In the morning, Xin arrived at the gate of Zone D of Shanghai World Expo Park, waiting for the opening of the park. The park opens at nine o'clock sharp. There is a 10n security inspection channel at the entrance of Zone D for tourists to enter the park through security inspection. Every minute, tourists keep arriving here according to the same number of people. Until noon 12, there is no queue at the gate of Zone D. Visitors can enter the park through security check as soon as they arrive. At 9: 20, when Xin entered the Shanghai World Expo Park through security inspection, he found that it took an average of 20 seconds for a person to enter the park through the security inspection channel.

Consider queuing

(1) If the letter is ranked at the 3000th position at 9: 00, how many security channels may there be at the entrance of Zone D?

(2) If the park opens at 9: 00: 00, the number of people waiting to enter the park in Zone D remains the same: the security check passage is twice as long as the existing 1.2 times, and the number of tourists arriving at the entrance of Zone D remains the same every minute, tourists can enter the park through security check as long as they arrive at the entrance of Zone D at noon1:00; When the number of tourists who arrive at the entrance of Zone D every minute increases by 50%, tourists are still required to enter the park at the entrance of Zone D from 12: 00, so the number of security inspection channels needs to be increased. (10)

Typical examples of senior high school entrance examination

1. (Xicheng District, Beijing) The symmetry axis of parabola y=x2-2x+ 1 is ().

(a) row x= 1 (B) row x=- 1 (C) row x=2 (D) row x=-2.

Test Center: Symmetry axis of quadratic function Y = AX2+BX+C. 。

Comments: Because the symmetry axis equation of parabola y=ax2+bx+c is: y=-, substituting a= 1 and b=-2 into the known parabola to get x= 1, so option A is correct.

Another method: the parabola formula can be in the form of y=a(x-h)2+k, the symmetry axis is x=h, and the known parabola formula is y=(x- 1)2, so the symmetry axis is x= 1, so A should be chosen.

2. (Dongcheng District, Beijing) has an image of a quadratic function, and three students described some characteristics of it:

A: The symmetry axis is a straight line x = 4；;

B: the abscissa of the two intersections with the X axis is an integer;

C: The ordinate intersecting with the Y axis is also an integer, and the area of the triangle with these three intersections as its vertices is 3.

Please write a quadratic resolution function that satisfies all the above characteristics.

Test center: the solution of quadratic function y=ax2+bx+c

Note: Let the analytical formula be y=a(x-x 1)(x-x2) and x 1 < x2. The two intersections between the image and the X axis are a (x 1, 0) and b (x2, 0) respectively, and the coordinates of the intersections with the Y axis are (0).

The symmetry axis of parabola is the straight line x=4,

∴x2-4=4-x 1, that is, x 1+ x2=8 ①.

∵S△ABC=3,∴(x2- x 1)？ |a x 1 x2|= 3，

Namely: x2- x 1= ②

① ② Two formulas are added and subtracted: x2=4+, x 1=4-

∵x 1, x2 is an integer, ax 1x2 is also an integer, ∴ax 1x2 is a divisor of 3, * * can be taken as: 1, 3.

When ax 1x2 = 1, x2=7, x 1= 1, and a =

When ax 1x2 = 3, x2=5, x 1=3 and a = 3.

So the analytical formula is: y = (x-7) (x- 1) or y = (x-5) (x-3).

That is, y=x2-x+ 1 or y=-x2+x- 1 or y=x2-x+3 or y=-x2+x-3.

Note: in this question, just fill in an analytical formula or guess and verify. For example, guess that the intersection with the X axis is A (5 5,0) and B (3 3,0). Then find out a from the conditions of the problem and see if c is an integer. If there is, the guess can be verified, just fill it in.

5. (Hebei Province) As shown in figure 13-28, if the image of quadratic function y=x2-4x+3 intersects with the X axis at points A and B, and intersects with the Y axis at point C, the area of △ABC is ().

a、6 B、4 C、3 D、 1

Test site: the image of quadratic function y=ax2+bx+c and the application of its properties.

Comments: From the function image, we can know that the coordinate of point C is (0,3), and then from x2-4x+3=0, we can get x1= kloc-0/,x2=3, so the distance between point A and point B is 2. Then the area of △ABC is 3, so C should be chosen.

Figure 13-28

6. Psychologists in Anhui Province have found that there is a functional relationship between students' ability to accept concepts y and the time to put forward concepts x (unit: minutes): Y =-0. 1x2+2.6x+43 (0 < x < 30). The greater the value of y, the stronger the acceptability.

In what range of (1)x, students' acceptance ability is gradually enhanced? In what range of X, students' acceptance is gradually decreasing?

(2) What is the acceptability of students when the score is 10?

(3) What scores do students accept the most?

