images
images listlengths 1
1
| problem
stringlengths 88
2.72k
| answer
stringclasses 5
values |
|---|---|---|
<image>As shown in the figure, the sector $$OAB$$ is the lateral surface development of a cone. If the side length of each small square grid is $$1$$ cm, then the radius of the base of this cone is ( )
A. $$\dfrac{1}{2}$$ cm
B. $$\dfrac{\sqrt{2}}{2}$$ cm
C. $$\sqrt{2}$$ cm
D. $$2\sqrt{2}$$ cm
|
B
|
|
<image>If the program flowchart shown in the figure is executed, then the output value of $S$ is （）
A. $-1$
B. $\frac{1}{2}$
C. $1$
D. $2$
|
D
|
|
<image>Given an algorithm, as shown in the flowchart, the output result is ()
A. 7
B. 9
C. 11
D. 13
|
B
|
|
<image>As shown in the figure, in parallelogram $ABCD$, which of the following conclusions is incorrect?
A. $\overrightarrow{AB}=\overrightarrow{DC}$
B. $\overrightarrow{AD}+\overrightarrow{AB}=\overrightarrow{AC}$
C. $\overrightarrow{AB}-\overrightarrow{AD}=\overrightarrow{BD}$
D. $\overrightarrow{AD}+\overrightarrow{CB}=\vec{0}$
|
C
|
|
<image>Given the values of $$x$$ and $$y$$ as shown in the table: From the scatter plot, $$y$$ is linearly related to $$x$$, and $$\hat{y}=0.95x+\hat{a}$$, then $$\hat{a}=$$（ ）
A. $$2.5$$
B. $$2.6$$
C. $$2.7$$
D. $$2.8$$
|
B
|
|
<image>In a $5\times 5$ grid paper, the position of shape $N$ from figure (1) after translation is shown in figure (2). The correct translation method is ( )
A. Move down 1 square first, then move left 1 square
B. Move down 1 square first, then move left 2 squares
C. Move down 2 squares first, then move left 1 square
D. Move down 2 squares first, then move left 2 squares
|
C
|
|
<image>As shown in the figure, a series of square patterns are formed using matchsticks. The first pattern uses 4 sticks, the second uses 12 sticks, and the third uses 24 sticks. Following this pattern, the number of matchsticks used to form the 6th pattern is ( ).
A. $$84$$
B. $$81$$
C. $$78$$
D. $$76$$
|
A
|
|
<image>A steel ball rolls up a slope with an angle of $31^{\circ}$ for $5$ meters. At this point, the height of the steel ball above the ground is (unit: meters) \left( \right)
A. $5\cos 31^{\circ}$
B. $5\sin 31^{\circ}$
C. $5\cot 31^{\circ}$
D. $5\tan 31^{\circ}$
|
B
|
|
<image>Mathematical conjectures are a powerful driving force behind the development of mathematical theories, being one of the most active, proactive, and positive factors in the development of mathematics, and the most creative part of human rationality. In 1927, a student at the University of Hamburg, Lothar Collatz, proposed a conjecture: for every positive integer, if it is odd, multiply it by 3 and add 1; if it is even, divide it by 2. This process, when repeated, will eventually result in 1. Below is a flowchart designed based on the Collatz conjecture, what is the output of $i$?
A. 5
B. 6
C. 7
D. 8
|
B
|
|
<image>As shown in the figure, it is known that $$\angle AOB=90^{ \circ }$$, and $$OC$$ is any ray within $$\angle AOB$$. $$OB$$ and $$OD$$ bisect $$\angle COD$$ and $$\angle BOE$$, respectively. Which of the following conclusions are correct: 1. $$\angle COD= \angle BOE$$; 2. $$\angle COE=3\angle BOD$$; 3. $$\angle BOE=\angle AOC$$; 4. $$\angle AOC+ \angle BOD=90^{ \circ }$$. ( )
A. 1.2.4.
B. 1.3.4.
C. 1.2.3.
D. 2.3.4.
|
A
|
|
<image>The front view and left view of a 3D shape made up of several small cubes are shown in the figure. The minimum number of small cubes that make up this 3D shape is ( )
A. $3$
B. $4$
C. $5$
D. $6$
|
B
|
|
<image>As shown in the figure, several students circled three consecutive numbers in a vertical column on a calendar and calculated their sum. Which of the following is incorrect?
A. $27$
B. $36$
C. $40$
D. $54$
|
C
|
|
<image>Two triangles as shown in the figure cannot be combined to form ( ).
A. Square
B. Parallelogram
C. Rectangle
|
A
|
|
<image>In a certain season, two basketball players, Player A and Player B, both participated in 11 games. Their scores in these 11 games are represented by the stem-and-leaf plot below. Let the median score of Player A be $$M_1$$, and the median score of Player B be $$M_2$$. Which of the following options is correct?
