(Time:120min)
Total score: 120)
Fill in the blanks (3 points for each small question, 30 points for * * *)
1, known score, when x
, the score is negative; When x
, the value of the score is;
2. Polynomial decomposition factor =
; The result of the calculation is
;
3. In order to know the service life of a batch of ballpoint pen refills, use them properly.
Investigate in some way; In order to know the height of the students in your class, it is recommended to adopt
Investigate in some way;
4, the range of a set of data is
; The variance is
5, the condition of the proposition "if" is
, the proposition is
Proposition (fill in "true" or "false");
6. If, then
7, known, then =
;
8. As shown in the figure, ①∠BAD =∠C, ②∠ADB =∠ CAB, ③, ④.
(5), (5) as a condition, the other as a conclusion, forming a true proposition, then the condition is
The conclusion is that
; (Just fill in the serial number)
9. As shown in the figure, at △ABC, DE//BC, AD = 3BD, then
10, known
, then
, you can get
Second, multiple-choice questions (3 points for each question, ***30 points)
1 1. If so, which of the following is correct?
(
)
A、
B,
C,
d、
12, the solution set of inequality group is
(
)
A、
B,
C,
d、
13, when x is an arbitrary real number, the following fraction must be meaningful.
(
)
A、
B,
C,
d、
14, the following proposition is wrong.
(
)
A, two isosceles triangles with an angle of 30 are similar.
Two isosceles triangles with a base angle of 40 are similar.
C, two isosceles right-angled triangles are similar
D, two equilateral triangles are similar
In 15 and △ABC, point D and point E are on AB and AC respectively, so it is impossible to determine DE//BC (
)
a、AD=2，AB=5，AE= 1，CE= 1.5
b、AD=4，AB=6，DE=2，BC=3
c、AB=3BD，AC=3CE
d、AD:AB= 1:3，AE:EC= 1:2
16. When Xiao Ming factorized the problem, he accidentally omitted to copy the exponent of x, only knowing that the exponent is a positive integer not greater than 10, and the problem can be decomposed by bisection formula. The formula he copied in the exercise book is ("O" stands for omitted indicator), so the possible situation of this indicator value is as follows.
(
)
One or two kinds
B, 3 kinds
C, 4 kinds
D, 5 kinds
17, known real number,, satisfies,,,
The value of is equal to (
)
Answer, 0
b、 1
c、2
D, uncertainty
18, as shown in the figure, the height of beer bottle is 0, and the height of wine noodles in the bottle is 0. If the bottle cap is fixed,
On the other hand, the height of the wine surface is (), and the volume of the wine bottle is the same as that of the bottle.
The volume ratio of wine is ()
(1)
(2)
(3)
(4)
19. In the known rectangular ABCD, AB = 3 and BC = 4. Fold the rectangle so that point C coincides with point A, and the length of the crease EF is ().
(1)
(2)
(3)
(4)
20. If there is a point P on the plane of the regular triangle ABC, so that ⊿PAB, ⊿PBC and ⊿PCA are isosceles triangles, then such a point P has ().
1
four
(C)7
10
Iii. Answering questions (60 points)
2 1, (10 points) Decomposition factor: (1)
(2)
22.(8 points) Solve the inequality group and express the solution set on the number axis;
23, (6 points) calculation
24.( 10 minute) As shown in the figure, in △ABC, AB = 8cm, BC = 16cm, point P starts from point A and wants to move to point B at a speed of 2cm/s, while point Q starts from point B and moves to point C at a speed of 4cm/s along BC. If P and Q are started at the same time, it will take several seconds. .
25.(6 points) There are 400 students in the eighth grade of a middle school. In order to enhance students' environmental awareness, the school conducted an environmental knowledge test in this grade. In order to understand the performance of this test, the school selected the performance of 50 students. After sorting out the obtained data, draw the frequency distribution histogram as follows:
(1) Among the above problems, the overall problem is
, the sample is
(2) Among the 50 students, the students who scored 60 ~ 70 points are
People, students with 90 ~ 100 points are
People;
(3) In this exam, the eighth-grade students in the whole school got about 70 ~ 80 points.
People.
26.( 10) In order to protect the environment, an enterprise decided to purchase 10 sets of sewage treatment equipment. There are two types of equipment, A and B. The price, monthly sewage treatment capacity and annual consumption fee of each equipment are as follows:
Type a and type b
Price (ten thousand yuan/set) 12 10
Sewage treatment capacity (ton/month) 240 200
Annual consumption expense (ten thousand yuan/set) 1 1
According to the budget, the funds used by enterprises to purchase equipment are not higher than 6.5438+0.05 million yuan.
(1) Please design several purchasing schemes for this enterprise;
(2) If the amount of sewage produced by an enterprise is 2,040 tons per month, which procurement scheme should be chosen to save money?
(3) Under the condition of (2), if the service life of each equipment is 10 year, and the sewage treatment fee of the sewage plant is per ton 10 yuan, please calculate how much ten thousand yuan the enterprise will save by treating the sewage by itself compared with discharging the sewage to the sewage plant. (Note: Enterprise sewage treatment expenses include equipment purchase expenses and consumption expenses)
27. Reading material: If two quadrangles are not only similar figures, but also each group of straight lines corresponding to the vertices pass through the same point, then such a figure is called a potential diagram, and this point is called the potential center. The similarity ratio at this time is called the potential ratio.
As shown in the figure, in the rectangular coordinate system, the coordinates of point A and point B are (3, 2) and (6, 4) respectively, the AC⊥x axis is at point C, and the BG⊥x axis is at point G, making a square ACDE and a square bgmn with AC and BG as sides respectively;
(1) Try to write the function expressions corresponding to straight line AB and straight line EN respectively;
(2) Verification: Square ACDE and Square BGMN are similar graphs;
(3) Given the coordinate of point P as (10,0), try to make a square with point P as one of its vertices, which is similar to the existing square (just do it as shown below); (10)