Test site: properties of quadratic function y = AX2+BX+C

Comment: parabola y=-0. 1x2+2.6x+43 changed to vertex: y =-0.1(x-13) 2+59.9. According to the properties of parabola, it can be known that the opening is downward. When x≤ 13, y increases with the increase of x, and when 13, y decreases with the increase of x. The range of independent variables of this function is: 0≤x≤30, so the two ranges should be 0 ≤ x ≤13; 13≤x≤30. Substitute x= 10 to find the function value. From the vertex analytic formula, the acceptance ability is the strongest at 13 minutes. The problem solving process is as follows:

Solution: (1) y =-0.1x 2+2.6x+43 =-0.1(x-13) 2+59.9.

Therefore, when 0≤x≤ 13, students' acceptance ability is gradually enhanced.

When 13 < x ≤ 30, students' acceptance ability gradually decreases.

(2) When x= 10, y =-0.1(10-13) 2+59.9 = 59.

When the score is 10, the students' acceptance ability is 59.

(3) When x = 13, y takes the maximum value.

Therefore, in the score of 13, students' acceptance ability is the strongest.

9. A store in Hebei Province sells an aquatic product at a cost of 40 yuan per kilogram. According to market analysis, if it is sold in 50 yuan per kilogram, it can sell 500 kilograms a month; For every increase in the unit sales price of 1 yuan, the monthly sales volume will decrease by 10 kg. Please answer the following questions about the sale of this aquatic product:

(1) When the sales unit price is set to 55 yuan per kilogram, calculate the monthly sales volume and monthly sales profit;

(2) Let the sales unit price be X yuan per kilogram and the monthly sales profit be Y yuan, and find the functional relationship between Y and X (it is not necessary to write the value range of X);

(3) The store wants to make a monthly sales profit of 8,000 yuan when the monthly sales cost does not exceed 1 10,000 yuan. What should the sales unit price be?

Solution: (1) When the sales unit price is set to 55 yuan per kilogram, the monthly sales volume is: 500-(55–50) ×10 = 450 (kg), then the monthly sales profit is

: (55–40) × 450 = 6750 (yuan).

(2) When the sales unit price is X yuan per kilogram, the monthly sales volume is [500-(x–50) ×10] kilograms, and the sales profit per kilogram is (x–40) yuan, then the monthly sales profit is:

y =(x–40)[500-(x–50)× 10]=(x–40)( 1000– 10x)=– 10x 2+ 1400 x-

The resolution function of y and x is: y =–10x2+1400x–40000.

(3) Make the monthly sales profit reach 8000 yuan, that is, y=8000, ∴–10x2+1400x–40000 = 8000,

Namely: x2–140x+4800 = 0,

Solution: x 1=60, X2 = 80.

When the sales unit price is set at one kilogram of 60 yuan, the monthly sales volume is: 500-(60-50)× 10 = 400 (kg), and the monthly sales cost is:

40×400= 16000 (yuan);

When the sales unit price is set at one kilogram of 80 yuan, the monthly sales volume is: 500-(80-50)× 10 = 200 (kg), and the monthly sales unit price cost is:

40×200=8000 (yuan);

Since 8000 < 10000 < 16000, and the monthly sales cost cannot exceed 10000 yuan, the sales unit price should be set at 80 yuan per kilogram.

2(08  Baiyin and other 9 cities) 28. (12 minutes) As shown in Figure 20, in the plane rectangular coordinate system, the quadrilateral OABC is rectangular, and the coordinate of point B is (4,3). A straight line m parallel to the diagonal AC starts from the origin O and moves at the speed of 1 unit length per second in the positive direction of the X axis. It is assumed that both sides of the straight line m intersect with the right-angled OABC respectively.

(1) The coordinates of point A are _ _ _ _ _ _ _, and the coordinates of point C are _ _ _ _ _ _ _ _ _;

(2) When t= seconds or seconds, MN = AC；;

(3) Let the area of △OMN be S, and find the functional relationship between S and T;

(4) Does the function S obtained in (3) have a maximum value? If yes, find the maximum value; If not, explain why.

Application of quadratic equation in one variable

Growth rate: (Huanggang City, 2009) In order to solve the problem of people's difficulty in seeing a doctor, the municipal government decided to reduce the price of drugs. After two consecutive price reductions, the price of a drug dropped from 200 yuan per box to 128 yuan. What is the average price reduction percentage of this medicine?

Commodity pricing: 40 yuan, a shopping mall, sells 30 yuan's desk lamps, with an average of 600 lamps per month. According to the survey, every time the price of this table lamp increases by 1 yuan, the sales volume will decrease by 10. In order to achieve the average monthly sales profit 10000 yuan, what should the price of this desk lamp be? How many lights should be put on at this time?

Travel problem: A and B start from A and B, which are 20 kilometers apart, and walk in opposite directions at the same speed. After they met, they moved on, and B's speed remained the same. A walking more than before 1 km per hour. In this way, after A arrives at B, B needs 30 minutes to arrive at A, and how many kilometers does B walk per hour?

