18. It is known that the side BC of rectangular ABCD is on the X axis, e is the midpoint of diagonal BD, and the coordinates of point B and point D are respectively

Images of b (1, 0), d (3 3,3) and inverse proportional function y = pass through point a,

(1) Write the coordinates of point A and point E;

(2) Find the analytical formula of inverse proportional function;

(3) Judge whether the point E is on the image of the function.

19. It is known that CD is the height on the hypotenuse of,,, (as shown in the figure). Verification:

Reference answer

1.D 2。 B 3。 A 4。 D 5。 C 6。 B 7。 C 8。 C 9。 C 10。 B

1 1.3

12.- 1 or y=-x- 1 or y=

13. 1

14. 19. 1 cm, 164.3 cm.

15. 1

16.2x- 1，3

17. Solution: (1) The number of people in the polluted area is 1 1. If the number of donations from polluted places is yuan, then

1 1 + 1460=50×38

Solution =40

Answer: (1) number of people in polluted areas 1 1, and the number of donations in polluted areas is 40 yuan.

(2) The median donation amount is 40 yuan, and most donations amount is 50 yuan.

18. solution: (1) A (1, 3), E (2 2,32)

(2) Let the functional relationship be y = kx.

Substitute x = 1 and y = 3 to get: k = 3× 1 = 3.

∴ y = 3x is an analytical formula.

(3) When x = 2, y = 32.

Point e (2, 32) is on the image of this function.

19. Proof: Left

In a right triangle,

in other words

frontage

Facts have proved that:

People's education printing plate eighth grade second volume mathematics final examination questions three

First, multiple choice questions

1, the results of the fifth national census show that the total population of our country has reached1.300 million. Using scientific notation to represent this figure, the correct result is ().

a . 1.3× 108 b . 1.3× 109 c . 0. 13× 10 10d . 13× 109

2. Without changing the value of the score, average the coefficients in the score into integers, and the result is ().

A, B, C, D,

3. If the current flowing through a resistor is 1 when the voltage across the resistor is 5, the approximate picture of the current flowing through the resistor changing with the voltage across the resistor is (hint:) ().

4. If both X and Y in the score are enlarged by 2 times, the value of the score ()

A, expand by 4 times; B, expand by 2 times; C, unchanged; D has been reduced by 2 times.

5. As shown in the figure, there is a right-angled triangular paper with two right-angled sides. Now fold the right-angled edge along a straight line so that it falls on the hypotenuse and coincides with it. It is equal to ()

、 、 、 、

6. Vertices A, B, C and D in the rectangular ABCD are arranged clockwise. If the coordinates corresponding to point B and point D are (2,0) and (0,0) respectively in the plane rectangular coordinate system, and point A and point C are symmetrical about X, the coordinates corresponding to point C are

(A)( 1， 1(B)( 1，- 1)(C)( 1，-2)(D)(2，-2)

7, the following graphics, is a central symmetry graphics, but not axisymmetric graphics is ().

(a) Square (b) Rectangular (c) Diamond (d) Parallelogram

8. As shown in the figure, e, f, g and h are the midpoints of the four sides of the quadrilateral ABCD respectively. To make the quadrilateral EFGH rectangular, the quadrilateral ABCD should meet the following conditions ().

(a) One set of edges is parallel and the other set is not parallel; (b) The diagonal lines are equal.

(c) Diagonal lines are perpendicular to each other; (d) Diagonal lines are equally divided.

9, the following proposition is wrong ()

A. The diagonals of parallelogram are equal. B. The diagonals of isosceles trapezoid are equal.

Two parallelograms with equal diagonals are rectangles.

D. The quadrilateral with diagonal lines perpendicular to each other is a diamond.

10, if the image of the function y = 2x+k intersects with the positive semi-axis of the y axis, the quadrant where the image of the function y = is located is ().

A, first and second quadrants b, third and fourth quadrants c, second and fourth quadrants d, first and third quadrants.

