The mid-term examination paper of the second volume of mathematics in the second day of junior high school has the answer.

Choose one carefully first (3 points for each small question, 30 points for * * *).

1. As shown in the figure, ∠ 1 and ∠2 are ()

A. Isomorphism angle B. Internal dislocation angle

C. ipsilateral internal angle D. None of the above

2. It is known that the circumference of an isosceles triangle is 29 and one side is 7, so the base of the isosceles triangle is ().

A.11b.7c.15d.15 or 7

3. The following axial symmetry graphics, the largest number of axis of symmetry is ().

A. line segment B. angle C. isosceles triangle D. equilateral triangle

Age131415 25 28 30 35 Others

No.30 533 17 12 20 9 2 3

4. In the investigation of a social organization, the following data were collected. What statistics do you think best reflect the age characteristics of organizations? ()

A. mean B. mode C. variance D. standard deviation

5. In the following conditions, it cannot be judged that two right-angled triangles are congruent ()

A. the two acute angles are equal. A right-angled side is equal to an acute angle.

C. two right-angled sides are equal. D. A right-angled side is equal to a hypotenuse.

6. The following figure can be folded into a cube is ().

7. In the samples of 20, 30, 40, 50, 50, 60, 70 and 80, the relationship among mean, median and mode is ().

A. average value >; Median > majority B. Median

C. mode = median = average D. average

8. As shown in the figure, in Rt△ABC, ∠ACB=90O, BC=6, and the area of square ABDE is 100, then the area of square ACFG is ().

A.64 B.36 C.82 D.49

9. As shown in figure ∠AOP=∠BOP= 15o, PC‖OA, PD⊥OA, if PC= 10, PD is equal to ().

A. 10 5 days BC 2.5

10. The picture shows an equilateral triangular wooden frame. Beetles crawl on the frame (except the ends). Let the sum of the distances from the beetle to the other two sides be, and the height of the equilateral triangle be, then the relationship with the size is ().

A.B.

C.d. is not sure

Second, concentrate on filling in (2 points for each small question, 20 points for * * *)

1 1. As shown in the figure, AB‖CD, ∠2=600, then ∠ 1 equals.

12. The internal angle of an isosceles triangle is 100, so its base angle is _ _ _ _.

13. Analyze the following four surveys:

① Understand the eyesight of our classmates; ② Understand the height of students in our school;

(3) Before boarding the plane, conduct safety inspection on passengers; ④ Understand the main forms of entertainment for primary and secondary school students;

Among them, what should be investigated is: (fill in the serial number).

14. The surface of the cubic carton printed with the words "Building a harmonious society"

As shown in the picture, the word "sword" is printed on the opposite side.

It has words printed on it.

15. As shown in the figure, in Rt△ABC, CD is the height on the hypotenuse AB, ∠ A = 25,

Then ∠ BCD = _ _ _ _

16. In order to develop the agricultural economy and become rich and well-off, Wang, a professional chicken farmer, raised 2,000 chickens in 2007. Before listing, he randomly selected 10 chickens. The statistics are as follows:

Mass (unit: kg) 2 2 2 2 5 2 8 3

Quantity (unit: only) 1 2 4 2 1

It is estimated that the total mass of these chickens is _ _ _ _ _ _ _ kg.

17. If the length of the midline on the hypotenuse of a right triangle is 5cm, then the length of the hypotenuse is _ _ _ _ _ cm.

18. As shown in the figure, affected by the strong typhoon "Rosa", there was a big tree 9 meters in front of Uncle Zhang's house, which broke and fell from 6 meters above the ground. The length of the falling part is10m. Will it hit uncle Zhang's house when it falls?

Answer: (Please choose one of "Yes" and "No")

19. As shown in the figure, OB and OC are bisectors of ∠ABC and ∠ACB of △ABC, respectively, and they intersect at points. If the intersection O is OE‖AB intersecting at BC point O, OF‖AC intersecting at BC point F, BC=2008, then the circumference of △OEF is _.

20. As shown in the figure, in the rectangular ABCD, AB=2, ∠ ADB = 30, folded along the diagonal BD (making △ABD and △EDB fall on the same plane), and the distance between point A and point E is _ _ _ _ _ _.

Third, answer with your heart (there are 7 questions in this small question, with ***50 points)

2 1. (6 points in this question) As shown in the figure, ∠ 1 = 100, ∠ 2 = 100, ∠ 3 = 120.

Find the degree of ∠4

22. (6 points in this question) The picture below is composed of five small squares with a side length of 1.

(1) Divide the graph into three pieces, so that the three pieces are combined into a square (drawn in the graph);

(2) Find the area s of the square.

23. (8 points in this question) As shown in the figure, AD is the height of ABC, E is the upper point of AC, BE passes through AD to F, DC=FD, AC=BF.

(1) Explain the reason of δ BFD δ ACD;

(2) If AB=, find the length of AD.

24. (5 points for this question) As shown in the figure, it can be seen that in △ABC, ∠A= 120? ，∠B=20？，∠C=40？ Please find a point P on the edge of the triangle, draw a line segment through the point P and a vertex of the triangle, and divide the triangle into two isosceles triangles.

