(Time: 120 minutes, full mark: 150 minutes)

First, multiple-choice questions (this big question * * 10 small questions, 3 points for each small question, 30 points for * * *)

1. The calculation result is ()

A.3x2 B.x6 C.x5 D.x8

3. The result of calculating (-8) 2× 0.253 is

A. 1 B.- 1 C.- D。

3. The correct factorization of XM-XM-2 is ().

a . XM-2(x2- 1)b . XM( 1-x2)c . XM-2(x- 1)(x+ 1)d . XM-2(x+ 1)

4. In Equation a3? a2？ () = A 1 1, and the algebraic expression in brackets should be ().

A.a7 B.a8 C.a6 D.a3

5. If is, the value of is ()

A.B.5 C. D.2

6. It is known that the three sides of a triangle are 2 and 4 respectively, so the value range is ().

A.B. C. D。

Once the number of sides of a polygon increases by 1, the polygon's ()

A. internal angle and increase of 3600b0. The outer corner has been increased by 3600b0.

C. add a D. inner corner on the diagonal, and add 1800.

⒏ The ray A shines on the plane mirror CD, and then reflects back and forth between the plane mirror AB and CD, and the reflection angle of the ray is equal to the incident angle.

Shooting angle. If ∠ 1 = 55 and ∠ 3 = 75 are known, ∠2= ().

50 years later.

(9) As shown in the figure, the straight line AB‖CD, of the following relationships about ∠B, ∠D and ∠E, the correct one is ().

A.∠b+∠D+∠E = 90° B .∠b+∠D+∠E = 180°c .∠B =∠E-∠D .∠B-∠D =∠E

⒑ As shown in the figure, it is a schematic diagram of the table top of a billiard table, and the shaded parts at the four corners in the figure represent four goal holes respectively. If you hit a ball in the direction shown in the figure (the ball can be reflected many times), then the ball bag that the ball will eventually fall into is ().

A. 1 bag B.2 bag C.3 bag D.4 bag

2. Fill in the blanks (this big question * * 10 small question, 3 points for each small question, 30 points for * * *).

5. If AM = 2, AN = 3, am+2n equals _ _ _ _ _ _ _ _ _.

⒓ =____________________.

⒔ It is known that x2+y2+4x-6y+ 13 = 0, where both x and y are rational numbers, then yx = _ _ _ _ _ _ _ _ _ _ _ _

The common factor of polynomials is _ _ _ _ _ _ _.

If a polynomial can be decomposed into the square of a binomial, then the value of m is.

As shown in the figure, if you want to ‖, then the conditions you need to add are: _ _ _ _ _ _ _ _ _ _ or _ _ _ _ _ _ _ _.

⒘ As shown in the figure, if AB‖CE, ∠C=370, ∠A= 1 150, then ∠ F = _ _ _ _ _ _ degrees.

Carpenter ⒙ has two pieces of wood, the length is 80 cm and 150 cm respectively. In order to find the third piece of wood, nail them into triangles. There are four pieces of wood with lengths of 70cm,105cm, 200m and 300m respectively. He can choose the length of _ _ _ _ _ _ _.

If two parallel straight lines are cut by a third straight line, then: ① A pair of bisectors with the same angle are parallel to each other; ② The bisectors of a pair of internal dislocation angles are parallel to each other; ③ A pair of bisectors at the inner corner of the same side are parallel to each other; ④ A pair of bisectors at the inner corner of the same side are perpendicular to each other.

The correct conclusion is. (Note: Please fill in the serial numbers of all conclusions that you think are correct)

⒛ When calculating the sum of the internal angles of a polygon with a calculator, Xiao Ming's result was 2005, and Xiao Fang immediately judged that his result was wrong. Xiao Ming calculated carefully, and sure enough, he found himself in an angle twice. According to the above facts, please write a correct conclusion _ _ _ _ _ _ _ _ _ _ _.

Third, answer questions.

2 1. Calculation: (5 points for each small question, ***20 points)

⑴ a3？ (-B3)2+(-ab2)3； ⑵(-2p-q)(-q+2p)；

⑶(3-4y)(4y+3)+(-3-4y)2； (3) Given a+A- 1 = 3, find the value of a4+.

22. Factorization (5 points for each small question, 20 points for * * *)

⑴- 15a 3 B2+9a2b 2-3a B3； ⑵3 x2+6xy+3 y2；

⑶ ; ⑷8 1(a+b)2- 16(a-b)2。

23. (The full mark of this question is 8)

Known: ADC =117 as shown in the figure. Try to find the degree of ∠ A+∠ B+∠ C.

24. (The full mark of this question is 8)

It is known that in △ABC, ∠ B = 40, ∠ BCD = 100, EC share ∠ACB,

Find the degree of ∠A and ∠ACE.

25. (The full mark of this question is 8)

Fold an aluminum wire with a length of 24 into a triangle, and each side is a positive integer. The three sides of this triangle are marked as A, B and C respectively, and A ≤ B ≤ C. Please write A, B and C that satisfy the meaning of the question as much as possible.

Fourth, inquiry activities (this big topic ***3 small questions, 26 questions 8 points, 27 questions 6 points, 28 questions 12 points, ***26 points)

26. Calculation: (2a-b) (a+2b), verify the correctness of the result by area method (draw a puzzle).

27. As shown in the figure, in quadrilateral ABCD, ∠ A = ∠ C = 90, BF and DE are divided by ∠ABC and ∠ ADC respectively. Judge whether BE and DF are parallel, and explain the reasons.