1 1. If expressed as an integer, the value of the integer a can be ().

1。

12. As shown in the figure, the side length of square cardboard ABCD is 4, and points E and F are the midpoint of AB and BC respectively. If you cut along the dotted line on the left to form a "small villa" on the right, the area of the shaded part in the figure is ().

a、2 B、4 C、8 D、 10

Second, fill in the blanks

13. It is known that the abscissa of the intersection between the image of the direct proportional function and the image of the inverse proportional function is, so the coordinates of their intersection are respectively.

14. The parts produced by machine tools A and B are sampled and measured, and the results of calculating the mean and variance are as follows:

Machine tool A: = 10, = 0.02; Machine tool B: = 10, =0.06, from which it can be seen that: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

15. There is a 9-meter-high tree with a 1 meter-high child under it. If the tree breaks (does not break) at a distance of 4 meters from the ground, it is safe for children to leave the tree at least meters away.

16, write an inverse proportional function, so that the function value in its quadrant increases with the increase of independent variables. The resolution function can be. (Just write one)

17, as shown in the figure, is a trademark pattern designed by Sunshine Company for a certain commodity. The shaded part in the figure is red. If the area of each small rectangle is 1, then the area of the red part is 5.

18, as shown in figure □ABCD, AE and CF are bisectors of ∠BAD and ∠BCD respectively. According to the existing drawing, please add a condition to make the quadrangle AECF diamond. You can add a condition (only write one, and no other "points" and "lines" can be added in the drawing).

19. As we all know, in the isosceles trapezoid ABCD, if ad∨BC, diagonal AC⊥BD,AD=3cm,BC=7cm, then the height of the trapezoid is _ _ _ _ _ cm.

20. As shown in the figure, the diagonal length of diamond-shaped ABCD is 2 and 5 respectively, P is any point on diagonal AC (point P is not coincident with point A and point C), PE∨BC intersects with AB in E, and PF∨CD intersects with AD in F, so the area of shaded part is _ _ _ _ _ _.

III. Answering and Proving Questions

2 1, (1) calculation:

(2) Simplify:

22. The known function y=y 1+y2, where y 1 is directly proportional to X, and y2 is inversely proportional to x-2. When x= 1, y =-1; When x=3 and y=5, the analytical expression of the function is obtained.

23. Simplify first, and then let you take a set of values and substitute them for evaluation.

24, solving equations

25. As shown in the figure, in a square ABCD, e is a point on the edge of the CD, f is a point on the extension line of BC, CE=CF, ∠ FDC = 30, and the number of times to find ∠BEF.

26. As shown in the figure, the typhoon center measured by the Meteorological Observatory of City A is located in B, 320km west of City A, and moving towards the BF direction of 60 northeast at a speed of 40km per hour. The area affected by the typhoon is within 200 kilometers of the typhoon center.

(1) Is City A affected by this typhoon? Why?

(2) If City A is affected by this typhoon, how long will City A be affected by this typhoon?

27. as shown in the figure, the image of the linear function y=kx+b and the image of the inverse proportional function y= ax intersect at point a and point b, intersect with the x axis at point c, and intersect with the y axis at point d. It is known that OA=5, the coordinate of point b is (12, m), the intersection point a is AH⊥x axis, and the vertical foot is H.

(1) Find the analytical expressions of inverse proportional function and linear function;

(2) Find the area of △AOB.

28. As shown in the figure, in quadrilateral ABCD, AC=6, BD=8, and AC⊥BD sequentially connects the midpoints of each side of quadrilateral ABCD to obtain quadrilateral A1b1c1d1; Then connect the midpoints of the sides of the quadrilateral A1B1C1D1in turn to get the quadrilateral A2B2C2D2…… .....................................................................................................

