mathematics
20 12.4
Description:
1. The whole volume is divided into two parts, the first part is multiple-choice questions, and the second part is non-multiple-choice questions, with a total of 4 pages. The examination time is 90 minutes, and the full mark is 100.
2. Candidates must answer according to the regulations on the answer sheet; The answer sheet must be kept clean and cannot be folded.
Please fill in the name, candidate number, examination room, etc. before answering the question. Use the specified pen in the specified position on the answer sheet.
4. The multiple-choice question in this volume is 1- 12. After choosing the answer for each question, use 2B pencil to black the answer label of the corresponding question in the multiple-choice answer area of the answer sheet; Non-multiple choice questions 13-23, answers (including auxiliary lines) must be written in the non-multiple choice area of the answer sheet with the designated pen according to the answer number.
The first part of multiple choice questions
1. Multiple choice questions (this question is * *, 12, with 3 points for each question and * * * 36 points for each question, and only one option is correct).
The reciprocal of 1 –3 Yes
3C。 D.
2. The front view of the geometric figure shown in Figure 1
According to the Shenzhen Special Zone Daily reported on February 28th, at the end of 20 1 1, the number of motor vehicles in our city was 2.008 million, ranking second in the country. Keep the data of 2.008 million to three significant figures, which are expressed by scientific symbols as follows.
A.B. C. D。
4. Below are some traffic sign patterns, in which the central symmetric pattern is not axisymmetric.
A.B. C. D。
5. According to Shenzhen Air Quality Times on March 3 1 20 12, some environmental monitoring stations in our district are "PM2.5".
The 24-hour moving average index is shown in the following table.
Name of monitoring station Baoan Shajing Songgang Fuyong Guanlan Longhua
PM2.5
24-hour moving average index 55 60 73 53 55 40
For this set of data, the following statement is wrong.
A. the average value is 56 B. The mode is 55 C. The median is 55 d. The variance is 7.
6. The following operation is correct
A.B.
C.D.
7. As shown in Figure 2, the turntable can rotate freely. The turntable is divided into three sectors with equal area, and each sector is marked with the number-2, 1, 2. After rotating the dial twice, the probability that the sum of the numbers in the area pointed by the pointer is positive is
A.B. C. D。
8. As shown in Figure 3, AE⊥BC is known at point E. If sinB= and AD = 6, the area of rhombic ABCD is
A. 12
9. A store sells two items, each 120 yuan, of which one made a profit of 20% and the other lost 20%. So in this transaction, the store
A. earned 10 yuan B. lost 10 yuan C. neither earned nor lost D. none of the above is correct.
10. As shown in Figure 4, Xiaoying climbs from point A to point B along the slope AB in the park, and then slides down from point B to point C along the slope. It is known that point A and point C are on the same horizontal line, ∠A = 45? ，∠C = 30？ , AB = 4m, then the length of BC is
American asset management company
China, MD.
1 1. Rotate the arrow symbol counterclockwise by 90 degrees? In this way, a series of "arrow symbols" as shown in Figure 5 are obtained. Then, according to this law, 20 12 "arrow symbol" is
A. The second century BC
12. As shown in Figure 6, the isosceles right triangle ABC moves to the right along the straight line L at the speed of 1cm/s, and stops when AB and EF overlap. Assuming that the overlapping area of xs, triangle and square is ycm2, then in the following figure, the functional relationship between y and x can be roughly expressed as follows.
A. the fourth century BC.
Part II Non-multiple choice questions
Fill in the blanks (4 small questions in this question, 3 points for each small question, * * * 12 points).
13. Due to simplification, please fill in the answer sheet.
14. If the single item and the single item are similar, mn = answer, please fill in the answer sheet.
15. As shown in Figure 7, it is known that A is a hyperbola (x >；; 0) At the last point, point A, as the axis AB//x, intersects the hyperbola (X
16. As shown in Figure 8, in trapezoidal ABCD, AD//BC and BE share ∠ABC equally, while
BE⊥CD is on E, and P is a moving point on BE. If BC = 6 and CE=2DE,
Then the maximum value of | PC-PA | is the answer. Please fill in the answer sheet.
