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<image>The partial graph of the function $f(x)=A\cos (\omega x+\varphi )(A > 0$, $\omega > 0$, $\varphi \in (-\pi ,0)$ is shown in the figure. To obtain the graph of the function $y=A\sin \omega x$, the graph of $f(x)$ needs to be ( )
A. Shifted left by $\frac{\pi }{12}$
B. Shifted left by $\frac{\pi }{6}$
C. Shifted right by $\frac{\pi }{12}$
D. Shifted right by $\frac{\pi }{6}$
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C
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<image>As shown in the figure, point $A$ is translated to point $O$ (as shown in the figure). If a point $P$ on the left figure has coordinates $\left(m,n\right)$, then the coordinates of the corresponding point $P'$ after translation in the right figure are ( )
A. $\left(m+2,n+1\right)$
B. $ \left(m-2,n-1\right)$
C. $ \left(m-2,n+1\right)$
D. $ \left(m+2,n-1\right)$
|
D
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<image>On the number line shown, the positions of the rational numbers a, b, and c are marked. Then ( )
A. -c < b-a < b-c
B. -b < b-c < a-c
C. -c < a-c < a-b
D. -c < b-c < b-a
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D
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<image>As shown in the figure, the radius of the circle is 5, and the area of the shaded part inside the circle is ( )
A. $\frac{175\pi }{36}$
B. $\frac{125\pi }{18}$
C. $\frac{25\pi }{6}$
D. $\frac{34\pi }{9}$
|
A
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<image>As shown in the figure, a worker has made a rectangular window frame $$ABCD$$, with $$E$$, $$F$$, $$G$$, and $$H$$ being the midpoints of the four sides. To stabilize it, a wooden strip needs to be nailed on the window frame, but it should not be nailed between ( ).
A. Between points $$AC$$
B. Between points $$EG$$
C. Between points $$BF$$
D. Between points $$GH$$
|
B
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<image>As shown in the figure, in $\vartriangle ABC$, it is given that $\angle C={{90}^{\circ }}$, $BC=6$, and $AC=8$. What is the radius of its inscribed circle?
A. $\frac{\sqrt{3}}{2}$
B. $\frac{2}{3}$
C. $2$
D. $1$
|
C
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<image>As shown in the figure, AB⊥BC, the degree of ∠ABD is 15° less than twice the degree of ∠DBC. Let the degrees of ∠ABD and ∠DBC be x° and y°, respectively. According to the problem, which of the following systems of equations is correct?
A. $\left\{ \begin{array}{*{35}{l}} x+y=90 x=y-15 \end{array} \right.$
B. $\left\{ \begin{array}{*{35}{l}} x+y=90 x=2y-15 \end{array} \right.$
C. $\left\{ \begin{array}{*{35}{l}} x+y=90 x=15-2y \end{array} \right.$
D. $\left\{ \begin{array}{*{35}{l}} x+y=90 x=2y+15 \end{array} \right.$
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B
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<image>As shown in the figure, the partial graph of the quadratic function $$y=a{{x}^{2}}+bx+c$$ intersects the coordinate axes at points $$A\left( 3,0 \right)$$ and $$C\left( 0,2 \right)$$, and the axis of symmetry is the line $$x=1$$. When the function value $$y>0$$, the range of the independent variable $$x$$ is ( ).
A. $$x<{}3$$
B. $$0\leqslant x<{}3$$
C. $$-2<{}x<{}3$$
D. $$-1<{}x<{}3$$
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D
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<image>In the figure shown, the geometric solids that are prisms are ( ).
A. 5
B. 4
C. 3
D. 2
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D
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<image>In the rectangular prism shown in the figure, the geometric body formed by the vertices $O, A, B, C, D$ is ( )
A. Triangular Pyramid
B. Quadrilateral Pyramid
C. Triangular Prism
D. Quadrilateral Prism
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B
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<image>The figures 1.~4. in the square grid are shown as follows, where the shaded triangles in figures 1. and 2. are right triangles with one angle of $60{}^\circ$, and the shaded triangles in figures 3. and 4. are acute triangles with one angle of $60{}^\circ$. Which of the following figures can form a regular triangular prism?
A. 1. and 4.
B. 3. and 4.
C. 1. and 2.
D. 2. 3. 4.
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A
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<image>As shown in the figure, the central angle of sector $$AOB$$ is $$120{}^\circ$$, point $$P$$ is on chord $$AB$$, and $$AP=\frac{1}{3}AB$$. Extend $$OP$$ to intersect arc $$AB$$ at $$C$$. If a point is randomly thrown into sector $$AOB$$, what is the probability that the point falls within sector $$AOC$$?