(1) It is proved that quadrilateral A1b1c1d1is a rectangle;

(2) Write the area of quadrilateral A1b1c1d1and quadrilateral A2B2C2D2;

(3) Write the area of quadrilateral AnBnCnDn;

(4) Find the perimeter of the quadrilateral A5B5C5D5.

Reference answer

First, multiple choice questions

1、B2、B 3、D 4、B 5、B 6、B 7、D8、C9、D 10、D 1 1、D 12、B 13 、(- 1，2) 14。 A15,416, Y =- 1x (the answer is not unique)17,518, AE=AF (the answer is not unique)19,65444.

2 1, solution: (1) Original formula = 4-8× 0.125+1+1= 4-1+2 = 5 (2)-m.

22. Solution: Setup

; When,; When,,

23. Solution: Original formula

Evaluation: take a set of values and substitute them for evaluation.

24. Solution:

Multiply on both sides of the equation at the same time.

Solution: Test: When,

Is the solution of the original fractional equation.

25. 105 proved that ∠ EBC = ∠ FDC = 30 of △ BCE △ DCF, and ∠ BEC = 60 can be obtained.

26. Solution: (1) will be affected by typhoon, because the distance from P to BF is 160 km.

(2) The impact time is 6 hours.

27. Solution:

The point is on the image of the inverse proportional function.

for

Will,

∴ Once the resolution function was

28( 1) proves that ∵ points A 1 and D 1 are the midpoint of AB and AD respectively, and ∴A 1D 1 is the midline of △ABD.

∴A 1D 1∥BD, similarly: b 1c 1∑BD.

∴∥, =, ∴ quadrilateral is a parallelogram

∵AC⊥BD，AC∨a 1b 1，BD∨，∴ A 1B 1D。

A quadrilateral is a rectangle.

(2) The area of the quadrilateral is12; The area of quadrilateral is 6;

(3) The area of the quadrilateral is:

(4) Method 1: The length of the rectangle is 4 and the width is 3 from (1);

∵ rectangle ∽ rectangle; If a rectangle is 4 times longer and 3 times wider, then

Solve; ∴ ;

The perimeter of the rectangle =.

Method 2: Rectangular area/rectangular area

= (rectangular perimeter) 2/ (rectangular perimeter) 2

Namely: 12 = (perimeter of rectangle) 2: 142.

∴ The perimeter of the rectangle =

Eight grades, the second volume of mathematics final examination questions four.

1. Fill in the blanks carefully and make a final decision (only one of the four options given in each question is correct, please choose the correct option and fill it on the answer sheet).

1. As we all know, beehives built by bees are strong and save materials. Do you know the thickness of the hive? In fact, the thickness of the hive is only about 0.000073m, and this data is expressed as () by scientific counting method.

A, B, C, D,

2. If the two diagonals of a quadrilateral are equal, it is called a diagonal quadrilateral. The figure below is not a diagonal quadrilateral ()

A, parallelogram b, rectangle c, square d, isosceles trapezoid

3. The statistics of the maximum temperature in a certain place 10 day are as follows:

Maximum temperature (℃) 22 23 24 25

Days 1 234

The median and mode of this set of data is ()

a、24、25 B、24.5、25 C、25、24 D、23.5、24

4, the following operations, the correct is ()

A, B, C, D,

5. In the following groups, triangles with side lengths of A, B and C are not Rt△ but ().

a、a=2、b=3、c = 4 B、a=5、b= 12、c= 13

c、a=6、b=8、c = 10D、a=3、b=4、c=5

6. The range of a set of data 0,-1, 5, x, 3 and -2 is 8, so the value of x is ().

A, 6 B, 7 C, 6 or -3 d, 7 or -3

7, known point (3,-1) is a point on the hyperbola, then the following points are not on the hyperbola is ().

a、B、C 、(- 1，3) D 、( 3， 1)

8, the following statement is correct ()

The mode, median and average of a set of data cannot be the same number.

B, the average value of a set of data cannot be equal to any number in this set of data.

The median of a set of data may not be equal to any data in this set of data.

