20 19 Mathematics Examination Paper for Senior High School Entrance Examination in Zhuzhou City, Hunan Province
The score of the topic is one, two, three and four, and the total score is one. The reciprocal of multiple-choice questions (this big question is * * 10, and ***30.0) 1. -3 is ().
A.
B.
C. three-dimensional stereotactic instrument.
2.× =( )
A.B. 4 C. 23
3. In the following categories, similar to 3xy is ().
A.B.
C.
4. For any rectangle, the following statement must be correct ()
A. Diagonal lines are vertical and equal. B. The four sides are perpendicular to each other. C. the four corners are equal.
D it is an axisymmetric figure, but not a centrally symmetric figure.
5. The solution of the fractional equation with x-= 0 is ()
A. The 3rd day of the 2nd year BC
6. In the plane rectangular coordinate system, which quadrant is point A (2, -3) located? ( )
A. first quadrant B. second quadrant C. third quadrant D. fourth quadrant 7. If the median and average of a set of data x, 3, 1, 6, 3 are equal, the value of x is ().
A.2b 3c 4d 58。 The factorization of the following options is correct ().
A.
C.B. D。
9. As shown in the figure, in the rectangular plane coordinate system Oxy, three points A, B and C are not on the inverse proportional function y = (k > 0).
The same three points, connecting OA, OB, OC, passing through point A at point D is the AD⊥y axis, passing through point B and point C respectively is the BE, and CF and OC perpendicular to the X axis at points E and F intersect with BE at point M, and the areas of △AOD, △BOM and quadrilateral CMEF are respectively marked as S 1, S2, S3, then ().
A.
B.C. D。
10. Choose two different numbers from four numbers-1, 1, 2,4 to form an array MK = {ak,
Bk} (where k = 1, 2 … s, and {ak, bk} and {bk, ak} are regarded as the same array), if it is satisfied that for any Mi={ai, bi} and Mj={ai, bj}(i≠j, 65438+).
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A. 10
2. Fill in the blanks (this big topic is ***8 small questions, ***24.0 points)
2
1 1. If the image opening of the quadratic function y=ax+bx is downward, then a _ _ _ 0 (fill in "=" or ">" or "
Randomly draw a ball from it and the probability of getting a white ball is _ _ _ _.
CM is the midline on the hypotenuse AB, and e and f are MB and 13 respectively. As shown, in Rt△ABC, ∠ ACB = 90.
The midpoint of BC, if EF= 1, then AB = _ _ _ _ _
14. If a is a rational number and the value of 2-a is greater than 1, then the value range of a is _ _ _ _.15. As shown in the figure, make a ray passing through the vertex B of the regular pentagon ABCDE and its inner angle.
∠ The angular bisector of ∠EAB intersects with point P, and∠ ∠ABP = 60°, then∠ APB = _ _ _ _
Degree.
16. As shown in the figure, AB is the diameter ⊙O, point C is on ⊙O, and OC⊥AB passes through it.
The chord CD of point C intersects with the line segment OB at point E, and satisfies ∠ AEC = 65. If it is connected with AD, ∠ Bad = _ _ _ _ _ degrees. 17. Nine Chapters of Arithmetic is a famous mathematical work with rich contents in ancient China. The book has the following problems: "Today, the good ones walk a hundred paces, but the bad ones walk.
And then what? "It means: the fast man walks 100 step, and the slow man only walks 60 steps. Now the slow man walks first 100 step, and the fast man has to walk _ _ _ _ to catch up with the slow man. 18. As shown in the figure, in the plane rectangular coordinate system xOy,
A notch baffle II, where the notch is a line segment AB, where point A (0, 1) and point B are above point A, and AB= 1. Place a baffle III on the straight line x=- 1. The light emitted from the point O is reflected by the mirror I, and then shines on the baffle III through the notch AB, so the light falling on the baffle III.
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Third, the calculation problem (this big question * * 1 small question, ***6.0 points) 19. Simplify first, then evaluate:-
, where a =.
Fourth, answer the question (this big question is ***7 small questions, ***60.0 points)
20. Calculation: | |+π-2cos30.
2 1. Xiao Qiang's father is going out by car. When starting the car, the car alarm system showed that there was an obstacle in front of him. At this time,
The depression angle of the automobile front end F measured at the viewpoint A is α, and tanα=. If the straight line AF intersects the ground l 1 at point B, assuming that the horizontal line l2 at point A is parallel to the ground l 1, the length of the vertical line segment AC from point A to the ground l 1 is1.6m..
(1) Find the length of BC;
(2) If the point M on the obstacle is located at the midpoint of the line segment BC (the cross section of the obstacle is rectangular)
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Shape, and the line segment MN is the edge of the front end of this rectangle), MN⊥l 1. If Xiao Qiang's father backs up 0.6 meters along the straight line l 1, he can just see the top N point of the obstacle through the front of the car (point D is the corresponding point of point A, and point F 1 is the corresponding point of point F) and find the corresponding point of the obstacle.
22. A dessert shop plans to order a kind of fresh milk. According to previous sales experience, the demand for that day is the highest.
The temperature t is related. The statistics of June last year (calculated by 30 days) are as follows: (Statistical table of maximum temperature and demand) Maximum temperature t (unit: c) Demand (unit: cup) t < 25 25 ≤ t < 30t ≥ 30 200 250 400 (1) Last June, the maximum temperature was not lower than 30℃.
(2) If the probability that the highest temperature is in each interval is estimated, the probability that the daily demand for this kind of fresh milk in June last year does not exceed 200 cups is obtained;
(3) If the purchase volume is 350 cups on June this year, the price of each cup is 4 yuan, and the price is 8 yuan, the unsold fresh milk manufacturers will take it back and destroy it at the price of 1 yuan. Assuming that the situation this year is basically the same as last year, if the highest temperature t on a certain day in June this year meets 25 ≤ t < 30 (unit:℃), try to estimate the profit of selling this kind of fresh milk on that day.
23. As shown in the figure, it is known that the vertex O of the square OEFG is the intersection of the diagonal AC and BD of the square ABCD.
Connect CE and DG.
(1) verification: △ dog △ COE;
AM=, (2) If DG⊥BD, the side length of square ABCD is 2, and line segment AD and line segment OG intersect at point M, find the side length of square OEFG.