A. $$\frac{1}{4}$$
B. $$\frac{1}{3}$$
C. $$\frac{2}{7}$$
D. $$\frac{3}{8}$$
|
A
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<image>As shown in the figure, in $\Delta ABC$, $AB=AC$, $AD\bot BC$, with the foot of the perpendicular at $D$. $E$ is any point on $AD$. Then, the number of pairs of congruent triangles is ( )
A. 2
B. 3
C. 4
D. 5
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B
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<image>As shown in the figure, in $\vartriangle ABC$, DE and FG are the perpendicular bisectors of sides AB and AC, respectively. Given that $\angle BAC=100{}^\circ$ and $AB > AC$, the measure of $\angle EAG$ is
A. $10{}^\circ$
B. $20{}^\circ$
C. $30{}^\circ$
D. $40{}^\circ$
|
B
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<image>Execute the program flowchart as shown. If the input value of N is 6, then the output value of p is ( )
A. 15
B. 105
C. 120
D. 720
|
B
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|
<image>As shown in the figure, which of the following statements is incorrect?
A. ∠A and ∠C are consecutive interior angles
B. ∠1 and ∠3 are corresponding angles
C. ∠2 and ∠3 are alternate interior angles
D. ∠3 and ∠B are consecutive interior angles
|
B
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<image>The positions of the real numbers $$a$$ and $$b$$ on the number line are shown in the figure. Among $$a+b$$, $$b-2a$$, $$|b|-|a|$$, $$|a-b|$$, and $$|a+2|-|b-4|$$, the number of negative values is ( ).
A. $$3$$
B. $$1$$
C. $$4$$
D. $$2$$
|
A
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<image>As shown in the figure, a square ABCD with side length of 8 cm is folded so that point D falls on the midpoint E of side BC, and point A falls on point F. The crease is MN. What is the length of segment CN?
A. 3 cm
B. 4 cm
C. 5 cm
D. 6 cm
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A
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<image>A city has implemented a peak and off-peak electricity policy with the following rates: It is known that Mr. Wang's family used 75 kWh of peak electricity and 30 kWh of off-peak electricity in April. The total electricity bill is ( ) yuan.
A. $$number{32.3}$$
B. $$number{50.4}$$
C. $$number{43.4}$$
D. $$38$$
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B
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<image>As shown in the figure, this is the string diagram provided by Zhao Shuang from the Han Dynasty in the 3rd century when he annotated the 'Zhou Bi Suan Jing'. It was also selected as the emblem for the International Congress of Mathematicians held in Beijing in 2002. There are four congruent right-angled triangles inside the square ABCD. If a point is randomly chosen within the square, what is the probability that this point is from the smaller central square?
A. $$\frac{1}{4}$$
B. $$\frac{1}{25}$$
C. $$\frac{3}{4}$$
D. $$\frac{24}{25}$$
|
B
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<image>The graph of the quadratic function $$y=a{{x}^{2}}+bx+c(a\ne 0)$$ is shown in the figure below, then which of the following statements is correct?
A. $$a>b>c$$
B. The graph of the linear function $$y=ax+c$$ does not pass through the fourth quadrant
C. $$m(am+b)+b<a$$ (where $$m$$ is any real number)
D. $$3b+2c>0$$
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D
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<image>To promote traditional Chinese culture, the student council of a middle school randomly surveyed 50 students out of 1,000 first-year high school students about their participation in traditional cultural activities during their free time. After organizing the data, the following list was created: Estimate the correct situation regarding the participation of first-year high school students in traditional cultural activities ( ).
A. The number of students who attended 3 activities is approximately 360.
B. The number of students who attended 2 or 4 activities is approximately 480.
C. The number of students who attended no more than 2 activities is approximately 280.
D. The number of students who attended 4 or more activities is approximately 360.
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D
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<image>While doing his homework, Xiao Ming accidentally dropped ink on the number line. Based on the values in the image, determine how many integers are covered by the ink.
A. 8
B. 9
C. 10
D. 11
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B
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<image>As shown in the figure, let $$P$$ be a point on the surface (including edges) of a regular tetrahedron $$A-BCD$$ that does not coincide with any vertex. The set of distances from point $$P$$ to the four vertices is denoted as $$M$$. If the set $$M$$ contains exactly 2 elements, then the number of points $$P$$ that satisfy this condition is ( )
A. $$4$$ points
B. $$6$$ points
C. $$10$$ points
D. $$14$$ points
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C
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<image>As shown in the figure, in the right triangle $ABC$, $\angle BAC=90^{\circ}$, $AD\bot BC$. If $AB=2$ and $BC=4$, then the length of $DC$ is ( )
A. $1$
B. $ \sqrt{3}$
C. $ 3$
D. $ 2\sqrt{3}$
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C
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<image>As shown in the figure, the area of the shaded part is ( )
A. $2\sqrt{3}$
B. $-2\sqrt{3}$
C. $\frac{35}{3}$
D. $\frac{32}{3}$
|
D
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<image>As shown in the figure, lines a and b are intersected by line c. Given the following four conditions: 1. ∠1 = ∠5; 2. ∠1 = ∠7; 3. ∠2 + ∠3 = 180°; 4. ∠4 = ∠7. Which conditions can be used to prove that a ∥ b?
