1. The following operation is correct ()
(A) (B) (C) (D)
2. Among the following artistic Chinese characters, the one that is not axisymmetric is ()
Zhong Qi Wang Xi
(A) (B) (C) (D)
by car
be on foot
Ride a bike
The way to school
16 people
Eight people
24 people
number of people
3. When the speed of satellite is 2.88×107m/,the speed of jet is 1.8× 106.
Then the speed of this artificial earth satellite is the speed of this jet ()
(A) 1600 times (B) 160 times (C) 16 times (D) 1.6 times.
4. The picture is drawn after investigation in Class Two, Grade Eight, Lei Feng Middle School.
Bar chart, then the students in walking to school in this class are better than those who go to school by bike ().
(a) Eight people were missing; (b) Eight people were added; (c) 65,438+06 people were missing; (d) 65,438+06 people were added.
5. The fan-shaped statistical chart of the number of students in three grades in a school accounts for the number of students in the whole school is shown in the figure.
(Figure 4)
The degree of the central angle of the sector where Grade 8 is located is ()
Grade?Seven
Grade?Eight
Grade?Nine
frequency
150.5
50.5
75.5
100.5
125.5
30o(B)45o(C) 60o(D)72o
6. The picture shows 40 students in a class skipping rope for one minute.
Frequency distribution of test scores (integer multiple)
Histogram, first, second, third and fourth from the left.
The height ratio of the small rectangle is 1: 4: 3: 2,
Then the number of skipping ropes in one minute in this class is 100.
The students in the class have ()
(Figure 5)
(A)6 people (B)8 people
(Figure 6)
(C) 16 people (D)20 people.
7. In △ABC and △A 1B 1C 1, the following contents are given.
Four sets of conditions are given, among which it may be uncertain whether △ ABC △ a1b1c1is ().
(A)AB=A 1B 1，BC=B 1C 1，CA=C 1A 1
(B)∠C=∠C=90，AB=A 1B 1，BC=B 1C 1
A
C
B
P
1
No.2 package
No.3 Bao
The fourth bag
O
D
ordinary
M
C
1
Figure 8
Question 9
Map number 10
(C)AB=A 1B 1，，CA=C 1A 1，∠B=∠B 1
(D)AB=A 1B 1，，CA=C 1A 1，∠A==∠A 1
8. As shown in the figure, P is a point on the BC side of △ABC, and BP=PA=AC=PC.
Then the degree of ∠B is ()
20O (B)30O (C)40O (D)50O
9. The picture is a schematic plan view of the reformed billiard table (dotted line is a square grid), and the shadows on the four corners of the picture are displayed respectively.
Four ball holes are shown. If the ball is hit in the direction shown in the figure,
Hit (the ball can bounce many times), and then the ball finally falls.
The ball bag is ()
1 bag (B)2 bags (C)3 bags (D)4 bags
10. As shown in the figure, point M is a point on the bisector of ∠COD, point M is MC⊥OC of point C, MD⊥OD of point D, and the connection CD of point N is OM, then
Draw the following conclusions:
① MC=MD,②∠CMO=∠DMO,③OM⊥CD, and NC=ND,
(4) If ∠ 1 = 300 and OD=2MD, the correct one is ().
(A)①②③ (B)①②④ (C)③④(D)①③④
Fill in the blanks (3 points for each small question, *** 18 points)
1 1. Write a function whose function value decreases with the increase of independent variables.
(Just write one)
12. Calculation.
13. The following are the structural formulas and chemical formulas of three compounds, so the chemical formula of the fourth compound is.
H
H
H
C
H
C
C
H
H
H
H
H
H
H
H
H
C
C
H
H
H
H
C
H
Structural formula:
C2H6
C3H8
methane
Chemical formula:
Map number 15
14. Decomposition factor:.
15. As shown in the figure, in △ABC and △ADC, ∠B=∠D=90O,
Map number 14
To make △ ABC△ ADC, one more condition needs to be added.
Just write one.
16. As shown in the figure, the side length of the square ABCD is 3, and the point E is on AB.
Point f is on the extension line of BC, AE=AF, then quadrilateral EBFD.
The area of is:.
Iii. Answers and proof questions (this question is ***4 small questions, ***32 points)
17.(8 points) Find the value of algebraic expression, where
18.(8 points) As shown in the figure, points C, E, B and F are on a straight line, AB⊥CF is in B,DE⊥CF is in E, and AC = DF.
AB=DE .
Verify ce = cf
△ABC's graph about X axis symmetry
△ABC's graph about Y axis symmetry
19.(8 points) As shown in the figure, the figure of △ABC about the X axis and Y axis symmetry is made by using the coordinate characteristics of points about the axis symmetry.
20.(8 minutes) As shown in the picture, a ship departed from Island A at 9: 00 a.m. and sailed due north at a speed of 20 knots. 1 1 arrived at B. Looking at Lighthouse C from A and B respectively, I found NAC = 32O and NBC = 64o, so I found it from B..
