Time: 120 minutes Total score: 150 minutes

Choose an option carefully first ((this big question * * 10 small question, 4 points for each small question, out of 40 points).

The arithmetic square root of 1 and 9 is ()

A.3 B. 3

C.D.

2. The irrational number in the following figures is ()

-0.333…,-,3,3. 1 4 1 5, 2.01… (there are1zeros between two adjacent1), 76.066.

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

As the picture shows, it is a rectangular concrete playground in our school. if

A student should walk from Angle A to Angle C, at least ()

A.80 meters B.90 meters

C.100m D.110m

4. It is known that the diagonal drawn from a vertex of a polygon divides the polygon into 10 triangles, so the sum of the internal angles of the polygon is ().

14400

2 1600d 16200

5, the following proposition, the correct is ()

A. The diagonals of rectangles are perpendicular to each other.

B.the diagonal lines of diamonds are equal.

Diagonal lines of a square are vertically bisected and equal to each other.

D. diagonal bisection of isosceles trapezoid.

6. Among the following five banking standards, () is an axisymmetric figure with central symmetry.

1。

7. On the physical education class, Miss Liu put three on the basketball court.

Three basketballs, A, B and C, are not on the same line.

Now put the basketball D in, so that A, B, C, D.

Four basketballs form a parallelogram. Ask.

Basketball D has () in the picture.

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

8, the following four graphics, cannot be translated by graphics is ().

9. As shown in the figure, in the isosceles trapezoid ABCD, AD‖BC, AD=5,

AB=6，BC=8，AB‖DE，

The circumference of △DEC is ()

12 C. 15 D. 19

10. As shown in the figure, the rectangular ABCD is folded along AE, so that the D point falls on the F point on the BC side.

If ∠BAF=60ο, ∠DAE equals ()

A. 15

C.45 D.60

Second, fill in carefully (this big question * * 10 small question, 3 points for each small question, out of 30 points)

1 1, simplification: (1)=(2)=(3)= _ _ _.

12, if; If so, then;

.

13, as shown in the figure, is a cube with a side length of 3cm, and all faces are

Divide into three small squares. Its side length is 1 cm,

Suppose an ant crawls 2 cm per second, then it crawls from the bottom.

Point a crawls along the surface to point b on the side,

It will take at least two seconds.

14, △ABC and △DCE are equilateral triangles, as shown in the figure.

△ACE rotates counterclockwise around the point.

You can get delta by rotating.

15, the area of the diamond is 24㎝2, the length of one diagonal is 6㎝, the length of the other diagonal is, the side length is, and the distance between a group of opposite sides is.

16, a, b, c and d are in the same plane, from ① ab ‖ CD; ②AB = CD； ③ BC ‖ AD;

④ Choose two of the four conditions BC = AD to make the quadrilateral ABCD a parallelogram.

There are _ _ _ _ kinds of selection methods.

17. To judge that a diamond is a square, the condition that can be added is _ _ _ _ _ _ _ _ _ _ (only write one condition).

18, as shown in the figure, is the herringbone frame of the factory roof.

(isosceles triangle), its span BC =12m,

Zhongzhu advertisement is 2.5 meters, Zhongzhu AD⊥BC,

The vertical foot D is the midpoint of BC, which is also commonly known as the length of the factory building.

10 meter, in order to prevent rain, it is necessary to cover the roof with linoleum. (width of each roll of linoleum 1m, length 10m)

If you buy from this factory, you need to buy _ _ _ _ _ _ _ _ linoleum rolls.

19 As shown in the figure, the quadrilateral ABCD is a square with a side length of 1.

P is any point on the CD beside ABCD, PE⊥DB.

At point E, PF⊥AC is at point F, then PE+PF=.

20. As shown in the figure, in the trapezoid, ABCD, AD‖BC, and AB=8, AD=3, CD=6, and ∠B+

∠C=900, then the trapezoidal area s trapezoidal ABCD=.

Third, be patient: (This big question is ***8 questions, ***80 points)

2 1, simplification (5 points for each small question, * * * 20 points)

( 1)(2 - ) (2)( +2)( -2)

(3) (4)

22. (This small question is 8 points) To make a picture, first translate the letter "H" in the picture to the right by 3 squares, and then rotate the translated pattern clockwise by 900 degrees around the vertex in the lower left corner.

23. (8 points in this small question) As shown in the figure, it is a hanger made of quadrilateral instability. It is known that the side length of each diamond is 20㎝, and the distance between the two nails A and B of the clothes hanger on the wall is ㎝, so find ∠ 1.

24. Xiaoming and Xiaodong often play on the lawn of isosceles triangle. One day, they found an interesting phenomenon: the lawn as shown in the figure is isosceles △AB=AC, AB=AC, both of which are small P beside BC. Then Xiaoming goes to A along AC parallel lines PE (point E is on AB) and EA, and Xiaodong goes to A along BA parallel lines PF (point F is on AC) and FA. When the walking speed is constant, the time to arrive at A is exactly the same. Do you know why? Tell me your reasons.