A. 1.2.
B. 1.3.
C. 1.4.
D. 3.4.
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A
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<image>As shown in the figure, the line $$y=-x+3$$ intersects the $$y$$-axis at point $$A$$, and intersects the graph of the inverse proportion function $$y=\dfrac{k}{x}(k≠0)$$ at point $$C$$. A perpendicular is drawn from point $$C$$ to the $$x$$-axis, meeting it at point $$B$$. If $$AO=3BO$$, then the equation of the inverse proportion function is ( )
A. $$y=\dfrac{4}{x}$$
B. $$y=-\dfrac{4}{x}$$
C. $$y=\dfrac{2}{x}$$
D. $$y=-\dfrac{2}{x}$$
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B
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<image>To protect the environment and strengthen environmental education, a middle school organized students to participate in a voluntary activity to collect used batteries. Below is a statistical summary of the number of used batteries collected by 40 randomly selected students. Based on the number of used batteries collected by the students, determine which of the following statements is correct ( ).
A. The sample is 40 students
B. The mode is 11 batteries
C. The median is 6 batteries
D. The mean is 5.6 batteries
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D
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<image>As shown in the figure, in $\triangle ABC$, $\angle CBA = \angle CAB = 30^{\circ}$. The altitudes from $AC$ and $BC$ are $BD$ and $AE$, respectively. The sum of the reciprocals of the eccentricities of the ellipse and hyperbola with foci at $A$ and $B$ and passing through $D$ and $E$ is ( )
A. $\sqrt {3}$
B. $1$
C. $2\sqrt {3}$
D. $2$
|
A
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<image>The three views of a geometric solid are shown in the figure. The volume of the solid is ( )
A. $30\sqrt{3}$
B. $20\sqrt{3}$
C. $10\sqrt{3}$
D. $5\sqrt{3}$
|
B
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<image>As shown in the figure, $$BD$$ bisects $$\angle ABC$$, point $$E$$ is on $$BC$$, and $$EF \parallel AB$$. If $$\angle CEF = 100^{\circ}$$, then the measure of $$\angle ABD$$ is ( ).
A. $$60^{\circ}$$
B. $$50^{\circ}$$
C. $$40^{\circ}$$
D. $$30^{\circ}$$
|
B
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<image>In the parallelogram $$ABCD$$, point $$E$$ is on $$AD$$, and line $$CE$$ is extended to intersect the extension of $$BA$$ at point $$F$$. If $$AE=2ED$$, which of the following conclusions is incorrect?
A. $$EF=2CE$$
B. $${{S}_{triangle AEF}}=\frac{2}{3}{{S}_{triangle BCF}}$$
C. $$BF=3CD$$
D. $$BC=\frac{3}{2}AE$$
|
B
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<image>As shown in the figure, in the rectangular prism $$ABCD-A_1B_1C_1D_1$$, points $$E$$ and $$H$$ are on the edges $$A_1B_1$$ and $$D_1C_1$$ respectively (point $$E$$ does not coincide with $$B_1$$), and $$EH//A_1D_1$$. The plane through $$EH$$ intersects the edges $$BB_1$$ and $$CC_1$$ at points $$F$$ and $$G$$ respectively. Given that $$AB=2AA_1=2a$$, $$EF=a$$, and $$B_1E=B_1F$$, if a point is randomly selected within the rectangular prism $$ABCD-A_1B_1C_1D_1$$, what is the probability that the point lies within the geometric figure $$A_1ABFE-D_1DCGH$$?
A. $$\frac{11}{16}$$
B. $$\frac{3}{4}$$
C. $$\frac{13}{16}$$
D. $$\frac{7}{8}$$
|
D
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<image>As shown in the figure, line $m$ intersects line $n$ at point $C\left( 1,\sqrt{3} \right)$, line $m$ intersects the $x$-axis at point $D\left( -2,0 \right)$, line $n$ intersects the $x$-axis at point $B\left( 2,0 \right)$, and intersects the $y$-axis at point $A$. Which of the following statements is incorrect?
A. $m \perp n$
B. $\Delta AOB \cong \Delta DCB$
C. $BC=AC$
D. The function expression of line $m$ is $y=\frac{\sqrt{3}}{3}x+\frac{\sqrt{3}}{3}$
|
D
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<image>The figure shows the share of pages for each section in a newspaper bound volume. The newspaper bound volume has a total of 208 pages. Therefore, the International News section has approximately ( ) pages.
A. 70
B. 52
C. 34
D. 104
|
A
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<image>As shown in the figure, it is known that $\angle ACB=\angle B$, $BC$ bisects $\angle ACD$, and $\angle A=120{}^\circ$. What is the degree measure of $\angle BCD$?
A. $30{}^\circ$
B. $25{}^\circ$
C. $20{}^\circ$
D. $40{}^\circ$
|
A
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<image>A school needs to select one student from four students, Jia, Yi, Bing, and Ding, to participate in the district-organized 'My Chinese Dream' speech contest. After multiple rounds of selection within the school, the average scores $$\overline x$$ and variances $$S^2$$ of each student are shown in the table. If the school wants to choose a student with a high average score and stable performance, then this student should be ( ).
A. Jia
B. Yi
C. Bing
D. Ding
|
B
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<image>As shown in the figure, $$D$$ is a point on the hypotenuse $$BC$$ of $$Rt\triangle ABC$$, and $$AB=AD$$. Let $$\angle CAD=α$$ and $$\angle ABC=β$$. If $$α=10^{\circ}$$, then the measure of $$β$$ is ( ).