A. $$M_1=18,,M_2=12$$
B. $$M_1=81,,M_2=12$$
C. $$M_1=8,,M_2=2$$
D. $$M_1=3,,M_2=1$$
|
A
|
|
<image>As shown in the figure, in the right triangle $${\rm Rt}\triangle ABC$$, $$\angle BAC = 90\degree$$, $$\angle B = 35\degree$$, $$AD$$ is the median of the hypotenuse $$BC$$. When $$\triangle ACD$$ is folded along $$AD$$, point $$C$$ lands on point $$F$$. The line segment $$DF$$ intersects $$AB$$ at point $$E$$. What is the measure of $$\angle FAE$$?
A. $$105\degree$$
B. $$75\degree$$
C. $$40\degree$$
D. $$20\degree$$
|
D
|
|
<image>As shown in the figure, which of the following statements is correct?
A. The number of students in Grade 7 is the highest.
B. The number of boys in Grade 9 is twice the number of girls.
C. The number of girls in Grade 9 is more than the number of boys.
D. The number of students in Grade 8 is more than the number of students in Grade 9.
|
B
|
|
<image>The test scores of two individuals, A and B, over the last 5 tests are shown in the following graph. Which of the following statements is incorrect?
A. B's score on the 2nd test is the same as on the 5th test
B. On the 3rd test, A's score is the same as B's score
C. On the 4th test, A's score is 2 points higher than B's score
D. Over 5 tests, A's average score is higher than B's average score
|
A
|
|
<image>Execute the program flowchart as shown in the figure, input $n=1$. If the output ${{3}^{m}}+{{2}^{m}}$ is required to be the largest odd number $m$ not exceeding 500, then the box labeled with a diamond should contain
A. $Age 2500?$
B. $Ale 500?$
C. $Age 500?$
D. $Ale 2500?$
|
C
|
|
<image>Given the coordinates of the vertices of the tetrahedron P-ABC are P (0, 0, 5), A (3, 0, 0), B (0, 4, 0), C (0, 0, 0), the volume of the tetrahedron P-ABC is ( )
A. \frac{1 0} {3}
B. 5
C.
D. 10
|
D
|
|
<image>The partial graph of the function $$f(x)=A\sin(2x+\varphi)$$ ($$A>0$$, $$\varphi\in \bf{R}$$) is shown in the figure below. Then, $$f(-{\pi\over 24})=$$ ( ).
A. $$-1$$
B. $$-{1\over 2}$$
C. $$-{\sqrt3\over 2}$$
D. $$-\sqrt2$$
|
D
|
|
<image>Based on the corresponding values in the following table, determine the range of one solution for the equation $$ax^2+bx+c=0$$ ($$a\neq0$$, $$a$$, $$b$$, and $$c$$ are constants).
A. $$3<x<3.23$$
B. $$3.23<x<3.24$$
C. $$3.24<x<3.25$$
D. $$3.25<x<3.26$$
|
C
|
|
<image>As shown in the figure, $AD$ is the median of $\triangle ABC$, $\angle ADC=60^{\circ}$, $BC=6$. When $\triangle ADC$ is folded along the line $AD$, point $C$ lands on point $E$. Connecting $BE$, the length of $BE$ is ( )
A. $3$
B. $4$
C. $5$
D. $2$
|
A
|
|
<image>As shown in the figure, $$DE$$ is the midline of $$\triangle ABC$$, and $$BE$$ and $$CD$$ intersect at point $$O$$. If $$S_{\triangle ODE}=1$$, then $$S_{\triangle OBC}=$$ ( )
A. $$2$$
B. $$3$$
C. $$4$$
D. $$9$$
|
C
|
|
<image>As shown in the figure, the parabola $$y=-2x^{2}-1$$ is shifted upward by several units so that the parabola intersects the coordinate axes at three points. If these intersection points can form a right triangle, then the distance of the shift is ( )
A. $$\dfrac{3}{2}$$ units
B. $$1$$ unit
C. $$\dfrac{1}{2}$$ unit
D. $$\sqrt{2}$$ units
|
A
|
|
<image>As shown in the figure, $\angle AOB=\angle COD=90^{\circ}$, $\angle AOD=126^{\circ}$. Then $\angle BOC$ equals ( )
A. $54^{\circ}$
B. $64$
C. $74^{\circ}$
D. Cannot be determined
|
A
|
|
<image>As shown in the figure, in the Cartesian coordinate system $$xOy$$, the parabola $$y=x^{2}+bx+c$$ intersects the $$x$$-axis at only one point $$M$$, and intersects a line $$l$$ parallel to the $$x$$-axis at points $$A$$ and $$B$$. If $$AB=3$$, then the distance from point $$M$$ to line $$l$$ is ( )