Iii. Answering questions (this question is entitled ***7, in which 17 5, 18 6, 19 7, 20 questions 8, 2 1 8, 22 questions 8 and 23 questions 10.
17. Calculation:
18. Solve the inequality group and express its solution set on the following number axis.
19. With the enhancement of citizens' environmental awareness, more and more citizens choose to travel by bus. Xiaoying randomly surveyed some citizens who took buses, counted their waiting time, and drew the following chart. "3~6" in the table means that the bus waiting time is greater than or equal to 3 minutes but less than 6 minutes, and others are similar.
Time period/minute frequency/number of people frequency
3~6 6 0. 1
6~9 2 1 0.35
9 ~ 12a 0.25
12 ~ 15 12b
15~ 18 6 0. 1
Total c 1.0
(1) The survey method used here is: (1)
(2) In the table, the value of A is _ _ _ _ _, the value of B is _ _ _ _ _ _, and the value of C is _ _ _ _ _ _ _; (3 points)
(3) Please fill in the histogram of full frequency distribution; ( 1)
(4) In this survey, the median time period is ~ minutes. (2 points)
20. as shown in figure 10, it is known that in ⊙O, the radius OC⊥ chord AB is at point d, and ∠AOC=60? .
(1) verification: △ oad △ CBD; (4 points)
(2) If AB=2, find the area of the shaded part in the figure. (4 points)
2 1. A company organized 20 A and B workers to make some souvenirs. As we all know, Class A workers produce two more souvenirs per hour than Class B workers, and Class A workers produce 24 souvenirs in the same time as Class B workers produce 20 souvenirs.
(1) How many souvenirs will A and B workers produce per hour? (4 points)
(2) According to the arrangement of the company, the number of Class B workers is required to be not less than 3 times that of Class A workers. For every souvenir sold, the company can make a profit 10 yuan. Assuming that the souvenirs produced can be sold, how should the company arrange the number of workers in Class A and Class B to maximize the profit per hour? What is the maximum profit? (4 points)
22. As shown in figure 1 1- 1, it is known that in a rectangular ABCD, O is the center of the rectangular ABCD, and the intersection point O is OE⊥AB in E and OF⊥BC in F, so that the rectangular BEOF. Got it.
(1) The quantitative relationship between AE and CF is _ _ _ _ _, and the positional relationship between AE and CF is _ _ _ _ _ _ _; (2 points)
(2) Fix the rectangular ABCD and rotate the rectangular BEOF clockwise around point B to the position shown in figure 1 1-2 to connect AE and CF. Then, is the conclusion in (1) still valid? Please explain the reasons; (3 points)
(3) If AB=8, when the rectangular BEOF rotates to the O point on the CF (as shown in figure 1 1-3), let OE and BC intersect at the P point and find the length of PC. (3 points)
23. As shown in figure 12, it is known that the parabola intersects the X axis at two points A and B (point A is to the left of point B) and intersects the Y axis at point C, with OB = 2OA = 4. ..
(1) Find the function expression of parabola; (3 points)
(2) Let p be the moving point on the parabola in (1), take p as the center and r as the radius ⊙P, and find the coordinates of the point when ⊙P is tangent to the parabola symmetry axes L and X. (4 points)
(3) Moving point E starts from point A and moves to end point B at a speed of/kloc-0 per unit length per second, while moving point F starts from point B and moves to end point C at a speed of/kloc-0 per unit length per second. The passing point e is the EG//y axis, and AC intersects with the point g (as shown in Figure 65,438+02-2). If point e and point f start at the same time, the movement time is t.
Is the area of △EFG the area of △ABC? (3 points)