A. $$40^{\circ}$$
B. $$50^{\circ}$$
C. $$60^{\circ}$$
D. Cannot be determined
|
B
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<image>As shown in the figure, the side length of the regular octagon $$A_{1}A_{2}A_{3}A_{4}A_{5}A_{6}A_{7}A_{8}$$ is $$2$$. If $$P$$ is a moving point on the edge of the regular octagon, then the range of $$\overrightarrow{ A_{1}A_{3}}\cdot \overrightarrow{A_{1}P}$$ is ( ).
A. $$\left \lbrack 0,8+6\sqrt{2}\right \rbrack $$
B. $$\left \lbrack -2\sqrt{2},8+6\sqrt{2}\right \rbrack $$
C. $$\left \lbrack -8-6\sqrt{2},2\sqrt{2}\right \rbrack $$
D. $$\left \lbrack -8-6\sqrt{2},8+6\sqrt{2}\right \rbrack $$
|
B
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<image>As shown in the figure, four line segments are connected end-to-end to form a frame, where $$AB=12$$, $$BC=14$$, $$CD=18$$, $$DA=24$$. The maximum distance between any two points among $$A$$, $$B$$, $$C$$, $$D$$ is ( )
A. $$24$$
B. $$26$$
C. $$32$$
D. $$36$$
|
C
|
|
<image>The number of geometric solids that belong to the category of prisms is ( ).
A. $$3$$
B. $$4$$
C. $$5$$
D. $$6$$
|
C
|
|
<image>A little mouse entered a maze, where every door is identical; at the other end of the maze, there are $4$ buttons, all of which look the same, with the $3$rd button being the switch for the maze. Pressing this button will automatically open the exit of the maze. What is the probability that the little mouse will find the maze switch on the first try? $\left( \right)$
A. $\dfrac{1}{4}$
B. $ \dfrac{1}{2}$
C. $ \dfrac{1}{3}$
D. $ \dfrac{1}{5}$
|
A
|
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<image>The three views of a geometric solid are shown in the figure: The front view and side view are both right-angled triangles with a hypotenuse of length $$2$$, and the top view is a quarter circle with a radius of $$1$$ and two radii. The surface area of this geometric solid is ( ).
A. $$\frac{\pi}{2}+\sqrt{3}$$
B. $$\frac{3\pi}{4}+\sqrt{3}$$
C. $$\frac{5\pi}{4}+\sqrt{3}$$
D. $$\frac{9\pi}{4}+\sqrt{3}$$
|
B
|
|
<image>Lines $$AB$$, $$BC$$, $$CD$$, and $$EG$$ are shown in the figure. $$ \angle{1} = \angle{2} = 80° $$, $$ \angle{3} = 40°$$. Which of the following conclusions is incorrect?
A. $$AB \parallel CD$$
B. $$\angle{EBF} = 40° $$
C. $$ \angle{FCG} + \angle{3} = \angle{2} $$
D. $$EF > BE$$
|
D
|
|
<image>Among the following curves, which one passes through the origin?
A. y=2(x-1)²
B. (x+1)²+(y-1)²=2
C.
D. (x-3)²+(y-2)²=4
|
B
|
|
<image>As shown in the figure, in parallelogram $$ABCD$$, the bisector of $$\angle ABC$$ intersects $$AD$$ at $$E$$, and $$\angle BED=150\degree$$. What is the measure of $$\angle A$$?
A. $$150\degree$$
B. $$130\degree$$
C. $$120\degree$$
D. $$100\degree$$
|
C
|
|
<image>As shown in the figure, $$\triangle ABC$$ and $$\triangle EFG$$ are both equilateral triangles with side lengths of $$2$$. Point $$D$$ is the midpoint of sides $$BC$$ and $$EF$$. The lines $$AG$$ and $$FC$$ intersect at point $$M$$. When $$\triangle EFG$$ rotates around point $$D$$, the minimum length of segment $$BM$$ is ( )
A. $$2-\sqrt{3}$$
B. $$\sqrt{3}+1$$
C. $$\sqrt{2}$$
D. $$\sqrt{3}-1$$
|
D
|
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<image>The graphs of the linear functions $$y=ax-1$$ and $$y=bx+5$$ are shown in the figure below. The values of $$a$$ and $$b$$ are ( )
A. $$a=3$$, $$b=2$$
B. $$a=2$$, $$b=3$$
C. $$a=1$$, $$b=-1$$
D. $$a=-1$$, $$b=1$$
|
C
|
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<image>As shown in the figure, $$PT$$ is tangent to circle $$O$$ at point $$T$$, $$PA$$ intersects circle $$O$$ at points $$A$$ and $$B$$, and intersects the diameter $$CT$$ at point $$D$$. Given that $$CD=3$$, $$AD=4$$, and $$BD=6$$, then $$PB=$$ ( ).