25. (9 points for this question) Eight-grade students in a school started a shuttlecock kicking competition, and each class sent five students to participate. According to the total score of the group, each student plays more than 100 (including 100) within the specified time. The following table is the competition data of five students in Class A and Class B with the best performance (unit: 1).

1 second, third, fourth and fifth total score

Grade a 89100 96118 97 500

Class b1009611091104500.

Statistics show that the total scores of the two classes are equal. At this time, some students suggested that you can use other information in the exam materials as a reference. Please answer the following questions:

(1) Calculate the excellent rate of Class II; (2) Find the median of two kinds of competition data;

(3) calculating the variance of two kinds of competition data;

(4) Which class do you think should be the champion? Why?

26. (6 points in this question) Graphics are three views of a geometric body, and the volume of the geometric body (unit: cm, take

3. 14, and the result retains 3 significant figures).

27. (This question 10) As shown in the figure, P is a point in the equilateral triangle ABC, connecting PA, PB and PC, and making an equilateral triangle BPM with BP as the edge and CM as the edge.

(1) Observe and guess the relationship between AP and CM, and explain your conclusion;

(2) If PA=PB=PC, then △PMC is a _ _ _ _ _ triangle;

(3) If PA:PB:PC= 1:, try to judge the shape of △PMC and explain the reasons.

Fourth, choose your own topic (5 points for this topic, the score of this topic can be recorded in the total score, if the total score exceeds 100, it will still be recorded as 100).

28. at Rt⊿ABC, ∠c = 90, while the relative lengths of ∠A, ∠B and ∠ c are a, b and c respectively. Let ⊿ABC have an area of s and a circumference of.

(1) Fill in the form:

Three-sided A, B and C

a+b-c

3、4、5 2

5、 12、 13 4

8、 15、 17 6

(2) If a+b-c=m, observe the conjecture in the above table: =, (expressed by an algebraic expression containing m);

(3) Explain the reasons for the conclusion in (2).

Reference Answers and Grading Opinions of the Mid-term Examination Paper in Grade Eight Mathematics

First, choose an option carefully.

The title is 1 23455 6789 10.

Answer B B D B A D C A C A

Second, concentrate on filling in.

11.12012.4013.③14. She15.2516.5000/kloc

19.2008 20.2

Third, answer patiently.

2 1. (6 points in this question) Solution: ∫∠2 =∠ 1 = 100, ∴ m ‖ n................3 points.

∴∠ 3 =∠ 5. ∴∠ 4 =180-∠ 5 = 60 ... 3 points.

22. (6 points for this question)

Solution: (1) The puzzle is correct (as shown in the figure); ............................., 3 points.

(2) S = 5 ........................................ 3 points.

23. (8 points for this question)

Solution: (1)∵AD is the height of ABC, ∴△ACD and △BFD are right triangles. ..........................................................................................................................

In Rt△ACD and Rt△BFD.

∵

∴ RT△ ACD ≌ RT△ BFD .............................................................................................................. 3 points.

(2)∫Rt△ACD≌Rt△BFD

∴ ad = BD ..........................................................................1min.

In Rt△ACD, ∫ad2+bd2 = ab2, ∴ 2AD2 = AB2, ∴ AD =...3 points.

24. (5 points for this question)

Give a division and get 2 points (angle label 1 minute).

25. (9 points for this question)

Solution: (1) Excellent rate of Class A: 2÷5=0.4=40%, Excellent rate of Class B: 3 ÷ 5 = 0.6 = 60%... 1 min.

(2) The average score of five students in Class A is 97.

The average score of five students in Class B is100. .............................. has 2 points.

(3), ............................. 2 points, ........................... 2 points.

∴S a 2 > Sao Paulo b 2

(4) Class B is the champion. Because the excellent rate of five students in class B is higher than that in class A, the median is higher than that in class A, and the variance is lower than that in class A, so the comprehensive evaluation of shuttlecock kicking level in class B is better ... 2 points.

26. (6 points in this question) Solution: This geometric figure consists of two parts: a cuboid and a cylinder.

Therefore, v = 8× 6× 5+= 240+25.6 ≈ 320cm3. ........................................................................................................................................

27. (This title is 10) Solution: (1) AP = cm ....................................................................................................1.

∫△ABC and △BPM are equilateral triangles, ∴ AB=BC, BP=BM, ∠ABC=∠PBM=600.

∴∠abp= ∴∠abp+∠pbc=∠cbm+∠pbc=600。

∴△ headquarters base△ coalbed methane. ∴ AP = cm ...................................................... 3 points.

(2) 2 points for an equilateral triangle.

(3) △PMC is a right triangle ................................................... 1 min.

Ap = cm, BP = PM, PA: Pb: PC = 1:, ∴ cm: PM: PC =1:... 2 points.

Let CM=k, then PM= k, PC= k, ∴ CM2+PM2=PC2,

∴△PMC is a right triangle, ∠ PMC = 900 ..................................1min.

Fourth, choose your own topic (5 points for this small question)

( 1), 1, .......................................... 1.

(2) ...........................................1min.