First-year math test papers and answers 1. Multiple choice questions (30 points)
The reciprocal of 1 and 3022 is ()
a . 3022； b .-3022； c； d；
2, the following statement is correct ()
A. Numbers whose absolute values are positive; B. The reciprocal number is1;
C. the square is its own number is 0; D. The number of a cube equal to itself is1;
3. if A < 0, B > 0, the largest number among b, b+a and b-a is ().
a . b-a； b . b+ a； C.ad not sure;
4. Excessive packaging wastes resources and pollutes the environment. According to estimates, if China reduces the amount of excessive packaging paper by 10% every year, it can reduce carbon dioxide by 3120,000 tons, which is expressed as () by scientific notation.
a . 3. 12× 105； b . 3. 12× 106； c . 3 1.2× 105； d . 0.3 12× 107；
5. If the equations about x 3x+5 = m and x-2m=5 have the same solution, then the value of x is ().
A.3b .-3； C.4d .-4；
6.A walks at a speed of 5 km/h 16 minutes, and B catches up with A at a speed of 13 km/h, so how many hours does it take B to catch up with A ()?
a . 10； B.6c； d；
7, the following formula in parentheses is correct ()
A.； b；
C.； d；
8, the following statement is correct ()
A. straight line AB and straight line BA are two straight lines; B. ray AB and ray BA are two rays; C segment AB and segment BA are two segments; D straight line AB and straight line a cannot be the same straight line;
9. If ∠ α and ∠βare complementary, and ∠α > ∠β, then the following formula represents the complementary angle of ∠β:
①90 -∠β; ②∠α-90 ; ③(∠α+∠β); (4) (∠ α-∠ β) is correct ()
A.4B.3C.2d . 1；
10. On the opening day of "Langshan Tourism Festival" in Hunan, China, from 8:00 am, the number of tourists entering the scenic spot every hour was about 1000, and the number of people leaving the scenic spot every hour was about 600. It is known that the number of tourists in Langshan Scenic Area is about 2000, so the time for tourists to reach saturation on the opening day of the scenic area is about ().
a . 10:00； b . 12:00； C. 13 point; D. 16 point;
Two. Fill in the blanks (24 points)
1 1, calculation: 0×(-2)-7=.
12, according to the new website Shanghai in June 1: Since the opening of the World Expo one month ago, the passenger flow has been stable, and the cumulative number of visitors on that night 19 exceeded 8 million, which is 8 million = 8 million by scientific counting method.
13, as shown in the figure, the whole circle represents the total number of people participating in extracurricular activities in a class.
The number of people skipping rope accounts for 30%, which means that the fan-shaped central angle of kicking shuttlecock is 60.
The ratio of the number of shuttlecock players to basketball players is 1:2, which means to participate in "others"
The number of active people accounts for% of the total number.
14、。
15, the price of an apple is x yuan per kilogram, and the face value is 100 yuan.
I bought 5 kilograms, so I should get my yuan back.
16. It is known that ∠A and ∠B are complementary. If ∠ A = 70, then ∠B is.
17, as shown in the figure, if CB=4cm and DB=7cm,
And d is the midpoint of AC, then AC=
18, the 10 th pattern is made of black and white square paper.
There are some pieces of white paper in the pattern.
Iii. Answering questions (22 points)
19, (6 points) calculation:
20.(8 points) Solving equations:
2 1, (8 points),
If, and B-2A=a, find the value of a.
Four, the application problem (24 points)
22.(8 points) The Youth League Committee of a middle school initiated the charity donation activity of "Caring for Disabled Children", and the teachers and students of the whole school enthusiastically donated 3,000 books of all kinds. In order to understand the distribution of all kinds of books, some books are randomly selected and counted according to four categories: a. Art; B. literature; C. popular science; D. others. And draw the statistical results into two incomplete statistical charts as shown in the figure:
(1) This statistic * * * extracted a book, and the degree of m= and ∠ α in the pie chart is.
(2) Please complete the bar chart.
(3) How many literary books are expected to be donated by all teachers and students?
23.(8 points) The 7th China Expo with the theme of "Open Rise and Green Development" ended successfully in Changsha, Hunan on May 20th, 20 12. As the host, Hunan Province has signed 348 overseas and domestic investment cooperation projects, of which the number of overseas investment cooperation projects is twice that of domestic investment cooperation projects outside the province, 5 1 more.
(1) How many overseas and domestic investment cooperation projects have Hunan signed?
(2) If the average investment cooperation projects abroad and outside the province are 600 million yuan and 750 million yuan respectively, how many billion yuan will Hunan Province, the host of this "China Expo", introduce?
