First, multiple-choice questions (3 points for each small question, ***24 points)
1. In the following categories, the correct calculation is ().
(A) (B) (C) (D)
Xiao Ming stood in front of the mirror and saw the electronic watch hanging on the wall opposite the mirror, and its reading was as shown in the figure.
The actual time of the electronic watch is ()
1(B) 1(C) 1(D) 1
3. If known, the value of is ().
(A) 49 (B) 39 (C) 29 (D) 19
4. A class is organizing students to discuss: measure the thickness of 1 piece of paper. The following four views have emerged. What you think is reasonable and feasible is ().
(a) directly measure the thickness of 1 sheet with a triangular ruler;
(b) firstly, measuring the thickness of two pieces of paper of the same type with a triangular ruler;
(c) First, measure the thickness of 50 pieces of paper of the same type with a triangular ruler;
(d) First, measure the thickness of the same type 1000 sheets with a triangular ruler.
5. As shown in the figure, in the following conditions, it cannot be judged that the straight line ∨ is ().
(A)≈ 1 =∠3(B)≈2 =∠3(C)≈4 =∠5(D)≈2+∠4 = 1800
6. Divide a cube with painted faces into 27 small cubes with the same size, and choose one of these cubes, and the probability that just three faces are painted with color is ()
(A) (B) (C) (D)
7. As shown in the figure, AB∨DE, CD=BF, if you want to prove △ ABC △ EDF, you need to add it.
The condition is ()
a、AB = EDb、AC = EFc、∠B =∠E； D, no need to supplement;
As the picture shows, Xiao Liang is playing on the playground and walking along the path at a constant speed for a period of time. The function image that can approximate the relationship between the distance from Xiao Liang to the starting point and time is ().
Fill in the blanks (3 points for each small question, 24 points for * * *)
9.=
10. As shown in the figure, AB∑CD and straight line EF intersect AB and CD at points E, F and EG respectively.
∠BEF crosses CD at G ∠1= 50? Then ∠2 =
1 1. The scale of the map is 1: 100000. If someone walks 2000 meters on the ground, the distance on the map is meters (the result is expressed by scientific notation).
12. If you see in the rearview mirror that the last five digits of a car's license plate are:, then the last five digits of this car are actually.
13, a bird flies freely in the air and then falls into a square as shown in the figure (each square is exactly the same except for the color), then the probability that the bird stops in a black square is _ _.
14. As shown in the figure, in △ABC, ∠C=900, AC=BC, and AD is the angular bisector of △ABC.
DE⊥AB, the vertical foot is E, if AB= 10, the circumference of △BDE is
15. As shown in the figure, fold △ABC along the straight line AD passing through point A to locate the AC side.
The straight line coincides with the straight line of the AB side, and the point C falls on the point E of the AB side. If < b = 450,
∠BDE=200, then∠ C =∠ CAD =
16. "The tortoise and the rabbit race" is a fable that students are familiar with. The picture shows the distance s (meters) and time.
T (minutes), and then the rabbit slept for minutes in the game, and the tortoise was here.
The average speed of the second race is 100 m/min.
Three. (6 points for 17, 8 points for 18, 0/9 for 10, 20 points for * *, 32 points).
17. Calculation
18. If a person lives 1 10,000 hours, how old is he or she? Is this possible? The result is accurate to the tenth place, and the significant figure of the divisor is pointed out. )
19. There are red, green and yellow balls in the pocket, including 4 red balls and 5 green balls. The probability of randomly picking out 1 green ball is, what is the probability of finding a yellow ball?
20. As shown in the figure, E is on the straight line DF and B is on the straight line AC. If ∠AGB =∠EHF∠C =∠D, try to judge the relationship between ∠A and ∠F, and explain the reasons.
Iv. (For each small question 10, ***20)
2 1. Simplify first and then evaluate, among which
22. As shown in the figure, it is known that CD⊥AB, EF⊥AB, and the vertical feet are d, f, ∠ 1=∠2 respectively. Try to judge the positional relationship between DG and BC and explain the reasons.