A. $$6$$
B. $$8$$
C. $$10$$
D. $$14$$
|
D
|
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<image>On May 12, a strong earthquake of magnitude 8.0 struck Wenchuan County, Sichuan, causing huge losses to the local people. A school actively organized a donation drive to support the disaster area. In Class 8 of Grade 7, all 56 students donated a total of 4500 yuan. The donation details are as follows: Donation (yuan) 200 100 50 20, Number of people 5 10. The number of people who donated 100 yuan and 50 yuan was accidentally stained by ink and is unclear. If we let the number of students who donated 100 yuan be x and the number of students who donated 50 yuan be y, according to the problem, the system of equations is ( )
A. $\left\{\begin{array}{l}x+y=41\\100x+50y=3300\end{array}\right.$
B. $\left\{\begin{array}{l}x+y=41\\100x+50y=4000\end{array}\right.$
C. $\left\{\begin{array}{l}x+y=41\\50x+100y=3300\end{array}\right.$
D. $\left\{\begin{array}{l}x+y=41\\50x+100y=4000\end{array}\right.$
|
A
|
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<image>As shown in the figure, in the rectangular prism $ABCD-{{A}_{1}}{{B}_{1}}{{C}_{1}}{{D}_{1}}$, $E$ is a point on edge $C{{C}_{1}}$ such that $CE=\frac{1}{3}C{{C}_{1}}$. The plane passing through points $B, D, E$ divides the rectangular prism $ABCD-{{A}_{1}}{{B}_{1}}{{C}_{1}}{{D}_{1}}$ into two parts. Let the volume of the polyhedron $ABED{{D}_{1}}{{A}_{1}}{{B}_{1}}{{C}_{1}}$ be ${{V}_{1}}$, and the volume of the tetrahedron $E-BCD$ be ${{V}_{2}}$. Then $\frac{{{V}_{1}}}{{{V}_{2}}}=$ ( )
A. 14
B. 15
C. 16
D. 17
|
D
|
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<image>As shown in the figure, in $$\triangle ABC$$, $$\angle ACB=90^{ \circ }$$, $$AC > BC$$. Squares $$ABDE$$, $$CMNB$$, and $$FGCA$$ are constructed outward on the sides $$AB$$, $$BC$$, and $$CA$$ of $$\triangle ABC$$, respectively. Connect $$EF$$, $$GM$$, and $$ND$$. Let the areas of $$\triangle AEF$$, $$\triangle CGM$$, and $$\triangle BND$$ be $$S_{1}$$, $$S_{2}$$, and $$S_{3}$$, respectively. Which of the following conclusions is correct?
A. $$S_{1}=S_{2}=S_{3}$$
B. $$S_{1}=S_{2} < S_{3}$$
C. $$S_{1}=S_{3} < S_{2}$$
D. $$S_{2}=S_{3} < S_{1}$$
|
A
|
|
<image>The following figures are all composed of black triangles of the same size arranged according to a certain pattern. In the 1st figure, there are a total of 4 black triangles; in the 2nd figure, there are a total of 8 black triangles; in the 3rd figure, there are a total of 13 black triangles; …, following this pattern, the number of black triangles in the 8th figure is ( )
A. 33
B. 34
C. 43
D. 53
|
D
|
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<image>The daily minimum temperatures for a week in Suzhou are recorded in the following table. What are the mode and median of the daily minimum temperatures for these seven days?
A. $4$, $4$
B. $5$, $4$
C. $4$, $3$
D. $4$, $4.5$
|
A
|
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<image>Read the flowchart shown below. If the output is $$k=5$$, then the condition that should be filled in the blank judgment box is ( ).
A. $$S>-25$$
B. $$S<-26$$
C. $$S<-25$$
D. $$S<-24$$
|
D
|
|
<image>As shown in the figure, the slant height of the cone is 5 cm, and the radius of the base is 3 cm. The lateral surface area of the cone is ( )
A. 15πcm²
B. 20πcm²
C. 12πcm²
D. 30πcm²
|
A
|
|
<image>In the figure, $D$, $E$, and $F$ are the midpoints of the three sides of $\triangle ABC$. How many triangles are congruent to $\triangle DEF$?
A. $1$
B. $2$
C. $3$
D. $5$
|
C
|
|
<image>Arrange the positive integers from $$1$$ to $$2018$$ according to a certain pattern as shown in the table: By moving the shaded frame in the table, the sum of the three numbers in the frame could be ( ).
A. $$2019$$
B. $$2018$$
C. $$2016$$
D. $$2013$$
|
D
|
|
<image>The positions of rational numbers a and b on the number line are shown in the figure. Simplify the result of a + b + |a + b| ( ).
A. 2a + 2b
B. 2b
C. 0
D. 2a
|
C
|
|
<image>As shown in the figure, the graph of the quadratic function $$y=ax^2+bx$$ passes through the origin, and the y-coordinate of the vertex is $$2$$. If the quadratic equation $$ax^2+bx+k=0$$ has real roots, then the range of $$k$$ is ( ).
A. $$k<-2$$
B. $$k>-2$$
C. $$k\leqslant-2$$
D. $$k\geqslant-2$$
|
D
|
|
<image>The numbers $$a$$ and $$b$$ are positioned on the number line as shown in the figure. Then $$a+b$$ is ( ).
