1. The following figure is both axisymmetric and centrally symmetric ().

A. equilateral triangle B. parallelogram C. regular Pentagon D. square

Test center: central symmetrical figure; Axisymmetric graph.

Analysis: According to the concepts of axisymmetric figure and central symmetric figure.

Solution: Solution: A, it is an axisymmetric figure, not a central symmetric figure, so it is wrong;

B, it is not an axisymmetric figure, but a centrally symmetric figure. Therefore, it is wrong;

C is an axisymmetric figure, not a centrally symmetric figure. Therefore, it is wrong;

D, an axisymmetric figure, is also a centrally symmetric figure. So, it is correct.

So choose D.

Comments: This topic examines the concepts of central symmetric graphics and axisymmetric graphics: the key of axisymmetric graphics is to find the axis of symmetry, and the two parts of the graphics can overlap after being folded along the axis of symmetry; The central symmetric figure is to find the symmetric center, and it will overlap with the original figure after rotating 180 degrees.

2. If △ABC is similar to △A? b？ c？ , the area ratio is 1: 2, then △ABC and △A? b？ c？ The similarity ratio of is ()

A. 1:b . 1:4 c . 4: 1d .: 1

Test center: the nature of similar triangles.

Analysis: from △ABC to △A? b？ c？ The area ratio is 1: 2. According to the fact that the area ratio of similar triangles is equal to the square of the similarity ratio, the answer can be obtained.

Answer: Solution: ∫△ ABC Similar△ A? b？ c？ , the area ratio is 1: 2,

? △ABC and△ a? b？ c？ The similarity rate is: 1:.

So choose a.

Comments: This question examines the nature of similar triangles. This problem is relatively simple, and the memory theorem is the key to solve it.

3.(3 points) (20 12? Liaocheng)? Throw a uniform coin and land face up? This event is ()

A. inevitable events B. random events C. definite events D. impossible events

Test location: random events.

Analysis: According to the definition of random events, random events are events that may or may not occur and can be judged.

Answer: Solution: Throw 1 even coins, which may be face-up or face-up after landing.

Therefore, throwing 1 even coins and landing face up is a random event.

So choose B.

Comments: This topic mainly examines the understanding of the concept of random events. To solve this kind of problem, we should learn to pay attention to the things around us and analyze, treat and solve the problem with mathematical ideas and methods, which is relatively simple.

4. If the radius of a sector is 1 and the arc length is, then the central angle of this sector is ().

A.30? B. 45？ C. 60？ D. 90？

Test center: arc length calculation.

Topic: the finale.

Analysis: According to the arc length formula l=, it can be solved.

Solution: let the central angle be n degrees, according to the meaning of the question.

= ,

Solution: n=60.

So choose: C.

Comments: This question examines the arc length formula of the sector, which is a basic question.

5. The unary quadratic equation x2-2x = m always has real roots, so the condition that m should meet is ().

A.m & gt﹣ 1 B. m=﹣ 1 C. m？ -1Tim? 1

Test center: discriminant of roots.

Special topic: calculation problems.

Analysis: The quadratic equation with one variable has real roots, and the discriminant of the roots is greater than or equal to 0, so the range of m can be found.

Solution: Solution: The unary quadratic equation x2-2x-m = 0 always has real roots.

? △=4+4m？ 0,

Solution: m? ﹣ 1,

So choose C.

Comments: This question examines the discriminant of roots and the discriminant of quadratic equations with real roots greater than or equal to 0.

6. The image of quadratic function y=ax2+bx+c is shown in the figure, so the following conclusion is correct ().

A.a & gt0

B The unary quadratic equation ax2+bx+c=3 about X has two equal real roots.

C.c & lt0

D. when x? 0, y decreases with the increase of x.

Test site: the nature of quadratic function.

Special topic: combination of numbers and shapes.

Analysis: A is judged according to the opening direction of parabola; Judging b according to the coordinates of parabola vertices; C according to the position of the intersection of parabola and Y axis; According to the properties of quadratic function, judge d.

Solution: Solution: A, the parabolic opening is downward, then A.

B, because the maximum value of parabola is 3 when x= 1, and the unary quadratic equation ax2+bx+c=3 about x has two equal real roots x 1=x2= 1, so option b is correct;

C. if the intersection of parabola and x axis is above x axis, then c >；; 0, so the c option is wrong;

D. when x> is at 1, y decreases with the increase of x, so the d option is wrong.

So choose B.

