Don't lose yourself in your busyness. After studying, enjoying life will make your mood bloom like a flower. The following is the final examination paper (including the answers) of the eighth grade last semester, which I compiled from 20 16-20 17. Welcome to refer to.

1. Multiple choice questions: (This question 10 is a small question, with 3 points for each small question and 30 points for * * *).

1.(20 15? Mianyang) Among the following patterns, the axisymmetric figure is ()

2. The following statement is true ()

The square root of A.4 is; The cube root of B.8 is; c； d；

3. What is the point in the fourth quadrant in the plane rectangular coordinate system? ( )

A.( 1，2) B.( 1，-2)c .( 1，2)d .( 1，-2)

4. In △ABC and △DEF, it is known that AC=DF,? C=？ F, after adding the following conditions, it cannot be determined that △ ABC△ def is ().

A.BC=EF B.AB=DE C？ A=？ D D？ B=？ E

5. Among the following numbers: 0.32, -4, and what are the numbers with square roots? ( )

A.3B.4C.5D.6

6.△ ABC that meets the following conditions is not a right triangle ()

A.BC= 1，AC=2，AB =； b . BC \u AC \u AB = 3 \u 4 \u 5；

C.？ A+？ B=？ c； d？ A: Huh? b∴？ c = 3∶4∶5；

7.(20 14? Qiannan Prefecture) Positive proportional function y=kx(k? 0) in the second and fourth quadrants, then the image of linear function y=x+k is roughly ().

A.B. C. D。

8.(20 14? Yibin) As shown in the figure, a linear function intersects at point B through the image of point A and the image of a proportional function y=2x, so the analytical formula of this linear function is? ( )

a . y = 2x+3 b.y=x﹣3 c.y=2x﹣3 d.y=﹣x+3

9. As shown in the figure, in △ABC, AB=AC= 10, BC=8, and AD is equally divided? When BAC intersects BC at point D, point E is the midpoint of AC, and DE is connected, the circumference of △CDE is ().

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10.(20 15? Qiannan prefecture) as shown in figure 1, in the rectangular MNPQ, the moving point r starts from point n and runs along n? p？ q？ The movement in the m direction stops at point m, let the distance of point R move be x, and the area of △MNR be y. If the function image of y relative to x is shown in Figure 2, then when x=9, point R should move to ().

Morning; B.N place; C.p .d . Q；

Fill in the blanks: (There are 8 small questions in this question, with 3 points for each small question and 24 points for * * *).

1 1. The irrational numbers in real numbers,, and are.

12.(20 15? Wuxi) The coordinates of the intersection point between the image of the linear function y = 2x-6 and the X axis are.

13. point a (? 3, 1) is about an axisymmetric point. The coordinates are.

14.(20 14? Taizhou) After the image with linear function y = 3x ~ 1 is translated by 3 units along the y axis, the corresponding functional relationship of the obtained image is.

15. The value range of variables in function = is.

16. The graph of function sum intersects at point A (,3), then the solution set of inequality is.

17. As shown in the figure, in △ABC, the middle vertical line of BC side passes through BC in D and AB in E. If CE is equally divided? ACB？ B=40？ And then what? A = _ _ _ _ _ _ _ _ degrees.

18. As shown in the figure, in the plane rectangular coordinate system,? AOB=30？ The coordinate of point A is (2,0). OB, the vertical foot is; Overwork? X axis, vertical foot is; Do more work? OB, the foot is the key; Do more work? X-axis, vertical foot? ; If you keep doing this, the ordinate of is.

Iii. Answering questions: (The score for this big question is ***76)

19.( 10) (1) Calculation:. (2) Known calculated values.

20. (The full mark of this question is 7) It is known that sum is the square root of a positive number, and its cube root is -2.

(1):,;

(2) Find the arithmetic square root of.

2 1. (The full mark of this question is 7) As shown in the figure, in Rt△ABC,? ACB=90？ , point D and point F are on AB and AC respectively, CF=CB, connect the CD, and rotate the segment CD clockwise around point C by 90? CE followed by EF.

(1) Verification: △ BCD △ FCE;

(2) if EF∨CD, ask? The degree of BDC.

22. (The full mark of this question is 7) It is known that y-3 is directly proportional to x+5. When x=2, y= 17. Find:

(1) the functional relationship between y and x;

(2) When x=5, the value of y 。

23. (The full mark of this question is 7) Known: A (0, 1), B (2 2,0), C (4 4,3).

(1) Trace all points in the coordinate system and draw △ABC.

(2) Find the area of △ABC;

(3) Set point p on the coordinate axis and the plane of △ABP and △ABC.

If the products are equal, find the coordinates of point P.

24. (The full mark of this question is 6) It is known that the function y=-2x+6 and the function y=3x-4.

(1) Draw the images of these two functions in the same plane rectangular coordinate system;

(2) Find the intersection coordinates of these two function images;

(3) According to the image answer, when the value of x is in what range, the image of function y=-2x+6 is above the image of function y=3x-4?

25. As shown in the figure, the side length of each small square in the square grid is 1, and the vertex of each small cell is called the grid point.

(1) Draw a square with an area of 1 0 with grid points as vertices in the diagram1;

(2) Draw a triangle with the grid point as the vertex in Figure 2, so that the three sides of the triangle are 2, 0, etc.

