First, the requirements for the senior high school entrance examination:

1. Go through the process of abstract generalization of concepts such as functions and linear functions, understand the ideas of functions and variables, and further develop the ability of abstract thinking; Through the exploration of function images and their properties, we can develop cooperation consciousness and ability in cooperation and exchange activities.

2. Experience the process of solving practical problems by using linear functions and their images, and develop mathematical application ability; Experience the process of identifying and applying function image information, and develop image thinking ability.

3. Understand the concept of linear function; Understand the related properties of linear functions and their images; Understand the relationship between equations and functions.

4. Can determine the function expression according to the given information; Can make images of functions at one time and use them to solve simple practical problems.

Research on the Second and Second Examination Papers

(A) the examination of knowledge points in the senior high school entrance examination:

The knowledge points involved in the 2004 and 2005 senior high school entrance examinations in some provinces and cities are as follows:

Proportion of knowledge points tested by serial number

The meaning, image and properties of 1 linear function are 2.5~3%.

The solution of linear function expression is 2.5~7.5%

3 linear function for solving practical problems 2.5~ 10%

(2) Hot spots of senior high school entrance examination:

The knowledge of linear function is the key knowledge in the senior high school entrance examination every year, and it is the main content of each volume. This chapter mainly examines the image, nature and application of linear function, which can examine the comprehensive ability of candidates and their ability to solve practical problems. Therefore, the practical application of linear function is a hot spot in the senior high school entrance examination, and the comprehensive problem composed of geometry and equation is a hot spot in the senior high school entrance examination.

Third, the trend of senior high school entrance examination proposition and review countermeasures

Linear function is one of the important contents in mathematics. The number of questions accounts for about 5% ~ 10% of all questions, and the score accounts for about 5% ~ 10% of the total score. The test questions include low-level fill-in-the-blank questions and multiple-choice questions, medium-level analytical questions, and a large number of comprehensive questions. In recent years, reading comprehension questions with novel design, close to life and reflecting the characteristics of the times have appeared in the senior high school entrance examination papers.

In view of the trend of senior high school entrance examination, we should first understand the concept of function, master its properties and images, and pay attention to the practice of practical application of function.

20 10-8- 12

★★★★ (1) Breakthrough of test sites ★★★★

Test site 1: the meaning of linear function and its images and properties

First, the test site explanation:

1. linear function: if the relationship between two variables x and y can be expressed in the form of Y = KX+B (where k and b are constants and k ≠0), then y is said to be a linear function of x (where x is an independent variable and y is a dependent variable). In particular, when b=0, y is said to be a proportional function of x 。

2. Image of linear function: the image of linear function y=kx+b is a straight line passing through points (0, b) and (-bk, 0), and the image of proportional function y=kx is a straight line passing through the origin (0, 0), as shown in the following table.

3. Properties of linear function: y = kx+b (k and b are constants, k ≠0). When k > 0, the value of y increases with the value of x; When k < 0, y value decreases with the increase of x value.

4. The relationship between the position of the straight line Y = KX+B (where k and b are constants and k ≠0) in the coordinate plane and k 。

(1) The straight line passes through the first, second and third quadrants (the straight line does not pass through the fourth quadrant);

(2) The straight line passes through the first, third and fourth quadrants (the straight line does not pass through the second quadrant);

(3) The straight line passes through the first, second and fourth quadrants (the straight line does not pass through the third quadrant);

(4) The straight line passes through the second, third and fourth quadrants (the straight line does not pass through the first quadrant);

Second, the classic exam analysis:

Examination 1- 1 (Guiyang, 2004, 4 points) shows that the image of the primary function y=kx+b is as shown in figure 1-6- 1. When x < 0, the value range of y is ().

A.y>0 B、y 12

9. Two linear functions y 1 = MX+n.y2 = NX+n, and their images in the same coordinate system may be () in Figure l-6-2.

10 Xiao Li bought several kilos of watermelons from the wholesale market at the price of one kilo of 0.8 yuan and sold them in the market. Some watermelons were sold, and the rest were sold out at a reduced price in 0.4 yuan. The relationship between the sales amount and the kilograms of melons sold is shown in Figure L-6-3, so Xiao Li earned ().