A. Positive
B. Zero
C. Negative
D. Any of the above
|
C
|
|
<image>As shown in the figure, AB and CD are diameters of circle O, arc $AE=$ arc $BD$. If ∠AOE=32°, then the measure of ∠COE is ( )
A. 32°
B. 60°
C. 68°
D. 64°
|
D
|
|
<image>Execute the program flowchart as shown. If the input value is $$1$$, then the output value is （）.
A. $$1$$
B. $$2$$
C. $$3$$
D. $$4$$
|
B
|
|
<image>A school needs to select one student from four to participate in the city's 'Young Talent Show Host' competition. The average score $$\bar{x}$$ and variance $${{s}^{2}}$$ of each student in the selection competition are shown in the table. If a student with high scores and stable performance is to be chosen, which student should be selected?
A. Student A
B. Student B
C. Student C
D. Student D
|
B
|
|
<image>According to the 'Road Traffic Safety Law of the People's Republic of China': if the blood alcohol concentration of a vehicle driver is 80 mg/100 ml (including 80) or higher, it is considered driving under the influence of alcohol. In a certain place, 28,800 people suspected of driving after drinking were tested for blood alcohol concentration, and the frequency distribution histogram based on the test results is shown in the figure. How many of these 28,800 people are considered to be driving under the influence of alcohol?
A. 8640
B. 5760
C. 4320
D. 2880
|
C
|
|
<image>The power generation of the three commonly used refrigerants in air conditioners is shown in the table below. Arrange these three refrigerants in order of boiling point from lowest to highest ( ).
A. $$R22$$, $$R12$$, $$R410A$$
B. $$R12$$, $$R22$$, $$R410A$$
C. $$R410A$$, $$R12$$, $$R22$$
D. $$R410A$$, $$R22$$, $$R12$$
|
D
|
|
<image>Given the graph of the quadratic function y=ax$^{2}$+bx+c as shown in the figure, which of the following conclusions are correct: 1. abc>0; 2. b<a+c; 3. 4a+2b+c>0; 4. a+b+c>m(am+b)+c (where m is a real number not equal to 1). The number of correct conclusions is ( )
A. $1$
B. $2$
C. $3$
D. $4$
|
B
|
|
<image>As shown in the figure, the side AC of the equilateral triangle ABC is gradually transformed into an arc $\overset\frown{AC}$, with B as the center and BA as the radius, while the length remains unchanged. The lengths of AB and BC also remain unchanged. Then the measure of ∠ABC changes from 60° to ( ).
A. ($\frac{60}{\pi }$)°
B. ($\frac{90}{\pi }$)°
C. ($\frac{120}{\pi }$)°
D. ($\frac{180}{\pi }$)°
|
D
|
|
<image>As shown in the figure, in the rectangular paper piece $$ABCD$$, $$AB=9$$, $$BC=12$$. When $$\triangle BCD$$ is folded along the diagonal $$BD$$, point $$C$$ lands at point $$C'$$, and $$BC'$$ intersects $$AD$$ at point $$G$$. The value of $$\sin \angle ABG$$ is ( ).
A. $$\dfrac{25}{7}$$
B. $$\dfrac{7}{24}$$
C. $$\dfrac{24}{25}$$
D. $$\dfrac{7}{25}$$
|
D
|
|
<image>To understand the physical development of senior high school students in a certain area, the weight (unit: kg) of 100 senior high school students in the area was sampled, and the frequency distribution histogram is shown in the figure: According to the above figure, the number of students among these 100 students whose weight is in the range [56.5, 64.5) is ( )
A. 20
B. 30
C. 40
D. 50
|
C
|
|
<image>During this winter vacation, Xiao Ming visited the Chinese Fan Museum. As shown in the figure, she saw a paper fan and a round fan. It is known that the paper fan's bone handle length is 30cm, the width of the paper part of the fan surface is 18cm, and the angle of the paper fan when unfolded is 150°. If the areas of the fan surfaces of these two fans are equal, then the radius of the round fan is ( )
A. $6\sqrt{7}cm$
B. $4\sqrt{15}cm$
C. $6\sqrt{6}cm$
D. $3\sqrt{35}cm$
|
D
|
|
<image>As shown in the figure, the points representing 3 and $\sqrt{13}$ on the number line are C and B, respectively. Point C is the midpoint of AB. The number represented by point A is ( )
A. -$\sqrt{13}$
B. 3-$\sqrt{13}$
C. 6-$\sqrt{13}$
D. $\sqrt{13}$-3
|
C
|
|
<image>Given the solution sets of two inequalities represented on the number line as shown in the figure, the solution set of the system of inequalities formed by these two inequalities is ( )
A. $x\geqslant 1$
B. $x \gt -1$
C. $x \gt 1$
D. $-1\leqslant x\leqslant 1$
|
C
|
|
<image>Translate $$\triangle ABC$$ in the direction of $$BC$$ to get $$\triangle A'B'C'$$. As the translation distance continuously increases, the change in the area of $$\triangle A'CB$$ is ( )
A. Increase
B. Decrease
C. Remain unchanged
D. Uncertain
|
C
|
|
<image>In the figure, the base area of the bottle bottom and the area of the conical cup's opening are equal. If all the liquid in the bottle is poured into the cups, it can fill ( ) cups.
