7 Summer Mathematics Beijing Normal University

Mid-term examination paper of the second semester of grade seven.

(100 minutes 90 minutes)

1. Multiple choice questions: (3 points for each question, ***33 points)

1. As shown in the figure, AB‖ED, ∠B+∠C+∠D= ()

A. 180？ B.360？ C.540？ D.270

2. If point A (x, 3) and point B (2, y) are axisymmetrical about x, then ()

A.x=-2，y =-3； B.x=2，y = 3； C.x=-2，y=3？ ; D.x=2，y=-3

3. An outer angle of a triangle is less than its adjacent inner angle, then the triangle is ().

A. acute triangle? B. obtuse triangle; C. right triangle? D. unable to determine

4. The triangle with two equal sides is 3 cm long and 5 cm long, so its circumference is ().

A.8cm？ B. 1 1cm？ C. 13cm？ D. 1 1 cm or13cm

5. If point A (m, n) is in the second quadrant, then point B (-m, │n│) is in ().

A. the first quadrant? B. the second quadrant; C. the third quadrant? D. the fourth quadrant

6. It is known that point P is in the third quadrant, the distance to the X axis is 3, and the distance to the Y axis is 5, so the coordinate of point P is ().

A.(3,5)? B.(-5，3)？ C.(3，-5)？ D.(-5，-3)

7. As shown in the figure, if ef ‖ BC and eh ‖ AC are known, the complementary angle of ∠ 1 in the figure is ().

A.3？ B.4？ C.5？ D.6

8. The triangle is ()

A. Connect a graph composed of any three points

B. a graph formed by connecting three line segments that are not on the same line end to end.

C. a diagram consisting of three line segments

D. None of the above statements is true.

9. Three straight lines with * * * points intersect with the fourth straight line, and one * * * has an antipodal angle of ().

A.8？ B.24？ C.7？ D. 12

At 10. △ABC, ∠A= ∠B= ∠C, then △ABC is ().

A. acute triangle? B. right triangle; C. obtuse triangle? This is possible.

1 1. On the school playground, the relationship between the flag-raising flagpole and the ground belongs to ().

A. the straight line is parallel to the straight line; ? B. the straight line is parallel to the plane; C. the straight line is perpendicular to the straight line; D. The straight line is perpendicular to the plane

Fill in the blanks: (3 points for each question, ***2 1 point)

12. As shown in the figure, AB‖CD intersects with straight line EF, and AB, CD are equally divided into e, f, f and EG ∠BEF, if ∠ 1 = 72, ∠ 2 = _ _ _ _ _ _ _.

13. The known points M(a,-1) and N(2, b) do not coincide.

(1) When points m and n are symmetric about _ _ _ _ _ _, a = 2 and b = 1.

(2) When point M and point N are symmetrical about the origin, a = _ _ _ _ _ _ _ _ _ and b = _ _ _ _ _ _.

14. if A(a, b) is on the bisector of the second quadrant and the fourth quadrant, the relationship between a and b is _ _ _ _ _ _ _ _.

15. The lengths of the two sticks are 5 and 7 respectively, so the third stick should be chosen to nail it into a triangle. If the length of the third stick is even, there are _ _ _ _ options.

16. If the sum of all internal angles of a polygon is 1680, then the number of sides of this polygon is _ _ _ _ _ _.

17.n The diagonal number of the polygon is _ _ _ _ _ _ _ _.

18. As shown in the figure, a bridge will be built between the banks of A and B, and the direction of the bridge from the bank of A is 50 northeast. If both sides of A and B start construction at the same time, the bridge construction on both sides of B should start in the direction of β _ _ _ _ _ _ _.

Three. Answer: (19-22, 9 points for each question, 23 questions 10, * * * 46 points)

19. As shown in the figure, in △ABC, AD ‖ BC and AE are divided into ∠ BAC, ∠ B = 20, ∠ C = 30, and the degree of ∠DAE is found.

20. Do you think it is possible that the abscissa of each point on a graph remains unchanged and the ordinate becomes the original reciprocal, while the graph at this time has not changed? For example, what if the abscissa and ordinate become the original opposites?

2 1. In the plane rectangular coordinate system, connect (-2, 1), (-2,-1), (2, -2), (2, 3) in turn, what figure will you get? Try to find the area of the graph.

22. As shown in figure AB‖CD, discuss the relationship between ∠APC and ∠ PAB and ∠ PCD in the following four figures respectively. Please choose any one of the obtained relationships to explain.

23. It is known that in △ABC, ∠ABC=∠C, BD is the bisector of ∠ABC, ∠ BDE = ∠ Bed, ∠ A = 100, and the number of times to find ∠DEC.

Answer:

1. 1.b dial: if you answer the picture, link BD.

Then ∠ Abd+∠ BDE = 180.

And ∠ 2+∠ CBD+∠ BDC = 180,

So ∠ABC+∠C+∠CDE.

=∠ABD+∠CBD+∠BDE+∠BDC+∠2

=360 .

2.d-point dialing: With respect to the two points of X axis symmetry, the abscissa is equal and the ordinate is opposite.

3.B-click: Because any external angle of acute triangle and right triangle is greater than or equal to its adjacent internal angle.

4. Dial D: There should be two situations:

When the length is 3 cm,

The circumference is: 3+3+5= 1 1 (cm);

When the length is 5cm, 3+5+5= 13(cm).

5. nudge: because point a is in the second quadrant,

So m < 0, n>0,

so-m & gt； 0，│n│& gt； 0,

So point b is in the first quadrant.

6.d disk: Because in the third quadrant, the distance to the X axis is 3, indicating that the ordinate is -3.

The distance to y is 5, that is, the abscissa is -5, that is, the coordinates of point P are (-5, -3).

7. A nudge: If you answer the picture, you will get ∠ 1=∠4 from AC‖EH.

∠ 2 +∠ 4 = 180 from ef ∠ BC,

∠2=∠3,∠ 1+∠5= 180 ,

So there are three complementary angles of ∠2, ∠3, ∠ 5, and ∠ 1

8. Point B: the definition of triangle.

9.d inching: Apply the definition of vertex angle.

10.b nudge: ∠C=4∠A,

∠B=3∠A，

So ∠ A+3 ∠ A+4 ∠ A = 180,

So ∠ A = 22.5, ∠ C = 90.

1 1.d nudge: apply the positional relationship between points, lines and surfaces.

Second, 12.54 nudge: because AB‖CD,

So ∠ 1+∠ BEF = 180,

So ∠ BEF = 180-∠ 1.

= 180 -72 = 108 .

And < 2 = < beg = < bef,

So < 2 = 54.

13.( 1)x axis; (2)-2, 1 inching: when two points are symmetrical about X axis, the abscissa is equal and the ordinate is opposite;

When the origin is symmetrical, the abscissa and ordinate are opposite.

14. Dial with opposite numbers: the absolute values of the abscissa and ordinate of the points on the bisector of the second and fourth quadrants are equal, but the signs are opposite.

15.4 inching: since the value range of the third side is greater than 2 and less than 12,

There are 4, 6, 8, 10 and 4 even numbers between 2 and 12, so there should be 4 cases.

16. 12 inching: let the remaining internal angle be x,

(n-2)？ 180 = 1680 +x，

n-2=，；

n=2+9+，

So n should be 12.

17.

Direction: the formula of diagonal number of polygon.

18. Northwest 130

Third, 19. Solution: Because ∠EAC= ∠BAC

= ( 180 -20 -30 )=65 ,