice |
func803 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/803.png | In a rectangular coordinate system, point A is a fixed point on the positive half of the x-axis, point P is a moving point on the hyperbola y = k/x (x > 0), and PB ⊥ the y-axis at point B. As the x-coordinate of point P gradually increases, the area of the quadrilateral OAPB will ( ). | C. Gradually decrease | ['Gradually increase', 'Remain unchanged', 'Gradually decrease', 'Increase first and then decrease'] | multi_choice |
func804 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/804.png | The weather is getting warmer, making it a great time for camping. On Saturday, Xiaolian and their family drove along a straight line from their home to a camping base 30 kilometers away. After driving for 0.5 hours, they reached the camping base. After spending some time at the base, they returned home along the same route. Due to increased traffic, the average speed on the return journey was 1/6 less than the average speed to the base. During the entire process, there is a functional relationship between Xiaolian's distance from home (x kilometers) and the time used (t hours), as shown in the figure. Which of the following statements is correct? ( )
A. The average speed to the base is 60 kilometers per hour
B. The time spent playing at the camp is 4 hours
C. The average speed on the return journey is 50 kilometers per hour
D. When 10 kilometers away from home, the value of x is 4.74 | D | ['The average speed to the base camp is 60 kilometers per hour', 'The time spent playing at the base camp is 4 hours', 'The average speed on the way back is 50 kilometers per hour', 'When the distance from home is 10 kilometers, the value of x is 4.74'] | multi_choice |
func805 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/805.png | Xiao Li's home, Xiao Ming's home, and the school are located in sequence on a straight line. One day, Xiao Li and Xiao Ming agreed to play ball and return to school to play after fetching their rackets from home. They set off from the school at the same time and traveled back home at a uniform speed, reaching their respective homes simultaneously. After Xiao Li reached home, he immediately picked up his racket and returned to the school at a different speed. Xiao Ming, on the other hand, rested for 4 minutes after retrieving his racket and then returned to the school at his original speed. Both arrived at the school at the same time (time spent finding the rackets is negligible). The relationship between the distance from the school (x, in meters) and the time of departure (t, in minutes) is shown in the graph. Among the following statements, which one is incorrect ( )?
A. Xiao Li's home is 1200m away from the school.
B. Xiao Ming's speed is 62.5m/min.
C. Xiao Li's return speed to the school is 600/7 m/min.
D. At the 16th minute after departure, the distance between Xiao Li and Xiao Ming is 320/7 m. | B | ["Xiao Li's home is 1200m away from the school", "Xiao Ming's speed is 62.5m/min", "Xiao Li's return speed is 600/7 m/min", 'When they left at 16 minutes, the distance between Xiao Li and Xiao Ming was 320/7 m'] | multi_choice |
func806 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/806.png | 9. Person A and Person B simultaneously set off from locations A and B, respectively, traveling toward each other at constant speeds toward Location B. They stopped for 4 minutes upon meeting and then continued to their destinations at their original speeds. The relationship between the distance y (m) between them and the time x (min) spent by Person A is as shown in the graph. Determine the correct conclusions: ① The distance between A and B is 1200m; ② At x=24 min, one of them reaches their destination; ③ b=800; ④ a=32. The number of correct conclusions is ( ).
A. 1 B. 2 C. 3 D. 4 | C | ['1个', '2个', '3个', '4个'] | multi_choice |
func807 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/807.png | To ensure safety, divers wear a depth gauge and a pressure gauge as shown in Figure 1. Figure 2 is a simplified circuit diagram of the working principle of the depth gauge, where the resistance of R1 (Ω) varies with the diving depth h (m), and its variation relationship is shown in Figure 3. The voltage reading of the voltmeter in the circuit changes accordingly. Given that the relationship between the voltmeter reading U(V) and the resistance R1 is U = 90 / (R1+15). Which of the following statements is incorrect?
A. As diving depth increases, the resistance of R1 continues to decrease
B. As diving depth increases, the value on the voltmeter continues to decrease
C. When diving depth is 10m, the resistance of R1 is 30Ω
D. When diving depth is 40m, the voltmeter reading is 3V | B | ['As the diving depth increases, the value of R1 continues to decrease.', 'As the diving depth increases, the reading of the depth gauge continues to decrease.', 'When the diving depth is 10m, the resistance of R1 is 30Ω.', 'When the diving depth is 40m, the reading of the depth gauge is 3V.'] | multi_choice |
func808 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/808.png | As shown in the figure, the line y = ax + b (a ≠ 0) passes through points A(0, 2) and B(3, 0). What is the solution set for the inequality ax + b > 0? | B. x < 3 | ['x > 3', 'x < 3', 'x > 2', 'x < 2'] | multi_choice |
func809 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/809.png | If the graph of the quadratic function y = (x + h)^2 + k is as shown in the figure, then the quadrant where point E(h, k) is located is ( ). | B. Second quadrant | ['First quadrant', 'Second quadrant', 'Third quadrant', 'Fourth quadrant'] | multi_choice |
func81 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/81.png | A biology group observed the growth of a plant and obtained the relationship between the plant's height y (unit: cm) and observation time x (unit: days). They plotted the function graph as shown in the figure. The plant stops growing at a height of ______ cm. | 16 | NULL | free_form |
func810 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/810.png | As shown in the figure, in the plane Cartesian coordinate system xOy, there are three points A(0,1), B(4,1), C(5,6). What is cos∠BAC? | C | ['1/2', '√13/5', '√2/2', '√3/2'] | multi_choice |
func811 | /home/yz979/scratch/chengye/math/data/original_set/funcset/images/images/811.png | As shown in the figure, point M is on the graph of the inverse proportion function y = -k/x. A perpendicular line MN is drawn from point M to the x-axis at point N, and OM is connected. Given that the area of △MNO is 1.9, what is the value of k? | C | ['-1.9', '1.9', '-3.8', '3.8'] | multi_choice |
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