A. $$\dfrac{5}{2}$$
B. $$\dfrac{9}{4}$$
C. $$2$$
D. $$\dfrac{7}{4}$$
|
B
|
|
<image>In the following figures, Figure 1 is a shaded triangle with an area of $$1$$. By connecting the midpoints of its sides, the middle triangle is removed to obtain Figure 2. Then, by connecting the midpoints of each remaining shaded triangle, the middle triangle is removed to obtain Figure 3. The same method is used to obtain Figure 4. Therefore, the area of the shaded part in Figure 4 is ( )
A. $$\dfrac{3}{4}$$
B. $$\dfrac{9}{16}$$
C. $$\dfrac{9}{64}$$
D. $$\dfrac{27}{64}$$
|
D
|
|
<image>As shown in the figure, $\angle ABC=31^{\circ}$, and the bisector of $\angle BAC$ intersects with the bisector of $\angle FCB$, $CE$, at point $E$. Then $\angle AEC$ is ( )
A. $14.5^{\circ}$
B. $ 15.5^{\circ}$
C. $ 16.5^{\circ}$
D. $ 20^{\circ}$
|
B
|
|
<image>As shown in the figure, in square $ABCD$, $\triangle PAD$ is an equilateral triangle. The degree measure of $\angle PBC$ is ( )
A. $15^{\circ}$
B. $ 20^{\circ}$
C. $ 25^{\circ}$
D. $ 30^{\circ}$
|
A
|
|
<image>As shown in the figure, it is known that $$AB$$, $$CD$$, and $$EF$$ are all perpendicular to $$BD$$, with the feet of the perpendiculars being $$B$$, $$D$$, and $$F$$ respectively, and $$AB=1$$, $$CD=3$$. What is the length of $$EF$$?
A. $$1/3$$
B. $$2/3$$
C. $$3/4$$
D. $$4/5$$
|
C
|
|
<image>The school bought 23 books, each costing 14 yuan. The vertical calculation below shows the total price of the 23 books. The result indicated by the arrow in the vertical calculation represents ( )
A. The price of 2 books
B. The price of 3 books
C. The price of 20 books
D. The price of 23 books
|
C
|
|
<image>A school conducted a survey to understand the extracurricular reading habits of its students. They randomly surveyed 50 students and collected data on the time each student spent reading outside of class on a particular day, as shown in the bar chart. Based on this bar chart, estimate the average extracurricular reading time for students on that day ( )
A. 0.96 hours
B. 1.07 hours
C. 1.15 hours
D. 1.50 hours
|
B
|
|
<image>As shown in the figure, in rhombus $$ABCD$$, $$DE \bot AB$$, and $$\cos A = \frac{3}{5}$$, then the value of $$\tan \angle DBE$$ is ( ).
A. $$\frac{1}{2}$$
B. $$2$$
C. $$\frac{\sqrt{5}}{2}$$
D. $$\frac{\sqrt{5}}{5}$$
|
B
|
|
<image>As shown in the figure, in parallelogram $ABCD$, after folding triangle $\Delta ADC$ along $AC$, point $D$ exactly lands on point $E$ on the extension of $DC$. If $\angle B = 60^\circ$ and $AB = 3$, then the perimeter of $\Delta ADE$ is ( )
A. 12
B. 15
C. 18
D. 21
|
C
|
|
<image>The positions of rational numbers a and b on the number line are shown in the figure. Among the following expressions: 1. ab > 0, 2. |b - a| = a - b, 3. a + b > 0, 4. 1/a > 1/b, the correct ones are ( )
A. 2
B. 3
C. 4
D. 1
|
A
|
|
<image>Given, as shown in the figure, point $C$ is on segment $AB$, and $AC=6\text{cm}$, $BC=14\text{cm}$. Points $M$ and $N$ are the midpoints of $AC$ and $BC$, respectively. The length of segment $MN$ is ( )
A. 10
B. 8
C. 4
D. 2
|
A
|
|
<image>As shown in the figure, in the right triangular prism $ABC-{A}'{B}'{C}'$, $\Delta ABC$ is an equilateral triangle with side length 2, and $A{A}'=4$. Points $E$, $F$, $G$, $H$, and $M$ are the midpoints of edges $A{A}'$, $AB$, $B{B}'$, ${A}'{B}'$, and $BC$, respectively. A moving point $P$ moves inside quadrilateral $EFGH$ and always remains parallel to the plane $AC{C}'{A}'$. What is the length of the trajectory of the moving point $P$?