Synthesis: (Chongqing, 2009) Machining needs oil lubrication to reduce friction. An enterprise processes a large-scale mechanical equipment, which consumes 90kg of oil and the oil reuse rate is 60%. According to this calculation, the actual fuel consumption for processing a large mechanical equipment is 36kg. In order to build a conservation-oriented society and reduce fuel consumption, both workshop A and workshop B of the enterprise organize personnel to tackle key problems and reduce actual fuel consumption.

(1) After the technical transformation of workshop A, the oil consumption for processing a large mechanical equipment was reduced to 70kg, and the oil reuse rate was still 60%. What is the actual fuel consumption of processing a large mechanical equipment after technical transformation in workshop A?

(2) After technical transformation, workshop B not only reduced the consumption of lubricating oil, but also improved the reuse rate of oil. It is found that on the basis of technological innovation, the reuse rate of oil will increase by 65,438 0.6% for every reduction of lubricating oil consumption by 65438±0kg. In this way, the actual fuel consumption of workshop B for processing a large mechanical equipment decreased to 12kg. After technical innovation, workshop b asked. What is the reuse rate of oil?

3. (Chongqing, 2009) Due to the lack of electricity, a certain place decided to use electricity at the wrong peak for the factory. It is stipulated that 7:00-24:00 every day is the peak period of electricity consumption, and the electricity price is A yuan /kW? h； 0: 00 to 7: 00 every day is the stable period of electricity consumption, and the electricity price is B yuan /kW? h； The following table shows the statistics of electricity consumption and electricity charges of a factory in April and May:

Monthly electricity consumption (ten thousand kilowatts? H) electricity fee (ten thousand yuan)

4 12 6.4

5 16 8.8

(1) If the electricity consumption in the stationary period in April accounts for the current month's electricity consumption, and the electricity consumption in the stationary period in May accounts for the current month's electricity consumption, find the values of A and B. 。

(2) What if the power consumption of the plant is expected to be 200,000 kilowatts in June? H, in order to explore the electricity bill between 654.38+ten thousand yuan and/kloc-0.06 million yuan (excluding 654.38+ten thousand yuan and/kloc-0.06 million yuan), what should be the range of electricity consumption in June?

2. (Neijiang City, 2009) A school wants to print a batch of complete materials. A printing company proposed a plate-making fee of 900 yuan, and each material was charged a printing fee of 0.5 yuan; Printing company B offered not to charge plate-making fees, but to charge 0.8 yuan for printing each material.

(1) Write the functional relationship between the charge y (yuan) of two printing companies and the number of printed matter x (copies) respectively.

(2) If the school is expected to print less than 5,000 promotional materials, which printing company should the school choose?

3. After a shopping mall bought two kinds of clothes, A and B, the price increased by 40%. During the Spring Festival, the shopping mall had a preferential promotion and decided to sell them at a 20% discount and a 10% discount respectively. A customer pays 182 yuan for two kinds of clothes, and the sum of the two kinds of clothes is 2 10 yuan.

4. (Yangzhou City, 2009) Baoying County, Yangzhou City, "the hometown of lotus roots in China", is rich in lotus root resources. A lotus root processing enterprise purchased 60 tons of lotus roots. According to market information, if the lotus root is roughly processed, it can be processed 8 tons per day, and the profit per ton is 1 10,000 yuan; If finishing is carried out, 0.5 tons can be processed every day, and the profit per ton is 5000 yuan. Due to the limitation of equipment conditions, the two treatment methods cannot be carried out at the same time.

(1) If the tonnage of finish machining is x tons, then the tonnage of rough machining is _ _ _ _ _ _ _ _ _ _. It takes _ _ _ days to process this batch of lotus roots, and it can make a profit of _ _ _ _ _ yuan (expressed by an algebraic expression with X).

(2) In order to keep fresh, enterprises must finish processing all lotus roots within one month (30 days). When the tonnage x of fine processing is within what range, the profit of processing lotus root is not less than 80 thousand yuan.

5. (Guizhou Province, 2009) In order to welcome the "Huangguoshu Waterfall Festival in Guizhou, China in 2009", the garden department decided to use the existing 3600 pots of first-class flowers and 2900 pots of second-class flowers, and put them on both sides of Yingbin Avenue with 50 gardening shapes of A and B. The following table shows the flowers needed to match each shape:

Modeling Jiayi

A piece of 90 pots and 30 pots.

B 40 pots 100 pots

(1) What are the matching schemes that match the meaning of the question?

(2) If the matching cost of model A is 1 1,000 yuan, and the matching cost of model B is 1, 200 yuan, which scheme has the lowest cost?

These are some of the topics I have done, which are not bad. You can go to the library below. There are many good topics.

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Please adopt! thank you