25. (8 points in this small question) When rural families lay the foundation, unlike the urban housing foundation with special instruments, they often use the indigenous method, first pull the rope into a quadrilateral, and measure the length a and width b of the housing foundation respectively (as shown in the figure). If AD = BC and AB = CD are measured, can the foundation be guaranteed to be rectangular? Please explain it with what you have learned. If it cannot be guaranteed to be rectangular, please explain what other processes are needed to ensure that the foundation is rectangular. (Name two methods)

26. (This small problem is 10) As shown in the figure, in the quadrilateral ABCD, AB=CD, BC=AD, E and F are two points on the diagonal AC, AE = CF, explain BE=DF.

27. When we were studying "real numbers", we drew a picture, that is, "Draw a square with a line segment with the unit length of'1'on the number axis, and then draw an arc with the origin o as the center and the diagonal length of the square as the radius at point A". Please answer the following questions according to the pictures:

What is the length of (1) line segment OA? (Write out the solution process)

(2) What is the purpose of this picture?

(3) This way of studying and solving problems embodies a new mathematical thinking method.

(Fill in the line with the following matching option serial numbers)

A. Combination of numbers and shapes B. Substitution C. Substitution D. Induction

8. As shown in Figure 10 and Figure 2, the quadrilateral ABCD is a square, and m is a point on the extension line of AB. One right-angled edge of the right-angled triangular ruler passes through point D, the right-angled vertex E slides on the edge of AB (point E does not coincide with points A and B), and the other right-angled edge intersects with the bisector BF of ∠CBM at point F.

(1) As shown in figure 1, when point E is at the midpoint of side AB:

① By measuring the length of DE and EF, we guess that the quantitative relationship between DE and EF is:

(2) The midpoint n between the connection point E and the AD side, and the quantitative relationship between NE and BF is guessed as follows;

Please explain the correctness of your above two conjectures.

(2) As shown in Figure 2, when point E is at any point on the side of AB, please find an n point on the side of AD to make NE=BF, and then guess what is the quantitative relationship between de and EF at this time.

Qijiang middle school eighth grade mathematics midterm exam answers

1. 1, A 2, B 3, C 4, B 5, C 6, B 7, C 8, D 9, C 10, a.

Second, 1 1,12,6; - ; 2,0 13、

14、C； ; BCD 15, 2006 16, 4 17, diagonal lines are equal (only one can be filled) 18, 7 19, 20,

2 1, solution: (1) Original formula =-1.

= 12+2-4-4 points.

= 14-4-5.

(2) The original formula =-2 points.

= 3-4-4-4 points.

=- 1-5 points.

(3) The original formula =-2 points.

=-4 points.

= 1-5 points.

④ The original formula =+-2 points.

=-5 points.

22. solution: add DQ, AE.

As can be seen from the figure, DQ=2AB=, then DF=

-Two points.

The quadrilateral ADEF is a diamond.

∴AE⊥DF, DO=OF, ao = OE-4 points.

Then DO=

In Rt△ADO, ∠ADO=900, AD=20㎝, DO=

According to Pythagorean theorem: ao = = 10 ㎝-6 points.

∴AE=2AO=20㎝

∴AD=DE=AE

Delta ade is an equilateral triangle.

∴∞- 1 = 600, 8 points.

23. Solution: Sketch.

Correct translation-4 points; Correct rotation -8 points.

24. solution: ∫PE‖ACPF‖AB? ∴ Quadrilateral AEPF is a four-point parallelogram.

∴ PE = AFPF = AE-8 points?

Xiao Ming and Xiao Dong are at the same speed?

Xiao Ming and Xiao Dong will arrive at point A at the same time-10.

25. Solution: There is no guarantee that the quadrilateral ABCD is a rectangle -2 points.

AD = BC，AB=CD？ ∴ Quadrilateral ABCD is a 4-point parallelogram.

Method 1: AC = BD (parallelograms with equal diagonals are rectangles) -7 points.

Method 2: A = 90? 0 (a parallelogram with right angles is a rectangle-10 minutes 26,

Solution: connect BD so that AC and BD intersect at O.

AB = CD BC = AD

∴ Quadrilateral ABCD is a parallelogram (two groups of quadrangles with equal opposite sides are parallelograms)-.

∴OA=OC, OB=OD (diagonal bisection of parallelogram) -5 points.

AE = CF

OE = of-6 points.

∴ quadrilateral BFDE is a parallelogram (quadrilaterals whose diagonals are bisected are parallelograms)-.

∴BE=DF (the opposite sides of a parallelogram are equal)-10.

27.( 1) Solution: ∵ = 2-65433.

∴OB=

∴ OA = OB =-2 points.

(2) Solution: There is a one-to-one correspondence between points on the number axis and real numbers-4 points.

(3) solution: A-.

28，( 1) ① de = ef -。

(2) ne = BF-2.

③ Solution: ∵ Quadrilateral ABCD is a square? ∴AD=AB,∠DAE=∠CBM=900？

∵ Points N and E are the midpoint of AD and AB respectively? ∴DN= AD，AE= AB

∴ DN = EB-3 points?

In，∠ ane = ∠ aen = 450？ ∴∠DNE= 1350？

∵BF split ∠CBM? ∴∠FBM=450？ ∴∠EBF= 1350

∴∠dne =∞-4 points?

∠∠FBM+∠DEA=900∠ Ade +∠DEA = 900?

∴∞-fbm =∠ade, 5 points?

∴△DNE≌△EBF？ ∴ de = ef ne = BF-6 points.

(2) Intercept an = AE, and connect NE to AD. The proof method is similar as above-10.

Without a map, we can make do.