A.32 yuan B. 36 yuan

C.38 yuan D. 44 yuan

1 1 With the support of the Re-employment Center, Sister Yang founded Runyang, a newspaper retail outlet, which provided the following information for an evening newspaper:

(1) Buy every 0.2 yuan and sell every 0.3 yuan;

(2) One month (counted as 30 days), 200 copies can be sold every day for 20 days, and only 120 copies can be sold every day for the remaining 10 days;

(3) Within one month, the number of newspapers bought from newspapers every day must be the same. Newspapers that can't be sold that day will be returned to the newspaper office at the rate of 0. 1 yuan per copy.

① Fill in the following table:

(2) If you buy X copies (120≤x≤200) of this evening paper from the newspaper every day, you will earn Y yuan every month. Try to find the function expression between y and x and find the maximum monthly profit.

Test point 2: the solution of linear function expression

First, the test site explanation:

1, undetermined coefficient method: first set the unknown coefficient in the formula, and then calculate the unknown coefficient according to the conditional column agenda or agenda group, thus writing this formula, which is called undetermined coefficient method, and the unknown coefficient is also called undetermined coefficient.

2. The general steps of finding the function watchcase formula by using the undetermined coefficient method are as follows: (1) Write.

General form of function expression; (2) Substitute the known conditions (corresponding values of independent variables and functions) into the expressions of common functions of order * * * to obtain the agenda or agenda group of undetermined coefficients; ⑶ Solve the equation (group) to get the value of the undetermined coefficient, and then write the expression of the function.

3. Solving the linear function expression: The undetermined coefficient method is often used to determine the linear function expression, in which only one pair of values of X and Y is needed to determine the proportional function expression, and two pairs of values of X and Y are needed to determine the linear function expression.

Second, the classic exam analysis:

Test 2- 1 (Qingdao, 2004) Biological research shows that the length y () of a certain snake is a linear function of its tail length x(cm), and when the tail length of the snake is 6cm, the snake length is 45.5 ㎝; When the tail length of the snake is 14cm, the snake length is105.5 ㎝; When the tail length of a snake is 10cm, the snake length is _ _ _ _ _ _ \

Question 2-2 (In 2004, Kaifu four provinces) The relationship between the number of times a cricket was found barking 1 minute and the local temperature was approximately a linear function. The following is a comparison table of cricket croaking times and temperature changes:

The number of crickets … 84 98 1 19 …

Temperature (? C) … 15 17 20 …

(1) Determine the relationship of linear functions according to the data in the table;

(2) If the cricket calls 63 times in 1 minute, what is the temperature at that time?

What's the temperature?

Solution: (1) Let the cricket call x times in 1 minute, then according to a resolution function, you can get y= 17 x+3.

2 when x=63, y= 17 ×63+3= 12.

Exam 2-3 (Ning 'an, 2004) As shown in the figure, in the plane rectangular coordinate system, the analytical formula of a straight line is that a quadratic equation with one variable has two equal real roots.

(1), and find the analytical formula of the straight line passing through points A(0,) and D (0);

(2) Take B and C points in turn on the line segment AD, so that AB=CD=, and try to judge the shape of △OBC;

⑶ Let the straight line intersect with the straight line AD at point P. Is there a triangle similar to △OAB in the figure? If it exists, please write directly; If it does not exist, please explain why.

Looking back14 (Wuhan, 2005, 8 points), a processing plant spent 3,000 yuan per ton.

Yuan price to buy 50 tons of raw materials for processing. If rough machining is carried out, the processing cost per ton is 600 yuan, which takes 13 days, and the price per ton is 4,000 yuan; If finishing is carried out, the processing cost per ton is 900 yuan, which takes 12 days, and the price per ton is 4,500 yuan. Now all 50 tons of raw materials have been processed.

(1) let x tons be coarsened to get y yuan, and find the functional relationship between y and x or (the range of independent variables is not required).

(2) If it must be completed within 20 days, how to arrange the production to get the maximum profit? What is the maximum profit?

Looking back at 1 5 (Jiangxi, 2005, 8 points), as shown in figure L-6-39, the straight line 1 and 2 intersect at point A, and the intersection coordinates of1and X axis are (-1 0), and the intersection coordinates of 2 and Y axis are (0).

(1) Find the expression of the linear function shown in the second line;

⑵ When x is what value, the function values of the two linear functions represented by 1 and 2 are both greater than 0?