A. $4$
B. $2\sqrt{3}$
C. $2\pi$
D. $2$
|
A
|
|
<image>As shown in the figure, in rectangle $ABCD$, points $E$, $G$, and $F$ are on sides $AD$, $BC$, and $AB$ respectively. Triangle $AEF$ is folded along $EF$ to $\Delta A'EF$, and quadrilateral $EDCG$ is folded along $EG$ to $E D' C' G$, such that the corresponding point $D'$ of point $D$ falls on $A'E$. Given that $\angle AFE = 70°$, the measure of $\angle BGC'$ is ( )
A. $20°$
B. $30°$
C. $40°$
D. $50°$
|
C
|
|
<image>In the figure, in △ABC, it is known that AB = 8, BC = 6, CA = 4, DE is the midsegment, then DE = ( )
A. 4
B. 3
C. 2
D. 1
|
B
|
|
<image>As shown in the figure, in the Cartesian coordinate system, the vertices of $$\triangle ABC$$ are all on the grid points of the graph paper. If $$\triangle ABC$$ is first translated 4 units to the right and then 1 unit down, to obtain $$\triangle A_1B_1C_1$$, then the coordinates of the corresponding point $$A_1$$ of point $$A$$ are ( )
A. $$\left(4,3\right)$$
B. $$\left(2,4\right)$$
C. $$\left(3,1\right)$$
D. $$\left(2,5\right)$$
|
D
|
|
<image>As shown in the figure, the width of the shaded ring is exactly equal to the radius of the smaller circle. The area of the shaded part is ( ) of the area of the larger circle.
A. $$\dfrac{1}{4}$$
B. $$\dfrac{2}{3}$$
C. $$\dfrac{3}{4}$$
|
C
|
|
<image>The graph of the linear function $$y=kx+b\left(k\neq 0\right)$$ is shown in the figure. When $$y>0$$, the range of values for $$x$$ is ( ).
A. $$x<0$$
B. $$x>0$$
C. $$x<2$$
D. $$x>2$$
|
C
|
|
<image>As shown in the figure, $$AB$$ is the diameter of circle $$\odot O$$, point $$C$$ is on circle $$\odot O$$, and $$\angle B=70^\circ$$. What is the measure of $$\angle A$$?
A. $$20^\circ$$
B. $$25^\circ$$
C. $$30^\circ$$
D. $$35^\circ$$
|
A
|
|
<image>In the figure, in △ABC and △ADE, ∠ACB = ∠AED = 90°, ∠ABC = ∠ADE, connecting BD and CE, if AC:BC = 3:4, then BD:CE is ( )
A. 5:3
B. 4:3
C. √5:2
D. 2:√3
|
A
|
|
<image>Execute the program flowchart as shown. If the input is $$m=4$$, $$n=6$$, then the output $$a=$$（ ）
A. $$4$$
B. $$8$$
C. $$12$$
D. $$16$$
|
C
|
|
<image>The front view and top view of a geometric solid are shown in the figure. If this geometric solid is composed of at most $$a$$ small cubes and at least $$b$$ small cubes, then $$a+b$$ equals ( )
A. $$10$$
B. $$11$$
C. $$12$$
D. $$13$$
|
C
|
|
<image>As shown in the figure, in rectangle ABCD, AB=2AD, E is a point on CD, and AE=AB. What is the degree measure of ∠CBE?
A. 30°
B. 5°
C. 15°
D. 10°
|
C
|
|
<image>As shown in the figure, in the right triangle $\triangle ABC$, $AB=AC=1$. If $\triangle BCD$ is an equilateral triangle, then the perimeter of quadrilateral $ABCD$ is ( ).
A. $2+3\sqrt{2}$
B. $2+2\sqrt{2}$
C. $1+3\sqrt{2}$
D. $1+2\sqrt{2}$
|
B
|
|
<image>As shown in the figure, the condition that cannot determine $$\triangle{ADB} \backsim \triangle{ABC} $$ is ( ).
A. $$\angle{ABD} = \angle{ACB} $$
B. $$\angle{ADB} = \angle{ABC} $$
C. $${AB}^{2} = AD \cdot AC$$
D. $${AD \over AB} = {AB \over BC}$$
|
D
|
|
<image>As shown in the figure, the side length of the small squares on the grid paper is 1. The three views of a certain geometric body are drawn using thick solid and dashed lines. The curves in the figure are semicircular arcs or circles. The volume of the geometric body is ( )
A. $\frac{25\pi}{3}$
B. $\frac{34\pi}{3}$
C. $\frac{43\pi}{3}$
D. $25\pi$
|
C
|
|
<image>As shown in Figure 1, there is a lamp controlled by sensor A to be installed on the wall above the door, 4.5 m above the ground. The lamp will automatically turn on when any object is within 5 m of it. How far from the wall must a student, who is 1.5 m tall, be for the lamp to just start glowing?
A. 4 meters
B. 3 meters
C. 5 meters
D. 7 meters
|
A
|
|
<image>As shown in the figure, line l$_{1}$∥l$_{2}$, points A and B are fixed on line l$_{2}$, and point C is a moving point on line l$_{1}$. If points E and F are the midpoints of CA and CB, respectively, which of the following values do not change as point C moves: 1. The length of segment EF; 2. The perimeter of △CEF; 3. The area of △CEF; 4. The degree measure of ∠ECF.
