1. Fill in patiently. (6, 7 points, 3 points for each small question, the remaining 2 points, ***22 points)
1. The morning temperature in a city 10℃, rising by 2℃ in the afternoon and falling at midnight (24: 00) 15℃. The temperature in the middle of the night is _ _ _ _.
2. On the number axis, the number represented by a point with a distance of 3 from the point representing-1 is _ _ _ _ _ _ _.
3. When learning the operation (+8)-(+ 10), a classmate made the following exploration: (-2)+(+ 10) =+8, so (+8)-(+10) =-2. On the other hand, (+8)+(- 10)=-2, so (+8)-(+10) = (+8)+(-10), thus summarizing an algorithm of rational numbers, which is _ _ _
4. Xiaohong painted the room, hired five workers, and it took 10 to finish it. Some kind of paint 150 liter was used, and the cost was 4800 yuan. The painting area is 150m2. At the time of final settlement, there are the following schemes:
Scheme 1: Pay according to work, with 30 yuan for each worker (1 person working one day is 1 worker);
Scheme 2: According to the painting cost, 30% of the painting cost is taken as the salary;
Option 3: Pay 12 yuan per square meter according to the painting area;
Ask Xiaohong's family for help. Choose _ _ _ _ scheme is the most cost-effective.
5. Write a linear equation with one variable satisfying the following conditions: ① The coefficient of an unknown quantity is; ② The solution of the equation is 3, and such an equation is _ _ _ _ _ _ _ _ _ _ _.
6. As shown in the figure, it is the surface development of a cubic carton. Please fill in the appropriate numbers in the other three boxes, so that after the pair is folded into a cube, the two numbers on the opposite side are opposite.
7. Xiaoming left from A to B 10m, and Xiao Liang also left from A.
Take 15m to c, and the BAC degree is 0.
8. When three straight lines intersect on a plane, there are at most a intersections and at least b intersections, then a+b = _ _ _ _ _ _.
9. In order to know the eyesight status of 400 seventh-grade students in a middle school, 40 students were randomly selected for investigation. In the survey, the general situation is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
10. A fruit company bought 10000 kg of citrus at the unit price of 2 yuan/kg. In order to reasonably determine the sales price, fruit companies need to convert the cost of damaged fruits in transportation into the price of undamaged fruits. Sales staff randomly selected some oranges from citrus and counted the damage of citrus. The results are as follows. If the company hopes to make a profit of 5000 yuan after selling all these oranges, then when selling oranges, it will be sold per kilogram.
Quality of Citrus (kg)
Damaged mass (kg) 5.50 19.42 5 1.54
Choose an option carefully (3 points for each small question, 30 points for * * *). The following questions all give four options, only one of which is correct. Please choose the serial number of the correct option and fill in the brackets after the question.
1 1, the following statement is incorrect ().
A has the smallest positive integer and no smallest negative integer. If a number is an integer, it must be rational.
C 0 is neither a positive rational number nor a negative rational number A positive rational number and a negative rational number make up a rational number.
12.from July to September, 2005, the top of the Three Gorges Dam was open to tourists for 92 days, with a daily reception quota of 1000 people. The maximum number of visitors during the whole opening period is expressed as () by scientific notation.
A 92× 103, b 9.2× 104, c 9.2× 103, d 9.2× 105.
13, in the following figures, the number of unequal groups is ()
①(-3)2 and -32 ②(-3)2 and 32 ③(-2)3 and -23 ④ 3 and ⑤(-2)3 and 3.
A.0 group B. 1 group C.2 group D.3 group
14, the calculation result is ()
A.B. C. D。
15. The car is driving on the expressway at a speed of 72 kilometers per hour, heading for the silent valley. The driver honked his horn and heard an echo four seconds later. How far is the car from the valley? It is known that the speed of sound propagation in the air is about 340m/s, assuming that the car is meters away from the valley when the echo is heard, according to the meaning of the question, the equation is listed as ().
A.B.
C.D.
16, a shop priced a commodity at the purchase price plus 20%, but it could not be sold; Later, the boss reduced the price by 20% according to the fixed price and sold it in 96 yuan, which was soon sold. Then the win-win situation of this business is ().
A. lose 4 yuan B. lose 24 yuan C. earn 6 yuan D. lose nothing.
17, the ratio of two angles is 7: 3, and their difference is 72, so the quantitative relationship between these two angles is ().
A. equality B. complementarity C. complementarity D. uncertainty
18, as shown in the figure, is a plane figure obtained by looking at a geometric body composed of the same small cubes from above, and the numbers in the small squares indicate the number of small cubes in this position, so the plane figure obtained by looking at the geometric body from the front is ().
19, the following survey is not suitable for sampling survey ()
A. investigate the passenger flow of a scenic spot within one year; B. Understand the situation of iodized salt in China;
C. Investigation on the germination rate of a new wheat variety: C. Investigation on the situation of a class of students riding bicycles to school;
20. As shown in the figure, the bar chart of skipping performance of grade seven students in a school (Class 3 * * *), then the correct answer below is ().