Review 16 (Zigong, 2005, 8 points) Observe the function image L-6-40, and answer the questions according to the information obtained:

(1) The dotted line OAB represents the function image of a practical problem. Please write an application problem that conforms to the meaning of the image;

(2) According to the application questions you gave, point out the meanings of X axis and Y axis respectively, and write the coordinates of A from two points;

⑶ Find the function expression of image AB and point out the range of independent variable X. 。

Looking back 17 (Linyi, 2005, 8: 00) A family needs to decorate the kitchen.

A certain brand of ceramic tile with the same specification 480. The tiles sold in the decoration materials shopping mall are packaged in large and small packages, each package is 50 pieces, and the price is 30 yuan; Small packages are 30 yuan each, and the price is 20 yuan. If you don't open large and small packaging retail, how to make a purchase plan to minimize the cost?

Looking back at the function y= in 18(2005, Henan, 3 points), the value range of the independent variable x is _ _ _ _ _ _ _ _.

Looking back at 19(2005, Henan, 3 points), the function picture between two variables y and x is as shown in figure L-6-4 1, so the value range of y is _ _ _ _ _ _ _ _ _.

★★★★ (3) mid-term examination forecast in 2006 ★★

(1 10 min 90 min) Answer (242)

First, the basic classic questions (50 points)

(a) multiple-choice questions (2 points for each question, ***28 points)

Note 1 In the following functions, X is the independent variable and Y is the dependent variable.

Quantity, b is a constant not equal to 0, and it is a linear function of ()

Note 2 The coordinate where the straight line y=2x+6 intersects the X axis is ().

A.(0，-3)B.(0，3)C.(3，0)d .(92， 1)

Note 3 is a linear function among the following functions, and the image passes through the origin.

Yes ()

Note 4 The straight line Y = 43 x+4 intersects with the X axis at A and the Y axis at B, and O is the origin, so the area of △AOB is ().

12

Note 5 Known functions: ① y =-x, ②y= 3x, ③ y = 3x- 1.

④y=3x2, ⑤y= x3, ⑤ y = 7-3x, where the proportional function is ().

A.①⑤ B.①④ C.①③ D.③⑥

Note 6 If each box contains 12 ballpoint pens, and the price is 6 yuan, the relationship between the ballpoint pen price y (yuan) and the number x (pieces) of ballpoint pens is ().

a . y = 12 b . y = 2x c . y = 6x d . y = 12x

Note 7 The quadrant that the image of linear function y = 3x-2 does not pass through is ().

A. the first quadrant b, the second quadrant c, the third quadrant d and the fourth quadrant

Note 8 The image of a linear function is shown in Figure L-6-42, so the expression of this linear function is ().

A.y=-2x+2

B.y=-2x-2

C.y= 2x+2

D.y=2x-2

Note 9 20 liters of oil is stored in the oil tank, and the oil comes from

When the oil tank flows out evenly and the flow rate is 0.2 L/min, the functional relationship between the remaining oil quantity q (L) in the oil tank and the outflow time t (min) is ().

A.Q=0.2t B.Q=20-2t

C.t=0.2Q D.t=20—0.2Q

Note 10 In the following function, the image passes through the origin and two quadrants or four quadrants.

Yes ()

a . y = 5x b . y =-X5 c . y = 5x+ 1d . y =-X5+ 1

Reference 1 1 sub-function y = kx+b, when -3 ≤ x ≤ 1

The y value of is 1≤y≤9, so k? The value of b is ()

A. 14b。 -6c。 -4 or 21d. -6 or 14.

Reference 12 Happiness Village runs a factory, and the function image of the total amount of a certain product c (pieces) produced in the first five months of this year against time t (months) is shown in Figure L-6-43, so the factory is () for this product.

A. 65438+ monthly total output10-March increased month by month, and decreased month by month from April to May.

B from 199 1 year to1March 1993, the total output increased month by month.

In addition, the total output in April and May was the same as that in March.

C. The total monthly output increased month by month from L to March, and stopped production in April and May.

D.1-The total production will remain unchanged in March, and production will be stopped in April and May.

Note 13 Given that the solution of the equations is 0, the coordinate of the intersection of the linear function y=2x+3 and y= 12 x+32 is ().

A.( 1，5)B.(- 1， 1)c .( 1，2)D.(4， 1)

One day, Xiaojun and his father went to climb the mountain and learned that the distance from the foot of the mountain to the top of the mountain was 300 meters. Xiaojun walked a long way before his father started. The two line segments in Figure L-6-44 show the relationship between the distance S (meters) between Xiaojun and his father from the foot of the mountain and the time t (minutes) taken to climb the mountain (from the time when his father started climbing the mountain). According to the image, the following are

A. when dad climbed the mountain, Xiaojun had already left.

50 meters

B. Dad left for five minutes, but Xiaojun stayed.

In front of dad.