A. 1.2.
B. 1.3.
C. 2.4.
D. 3.4.
|
B
|
|
<image>As shown in the figure, circle O intersects the sides OA and OE of the regular hexagon OABCDE at points F and G, respectively. The measure of the inscribed angle ∠FPG subtended by arc FG is ( )
A. 120°
B. 30°
C. 60°
D. 45°
|
C
|
|
<image>As shown in the figure, the radius of sector OAB is 12, OA is perpendicular to OB, and C is a point on OB. A semicircle O1 with OA as its diameter and a semicircle O2 with BC as its diameter are tangent at point D. The area of the shaded region in the figure is ( )
A. 6π
B. 10π
C. 12π
D. 20π
|
B
|
|
<image>Given the positions of rational numbers $a$ and $b$ on the number line as shown in the figure, which of the following four relations are correct: 1. a > 0, 2. -b < 0, 3. a - b > 0, 4. a + b > 0?
A. 4
B. 3
C. 2
D. 1
|
D
|
|
<image>As shown in the figure, the point sequences {A$_{n}$} and {B$_{n}$} are on the two sides of a certain acute angle, respectively, and $\left| {{A}_{n}}{{A}_{n+1}} \right|=\left| {{A}_{n+1}}{{A}_{n+2}} \right|,{{A}_{n}}\ne {{A}_{n+2}},n\in {{N}^{*}}$, $\left| {{B}_{n}}{{B}_{n+1}} \right|=\left| {{B}_{n+1}}{{B}_{n+2}} \right|,{{B}_{n}}\ne {{B}_{n+2}},n\in {{N}^{*}}$. (P ≠ Q indicates that point P does not coincide with Q) If ${{d}_{n}}=\left| {{A}_{n}}{{B}_{n}} \right|$, and ${{S}_{n}}$ is the area of $\vartriangle {{A}_{n}}{{B}_{n}}{{B}_{n+1}}$, then
A. ${{S}_{n}}$ is an arithmetic sequence
B. ${{S}_{n}^{2}}$ is an arithmetic sequence
C. ${{d}_{n}}$ is an arithmetic sequence
D. ${{d}_{n}^{2}}$ is an arithmetic sequence
|
A
|
|
<image>Given the function $f(x)=A\cos (wx+\phi )\left( w > 0,\quad |\phi | < \frac{\pi }{2} \right)$, part of its graph is shown in the figure below, where the coordinates of N and P are $\left( \frac{5}{8}\pi ,-\text{A} \right)$ and $\left( \frac{11}{8}\pi ,0 \right)$, respectively. Which of the following intervals cannot be the interval where the function $f(x)$ is monotonically decreasing?
A. $\left[ \frac{\pi }{8},\frac{5\pi }{8} \right]$
B. $\left[ -\frac{7\pi }{8},-\frac{3\pi }{8} \right]$
C. $\left[ \frac{9\pi }{4},\frac{21\pi }{8} \right]$
D. $\left[ \frac{9\pi }{8},\frac{33\pi }{8} \right]$
|
D
|
|
<image>The figure shows an 'H' formed with chess pieces. The first 'H' requires 7 pieces. The number of pieces required to form the x-th 'H' can be represented by an algebraic expression containing x ( ).
A. 5x
B. 5x-1
C. 5x+2
D. 5x+5
|
C
|
|
<image>As shown in the figure, the side length of the equilateral triangle $ABC$ is $L$, and points $A$ and $C$ move on the $x$-axis and $y$-axis, respectively. Let the maximum length of $OB$ be $L_{1}$ and the minimum length be $L_{2}$. Then the value of $L_{1} + L_{2}$ is ( )
A. $\sqrt {3}L$
B. $\dfrac{2\sqrt {3}}{3}L$
C. $\dfrac{3}{2}L + \dfrac{\sqrt {3}}{2}L$
D. $\dfrac{\sqrt {3}}{3}L$
|
C
|
|
<image>As shown in the figure, it is a partial 'petal' pattern. The complete 'petal' pattern is a very beautiful pattern; it is both an axisymmetric figure, a rotationally symmetric figure, and a centrally symmetric figure. How many axes of symmetry does the complete 'petal' pattern have? What is the minimum angle of rotation for the pattern to coincide with itself? The correct answer is ( )
A. It has 6 axes of symmetry, and must be rotated at least 60°
B. It has 12 axes of symmetry, and must be rotated at least 30°
C. It has 6 axes of symmetry, and must be rotated at least 30°
D. It has 12 axes of symmetry, and must be rotated at least 60°
|
B
|
|
<image>As shown in the figure: $\angle AOB:\angle BOC:\angle COD=2:3:4$, rays $OM$ and $ON$ bisect $\angle AOB$ and $\angle COD$ respectively, and $\angle MON=90^{\circ}$. Then $\angle AOB$ is ( )
A. $20^{\circ}$
B. $30^{\circ}$
C. $40^{\circ}$
D. $45^{\circ}$
|
B
|
|
<image>As shown in the figure, the diameter $$AB = 12$$ of circle $$ \odot O$$, $$CD$$ is a chord of $$ \odot O$$, $$CD \bot AB$$, and the foot of the perpendicular is $$P$$. Given that $$BP:AP = 1:5$$, the length of $$CD$$ is ( ).
