Name, class number
First, multiple-choice questions (this big question has 25 small questions, each with 3 points and each with 75 points).
1. Let a =, then the following formula is correct ()
2AB.2AC.2AD.A
2. If the function is increasing function in its domain, the quadrant that the image of the function passes through is ().
A. Quadrants 1, 2 and 3 b. Quadrants 1, 2 and 4 c. Quadrants 1, 3 and 4 d. Quadrants 2, 3 and 4.
3. As we all know, a>b>c, then the following formula must be correct ().
An ac & gtBCB. a-c>；; b-cC。 D.a+c=2b
4. If the function satisfies, then ()
A.3B. 1C.5D
5. In arithmetic progression, if, then ()
A. 14B
6. In the range of 0 ~ 360, the same angle as the 390 terminal edge is ().
2 10 D.330
7. Given two points A (a 1, 5) and B (3, 9), the midpoint coordinate of line segment AB is ().
A.( 1，7) B. (2，2) C. ( 1 2， 1 2) D. (2， 14)
8. Suppose, then the following statement is correct ()
A.p is a sufficient condition for q, but p is not a necessary condition for q.
B.p is a necessary condition for q, but p is not a sufficient condition for q.
Necessary and sufficient conditions for c.p to be q
D.p is neither a sufficient condition nor a necessary condition for q.
9. The solution set of inequality is ()
A.( 1 2，2) B. (2，3) C. ( 1，2) D. (3，4)
10. Given a plane vector, the values of are () respectively.
Asian Development Bank.
1 1. known, and then ()
Asian Development Bank.
12. The original price of a commodity is in 200 yuan. If it is sold after two consecutive price increases of 10%, the new price is ().
222 yuan 240 yuan 242 yuan 484 yuan
13. If four of the six candidates are elected as deputies to the National People's Congress, the number of people with different election results is ().
A. 15B.24C.30D.360
14. The eccentricity of hyperbola is ()
The 24th century AD.
15 13. The positional relationship between the straight line 3x-4y+ 12=0 and the circle x2+y2+ 10x-6y-2=0 is ().
A. intersection B. tangency C. separation D. intersection and passing through the center of the circle
16. Given that the straight line is perpendicular to the straight line, the value of a is ().
A.5b. 1c.3d
17. If, then = ()
A.4B.C.8D. 16
18. In the same rectangular coordinate system, when a >; At 1, the functions y = a–x and y=logax are like ().
A B C D
19, as shown in the figure, in the cube ABCD-a1b1c1d1,
The angle formed by two straight lines AC and B C 1 is ().
A.30 B.45
60-90 AD
20. Transform the image with function y = 3sin (2x–) into the image with function y = 3sin(2x-. This change is ().
A.b. translation unit to the left
C. translate the unit to the right. Translate the unit to the left.
2 1, the middle item of expansion is ()
A, B, C, D,
22. The inequality satisfied by the area represented by the shadow (including the straight line) in the figure is ().
a、x-y- 1≥0 B、x-y+ 1≥0
c、x-y- 1≤0 D、x-y+ 1≤0
23, from 10 any one basketball to test its quality, the sampling is ().
A, simple random sampling b, systematic sampling c, stratified sampling d and resampling.
24. An enterprise * * * has 150 employees, including 15 senior titles, 45 intermediate titles and 90 ordinary employees. 30 employees are selected by stratified sampling, and the number of each title in the sample is ().
a 5 10 15 B 3 9 18 C 3 10 17D 5 9 16
25. Five missiles of a certain type were randomly selected from 50 newly-developed missiles numbered 1-50 for launch test. Using the systematic sampling method with the same numbering interval, it was determined that the number of the selected five missiles might be ().
a 5 10 15 20 25 B 3 13 23 33 43 C 1 2 3 4 5D 6 15 27 34 48
II. Fill in the blanks (5 small questions in this big question, 4 points for each small question, 20 points for * * *)
26. The domain of the function is _ _ _ _ _ _ (expressed by interval).
27. There is a sample with a capacity of 20. After grouping, the interval and frequency of each group are: (10,20), 2; (20,30] ,4; (30,40] ,3; (40,50],5; (50,60],4; (60,70],2; .. (10,40) is equal to _ _ _ _
28. A shooter shoots 10 times under the same conditions, and the hit times are 7, 8, 6, 8, 6, 5, 9, 10, 7, 4, so the standard deviation of this sample is _ _ _ _.
29. The maximum value of this function is _ _ _ _ _ _ _ _
30. It is known that the lateral expansion of a cone is a semicircle with a radius of 4cm, so the volume of this cone is _ _ _ _ _ _ _.
Third, answer the question (this big question ***5 small questions, ***55 points)
3 1. (The full mark of this question is 10) Known function. Find:
( 1);
(2) Minimum positive period and maximum value of the function.
32. (The full mark of this question is 1 1) As shown in the figure, it is known that ABCD is square; P is a point outside that plane ABCD, and
Pa = ab = 3。 Find:
(1) The size of dihedral angle p-cd-a;
(2) the volume of the triangular pyramid P-Abd.
33. (The full mark of this question is 12) In the geometric series, it is known that,
(1) find the general term formula;
(2) If, find the sum of the previous items 10.
34. (Full score of this question 12) The known point is on the hyperbola, and the straight line L passes through the left focus F 1 of the hyperbola and is perpendicular to the X axis, and intersects the hyperbola at two points, A and B, so find:
The value of (1)m;
(2)|AB|。
35. At the beginning of this year, a machine tool factory bought a CNC machine tool with 980,000 yuan and put it into production immediately. The planned maintenance cost for the first year is 654.38+200,000 yuan. Starting from the second year, the annual maintenance cost will increase by 40,000 yuan over the previous year. After the machine tool is used, the total annual income is 500,000 yuan, and the profit after the NC machine tool is used for X years is 0,000 yuan.
(1) Write the functional relationship between y and x;
(2) When did the machine tool start to make profits (the profit amount is positive)? (14)