There are at least 40 people such as A.C..
B. There are 120 students in grade seven in this school.
C.A. and others account for 30% of the total number.
D.B. is the most, accounting for the total number of people.
Third, be careful.
1, (1) Calculate (-10) 3+;
(2) Solve the equation:
2. The Shanghai-Hangzhou maglev transportation project, which has attracted much attention at home and abroad, was recently approved by the State Council. After the completion of the Shanghai-Hangzhou maglev line, it is divided into two parts: the central city section and the suburban section, of which the length of the central city section is kilometers, accounting for the whole journey. The Shanghai-Hangzhou maglev train fare is set at RMB/km ~ RMB/km. Please estimate the fare range of Shanghai-Hangzhou maglev train.
3. As shown in the figure, O is a point on the straight line AB, OC is an arbitrary ray, and OD bisects ∠BOC.
OE shares ∠ AOC (1) points out the complementary angles of ∠AOD and ∠BOE in the graph;
5] Explain the quantitative relationship between ∠COD and ∠COE.
4. Yang Hui, a mathematician in the Song Dynasty, put forward the "Yang Hui Triangle" (as shown below) in the book "Detailed Explanation of Nine Chapters", which revealed the correlation between the number of terms and the coefficient of expansion (which is a non-negative integer).
For example:
It has only one term, and the coefficient is1;
It has two terms, the coefficients are 1 and 1 respectively, and the sum of the coefficients is 2;
It has three terms, the coefficients are 1, 2, 1 respectively, and the sum of the coefficients is 4;
It has four terms, the coefficients are 1, 3, 3, 1 respectively, and the sum of the coefficients is 8;
……
According to the above rules, answer the following questions:
(1) expansion * * * has terms, and the coefficients are respectively;
(2) The expansion * * * has a term, and the sum of the coefficients is.
With the improvement of people's living standards, more and more family cars enter the family. Xiao Ming bought a car and put it at home. He continuously recorded the distance he traveled in the sky every day (as shown in the table below). As a standard, the excess part is marked as "",the insufficient part as ""and the correct part as "".
Day one, day two, day three, day four, day five, day six and day seven.
Distance ()
(1) Please use your statistical knowledge to estimate how many kilometers Xiao Ming's family drives in January (within 30 days).
(2) If you need gasoline every time you travel, and the gasoline cost is RMB per liter, what is the annual (monthly) gasoline cost of Xiaoming's family? (Can be calculated by calculator)
6. The fruit wholesale department of a city wants to transport a batch of fruits from a city to the city for sale. There are two modes of transportation: train and car, and 200 yuan/hour is lost during transportation. Other main reference data are as follows:
Average speed in transit
Freight (km/h)
(Yuan/km) Loading and unloading expenses
(yuan)
Train 100 15 2000
Automobile 80 20 900
(1) If the total expenditure of cars is more than that of trains 1 100 yuan, do you know how many kilometers it is from this city to another? Please make an equation to solve it.
(2) If the distance between City A and City A is S kilometers, you know that the delay time of train and bus on the road is 2 hours and 3. 1 hour respectively. If you are the manager of the fruit wholesale department in City A, you want to transport this fruit to other areas for sale. Which mode of transportation would you choose is more economical?
Reference answer:
Third, be careful.
1.( 1)-968; (2)y=- 1 .
2. Yuan ~ Yuan. (Note: The total length is (1 min) km;
The scheduled fare is calculated in RMB/km, and the fare is
The scheduled fare is calculated in RMB/km, and the fare is
That is, the fare range is yuan ~ yuan. )
3. Complementary angles of (1) and ∠AOD ∠BOD, ∠COD
The angles ∠AOE and ∠COE are complementary to ∠BOE.
(2)COD+∠COE =∠AOB = 90。 (Hint: Because OD divides ∠BOC equally, ∠COD= ∠BOC.
And OE shares ∠AOC equally, so ∠COE= ∠AOC,
so∠COD+∠COE =∠BOC+∠AOC =∠BOC+∠AOC)，
So ∠ COD+∠ COE = ∠ AOB = 90. )
4.( 1) ; 1,4,6,4, 1;
(2) , .
5.( 1) 1500m； (2)6825.6 yuan
6.( 1) 400 meters (hint: suppose the distance between this city and a city is x kilometers, and it is 200 according to the meaning of the question? + 15x+2000=200？ +20x+900- 1 100 Solve this equation, x=400. )
(3) When the total cost of the train and the car is the same, there are
.
Solve this equation and get s= 160.
That is, when the distance between this city and a city is greater than 160 km, it is more economical to choose train transportation;
When the distance between this city and a city is equal to 160 km, you can choose two modes of transportation: train and car.
When the distance between this city and a city is less than 160 km, it is more economical to choose car transportation.