D, mode, median and average describe the fluctuation of a set of data from different angles.

9. As shown in Figure (1), it is known that the length of the diagonal of a rectangle is, and the midpoints of all sides are connected to form a quadrilateral, so the perimeter of the quadrilateral is ().

A, B, C, D,

10, the equation about x has no solution, and the value of m is ().

a 、-3 B 、-2 C 、- 1 D、3

1 1. In a square ABCD, diagonal AC=BD= 12cm, and point P is any point on the side of AB, then the sum of the distances from point P to AC and BD is ().

A, 6cm b, 7cm c, 4cm d, 5cm

12 As shown in Figure (2), the area of rectangular ABCD is 10, and its two diagonal lines intersect at a point, AB and its adjacent side are parallelograms, and AB and its adjacent side are parallelograms, ..., and so on, the area of parallelogram is ().

a、 1 B、2 C、D、

Fill it out carefully, I believe you can fill it out quickly and accurately.

13, if the image of the inverse proportional function decreases with the increase of x in each quadrant, then the value of k can be _ _ _ _ _ (just write a qualified k value).

14. Two classes of Grade One and Grade Two in a middle school took the same math exam. The average score and variance of the two classes are points and points respectively, and the score is _ _ _ _ _ (fill in "Class A" or "Class B").

15. As shown in Figure (3), in □ABCD, e and f are points on the sides of AD and BC respectively. If you add a condition _ _ _ _ _ _ _ _ _ _ _, the quadrilateral EBFD is a parallelogram.

16, as shown in figure (4) is a broken line statistical chart of a group of data. The average of this set of data is, and the range is.

17, as shown in figure (5), there is a right-angled trapezoidal part ABCD, AD∨BC, oblique waist DC= 10cm, D∞= 120, then the length of the other waist AB of this part is _ _ _ _ _ cm.

18, as shown in Figure (6), the quadrilateral is a diamond with a perimeter, and the coordinates of the points are, so the coordinates of the points are.

19. As shown in Figure (7), use two pieces of isosceles right-angled triangular paper with the same size to make a puzzle, and get the following figures: ① parallelogram (excluding rectangle, diamond and square); ② Rectangular (excluding square); ③ Square; ④ equilateral triangle; (5) isosceles right triangle, which must be able to spell the graphics are _ _ _ _ _ _ _ (only fill in the serial number).

20. Any positive integer n can be decomposed into: (s, t is a positive integer, s≤t). If in all these decompositions of n, the absolute value of the difference between the two factors is the smallest, we call it the optimal decomposition and stipulate that. For example, 18 can be decomposed into 1× 18, 2×9 and 3×6, and there it is. Combined with the above information, the following statements are given: ①; ② ; ③ ; (4) If n is a complete square number, then the correct statement is _ _ _ _ _ _ _. (Fill in serial number only)

Third, use your head, and you will be sure to get it right (the answer should be written in words, proof process or derivation steps)

2 1, solving the equation

22. Simplify first and then evaluate, where x=2.

23. Fifty students from Class 8 (1) of a school took part in the 2007 Jining Mathematics Quality Monitoring Examination. The results of the whole class are as follows:

Grade (score) 7174 78 80 82 83 85 86 88 90 9192 94

Number 12354553784332

Please answer the following questions according to the information provided in the table:

(1) What is the mode and median of the students in this class?

(2) Zhang Hua scored 83 points in this class. Can you say that Zhang Hua's grades are above average in the class? Try to explain why.

24. As shown in Figure (8), five small squares with the same size are arranged in the shape of the figure. Now, move one of the small squares, please click.

Graphs meeting the following requirements are drawn in Figure (8- 1), Figure (8-2) and Figure (8-3) respectively. (shadow)

(1) makes the obtained graph become an axisymmetric graph instead of a centrally symmetric graph;

(2) making the obtained figure change from an axisymmetric figure to a centrally symmetric figure;

(3) The obtained graph is both axisymmetrical and centrosymmetric.

