The second volume of the junior high school mathematics final examination paper Hebei Education Edition 1, multiple-choice questions (3 points for each question, * * * 30 points).
1. 3℃ above zero is 3℃, and 2℃ below zero is ().
A.2 B. C.2℃ D. 2℃
2. The inverse of the solution of this equation is ()
a . 2 B- 2 c . 3d-3
3. In recent years, China's high-speed rail has developed rapidly, and the high-speed rail technology has continuously gone abroad, becoming a new business card to show China's strength. It is estimated that by the end of 20 16, the operating mileage of China's high-speed railway will reach 18000 km. The scientific notation of 18000 should be ()
A. 18？ 10 B. 1.8？ 10 C. 1.8？ 10 D. 1.8？ 10
4. The following operation is correct ()
A.3x2+2x3=5x5 B.2x2+3x2=5x2
C.2x2+3x2 =5x4 D.2x2+3x3=6x5
5. If the value of the algebraic expression x-2y+2 is 5, the value of 2x-4y is ().
a . 3 B- 3 c . 6d-6
6. Given the position of the points represented by numbers A and B on the number axis as shown in the figure, the following conclusion is correct ().
a . a+b & gt； 0 Bachelor of Arts? b & gt0 C.|a| >| b | d . b+a & gt； b
7. To fix a horizontal batten on the wall, at least the number of nails is ().
A.1b.2c.3d. Any one
8. As shown in the figure, C and D are two points on the line segment AB, and D is the midpoint of the line segment AC. If AB= 10cm and BC=4cm, the length of AD is ().
A. 2 cm b. 3 cm c. 4 cm d. 6 cm
9. The degree of the angle that a pair of triangles can't be spliced is (splicing requirements: neither overlapping nor leaving gaps) ()
A.B. C. D。
10. Observe the following monomial about X and explore its laws: 2x, 4x, 6x, 8x, 10x, 12x,? According to the above law, the single item of 20 16 is ().
a . 20 16x b . 20 16x c . 4032 x d . 4032 x
Two. Fill in the blanks (3 points for each question, ***2 1 point)
1 1. The coefficient of single item is.
12.
13. If it is a similar project, _ _ _ _ _ _ _ _.
14. If the solution of the equation about is, then.
15. If the complementary angle is 76? 28? , then =
16. As we all know, it is the opposite of each other and the reciprocal of each other, so the value of is equal to _ _ _ _ _.
17. If the equation about x is linear, then.
III. Answering questions (42 points for this question, 6 points for each question)
18. Calculation: (1)
(2)
19. Solve the following equation:
( 1)5(x+8)=6(2x﹣7)+5
(2)
20. Simplify before evaluating: 5a2-4a2+a-9a-3a2-4+4a, where a=-.
2 1. The complementary angle of an angle is 30 smaller than that of this angle? Please work out the size of this angle.
22. The window of a room is as shown in the picture. The top decoration consists of two quarter circles and a semicircle (they have the same radius):
(1) What is the area occupied by decorations?
(2) What is the window area where sunlight can enter?
Fourth, comprehensive questions
23.(8 points) A company wants to transport a batch of goods to other places, and there are two modes of transportation to choose from:
Method 1: transport by courier company, loading and unloading fee 400 yuan, plus 4 yuan per kilometer;
Mode 2: Train transportation, loading and unloading fee of 820 yuan, plus 2 yuan per kilometer.
(1) If the total cost of the two modes of transportation is equal, what is the transportation distance?
(2) If the transportation distance is 800 kilometers, which transportation mode should the company choose?
24.(9 points) As shown in figure (1), stack the right-angled vertices c of two right-angled triangles together.
(1) try to judge? ACE and? The relationship between BCD size, and explain the reasons;
(2) What if? DCE=30？ , beg? ACB degree;
(3) guess? ACB and? The quantitative relationship of DCE, and explain the reasons;
(4) If the position of one of the triangular plates changes, as shown in Figure (2), does the conclusion in Item (3) still hold? (No need to give reasons)
25.( 10 minute) The distance between Station A and bilibili is 448 kilometers, and a local train starts from Station A with a speed of 60 kilometers per hour; An express train departs from Mile Mile at a speed of 80 kilometers per hour. Q:
(1) Two cars leave at the same time, in opposite directions. How many hours did they meet after departure?