A. $$4\sqrt{2}$$
B. $$8\sqrt{2}$$
C. $$2\sqrt{5}$$
D. $$4\sqrt{5}$$
|
D
|
|
<image>Referring to the flowchart shown, run the corresponding program. The output result is ( ).
A. $$-1$$
B. $$0$$
C. $$7$$
D. $$1$$
|
A
|
|
<image>As shown in the figure, a set of parallel lines, ${{l}_{1}}//{{l}_{2}}//{{l}_{3}}$, intersect line $a$ at points $A$, $B$, $C$; and intersect line $b$ at points $D$, $E$, $F$. If $AB:BC=2:3$ and $DF=15$, then $EF=$ ( )
A. 6
B. 8
C. 9
D. 10
|
C
|
|
<image>In ancient Chinese mathematical works, such as the 'Nine Chapters on the Mathematical Art,' there is a problem: 'There is a container of rice, the amount of which is unknown. The first person takes half of it, the second person takes one-third of what remains, and the third person takes one-fourth of what is left. There are 15 sheng (a unit of volume) of rice remaining. What was the original amount of rice?' The diagram below shows a flowchart for solving this problem. If the output $S=3$ (unit: sheng), then what is the value of the input $k$?
A. 4.5
B. 6
C. 9
D. 12
|
C
|
|
<image>As shown in the figure, the small squares have a side length of $$1$$. The three views of a geometric solid are shown in the figure. The surface area of the solid is ( ).
A. $$4\sqrt{5}\pi+96$$
B. $$(2\sqrt{5}+6)\pi+96$$
C. $$(4\sqrt{5}+4)\pi+64$$
D. $$(4\sqrt{5}+4)\pi+96$$
|
D
|
|
<image>$\vartriangle ABC$ is an equilateral triangle with side length 2, and $M$ is the midpoint of $AC$. $\vartriangle ABM$ is folded along $BM$ to the position of $\vartriangle PBM$. When the volume of the tetrahedron $P-BCM$ is maximized, the surface area of the circumscribed sphere of the tetrahedron $P-BCM$ is ( )
A. $\pi$
B. $3\pi$
C. $5\pi$
D. $7\pi$
|
C
|
|
<image>As shown in the figure, a dart is thrown at an equilateral triangle region. Assuming the dart is equally likely to hit any of the small triangular regions in the figure, what is the probability that the dart will hit the shaded area in one throw?
A. $\dfrac{1}{6}$
B. $ \dfrac{1}{4}$
C. $ \dfrac{3}{8}$
D. $ \dfrac{5}{8}$
|
C
|
|
<image>As shown in the figure, in △ABC, ∠BAC=90°, AB=AC, AE is a line passing through point A, and B, C are on opposite sides of AE. BD⊥AE at D, CE⊥AE at E, CE=3, BD=9, then the length of DE is ( )
A. $5$
B. $5.5$
C. $6$
D. $7$
|
C
|
|
<image>As shown in the figure, in parallelogram $ABCD$, diagonals $AC$ and $BD$ intersect at point $O$. If $AB=7$, $AC=8$, and $BD=10$, then the perimeter of $\Delta OCD$ is ( )
A. 12
B. 13
C. 15
D. 16
|
D
|
|
<image>As shown in the figure, in $\Delta ABC$, $\angle ACB={{90}^{\circ }}$, $CD\bot AB$, with the foot of the perpendicular at $D$, point $E$ is the midpoint of side $AB$, $AB=10$, $DE=4$, then ${{S}_{\Delta AEC}}=$（）
A. 8
B. 7.5
C. 7
D. 6
|
B
|
|
<image>As shown in the figure, $$AB$$ and $$AC$$ are two tangents to circle $$\odot{O}$$, with $$B$$ and $$C$$ being the points of tangency. If $$\angle{A}=70^{\circ}$$, then the measure of $$\angle{BOC}$$ is ( ).
A. $$100^{\circ}$$
B. $$110^{\circ}$$
C. $$120^{\circ}$$
D. $$130^{\circ}$$
|
B
|
|
<image>As shown in the figure, compared to the triangle in 1., the change in the triangle in 2. is ( )
A. Shifted 3 units to the left
B. Shifted 1 unit to the left
C. Shifted 3 units up
D. Shifted 1 unit down
|
A
|
|
<image>As shown in the figure, in the Cartesian coordinate system, the parabola y = (x + 1)(x - 3) intersects the x-axis at points A and B. If there are exactly three distinct points C$_{1}$, C$_{2}$, and C$_{3}$ on the parabola such that the areas of triangles ABC$_{1}$, ABC$_{2}$, and ABC$_{3}$ are all equal to m, then the value of m is ( )
A. 6
B. 8
C. 12
D. 16
|
B
|
|
<image>As shown in the figure, given $$\angle1 =\angle2$$, $$\angle BAD =\angle BCD$$, which of the following conclusions are correct: (1) $$AB \parallel CD$$; (2) $$AD \parallel BC$$; (3) $$\angle B=\angle D$$; (4) $$\angle D=\angle ACB$$. How many of these are correct?