25. A youth research institution randomly investigated the amount of winter vacation pocket money (the amount is integer yuan) of 0/00 students in a school, in order to study, analyze and guide students to establish a correct consumption concept. Now, according to the survey data, make a frequency distribution table as shown in the following figure.

(1) Please complete the frequency distribution table and frequency distribution histogram;

(2) The research thinks that students who spend more than 150 yuan should be advised to be frugal and reasonable. How many students in this school 1200 should be advised to spend this advice?

(3) What information can you get from the chart below? (Write at least one)

Median frequency in grouping (meta) groups

0.5~50.5 25.5 0. 1

50.5~ 100.5 75.5 20 0.2

100.5~ 150.5

150.5~200.5 175.5 30 0.3

200.5~250.5 225.5 10 0. 1

250.5~300.5 275.5 5 0.05

Total 100

26. As shown in the figure, the image of the linear function and the image of the inverse proportional function intersect at points M and N..

(1) According to the conditions in the figure, the analytical expressions of inverse proportional function and linear function are obtained;

(2) When x is what value, the value of the linear function is greater than that of the inverse proportional function?

27. As shown in the figure, fold the AD on one side of the rectangular ABCD so that the D point falls on the F point on the BC side. It is known that AB=8cm and BC= 10cm. Find the length of CE?

28. As shown in the figure, in the trapezoidal ABCD, AD∨BC, ∠ B = 90, AD=24 cm, BC=26 cm, the moving point P starts from point A and moves to point D along the AD direction at the speed of 1cm/s, and the moving point Q starts from point C at the speed of 3 cm/s.

How long did it take (1) quadrilateral PQCD to make a parallelogram?

(2) How long did it take for the quadrilateral PQBA to become a rectangle?

(3) How long did it take for the quadrilateral PQCD to be an isosceles trapezoid?

Reference answer

First, multiple-choice questions (3 points × 12=36 points)

The title is123455678911112.

The answer is BAADA, bad, CAD, taxi, bad.

Second, fill in the blanks (3 points ×8=24 points)

13, k > any value 4 (the answer is not unique); 14, _ _ class _ _ _ A 15, the answer is not unique; 16、 46.5 , 3 1 ;

17、cm； 18、 (0,3) ; 19、__①③⑤__; 20、 __①③④__.

Three, use your head, you can do it right (***60 points)

2 1, (6 points) solution: multiply both sides of the equation:

Solution:

Test: Substitution =0

So-2 is the root of the original equation, and the original equation has no solution.

22.(6 points) Solution: Original formula =

Substitute x=2 into the original formula =8.

23.(8 points) (1) mode 88, median 86;

(2) No, the reason is very short.

24.(6 points)

25.(9 points)

(1) omitted

(2) (name)

(3) Omission

26.(8 points) Solution: (1) The inverse analytic function is:

The analytical formula of linear function is:

(2) When the value of OR linear function is greater than the value of inverse proportional function.

27.(8 points) CE=3

28.(9 points) (1)(3 points) Suppose that the quadrilateral PQCD is a parallelogram, that is, PD = CQ.

So we have to

(2)(3 points) Suppose that the quadrilateral PQBA is a rectangle, that is, AP = BQ, so.

(3)(3 points) Suppose that the quadrilateral PQCD is an isosceles trapezoid.

Mathematics final exam of the second semester of the second day of junior high school

(Duration: 90 minutes; Full score: 120)

1. Multiple choice questions: (3 points× 6 =18 points)

1. As shown in the figure, the mass of each weight in the right plate of the balance is 1g, so the value range of the mass m(g) of object A can be expressed as () on the number axis.

2. The following figure is a schematic diagram of pinhole imaging principle. According to the size marked in the picture, the length of the image CD formed by this candle in the cassette is ().

