First, multiple-choice questions (this big topic * *10 small topic; 3 points for each small question, 30 points for * * *. )
1. The following figure is axisymmetric, but it is ().
(A) (B) (C) (D)
2. As shown in the figure (1), connect the midpoint O of two steel bars AA' and BB' together, so that AA' and BB' can freely rotate around the point O to make a measuring workpiece, then the length of A' B' is equal to the width of the inner groove AB, so the reason for judging △ OAB △ OAB is ().
(a) corner edge (b) corner edge
(c) side edge (d) corner edge
( 1)
3. It is known that the circumference of an isosceles triangle is 20cm, and the functional relationship between the base length y(cm) and the waist length x (cm) is y=20-2x, so the value range of the independent variable x is ().
A.0 & ltx & lt 10 b . 5 & lt； X<10 C. all real numbers d.x >; 0
4. As shown in the figure, the environmental protection team of a school collected 226 pieces of waste batteries on four Sundays in a month. The number of batteries collected on each Sunday is as follows:
Sunday order 1 2 3 4
Number of batteries collected 80 63 5 1 32
In the following four statistical charts about the number of waste batteries collected on four Sundays, the correct one is ().
5. It is known that points P 1 (A- 1, 5) and P2(2, b- 1) are axisymmetric with respect to X, so the value of (a+b)2007 is ().
In 2007
6. Turn on the switch of the washing machine. When washing clothes (there is no water in the washing machine), the washing machine goes through four continuous processes: water intake, washing, drainage and dehydration, in which the water volume y (liter) in the washing machine and time x (minute) satisfy a certain functional relationship, and the functional image is roughly ().
7.△ABC is an isosceles right triangle, ∠ C = 90, D is a point above BC, and AD=2CD, then ∠ DAB = ().
A.30 B.45 C.60 D. 15
8, the following operation is correct ()
A.B. C. D。
9. As shown in Figure (2), in △ABC, D and E are on BC, BD=DE=AD=AE=EC, then the degree of ∠BAC is _ _ _ _ _.
(2)
A.30 B.45 C.60 D. 15
10 As shown in the figure, in a square grid composed of 4×4 small squares, the ratio of the area of the shadow part to the area of the square ABCD is ().
a、5:8 B、3:4 C、9: 16 D、 1:2
Second, fill in the blanks (this big topic *** 10 small topic; 3 points for each small question, 30 points for * * *. Write the answer on the horizontal line of the question)
1 1, as shown in the figure, follow the rules and fill in the blanks:
12. Decomposition factor: _ _ _ _ _ _ _.
Page 2 * * * Page 8
13. According to the record of the highest temperature (℃) of a city in July last year, make a statistical chart as shown in the figure. According to the information in the picture, the number of days when the highest temperature reaches 35℃ (including 35℃) is _ _ _ _.
13 thematic map 14 thematic map
14, as shown in the figure, consists of two squares with side lengths A and B. By using different methods to calculate the shadow area in the figure below, one formula that can be verified is.
15, as shown below, Xiao Ming built 1, 2, 3 "goldfish" with matches, and it takes one match to build n "goldfish".
……
16 As shown in the figure, Yang Hui, a mathematician in the Song Dynasty, put forward the right table in his book "Detailed Explanation of the Nine Chapters Algorithm", revealing that
Coefficient law of (non-negative integer) expansion. For example:
It has only one term, and the coefficient is1;
The coefficients of the two terms are 1 and1respectively;
It has three terms, and the coefficients are 1, 2,1;
It has four terms, and the coefficients are 1, 3,3,1respectively;
According to the above laws, there are five items in the expansion formula * * *, and the coefficients are respectively.
As shown in the figure, 17 is a graph composed of four identical rectangular pieces of paper. Please write the identities about A and B with different representations of blank areas in the diagram.
Page 3 * * * Page 8
17, given that y=(m-2)x is a proportional function, then m=.
In the function y=, the value range of the independent variable x is _ _ _ _ _ _ _. The range of independent variables in the functional relationship is. In the function y=, the range of letters is _ _ _ _ _ _ _.
18. If the image of linear function y=kx+3 passes through point M(3, -4), then k=.
19. in the formula s=v0t+2t2(v0 is a known number), the constant is and the variable is.
20. In △ABC and △A 1B 1C 1, if AB = A 1C 1 and BC = B1C, then supplementary conditions are given.
You can get △ ABC △ a1b1c1.
Iii. Answer questions (***60 points). Please write down the necessary calculus process or reasoning steps when answering.
2 1.
⑴[(x+y)2-y(2x+y)-8x]÷2x； ⑵ Known values of:,,.
(3) It is known that the product sum of sum is a similar term, and the value of.
(4) Simplify first and then evaluate. (-24x 2+4a3x 3-a2 x4)÷(-a2 x2), where a= and x =-4.
(5) Factorization.
