This test paper has five pages. After the exam, return this paper together with the answer sheet.
Precautions:
1. Before answering the questions, candidates should fill in their names and admission ticket numbers clearly, and paste the bar code accurately in the bar code paste area of candidates' information.
2. Multiple choice questions must be filled in with 2B pencil; Non-multiple-choice questions must be written with a signature pen with 0.5 mm black handwriting, with neat font and clear handwriting.
3. Please answer in the answer area of each question on the answer sheet according to the order of the question number, and the answers written beyond the answer area are invalid; Draft paper and test paper are invalid.
4. The drawings can be drawn with pencil first, and must be blacked out with a black signature pen after confirmation.
5. Keep the card surface clean, do not fold, break or wrinkle, and do not use correction fluid, correction tape or paper scraper.
1. Multiple choice questions: This topic is *** 12, with 5 points for each question and 60 points for each question. Of the four options given in each question, only one meets the requirements of the topic.
Fill-in-the-blank question: There are 4 small questions in this question, each with 5 points and * * 20 points.
13. China high-speed railway has developed rapidly and advanced technology. According to statistics, among the high-speed trains that stop at one station, the punctuality rate of 10 train is 0.97, the punctuality rate of 20 train is 0.98, and the punctuality rate of 10 train is 0.99, so the average punctuality rate of all trains that stop at this station is estimated.
16. China epigraphy has a long history, and the seal is one of the representatives of epigraphy. Most seals are cuboids, cubes or cylinders, but the seal of Guandu in the Southern and Northern Dynasties is a "semi-regular polyhedron" (Figure 1). A semi-regular polyhedron is a polyhedron surrounded by two or more regular polygons. Semi-regular polyhedron embodies the symmetrical beauty of mathematics. Figure 2 is a graph. All its vertices are on the face of the same cube, and the side length of this cube is 1. Then the semi-regular polyhedron * * * has _ _ _ _ _ _ faces, and its side length is _ _ _ _ _ _ _. (The first space in this question is 2 points, and the second space is 3 points. )
Third, the answer: **70 points. The solution should be written in words, proof process or calculation steps. The number 17 ~ 2 1 is required, and candidates must answer every question. Questions 22 and 23 are multiple-choice questions, and candidates should answer as required.
(1) Required questions: **60 points.
17.( 12 points)
As shown in the figure, the bottom surface of the cuboid ABCD–a1b1c1is a square, the point e is on the edge AA 1, and BE⊥EC 1.
(1) proof: BE⊥ plane EB1c1;
(2) if AE = A 65438+E, find the sine of dihedral angle b–EC–c1.
18.( 12 points)
In the 1 1 table tennis match, you will get 1 points for each win. When a game is tied with 10: 10, the right to serve is exchanged for each ball, and the player who scores 2 points first wins and the game is over. Students A and B play singles. Suppose that the probability of a serving score is 0.
(1) find p (x = 2);
(2) Find the probability of the event "X=4, A wins".
(2) Multiple choice questions: ** 10. Candidates are asked to answer any one of questions 22 and 23. If you do too much, score according to the first question.
22. [Elective 4-4: Coordinate System and Parameter Equation] (10 score)
23. [Elective 4-5: Selected Lectures on Inequality] (10 mark)
20 19 Liaoning college entrance examination science mathematics reference answer
1.A 2。 C 3。 C 4 explosive D 5。 A six. C 7。 B 8。 D 9。 A 10。 B 1 1。 A 12。 B
13.0.98 14.–3
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