Five, (this question 12 points)
23. As shown in the figure, AB∑DE, AB=DE and AF=DC are known. How many pairs of congruent triangles are there in the picture? Please choose a pair to give proof.
Six, (this question 12 points)
24. As shown in the figure, in the L-shaped diagram composed of small squares, please use three methods.
Draw a small square in the picture below to make it an axisymmetric figure.
Seven, (this question 12 points)
25. Zhang Hua goes on a business trip by bike at 8: 00 in the morning, as shown in the figure, which is a function image between the distance s (kilometers) from home and the time spent (hours). According to this image, answer the following questions:
(1) When does Zhang Hua rest? How long did you rest? How far is it from home at this time?
When will he arrive at his destination? How long did you stay there? How far is the destination from home?
When will he come back? When will you go home? What is the average return speed?
Eight, (this question 14 points)
26. As shown in the figure, in △ABC, AC=BC, ∠ACB=900, D is a point above AC, the extension line of AE perpendicular to BD is at E, and AE= BD. Verify that BD is the bisector of ∠ABC.
Alternative questions:
1. Of the following four figures, the one that is not axisymmetric is ().
2. If 2x+5y-3=0, then 4x? The value of 32y is ()
A.6 B.8 C.9 D. 16
3. As shown in the figure, AB∨DE, ∠ABC=800, ∠CDE= 1400 are known.
Then BCD = _ _ _ _ _ _
A bamboo pole is 3.649 meters long, accurate to the tenth place.
There are 20 balls in the pocket, of which the number of red balls is twice that of white balls, and the rest are black balls. A randomly draws 1 ball from his pocket. If it is a red ball, A wins; A put the touched ball back in the bag, and B randomly touched 1 ball from the bag. If it's a black ball, B wins. If the game is fair to both sides, how many black balls should it be?
6. In △ ABC, AD is the center line of BC. Please explain: AB+AC > 2AD
Reference answer:
18.114 1.6 years old, which is impossible. The valid number is 1. 1.4,1.6.
19.* * * 15 ball, 6 yellow balls. The probability of finding 1 yellow ball is.
20. ∠ A = ∠ F. Reason: Because ∠AGB=∠DGF, ∠AGB=∠EHF.
So ∠DGF=∠EHF, so BD∨CE, so ∠C=∠ABD.
And ∠C=∠D, so ∠D=∠ABD, so DF∨AC, so ∠ A = ∠ F.
Four. 2 1. The simplified result of the original formula is:, and the value of the original formula is.
22.DG∨BC。 The reason is:
Vii. 25. (1) As can be seen from the figure, the rest time is 9: 00-9: 30; Rest for half an hour; Leave home at this time 15 km.
(2) Zhang Hua 1 1:00 arrives at the destination; I stayed there for 1 hour, and my destination was 30 kilometers away from home.
(3) He returned at 12:00; /kloc-arrive home at 0/4: 00; It takes 2 hours to return, 30 kilometers, and the average speed when returning is (km/h). A: The average speed of Zhang Hua's return is 15 km/h. 。
VIII. 26. As shown in the figure, extend the extension line of BC to AE at point F,
In △ACF and △BCD, ∠ FAC = 900-∠ F = ∠ DBC, AC = BC, ∠ACF =∠BCD = RT∞,
∴△ACF≌△BCD(ASA).∴AF=BD.AE= BD, that is, AE = AF. ∴ AE = F E
In △ABE and △FBE, AE = Fe, ∠aeb =∠feb = rt∞, Be = BE, ∴△ Abe △ FBE (SAS).
∴∠ABE=∠FBE. That is, BD is the bisector of∠∠ ∠ABC.
Alternative questions:
1.(D) Provide information; (b) and: 3.400; 4.3.6;
5. If there are white balls in the bag, there are two red balls and (20-3) black balls.
There are 20 balls in the bag, so the probability of A winning is, the probability of B winning is,
According to the fact that both sides of the game are fair, there is =, and if the solution is =4, then 20-3 =8.
Answer: There should be 8 black balls in the bag.