①(x+y)2-9 y2； ② 10b(x-y)2-5a(y-x)2；
③(a b+b)2-(a+ 1)2；
22.( 10) (picture title) As shown in the figure, it is a statistical chart of the number of medals won by China athletes in the Olympic Games from 1984 to 2000. Please answer the following questions according to the information provided by the statistical chart:
(1) How many medals did China athletes win in the five Olympic Games from 1984 to 2000?
(2) In which Olympic Games did China athletes win the most medals?
(3) According to the above statistics, how many medals can China athletes win in the 2004 Olympic Games?
(4) According to the above data, make a line chart to show the number of gold medals won by China athletes in 1984 ~ 2000 Olympic Games.
(5) You might as well make a fan-shaped statistical chart according to the data, compare it and experience the different characteristics of the three statistical charts.
23.(6 points) As shown in the figure, in △ABE and △ACD, the following four conclusions are given: (1) AB = AC; (2)AD = AE； (3)AM = AN； (4)AD⊥DC, AE⊥BE, according to three of them, fill in the "known" column below, and 1 conclusion, fill in the "verification" column below to form a true proposition, and write the proof process.
Known:;
Prove:
Page 5 * * * Page 8
24. As shown in the figure, L 1, L2 respectively represent the functional relationship between the cost y (cost = lamp price+electricity fee, unit: yuan) of incandescent lamps and energy-saving lamps and the lighting time x(h). Assuming that the service life of both lamps is 2000h, the lighting effect is the same.
(1) According to the image, the functional relationships of L 1 and L2 are obtained respectively.
(2) When the lighting time is what, the cost of two lamps is equal?
(3) Liang Xiao's room is planned to be illuminated for 2500h, and he bought an incandescent lamp and an energy-saving lamp. Please help him design the most economical way to use the lamp.
25. As shown in the figure, point E is the point on the CD beside the square ABCD, point F is the point on the CB extension line, EA⊥AF, and verification: DE = BF.
26. One product per piece 10 yuan. The relationship between the daily sales price (yuan) of each product and the daily sales volume (pieces) of the product in the trial sale stage is as follows:
(yuan)
15 20 25 30 …
(piece)
25 20 15 10 …
(1) Please draw points on the rectangular coordinate system, observe the distribution of points, and establish an appropriate sum function model.
(2) If you are required to sell 24 pieces a day, how much profit can you make this day?
27.(8 points) As shown in the figure, the straight line Y =-2x+4 intersects the X axis and the Y axis at points A and B respectively. If both ends of the line segment CD slide on the coordinate axis (point C is on the Y axis and point D is on the X axis), and CD = ab.
(1) When △COD and △AOB are equal, find the coordinates of C and D;
(2) Is there a straight line CD passing through the first, second and third quadrants to make CD⊥AB? If it exists, find the analytical formula of straight line CD; If it does not exist, please explain why.
Page 6 * * * Page 8
28.(8 points) A wholesaler wants to transport a batch of seafood from place A to place B, and both the automobile freight company and the railway freight company have started seafood transportation business. It is known that the transportation distance is 120km, and the speeds of cars and trains are 60km/h and 100km/h respectively. The charging items and standards of the two freight companies are shown in the following table:
Unit price of transportation fee of means of transport
(yuan/ton? Kilometers) unit price of refrigeration fee
(yuan/ton? Hourly) toll
(Yuan) Handling fee and management fee
(yuan)
Automobile 2 5 200 0
Train 1.8 5 0 1600
Note: "Yuan/ton? "Kilometers" means the freight per ton of goods per kilometer; "Yuan/ton hour" refers to the hourly refrigeration fee for each ton of goods.
(1) Assuming that the seafood to be shipped by the wholesaler is X (tons), the fees charged by the automobile freight company and the railway freight company are y 1 (yuan) and y2 (yuan) respectively, try to find the functional relationship between y 1 and y2 and X;
(2) If the wholesaler has no less than 30 tons of seafood to ship, which freight company should he choose to undertake the transportation business in order to save the freight?
29. The price of each brush of Xinhua Stationery is 25 yuan, and the price of each calligraphy exercise book is 5 yuan. Stationery stores have formulated two preferential measures to promote sales. Answer: If you buy a brush, you will get a calligraphy exercise book. B: 10% off the purchase amount.
Experimental middle school wants to buy 10 brush and x(x≥ 10) calligraphy exercise books for the school's calligraphy interest group.
(1) Please use the preferential method A to write the functional relationship between the actual payment amount Y A (yuan) and X (capital);
(2) Please write down the functional relationship between the actual payment amount Y, B (Yuan) and X (Ben) by the second preferential method;
(3) If you buy the same number of calligraphy exercise books, which preferential payment method would you choose to save money?
30.(8 points) As shown in the figure, the functional relationship between the straight line OC and BC is sum respectively, and the moving point P (0) moves on OB (0).
(1) Find the coordinates of point C, and answer when X takes what value >?
(2) Let the area on the left side of the straight line in△ △COB be S, and find the functional relationship between S and.
(3) At what value does the straight line bisect the area of △COB?