Four, comprehensive questions (this question 10)
2 1. It is known that the image of the linear function y=kx+b passes through the point (1, 1), and k and b satisfy k-b=-5.
(1) Try to find the analytical expression of this function. (5 points)
(2) If the image of the function intersects with the Y axis at point A, whether there is a point P on the image of the function, so that PA=PO, and if there is, the coordinates of the point P are requested; If it does not exist, please explain why. (5 points)
Verb (abbreviation of verb) comprehensive question (subject 10)
A
B
C
O
x
y
22. as shown in the figure, in the rectangular coordinate system xOy, the straight line y=kx+b passes through the positive semi-axis of the x axis at A(- 1, 0) and the positive semi-axis of the y axis at b, c is a point on the negative semi-axis of the x axis, ca = co, and the area of △ ABC is 6.
(1) Find the coordinates of point C. (3 points)
(2) Find the analytical formula of straight line AB (3 points)
C
O
x
F
E
D
y
(3)D is the moving point in the second quadrant, OD⊥BD, straight line BE, vertical line CD is on the forehead, and OF⊥CD intersects straight line BE at F. Does the size of ∠BDF change when the lengths of line segments OD and BD change? If yes, please explain the reasons; If not, please prove and find its value. (4 points)
Reference Answers and Grading Criteria for Grade 8 Mathematics
First, multiple-choice questions (3 points for each small question, 30 points for * * *)
Title number
1
2
three
four
five
six
seven
eight
nine
10
answer
D
A
C
B
D
D
D
C
B
B
Fill in the blanks (3 points for each small question, *** 18 points)
Title number
1 1
12
13
14
15
16
answer
The answer is not unique.
4x6y2
C4H 10
(p+2)(p-2)
The answer is not unique.
nine
Iii. Answers and proof questions (this question is ***4 small questions, ***32 points)
17 ...2 points
= (x2+2xy+y2-x2+2xy-y2+4x2xy) ÷ 4xy ... 4 points.
=(4xy+4x2y2)÷4xy
= 1+xy...6 points
∵ x=()，y=2
∴ Original formula =1+xy =1+1× 2 = 3 ... 8 points.
18. Proof: AB ⊥ CD, Germany ⊥ CF.
∴∠ ABC =∠ def = 90o...2 points.
In Rt△ABC and Rt△DEF.
∴ RT△ ABC ≌ RT△ def (HL)...6 points.
BC =EF
∴BC—BE=EF—BE
Namely: CE = BF...8 points.
19. Scoring description: 4 points for each symmetrical figure.
20. Solution: ∵ ∠NAC=32O, NBC=64O.
∴∠ C =∠ NBC —∠ NAC = 64o-32o = 32o...2 points.
∴∠C=∠NAC=32O
∴ BC = AC...6 minutes.
∫AB = 20×( 1 1-9)= 40 (nautical miles) ... 7 points.
∴BC=AC=40 (nautical mile)
The distance from b to c is 40 nautical miles. ..... 8 points
Four, comprehensive questions (this question 10)
2 1. solution: the image-passing point of (1)∫ linear function y=kx+b (1, 1) ... 1 min.
∴k+b= 1
..... 4 points
The analytical formula of this function is y =-2x+3...5 minutes.
(2) There is a little P(0.75, 1.5) on the image of this function, which satisfies PA=PC.
The analytical formula of this function is y=-2x+3, and when x=0, y=3.
So the coordinates of point A are (0,3) ... 6 points.
PA = PO
∵ Point P is on the vertical line of A0,
Therefore, the ordinate of point P is yp = 1.5 ... eight minutes.
When YP= 1.5,
-2xp+3= 1.5
Get XP = 0.75...9 points.
Therefore, the coordinate of point P is (0.75, 1.5)... 10 minute.
Verb (abbreviation of verb) comprehensive question (subject 10)
22.( 1) Solution: ∫a(- 1, 0), ∴ OA = 1... 1.
And CA= CO, ∴ (CA+AO)=CA can get ca = 3...2 points.
∴ coefficient = 4, ∴ coefficient (-4,0) ... 3 points.
(2) Solution: ∵× bo = 6, ∴ bo = 4 ∴ b (0 0,4) ... 4 points.
For A(- 1, 0), the analytical formula of straight line AB can be obtained by using the undetermined coefficient method: y = 4x+4...6 points.
(3) Solution: When the lengths of line segments OD and BD change, the size of ∠BDF remains unchanged.
Proof: You can prove △ COD △ BOF ... 8 points.
∴OD=OF and OD⊥OF.
∴∠ODF=450
* ∴∠bdo=90o⊥BD od
∴∠BDF=45O
That is to say, when the lengths of line segments OD and BD change, the size of ∠BDF is constant at 45o... 10.