A.b.1/3cm C.1/2cm d. 1 cm

3. The correct proposition in the following propositions is ()

A. If x, -2x+3

B. Two straight lines are cut by the third straight line, and the same angle is equal.

D congruent graphics must be similar graphics, but similar graphics are not necessarily congruent graphics.

5. The chart below shows the frequency distribution histogram of heartbeat times per minute in a class of Senior Two (all times are integers). It is understood that only five students in this class have their hearts beating 75 times per minute. Please observe the figure below and point out that the following statement is wrong ().

A. data 75 belongs to group 2.

The frequency of group B 4 is 0. 1.

D. data 75 must be an intermediate value.

6. Both Party A and Party B start from place A and arrive at place B by bike. It is known that the distance between the two places is 30 kilometers. Party A walks 3 kilometers more than Party B every hour and arrives 40 minutes earlier than Party B. Let B walk x kilometers every hour, and the equation can be listed as ().

2. Fill in the blanks: (3 points× 6 =18 points)

7. Decomposition factor: x3-16x = _ _ _ _ _ _ _ _ _ _.

8. As shown in the figure, if AB//CD is known, ∠B=68o, ∠CFD=7 1o, ∠ FDC = _ _ _ _ _ _ _ degrees.

9. The same number of students in Class A and Class B took the same math test. The class average and variance are as follows:

10. Point P is a point different from A and B on the hypotenuse AB of Rt△ABC. Do a straight PE cut △ABC through point P, and the triangle thus cut is similar to △ABC. Please draw a straight line that meets the following conditions, and briefly explain the vertical or parallel positional relationship between the straight line PE and the edge of △ABC under the corresponding graph.

Location relationship: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

12. in △ABC, AB= 10.

Three. Drawing questions: (5 points)

13. Draw with compasses and straightedge, but don't write the method, and keep the trace of drawing.

When Xiao Ming makes the corner of the class for the whole class, he should enlarge the figure on the original picture so that the ratio of the new figure to the corresponding line segment of the original picture is 2: 1. Ask the students to help Xiao Ming finish the work.

4. Answer: (***79 points)

14.(7 points) Please simplify it first, and then choose a number that makes the original formula meaningful and you like to substitute in the evaluation:

15.(8 points) Solve the following inequality groups, express the solution set on the number axis, and write its integer solution.

16.(8 points) The cost of producing one kilogram of fructose in Xishui Food Factory is 24 yuan, and its sales plan is as follows:

Scheme 1: If it is directly sent to the sales department of our factory in this city for sale, the price per kilogram is 32 yuan, but the sales department needs to pay related expenses of 2400 yuan per month;

Option 2: If sold directly to local supermarkets, the ex-factory price is 28 yuan per kilogram.

If only one scheme can be sold every month, and each scheme can sell the products of that month every month, then suppose that the monthly sales volume of this factory is X kilograms.

(1) If you are the factory director, how should you choose the sales plan to make the factory get more profits in that month?

(2) When the factory director listened to the summaries of various departments, the sales minister said that the best scheme was adopted for sales every month, so good work performance was achieved. However, after seeing the report on the relationship between sales volume and profit in the first quarter sent by the accountant (as shown in the following table), the factory director found that the sales volume written in the report did not match the actual profit. Please find out the difference and calculate the actual sales in the first quarter.

17.(8 points) Hao Hao's mother bought several bottles of yogurt at Yunli Supermarket for 12.50 yuan, but she found that the same yogurt was cheaper in Yunli Supermarket than in 0.2 yuan. So, when she bought yogurt the next day, she went to Liqun Supermarket to buy it. As a result, she bought it for 18.40 yuan.