A. 1
B. 2
C. 3
D. 4
|
C
|
|
<image>Let $$(x_{1},y_{1})$$, $$(x_{2},y_{2})$$, $$\cdots$$, $$(x_{n},y_{n})$$ be $$n$$ sample points of variables $$x$$ and $$y$$. The line $$l$$ is the linear regression line obtained by the least squares method from these sample points (as shown in the figure). Which of the following conclusions is correct?
A. Line $$l$$ passes through the point $$(\overline{x},\overline{y})$$
B. The correlation coefficient between $$x$$ and $$y$$ is the slope of line $$l$$
C. The correlation coefficient between $$x$$ and $$y$$ is between $$0$$ and $$1$$
D. When $$n$$ is even, the number of sample points distributed on both sides of $$l$$ must be the same
|
A
|
|
<image>Two squares, each with a side length of $$8$$ cm, are joined to form a rectangle. The perimeter of the resulting rectangle is ( ) cm.
A. $$48$$
B. $$64$$
C. $$56$$
|
A
|
|
<image>In the right triangle ABC, ∠C=90°, D is a point on BC, sin∠ADC=\frac{\sqrt{3}}{2}, AD=BD, BD=2, AB=2\sqrt{3}, then the length of AC is ( ).
A. \sqrt{2}
B. \sqrt{3}
C. 2\sqrt{3}
D. 3\sqrt{3}
|
B
|
|
<image>As shown in the figure, the graph (line ABCDE) describes the relationship between the distance s (kilometers) from the starting point and the driving time t (hours) of a car traveling on a straight line. Based on the information provided in the graph, which of the following statements is correct?
A. The car traveled a total of 120 kilometers
B. The average speed of the car throughout the journey was 40 kilometers per hour
C. The speed of the car on its return was 80 kilometers per hour
D. The car maintained a constant speed between 1.5 hours and 2 hours after departure
|
C
|
|
<image>As shown in the figure, in the right triangle ABC, ∠ABC = 90°. Semicircles are drawn with diameters AB, BC, and AC, with areas denoted as S$_{1}$, S$_{2}$, and S$_{3}$, respectively. If S$_{1}$ = 4 and S$_{2}$ = 9, then the value of S$_{3}$ is ( )
A. 13
B. 5
C. 11
D. 3
|
A
|
|
<image>As shown in the figure, a road is being constructed along the direction of $AC$. To accelerate the construction progress, work is also being carried out simultaneously on the other side of the hill. From a point $B$ on $AC$, $\angle ABD=150^{\circ}$, $BD=500$ meters, and $\angle D=60^{\circ}$. To make $A$, $C$, and $E$ in a straight line, the distance from the excavation point $E$ to point $D$ is ( )
A. $200$ meters
B. $250$ meters
C. $300$ meters
D. $350$ meters
|
B
|
|
<image>Execute the program flowchart shown in the figure, then the output value of $$s$$ is ( )
A. $$\dfrac{3}{4}$$
B. $$\dfrac{5}{6}$$
C. $$\dfrac{11}{12}$$
D. $$\dfrac{25}{24}$$
|
D
|
|
<image>The graphs of the linear function $$y=kx+b$$ and the inverse proportion function $$y=\dfrac{k}{x}$$ are shown in the figure. Which of the following statements is correct?
A. Their function values $$y$$ increase as $$x$$ increases
B. Their function values $$y$$ decrease as $$x$$ increases
C. $$k<0$$
D. Their independent variable $$x$$ can take all real numbers
|
C
|
|
<image>As shown in the figure, there is a largest circle inside a square, with a radius of $$4$$ decimeters. The side length of the square is ( ).
A. $$16$$ decimeters
B. $$80$$ decimeters
C. $$8$$ decimeters
D. $$4$$ decimeters
|
C
|
|
<image>In a shooting competition, two participants, A and B, each shot at the target 6 times. The bar charts of their scores are shown in the figure. The mode of A's scores and the median of B's scores are
A. 2, 2
B. 2, 5.5
C. 7, 5
D. 7, 5.5
|
D
|
|
<image>A certain region has a total of 100,000 households, with the ratio of urban to rural households being 4:6. According to stratified sampling, the refrigerator ownership of 1,000 households in the region was surveyed, and the results are shown in the table below. Therefore, the estimated total number of rural households without a refrigerator in the region is ( ).