C. Xiaojun arrived at the top of the mountain later than his father.

D. Dad climbed the mountain slower than Xiaojun in the first 10 minute, and faster than Xiaojun after 10 minute.

(2) Fill in the blanks (2 points for each question, *** 12 points)

Note 15 If the function y = (m-2) x+5-m is a linear function,

Then the condition that M meets is _ _ _ _ _ _ _.

Note 16 In the function y = 2x-6, the value of y increases with the value of x _ _

Note 17 If the image of the proportional function passes through (-l, 5), then the expression of this function is _ _ _ _ _ _ _ _ _ _, and the value of y decreases with the decrease of X and _ _ _ _ _ _ _ _.

Note 18 If the original function y = kx-3 crosses the point (3,0), then k=__

The image also passes through points (0,) and (,-2).

For the reference 19, the image of linear function y = 2x+4 is shown in figure 1-6-45. According to the image, when x_____, y > 0; When y>0, x = _ _ _ _ _

Note 20: 8 yuan starting fee is charged for taxis within 4 km (including 4 km) in a city. When the journey is more than 4km, 1.80 yuan will be charged for each trip exceeding 1 km. When the journey exceeds 4km, the functional relationship between the charging fee of Y yuan and the taxi mileage is _ _ _ _ _ _ _.

(3) Problem solving: (10)

Note 2 1 As shown in figure 1-6-46, the image of the proportional function passes through point A in the figure.

(1) Find the expression of this function;

(2) Find the value of x when y= 1.

Second, comprehensive questions within the discipline (7 points for each question, *** 14 points)

Note 22 It is known that the straight line Y = x+2 and the straight line y= 23 x+2 intersect at point C, the intersection of the straight line Y =-x+2 and the X axis is A, and the intersection of the straight line Y = 23 x+2 and the X axis is B. Find the area of △ABC.

Note 23: As shown in figure 1-6-47, find the expression of the graph of the straight line Y = 2x-L which is symmetrical about the X axis.

Iii. Interdisciplinary infiltration (10 score)

Reference 24 Sound travels in the air

Speed x (m/s) (sound speed for short) is

The temperature x(℃) is a linear function. Table below

A group of sound velocities at different temperatures are listed:

(1) Find the functional relationship between y and x;

When the temperature is (22℃), some people see smoke.

It takes 5 seconds for the flowers to be set off before they hear the sound. How far is this man from the place where fireworks are set off?

Iv. Practical application problems (10 score)

There are 20 workers in a workshop, each of whom processes Class A every day.

Type B has five or four parts. Among these 20 workers, X people are sent to process the parts of Type A, and the rest are processed the parts of Type B. It is known that processing a part of Type A can make a profit in 6 yuan, and processing a part of Type B can make a profit in 24 yuan.

(1) Write the functional expression between the daily profit y (yuan) and x (person) of this workshop;

(2) If the daily profit of the workshop is 1260 yuan, how many people need to be sent to process Class A parts?

V. Infiltrating the concept of the new curriculum standard (0/3 points for each question, ***26 points)

For the sake of students' health, the school was closed.

The heights of desks and stools are scientifically designed according to a certain relationship. Xiao Ming observed and studied a batch of desks and stools bought by the school and found that they can be adjusted according to the length of a person. So he measured the height of a set of desks and stools corresponding to the four gears and got the data shown in the following table:

(1) After exploring the data, Xiao Ming found that the height y of the table is a linear function of the height x of the stool. Please write the relationship of this linear function (the range of x is not required).

(2) Xiao Ming measured the desk and stool at home after he came home. The desk is 77 cm high and the stool is 43.5 cm high. Please judge whether the two are compatible and explain the reasons.

Preparation 27 (Reading comprehension questions) Read the following materials: Father and Son.

My son goes out for morning exercise at the same time. As shown in figure 1-6-48 (A), the solid line represents the function image of the distance (meters) and time (minutes) from home of the father; The dotted line represents the function image of the distance (meters) and time (minutes) for the son to leave home. According to the image, they first met at 10 minutes, when they were 400 meters away from home. After 30 minutes of morning exercise, they got home at the same time. "