(3) As shown in Figure 3, points A, B and C are the vertices of a small square. What? Degree of ABC

26. (The full mark of this question is 8) As shown in the figure, in △ABC,? ABC=45？ ，CD？ AB, is it? AC, the vertical foot is d, e, f is the midpoint of BC, and BE intersects DF and DC at points g, h,? ABE=？ CBE。

(1) Is the straight line BH equal to AC? If they are equal, give proof; If not, please explain the reasons;

(2) Verification:

27. (this question is full of 8 points) (20 15? Jining) Xiaoming goes to a clothing store to do social practice. The manager of the clothing store asked Xiaoming to help solve the following problems: The clothing store is going to buy two kinds of clothes, one is 80 yuan's price 120 yuan, and the other is 60 yuan's price 90 yuan. It is planned to buy two kinds of clothing/0/00 pieces of kloc, of which no less than 65 pieces of clothing.

(1) If the cost of buying this 100 clothes does not exceed 7500 yuan, how many clothes can A buy at most?

(2) Under the condition of (1), the clothing store offers a discount of a(0) for each garment.

28. (The full mark of this question is 9) As shown in the figure, in △ABC, AB=BC=AC= 12cm. At present, two points M and N start from point A and point B respectively and move along the edge of the triangle. It is known that the speed of point M is 1cm/s and the speed of point N is 2 cm/s. When point N reaches point B first,

How many seconds after (1) points m and n move, do the two points m and n coincide?

(2) After the points M and N move for a few seconds, the equilateral triangle △AMN can be obtained.

(3) When point M and point N move on the edge of BC, can an isosceles triangle with MN as the base be obtained? If yes, request the time when M and N move at this time.

Reference answer

First, multiple-choice questions:

1.d； 2.a； 3.b； 4.b； 5.a； 6.d； 7.b； 8.d； 9.c； 10.d；

Second, fill in the blanks:

1 1., , , ; 12.(3,0); 13.(-3,- 1); 14.； 15. and; 16.； 17.60; 18.；

Third, answer questions:

19.( 1)- 10; (2) ;

20.( 1) , ; The arithmetic square root of (2) is;

2 1.( 1) omitted; (2)90? ;

22.( 1) ; (2)23;

23.( 1) omitted; (2)4; (3 3) P (10/0,0) or p (-6,0);

24.( 1) omitted; (2)(2,2); (3) ;

25.( 1) as shown in the figure; (2) As shown in Figure 2;

(3) As shown in Figure 3, if AC and CD are connected, then AD=BD=CD= and ACB=90? , from Pythagorean theorem: AC=BC=,

ABC=？ BAC=45？ .

26.( 1)BH=AC for the following reasons:

∵CD？ AB, is it? Communication,

BDH=？ BEC=？ CDA=90？ ,

∵? ABC=45？ ,

BCD= 180？ -90? -45? =45? =? American Broadcasting Company Inc (ABC)

? DB=DC，

∵? BDH=？ BEC=？ CDA=90？ ,

A+？ ACD=90？ ,? A+？ HBD=90？ ,

HBD=？ ACD，

∫In△DBH and △DCA

,? △DBH?△DCA(ASA)，？ BH=AC。

(2) connecting CG,

According to (1), DB=CD, ∫F is the midpoint of BC,

? DF vertically divides BC. BG=CG，

∵? ABE=？ CBE, yes? AC，？ EC=EA，

In Rt△CGE, we get from Pythagorean theorem:

CE = AE，BG=CG，？ .

27. Solution: (1) Suppose a kind of clothing buys X pieces, then B kind of clothing buys (100-x) pieces.

According to the meaning of the question:

Solution: 65? x？ 75,? You can buy up to 75 clothes;

(2) Let the total profit be W yuan,

W = (120-80-a) x+(90-60) (100-x), that is, w=( 10-a)x+3000.

①00, w increases with the increase of x,

? When x=75, w has the maximum value, that is, 75 pieces of class A clothing and 25 pieces of class B clothing are purchased at this time;

(2) When a= 10, which scheme can be purchased?

③ When 10

When x=65, w has the maximum value, that is, 65 pieces of A-type clothes and 35 pieces of B-type clothes are purchased at this time.

28. Solution: (1) After moving point M and point N for x seconds, point M and point N coincide.

x？ 1+ 12=2x, the solution is: x =12;

(2) After the points m and n are moved for t seconds, the equilateral triangle △AMN can be obtained, as shown in Figure ①.

AM=t？ 1=t, AN=AB-BN= 12-2t, ∫ triangle △AMN is an equilateral triangle,? t= 12-2t，

The solution is t=4. After the points m and n move for 4 seconds, the equilateral triangle △AMN can be obtained.

(3) When point M and point N move on the edge of BC, an isosceles triangle with MN as the base can be obtained.

From (1), it can be seen that at 12 seconds, m and n coincide, just at c,

As shown in Figure ②, suppose △AMN is an isosceles triangle. AN=AM，AMN=？ ANM，

AMC=？ ANB，AB = BC = AC，？ △ACB is an equilateral triangle, C=? b，

At △ACM and △ABN,

∵ ,? △ACM?△ABN，？ CM=BN，

Suppose that when points M and N move on the edge of BC, the moving time of M and N is y seconds, and △AMN is an isosceles triangle.

? CM=y- 12, NB=36-2y, CM=NB, y- 12=36-2y, and the solution is y= 16. Therefore, the hypothesis holds.

? When point M and point N move on the edge of BC, an isosceles triangle with MN as the base can be obtained. At this time, the movement time of m and n is 16 seconds.

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