A. 16,000 households
B. 44,000 households
C. 17,600 households
D. 2,700 households
|
A
|
|
<image>As shown in the figure, CF is the bisector of the exterior angle ∠ACM of △ABC, and CF∥AB, ∠ACF=50°, then the measure of ∠B is
A. 80°
B. 40°
C. 60°
D. 50°
|
D
|
|
<image>As shown in the figure, $$EF$$ passes through the intersection point $$O$$ of the diagonals of rectangle $$ABCD$$, and intersects $$AB$$ and $$CD$$ at $$E$$ and $$F$$, respectively. The area of the shaded region is ( ) of the area of rectangle $$ABCD$$.
A. $$\frac{1}{5}$$
B. $$\frac{1}{4}$$
C. $$\frac{1}{3}$$
D. $$\frac{3}{10}$$
|
B
|
|
<image>As shown in the figure, ⊙O is the circumcircle of △ABC. Given that ∠OAB = 30°, then ∠ACB is ( )
A. 50º
B. 60°
C. 70°
D. 80°
|
B
|
|
<image>As shown in the figure, given triangle $$ABC$$, $$AB=10$$, $$AC=8$$, $$BC=6$$, $$DE$$ is the perpendicular bisector of $$AC$$, $$DE$$ intersects $$AB$$ at $$D$$, and $$CD$$ is connected. $$CD=$$ （ ）
A. $$3$$
B. $$4$$
C. $$4.8$$
D. $$5$$
|
D
|
|
<image>The three views of a geometric solid are shown in the figure below. The volume of the solid is ( ).
A. $$16$$
B. $$8$$
C. $$10$$
D. $$24$$
|
B
|
|
<image>The three views of a geometric solid are shown in the figure. The front view and side view are both equilateral triangles with a side length of $2$, and the top view is a square. The total surface area of the geometric solid is ( )
A. $4$
B. $8$
C. $12$
D. $4+4\sqrt {3}$
|
C
|
|
<image>As shown in the figure, Tian Liang used scissors to cut along a straight line to remove a part of a flat leaf and found that the perimeter of the remaining leaf is smaller than the original leaf's perimeter. The mathematical knowledge that can correctly explain this phenomenon is ( )
A. The shortest distance between two points is a straight line
B. Through a point, there are infinitely many lines
C. Through two points, there is exactly one line
D. A part is less than the whole
|
A
|
|
<image>King Tiger organized a fruit exchange activity for the little animals using a seesaw. The little monkey brought 12 cherries. According to the exchange rules below, it can exchange for ( ) pears.
A. 1
B. 2
C. 3
D. 4
|
B
|
|
<image>As shown in the figure, in quadrilateral $$ABCD$$, $$\angle ABC=90^{ \circ }$$, $$AB=BC=2\sqrt{2}$$, $$E$$ and $$F$$ are the midpoints of $$AD$$ and $$CD$$ respectively. Connecting $$BE$$, $$BF$$, and $$EF$$. If the area of quadrilateral $$ABCD$$ is $$6$$, then the area of $$\triangle BEF$$ is ( )
A. $$2$$
B. $$\dfrac{9}{4}$$
C. $$\dfrac{5}{2}$$
D. $$3$$
|
C
|
|
<image>Given a plane quadrilateral ABCD, its oblique axonometric drawing (with ∠x'O'y' = 45°) is a square A'B'C'D' with a side length of 1 (as shown in the figure), then the area of the original plane quadrilateral ABCD is ( )
A. $\sqrt{5}$
B. $\sqrt{3}$
C. $2\sqrt{2}$
D. $2\sqrt{5}$
|
C
|
|
<image>In the right triangle $ABC$, $\angle ACB=90{}^\circ $, $CD$ is the altitude, $\angle A=30{}^\circ $, and $BD=2cm$. What is the length of $AB$?
A. $10cm$
B. $8cm$
C. $6cm$
D. $4cm$
|
B
|
|
<image>In statistics, there is a very useful statistic $$k^2$$, which can be used to determine the extent to which we can believe that 'two categorical variables are related.' The following table reflects the results of a math exam for two parallel classes (Class A taught by Teacher A, Class B taught by Teacher B), categorized by whether students passed or failed the exam, in a $$2\times2$$ contingency table: Based on the value of $$k^2$$, what is the approximate confidence level that the number of failures is related to the different teachers?
A. $$99.5%$$
B. $$99.9%$$
C. $$95%$$
D. Insufficient evidence
|
A
|
|
<image>As shown in the figure, if $$\angle 1 + \angle 2 = 180^{\circ}$$, then ( ).
A. $$ \angle 2 + \angle 4 = 180^{\circ}$$
B. $$ \angle 3 + \angle 4 = 180^{\circ}$$
C. $$ \angle 1 + \angle 3 = 180^{\circ}$$
D. $$ \angle 1 = \angle 4$$
|
C
|
|
<image>The three views of a geometric solid are a square, a rectangle, and a semicircle, with the sizes as shown in the figure. The volume of the geometric solid is ( )
A. $\frac{\pi}{2}$
B. $\frac{2\pi}{3}$
C. $\pi$
D. $2\pi$
|
C
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.