A. $$4$$
B. $$5$$
C. $$6$$
D. $$7$$
|
C
|
|
<image>From the time shown on the clock below, what time will it be after 25 minutes?
A. 10:20
B. 11:20
C. 11:25
|
A
|
|
<image>The 'Pythagorean Theorem' in the West is known as 'Pythagoras Theorem.' During the Three Kingdoms period, the mathematician Zhao Shuang from the State of Wu created a 'Pythagorean Circle and Square Diagram' which provided a detailed proof of the Pythagorean Theorem using a combination of numbers and shapes. In the 'Pythagorean Circle and Square Diagram' shown below, four identical right-angled triangles and a small square in the middle form a large square with a side length of $$2$$. If the smaller acute angle $$\alpha = {\pi \over 6}$$ in the right-angled triangle, what is the probability that a dart randomly thrown into the large square will land inside the small square?
A. $${\sqrt{3} \over 4}$$
B. $${\sqrt{3} \over 2}$$
C. $${2-\sqrt{3} \over 2}$$
D. $${4-\sqrt{3} \over 4}$$
|
C
|
|
<image>In the figure, $\vartriangle ABC$ has $DE \parallel AC$ and $EF \parallel AB$. Points $D$, $E$, and $F$ are on the sides of $\vartriangle ABC$. If $AD:BD = 3:5$, then the value of $AF:CF$ is ( )
A. 3:2
B. 5:3
C. 4:3
D. 2:1
|
B
|
|
<image>The rose window (as shown in the figure) is one of the characteristics of Gothic architecture, with its colorful glass giving a splendid impression. The patterns that make up the window include trefoils, quatrefoils, cinquefoils, sexfoils, and octofoils, among others. The figure below is a quatrefoil composed of four semicircles, with the connection points of the semicircles forming a square ABCD. If a point is randomly taken within the entire figure, what is the probability that this point is taken from the square region?
A. $\frac{2}{\pi +2}$
B. $\frac{1}{\pi +1}$
C. $\frac{4}{\pi +2}$
D. $\frac{2}{\pi +1}$
|
A
|
|
<image>As shown in the figure, the side length of the small squares on the grid paper is 1. The thick solid lines draw the three views of a certain geometric body. The volume of the geometric body is ( )
A. $\pi +6$
B. $\frac{2\pi }{3}+6$
C. $\frac{\pi }{3}+6$
D. $\frac{\pi }{3}+2$
|
C
|
|
<image>As shown in the figure, $AB=AC$, $\angle A=40^{\circ}$, the perpendicular bisector $MN$ of $AB$ intersects $AC$ at point $D$ and $AB$ at point $M$. Then $\angle 2$ equals ( )
A. $20^{\circ}$
B. $25^{\circ}$
C. $30^{\circ}$
D. $40^{\circ}$
|
C
|
|
<image>Read the flowchart shown in the figure. Run the corresponding program. If the output result is $$s=9$$, then the content that should be filled in the diamond is ( ).
A. $$n<2$$
B. $$n<3$$
C. $$n<4$$
D. $$a<3$$
|
B
|
|
<image>Mercedes-Benz was founded in 1900 and is one of the world's most successful premium car brands. Its classic 'three-pointed star' logo symbolizes mechanization on land, sea, and air. It is known that the logo consists of 1 circle and 6 congruent triangles (as shown in the figure). Point O is the center of the circle, and ∠OAB = 15°. If a point is randomly selected within the circle, what is the probability that this point falls within the shaded area?
A. $${2\sqrt{3} -3\over 2\pi } $$
B. $${2\sqrt{3} -3\over 4\pi } $$
C. $${6\sqrt{3} -9\over 2\pi } $$
D. $${6\sqrt{3} -9\over 4\pi } $$
|
D
|
|
<image>Which path is the shortest for the cat to catch the mouse? ( )
A. The 1st path
B. The 2nd path
C. The distances are the same
|
C
|
|
<image>If the base of a triangular prism is an equilateral triangle, and its front (main) view is shown in the figure, then its volume is ( ).
A. $$\sqrt{3}$$
B. $$2$$
C. $$2\sqrt{3}$$
D. $$4$$
|
A
|
|
<image>As shown in the figure, $A$ and $B$ are any two points on a hyperbola, $AM \bot y$-axis, $BN \bot x$-axis, and $M$, $N$ are the feet of the perpendiculars. Let the areas of $\triangle AOM$ and $\triangle BON$ be $S_{1}$ and $S_{2}$, respectively. Then their size relationship is ( )
A. $S_{1} \gt S_{2}$
B. $S_{1}=S_{2}$
C. $S_{1} \lt S_{2}$
D. Cannot be determined
|
B
|
|
<image>As shown in the figure, point $$C$$ is a moving point on line segment $$AB$$, with $$AB=1$$. Squares are constructed on $$AC$$ and $$CB$$ respectively. Let $$S$$ represent the sum of the areas of these two squares. Which of the following statements is correct?