28.( 1) As shown in figure 1, the bisectors of ∠ABC∠ACB intersect at point O in △ABC, try to explain ∠ BOC = ∠ A+90;

(2) As shown in Figure 2, if O is the intersection of two bisectors of external angles of △ABC, does the relationship in (1) hold? If yes, please explain the reasons;

If not, what is the relationship between ∠BOC and ∠A?

(3) Imitate (1) and (2), can you put forward a new problem and solve it?

or

Midterm exam questions

I. Multiple-choice questions: (3 points for each small question, ***24 points)

1. In the figure below, opposite to the vertex angle, and ().

2. When Xiao Ming and Xiao Gang are discussing math problems, they have the following dialogue:

Xiaoming: There is one and only one straight line parallel to the known straight line L. 。

Xiao Gang: Beyond point A, there is only one straight line perpendicular to the known straight line L. 。

Who do you think is right, Xiaoming or Xiaogang? ()

A. Xiaoming is right. B. Xiaogang is right. C. Xiaoming and Xiaogang are both right. D. Neither is correct.

3. Observe the cuboid as shown in the figure, and there are () sides parallel to the side AB.

A.4 B. 3 C. 2 D. 1

4. As shown in the figure, when a highway is built to the lake, it needs to go around the lake. If the first rotation angle a is

120, the second turning angle ∠B is 150, and the third turning angle ∠ C, at this time, the road is just the same as

The road before the first turn is parallel, so ∠C is ()

A. 120 b . 130 c . 140d . 150

5. The number below each group is the length of three small sticks, in which () can be put into a triangle.

A.B.

C.D.

6. As shown in the figure: Yes, yes. In the figure, there is a () with complementary angle.

a，0 b， 1 c，2 d，3。

7 It is known that point P is located on the right side of the axis, 3 unit lengths off the axis and 4 unit lengths above the axis, so the coordinate of point P is _ _ _

A.(-3，4B。 (3，4) C.(-4，3) D. (4，3)

8. As shown in the figure, the side AB of the rectangular ABCD is on the Y axis, and the point O is the midpoint of AB. As we all know.

Ab = 4, and the edge CD intersects the X axis at point E, then the coordinate of point C is ().

A.()B. ( ) C. ( ) D .()

Fill in the blanks: (3 points for each small question, * * * 30 points)

9. As shown in the figure, when a straight line intersects with a straight line at,, and, it can be made into//.

10. Point p () is on _ _ _ _ _ _ _. (Fill in "X axis" or "Y axis").

The coordinate of point 1 1.A is (3, -4), which means that point A is in the _ _ _ quadrant.

12. If point P(a, b) is in the second quadrant, then point Q(b, a) is in the fourth quadrant.

13. It is known that the lengths of two sides of an isosceles triangle are 8 cm and 3 cm respectively. Then it's

The circumference is _ _ _ _ _ _ _ cm.

14. A polygon with equal inner and outer angles is a _ _ _ _ _ polygon.

15 is known, as shown in figure, =, =,

. So, = _ _ _

16. The shape of the triangular wooden frame will not change, but the shape of the quadrilateral wooden frame will change, indicating that the triangle exists.

17. in △ABC, if ∠B=∠A+∠C, △ ABC is a triangle.

18. As shown in the figure, put a pair of commonly used triangular plates together as shown in the figure.

Then ∠ADE in the graph is a degree.

Iii. Answer: (***66 points)

19.( 10 minute) Find the value of x in the figure. (//)

20.( 10) As shown in the figure, B is 57 southwest of A, C is southeast of A15, and C is 82 northeast of B. Find the degree of ∠ C. 。

2 1( 12 points)

Given the position of points and points in the plane rectangular coordinate system as shown in the figure, then:

(1) Write the coordinates of these two points: (,), (,);

(2) Find the area of δ.

22( 12 points), there are many different methods to prove the theorem of triangle interior angle sum, and the following proof process is completed:

(1) As shown in figure 1, the passing point A is DE‖BC,

Because in BC,

Therefore ... ∠2=∠ ,∠3=∠ ()

Because ∠ 1+∠4+∠5= (boxer definition)

So ∞ +∞ +∞ = (equivalent substitution)

(2) extend BC to E, so that CD‖AB is behind point C,

Because CD‖AB,

So ∠ 1 =∞ ()

∠2=∠ ( )

Because ∠3+∠4+∠5= (flat angle definition)

So ∞ +∞ +∞ = (equivalent substitution)

(

23.( 10) Use counterexamples to show that the following examples are false examples.

(1) if A < B, then AC < BC,

(2) Two equal angles must be antipodal angles.

24.( 12 points) It is known that the straight line AB‖CD, E is a point between AB and CD, connecting EA and EC.

(1) As shown in Figure ①, if ∠ A = 200 and ∠ C = 400, ∠ AEC = 0.

(hint: if e is EF‖AB, then EF‖CD)

(2) If ∠ A = and ∠ C =, ∠ AEC = 0.

(3) As shown in Figure (3), if ∠ A = ∠ C =, what is the equivalent relationship with ∠AEC? And briefly explain.