The two cars are driving in opposite directions. The local train will drive for 28 minutes first. A few hours after the express train left, the two cars met.
Hebei Education Edition, Grade One, Volume Two, Mathematics Final Examination Paper Reference Answer 1 Multiple Choice Questions
1- 10
Two. Fill in the blanks (3 points for each question, ***2 1 point)
1 1. 12.-2 13.5 14.- 1 15. 103? 32' 16. 17.2
III. Answering questions (42 points for this question, 6 points for each question)
18. Solution: (1) Original formula =-3 points.
=- 12+ 16-6
=-2-6 points.
(2) The original formula =- 1-? (2-9)-3 points.
=- 1- ? (-7)
=-6 points.
19. Solution: (1) If the brackets are removed, 5x+40 = 12x-42+5-2 points.
If the transferred project is merged with similar projects, 7x =-4 points.
If the coefficient is 1, x = 1 1-6 points.
(2) If the denominator is removed, 3 (x+2)-2 (2x-3) = 12-2 points.
If the brackets are removed, 3x+6-4x+6 =12-4 points.
Used to move items to merge similar items. ﹣x=0.
If the coefficient is 1, x = 0-6 points.
20. Solution: The original formula =-3 points.
When a=-, the original formula =
=
=-6 points.
2 1. solution: let the degree of this angle be x? ,
From the meaning of the question:-4 points.
Solution: x = 80-5 points.
A: What's the degree of this angle? -Six points.
22. Solution: (1) According to the meaning of the question, the area of the ornament is exactly equal to the area of a circle with a radius of.
That is =; -Three points.
(2) According to the meaning of the question, the part area that can penetrate sunlight = window area-decoration area,
So the area of the part that can penetrate sunlight =-6 points.
Fourth, comprehensive questions
23.(8 points) Solution: (1) Assuming the transportation distance is X kilometers, according to the meaning of the question.
400+4x = 820+2x-3 points.
The solution is x = 2 10-5 minutes.
Answer: If the total cost of the two modes of transportation is equal, the transportation distance is 2 10 km;
(2) If the transportation distance is 800 kilometers,
The total transportation cost of scheme 1 is: 400+4? 800=3600 (yuan)
The total transportation cost of scheme 2 is: 820+2? 800=2420 (yuan)
2420 & lt3600,
Therefore, if the transportation distance is 800 kilometers, the company should choose the second mode of transportation. -Eight points.
24.(9 points) Solution: (1)? ACE=？ Alkaline catalytic decomposition for the following reasons:
∵? ACD=？ BCE=90？ ,? ACE+？ ECD=？ BCD+？ ECD=90？ ,
ACE=？ BCD- 2 points.
(2) What if? DCE=30？ ,? ACD=90？ ,
ACE=？ ACD﹣？ DCE=90？ ﹣30? =60? ,
∵? BCE=90？ And then what? ACB=？ ACE+？ BCE，
ACB=90？ +60? = 150? ; -Five points.
(3) guess? ACB+？ DCE= 180？ -Six points.
The reason for this is the following：
∵? ACD=90？ =? ECB，？ ACD+？ ECB+？ ACB+？ DCE=360？ ,
ECD+？ ACB=360？ ﹣(? ACD+？ ECB)=360？ ﹣ 180? = 180? ; -Eight points.
(4) established. -Nine points.
25.( 10) (1) Solution: Let the two cars meet after x hours.
According to the meaning of the question: 60x+80x=448,-3 points.
The solution is x=3.2.
A: The two cars set off at the same time, in opposite directions, and met 3.2 hours after the departure. -Five points.
(2) Solution: Suppose that two cars meet after the express train leaves for y hours.
According to the meaning of the question: 60 (+y)+80y = 448-8.
The solution is y=3.
Attendant: Three hours after the express train left, two cars met. -10.