1. Multiple-choice questions: (This big question has a total of 10 small questions, with 3 points for each small question and 30 points for * * *).
1. If m >- 1, the error in the following categories is ().
a . 6m >-6 b .-5m 0d . 1-m < 2
2. In the following categories, the correct one is ()
A.= 4 B. =4 C. =-3 D. =-4
3. It is known that a > b > 0, so the following inequalities have no solution ().
A.B. C. D。
4. A car driving on the highway, after two turns, is still driving in parallel in the original direction, then the angles of these two turns may be ().
(a) Turn right 50, then turn right 40 (b) Turn right 50, then turn left 40.
(c) Turn right 50, then turn left 130 (d) Turn right 50, then turn left 50.
5. The equation solved is ()
A.B. C. D。
6. As shown in the figure, in △ABC, ∠ABC=500, ∠ACB=800, BP shares ∠ABC, CP shares ∠ACB, then the scale of ∠BPC is ().
A. 1000？ B. 1 100？ C. 1 150？ D. 1200？
( 1) (2) (3)
7. The lengths of the four line segments are 3, 4, 5 and 7 respectively, so the number of different triangles that can be formed from end to end is ().
A.4 B.3 C.2 D. 1
8. In a polygon with equal internal angles, if an external angle is equal to an internal angle, then the number of sides of the polygon is ().
A.5 B.6 C.7 D.8
9. As shown in the figure, △A 1B 1C 1 is obtained by shifting △ABC to the direction of BC by half the length of BC. If the area of △ABC is 20 cm2, the area of quadrilateral A 1dc 1 is ().
A. 10 cm2 B. 12 cm2 C. 15 cm2 D. 17 cm2
10. At rest, the positions of Xiaohua, Xiaojun and Xiaogang are as shown in figure 1. Xiaohua said to Xiaogang that if my position is represented by (0,0) and Xiaojun's position is represented by (2, 1), then your position can be represented by ().
A.(5，4) B.(4，5)？ C.(3，4)？ d .(4.3)
Fill-in-the-blank question: This big question has ***8 small questions, each with 3 points and ***24 points. The answer is written directly on the horizontal line of the answer sheet.
The square root of 1 1.49 is _ _ _ _ _, the arithmetic square root is _ _ _ _ _, and the cube root of -8 is _ _ _ _ _.
12. The solution set of inequality 5x-9≤3(x+ 1) is _ _ _ _ _.
13. If point P(a, 2) is in the second quadrant, then point Q(-3, a) is in _ _ _ _ _.
14. As shown in Figure 3, there is a Lizhuang near the railway, and now a railway station is to be built. In order to make it most convenient for Lizhuang people to take the train (that is, the shortest distance), please choose a point near the railway to build a railway station (the location has been selected) and explain the reason: _ _ _ _ _ _ _.
15. If you drive from A to B at 60 east-north direction, and then drive from B to C at 20 west-south direction, then ∠ ABC = _ _ _ _ _ _
16. As shown in the figure, AD∨BC, ∠ D = 100, and CA shares ∠BCD, then ∠ DAC = _ _ _ _ _ _
17. Give the following regular polygons: ① regular triangle; ② Square; ③ Regular hexagon; ④ Regular octagon. Can fill the ground with one of the regular polygons is _ _ _ _ _ _ _. (Fill in the serial numbers of all answers)
18. If │x2-25│+ =0, then x = _ _ _ _ _ _, and y = _ _ _ _ _ _.
Three. Solution: This big question has ***7 small questions, with a score of ***46. The solution should be written in words, proof process or calculus steps.
19. Solve the inequality group: and express the solution set on the number axis.
20. Solve the equation:
2 1. As shown in the figure, AD∨BC and AD share ∠EAC equally. Can you determine the quantitative relationship between ∠B and ∠C? Please provide a justification for the answer.
22. As shown in the figure, it is known that D is a point on the BC extension line beside △ABC, DF⊥AB intersects AC at F and E, ∠ A = 35, ∠ D = 42, and the degree of ∠ACD is found.
23. As shown in the figure, it is known that A(-4,-1), B(-5, -4), C(- 1, -3) and △ABC are translated to get △ a ′ b ′ c ′ and △ ABC (x 1).
(1) Please make △ a ′ b ′ c ′ in the drawing; (2) Write the coordinates of points A', B' and C'.
24. The ticket price of a park in Changsha is shown in the following table:
The number of ticket buyers is1~ 50,51~ 100, which exceeds100.
Ticket price 10 yuan/8 yuan/5 yuan/person.
More than 50 students from Class A and Class B 100 of Grade 9 in a school went to the park to hold a graduation party, and less than 50 students from Class A and Class B. If tickets were bought separately according to classes, the two classes would have to pay 920 yuan. If two classes buy tickets together, one class has to pay 5 15 yuan. How many people are there in Class A and Class B respectively?
25. A storage and transportation station has Class A goods 1.530 tons and Class B goods 1.500 tons. Arrange to transport these goods to Qingdao by freight train, and 50 freight cars with different specifications of A and B can be hung. It is known that 35 tons of Class A goods and 1.5 tons of Class B goods can fill a Class A freight car. Please design it.
Answer:
I. Multiple choice questions: (***30 points)
BCCDD，CBBCD
Two. Fill in the blanks: (***24 points)
1 1.7,7,-2 12.x≤6
13.3 14. The vertical segment is the shortest.
15.40 16.400
17.①②③ 18.x= 5，y=3
Three. Answer: (***46 points)
19. Solution: The first inequality can be simplified as
X-3x+6 ≥ 4, and its solution set is X ≤ 1.
The second inequality can be simplified as follows
2(2x- 1)-7。
The solution set of the original inequality group is -7 < x ≤ 1.
Representing the solution set on the number axis are:
20. Solution: The original equation can be simplified as follows
∴
Subtract the two equations and you can get 37y+74=0.
Y =-2。 Therefore.
Therefore, the solution of the original equation is
21.∠ b = ∠ C. Reason:
∫ AD ∨ BC
∴∠ 1=∠B,∠2=∠C
∵∠ 1=∠2
∴∠B=∠C
22.？ Solution: Because ∠ AFE = 90,
So AEF = 90-A = 90-35 = 55.
So ∠ CED = ∠ AEF = 55,
So ∠ ACD =180-∠ ced-∠ d.
= 180 -55 -42=83 .
23.a′(2，3)，B′( 1，0)，C′(5， 1)。
24. Solution: There are X people and Y people in Class A and Class B respectively.
According to the meaning of the question
solve
So there are 55 students in Class A and 48 students in Class B. 。
25. Solution: If the X part of Type A cargo hold is used, the (50-x) part of Type B cargo hold is used.
The solution is 28 ≤ x ≤ 30.
Because x is an integer, x can only take 28, 29 and 30.
Therefore, the value of (5O-x) is 22,265,438+0,20.
So * * * there are three transportation schemes.
Transport scheme 1: 28 sections for A-type trucks and 22 sections for B-type trucks;
The second transportation scheme: 29 sections for type A trucks and 2 1 section for type B trucks;
The third transportation scheme: 30 sections for A-type trucks and 20 sections for B-type trucks.