24. (8 points) (1) As shown in the figure, point C is on line segment AB, with line segments AC=6cm and BC=4cm, and points M and N are the midpoint of AC and BC respectively. How long is the line segment MN?
(2) According to the calculation process and results of (1), let AC+BC=a, and other conditions remain unchanged. Can you guess the length of MN? Describe the law you found in one sentence?
(3) For (1), if it is expressed as: "Given that the line segment AC=6cm, BC=4cm, point C is on the straight line AB, and point M and point N are the midpoint of AC and BC respectively, how can we find the length of line segment MN?" Will the result change? If so, find out the result.
Verb (abbreviation of verb) comprehensive question (20 points)
25.( 10) It is known that point O is a point on straight line AB, ∠ Coe = 90, and OF is the bisector of ∠AOE.
(1) When points C, E and F are on the same side of straight line AB (as shown in Figure ①), try to explain that ∠ BOE = 2 ∠ COF;
(2) When point C, point E and point F are on both sides of straight line AB (as shown in Figure ②), does the conclusion in (1) still hold? Please give your conclusion and explain the reasons.
(3) Rotate the ray in Figure ② clockwise around point O by m (0 < m < 180) to get ray OD, let ∠ AOC = n, and if ∠ BOD = 0, what is the degree of ∠DOE? (expressed by a formula containing n)
26.( 10) During the "Eleventh" period, Ping Li, Wang Li and other students went to a park with their parents. The following is a conversation between Li Ping and his father when they buy tickets. Try to answer the following questions according to the information in the picture:
(1) How many adults did Li Ping go to? How many students?
(2) Please help us to think about which way to buy tickets is more economical? Explain why.
(3) After purchasing tickets, Li Ping found that 8 students including Zhang Ming and their 12 parents ***20 people also came to buy tickets. Please design a more economical ticket purchase scheme for them and work out the ticket purchase cost at this time.
Reference answer:
1. Multiple choice questions: 1, b; 2、B； 3、A； 4、B； 5、B； 6、C；
7、C； 8、B； 9、B； 10、C；
2. Fill in the blanks: 1 1,-7; 12、8× 106; 13、20; 14、5x y2-3x2y； 15、 100-5x；
16、20 ; 17、6cm 18、3 1;
3. Answer:19,0; 20、x =-8；
2 1、B-2A=-2()=7x-5y
From: x=2a, y = 3；; B-2a = 7x-5y =-14a-15 = a, and the solution is a=- 1.
Fourth, application problem 22, (1) 40 ÷ 20 = 200; 80÷200=0.4=40﹪;
(2) The number of B: 200-40-80-20=60, the figure is omitted:
(3)3000×900 (Ben)
23.( 1) Setting up X overseas investment cooperation projects, the result is 2x-(348-x)=5 1, and the solution is x= 133.
Therefore, investment cooperation projects outside the province: 348- 133=2 15 (1) A: omitted.
(2) Total amount of introduced funds: 65,438+033× 6+265,438+05× 7.5 = 2,465,438+00.5 (100 million yuan).
24 、( 1)MN=5cm，(2)MN=a
(3) there will be changes. When point C is on the AB line, Mn = 5cm；;
When point C is on the extension line of line AB, Mn =1cm;
Verb (abbreviation of verb) Comprehensive question: 25. (1) As shown in Figure ①, if ∠COF=α, ∠ EOF = 90-α.
Because it is the bisector of ∠AOE, AOF = EOF = 90-α.
Therefore, ∠ AOC = (90-α)-α = 90-2α.
∠ BOE =180-∠ COE-∠ AOC =180-90-(90-2α) = 2α, that is, ∠ BOE = 2 ∠ COF;
(2) established. As shown in Figure ②, if ∠AOC=β, ∠AOF=,
So ∠ COF = ∠ AOC+∠ AOF = β+= (90+β).
And ∠ BOE =180-∠ AOE =180-(90-β) = 90+β, that is ∠ BOE = 2 ∠ COF;
(3) because ∠ doe =180-∠ AOE-∠ BOD =180-(90-n)-=
26.( 1) If there are x adults, there are (12-x) students, and the result is: 35x+35x0.5 (12-x) = 350.
Solution: x=8, so there are 4 students.
(2) If the group ticket is 35×0.6× 16=336 yuan, it can save money.
(3) The most economical way is to buy group tickets for 16 people and student tickets for 4 people.
Ticket purchase fee: 35×0.6× 16+4×35×0.5=406 (RMB).