Comments: This question examines the nature of quadratic function: quadratic function y=ax2+bx+c(a? The vertex coordinates of 0) are (﹣,), the symmetry axis straight line x=﹣, and the quadratic function y=ax2+bx+c(a? 0) has the following properties: when A >；; 0, parabola y=ax2+bx+c(a? 0) the opening is upward, x < ﹣, y decreases with the increase of x; X>﹣, y increases with the increase of x; When x=﹣, y takes the minimum value, that is, the vertex is the lowest point of parabola. When a man

Answer? 0) downward opening, x

7. A sealed container with variable volume contains a certain amount of gas. When the volume of the container changes, so does the density of the gas. Density? Does (unit: kg/m3) meet the functional relationship with volume V (unit: m3)? = (k is a constant, k? 0), the image is as shown in the figure, so when v? 6m3, the density of gas? The value range of (unit: kg/m3) is ()

A. 1.5 kg/m3 b. 0 kg/m3 < & lt 1.5 kg/m3

C. 1.5kg/m3·d？ & gt 1.5 kg/m3

Test center: the application of inverse proportional function.

Analysis: According to the image, the inverse proportional function image passes through the point (6, 1.5), the function solution is obtained by using the undetermined coefficient method, and then the value of k is obtained according to V? 6m3 solution is enough.

Solution: Solution: According to the image, the function image passes through the point (6, 1.5).

Let the inverse proportional function be? = ,

Then 1.5=,

The solution is k=9,

So the analytical formula is:? = ,

When V=6, what? = 1.5,

So choose B.

Comments: This topic mainly examines the image recognition and the undetermined coefficient method to find the resolution function. Students should observe the images carefully.

8. Organize a basketball invitational tournament, one for every two teams. According to the venue, time and other conditions, it is planned to arrange 28 performances. If the tournament organization * * * invites X pairs to participate in the tournament, the equation can be listed as ().

A.x(x﹣ 1)=28 b . x(x+ 1)= 28 c . x(x﹣ 1)=28 d . x(x+ 1)= 28

Test center: abstract a quadratic equation from practical problems.

Analysis: If the competition organization * * * invites X pairs to participate in the competition, then each team will participate in the competition of (x | 1) pairs, but the competition between the two teams is only1. According to * * *, arrange 28 games and make an equation.

Solution: If the competition organization * * * invites X pairs to participate in the competition, then each team will participate in (x- 1) pairs of competitions.

From the meaning of the question, x (x- 1) = 28.

So choose a.

Comments: This question examines the quadratic equation of one variable abstracted from practical problems. The key to solve this problem is to understand the meaning of the problem, set the unknown, find out the appropriate equivalence relationship and list the equations.

9. As shown in the figure, O is the circumscribed circle of △ABC. B=60？ , AC=8, then the length ⊙O of the diameter AD is ()

A. 16 B. 4 C. D

Test site: fillet theorem; Pythagorean theorem

Analysis: first connect the CD, because AD is the diameter ⊙O, and the circumferential angle corresponding to the diameter is a right angle, which can be obtained. ACD=90？ , and from the angle theorem of circle, we can draw? D=？ B=60？ Then using trigonometric function, the diameter ⊙O and the length of AD are obtained.

Answer: Solution: Connect the CD,

∵AD is the diameter⊙ o,

ACD=90？ ,

∵? D=？ B=60？ ，AC=8，

? AD= =。

So choose D.

Comments: This topic examines the theorem of circle angle and trigonometric function. This question is not difficult. Pay attention to the method of auxiliary lines and the application of the idea of combining numbers with shapes.

10. As shown in the figure, point P(x, y) (x >; 0) is the inverse proportional function y =(k >；; 0), the circle with point P as the center and OP as the radius intersects with the positive semi-axis of X axis at point A. If the area of △OPA is S, the change of S is () when X increases.

The value of A. S increases and the value of B. S decreases.

The value of C. S first increases and then decreases, while the value of D. S remains unchanged.

Test site: the geometric meaning of the inverse proportional function coefficient K.

Special topic: calculation problems.

Analysis: do PB? OA is in b, as shown in the figure. According to the vertical diameter theorem, OB=AB, then S△POB=S△PAB, and according to the geometric meaning of the inverse proportional function K, S△POB= |k|, so S=2k is a constant value.

Answer: Solution: Do PB? OA is in b, as shown in figure,

Then OB=AB,

? S△POB=S△PAB，

∫S△POB = | k |，

? S=2k，

? The value of s is a fixed value.

So choose D.

Comments: This question examines the geometric meaning of the inverse proportional function coefficient k: take any point in the inverse proportional function y= image, and make vertical lines on the X axis and the Y axis respectively after passing this point, and the rectangular area enclosed with the coordinate axis is constant |k|.