18.(8 points) The ideological and moral construction of minors has attracted more and more attention from the society. In order to guide students to establish a correct concept of consumption, a youth research institute randomly investigated the amount of pocket money (the amount is integer yuan) of 0/00 students in a school in Dalian during the winter vacation. According to 100 survey data, make frequency distribution table and frequency distribution histogram:

(1) Complete the frequency distribution table and frequency distribution histogram; In the table, a = _ _ _ _ _, b = _ _ _ _ _ _ and c = _ _ _ _ _ _

(2) The example of this question is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

(3) The Institute believes that students who spend more than 150 yuan should be advised to be thrifty. Of the 1000 students in this school, how many students should be advised to be frugal?

19.(8 points) (1) A classmate wants to measure the height of a tree with its shadow. At a certain moment, he measured the height of a column as 1 m and the length of the shadow as 0.9 m, but when he went to measure the shadow, he found that the upper part of the shadow fell on the CD on the wall. (pictured) He measured BC=2.7 meters. Can you help him find out how tall the tree is?

(2) Can you help him find other measuring methods (ruler, benchmark and mirror) within 24 hours a day? Please draw a schematic diagram and combine it with your graphic description:

Experimental equipment used: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Line segment whose length needs to be measured: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

20.(8 points) A certain district raises funds 1.600 yuan, and plans to paint on the trapezoidal open space with the upper and lower floors of10m and 20m respectively for decoration. As shown in the figure, (1) the unit price of the paint they sprayed in △AMD and △BMC areas is 8 yuan /m2. When the △AMD area is covered (shaded part in the figure), * * * cost 160 yuan. Please calculate the cost of covering △BMC area. (2) If there are two brands of paints to choose from in other regions, and the unit prices are 12 yuan /m2 and 10 yuan /m2 respectively, which paint should I choose just after the raised funds are used up?

2 1.( 12 points) Explore and innovate:

As shown in the figure, there are two parallel straight lines AB and CD in the known plane, and P is the moving point outside the straight lines AB and CD in the same plane. (1) When point P moves to the left of two points of the line segment AC between AB and CD, as shown in figure (1), what is the relationship between ∠P, ∠A and ∠C?

Please prove your conclusion:

(2) When the point P moves to the right of two points of the line segment AC between AB and CD, as shown in Figure (2), what is the relationship between ∠P, ∠A and ∠C? (No proof is required. ) a:

(3) With the movement of point P, can you find out the other two different positional relationships, draw corresponding graphs, and write the relationships between ∠P, ∠A and ∠C at this time? Choose one of them to prove it.

Practice and application:

Fold a rectangular piece of paper ABCD (as shown in the figure) along EF, so that point B falls on B 1, point C falls on C 1, and point B 1C 1 meets point G. Fill in the blanks according to the above conclusions:

22.( 12 points) Factorization with geometric figures, through the combination of numbers and shapes, can help us understand the problem well.

(1) For example, add an appropriate number to the horizontal line below to make it completely flat.

As shown above, "x2+8x" is based on a square with a side length of x, plus two small rectangles with a length of x and a width of 4. In order to make it completely flat (that is, the figure becomes a square), a small square with a side length of 4 must be added. That is x2+8x+42=(x+4)2.

Please draw a picture on the horizontal line below and explain the practice of x2-4x+_ _ _ _ = (x-_ _ _ _) 2 in words and fill in the blanks.

Description:

(2) It is known that the sum of the areas of a square with a side length of x and a rectangle with a length of x and a width of 8 is 9. Look at the picture and find the side length of x: (add the corresponding numerical or algebraic expressions to the letters a, b, c and x).

a = _ _ _ _ _ _ _ _ _ _ _ _，B=_______

c = _ _ _ _ _ _ _ _ _ _ _ _，x=_______

(3) The complete square formula can be expressed by the area of plane geometry. In fact, some algebraic formulas can also be decomposed in this form, such as using the area decomposition factor: a2+4ab+3b2,

So: a2+4ab+3b2=(a+b)(a+3b).

Write an algebraic expression with letters A and B, draw a geometric figure, and write the result of factorization with geometric figures. Provide the following three kinds of graphics: a square with side lengths A and B, and a rectangle with length A and width B (use each at least once).