A. When $$C$$ is the midpoint of $$AB$$, $$S$$ is minimized.
B. When $$C$$ is the midpoint of $$AB$$, $$S$$ is maximized.
C. When $$C$$ is one of the trisection points of $$AB$$, $$S$$ is minimized.
D. When $$C$$ is one of the trisection points of $$AB$$, $$S$$ is maximized.
|
A
|
|
<image>The figure shown is the 'Zhao Shuang String Diagram' drawn by the Han Dynasty mathematician Zhao Shuang when annotating the 'Zhou Bi Suan Jing'. The diagram consists of four congruent right-angled triangles and a small square in the middle, forming a larger square. This is the earliest proof of the Pythagorean theorem in China. Let the smaller acute angle in the right-angled triangle be $\theta$, and $\cos 2\theta =\frac{7}{25}$. If a point is randomly selected within the larger square, the probability that this point is within the smaller square is ( )
A. $\frac{1}{5}$
B. $\frac{4}{25}$
C. $\frac{1}{25}$
D. $\frac{3}{5}$
|
C
|
|
<image>Xiao Ming bought a new 'Harmony' brand bicycle. The user manual provides the following instructions for the tires: After reading the manual, Xiao Ming discussed with his father: After calculation, Xiao Ming concluded that the maximum distance this pair of tires can travel is ( )
A. $9.5$ thousand kilometers
B. $ 3\sqrt{11}$ thousand kilometers
C. $ 9.9$ thousand kilometers
D. $ 10$ thousand kilometers
|
C
|
|
<image>In a class, the extracurricular reading volume (unit: books) of all students from January to August last year during the 'Scholarly Campus' activity is shown in the following line chart. Which of the following statements is correct?
A. The median is 58
B. The range is 47
C. The mode is 42
D. The number of months with reading volume exceeding 60 is 4
|
A
|
|
<image>Read the flowchart on the right, run the corresponding program, and the output result is
A. $\frac{13}{11}$
B. $\frac{21}{13}$
C. $\frac{8}{13}$
D. $\frac{13}{8}$
|
D
|
|
<image>As shown in the figure, in the Cartesian coordinate system $$xOy$$, it is known that $$AD$$ bisects $$\angle OAB$$, $$DB \bot AB$$, $$BC$$ is parallel to $$OA$$, the coordinates of point $$D$$ are $$D(0, \sqrt3)$$, and the x-coordinate of point $$B$$ is $$1$$. Then, the coordinates of point $$C$$ are ( ).
A. $$(0,2)$$
B. $$(0,\sqrt3 + \sqrt2)$$
C. $$(0,\sqrt5)$$
D. $$(0,5)$$
|
B
|
|
<image>As shown in the figure, AD is the angle bisector of ∠BAC in △ABC, DE is perpendicular to AB at point E, and DF is perpendicular to AC intersecting AC at point F. The area of △ABC is 7, DE = 2, and AB = 4. What is the length of AC?
A. 4
B. 3
C. 6
D. 5
|
B
|
|
<image>Yichang High School has launched a 'Sunshine Sports Activity'. All students in Class 1, Grade 9 participated in three activities: Bashan Dance, Table Tennis, and Basketball on April 18, 2011, at 16:00. Teacher Chen counted the number of students participating in these three activities at that time and created the frequency distribution histogram and pie chart shown in the figure. According to these two statistical charts, the number of students participating in the Table Tennis activity at that time is ( ).
A. $$50$$
B. $$25$$
C. $$15$$
D. $$10$$
|
C
|
|
<image>If the real numbers $a, b, c, d$ are represented on the number line as shown in the figure, which of the following conclusions is correct?
A. $a < -5$
B. $b+d < 0$
C. $|a|-c < 0$
D. $c < \sqrt{d}$
|
D
|
|
<image>As shown in the figure, $$AB=BC=CD=DE=1$$, and $$BC\perp AB$$, $$CD\perp AC$$, $$DE\perp AD$$, then the length of line segment $$AE$$ is ( ).
A. $$\frac{3}{2}$$
B. $$2$$
C. $$\frac{5}{2}$$
D. $$3$$
|
B
|
|
<image>The following figures are all composed of parallelograms of the same size arranged according to a certain pattern. In the 1st figure, there is a total of $$1$$ parallelogram, in the 2nd figure, there is a total of $$5$$ parallelograms, in the 3rd figure, there is a total of $$11$$ parallelograms, ... then the number of parallelograms in the 6th figure is ( ).
A. $$55$$
B. $$42$$
C. $$41$$
D. $$29$$
|
C
|
|
<image>As shown in the figure, point $$A$$ is on the graph of the inverse proportion function $$y={k\over x}$$ ($$x<0$$). A perpendicular line is drawn from point $$A$$ to the y-axis, with the foot of the perpendicular being point $$B$$. If the area of $$\triangle OAB$$ is $$3$$, then the value of $$k$$ is ( ).
A. $$3$$
B. $$-3$$
C. $$6$$
D. $$-6$$
|
D
|
|
<image>As shown in the figure, a square piece of paper $$ABCD$$ with a side length of $$8cm$$ is folded so that point $$D$$ falls on the midpoint $$E$$ of $$BC$$, and point $$A$$ falls on $$F$$. The fold line is $$MN$$. What is the length of segment $$CN$$?
A. $$2$$
B. $$3$$
C. $$4$$
D. $$5$$
|
B
|
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