Scientific mathematics (including answers)
This paper is divided into two parts: the first volume (multiple choice questions) and the second volume (non-multiple choice questions). Volume 1 1 to 2 pages. Volume II, pages 3-4. After the examination, the examination paper of Compendium of Materia Medica and the answer sheet should be returned together.
volume one
Precautions:
1. Before answering questions, candidates must clearly fill in their name and admission ticket number on the answer sheet with a black ink pen with a diameter of 0.5 mm, and affix the bar code. Please carefully approve the admission ticket number, name and subject on the bar code.
2. After choosing the answer to each small question, black the answer label of the corresponding question on the answer sheet with 2B pencil. If you need to change it, clean it with an eraser, and then choose another answer label. Answering on the test paper is not efficient.
3. Volume 1 *** 12 is a minor problem, the first minor problem is 5 points, and * * * 60 points. Of the four options given in each question, only one meets the requirements of the topic.
Reference formula:
If events A and B are mutually exclusive, then the surface area formula of the ball
If events A and B are independent of each other, then R represents the radius of the ball.
Volume formula of ball
If the probability of event A in the experiment is p, then
The probability that event A happens exactly k times in n independent repeated tests, where r represents the radius of the ball.
I. Multiple choice questions
(1) Complex number =
(1). I (b). -I(C). 12— 13i(D). 12+ 13i
(2) let cos (-80) = k, then tan 100 =
(1). (2). —
(C.) (D)。 —
(3) If the variables x and y satisfy the constraint conditions, the maximum value of z = x-2y is
(A).4 (B)3 (C)2 (D) 1
(4) if a 1a2a3=5 and a7a8a9= 10, then a4a5a6=
5 (B) 7 (C) 6 (D) 4
(5) The coefficient of X in the expansion of (1+2) 3 (1-) 5 is
(A) -4 (B) -2 (C) 2 (D) 4
(6) A school offers 3 elective courses of Class A and 4 elective courses of Class B, and a classmate chooses 3 courses from them. If at least one of the two courses is required, then the different choice method is * * *.
(A)30 species (B)35 species (C)42 species (D)48 species.
(7) In a cube, the cosine of the included angle with the plane is
(A) (B) (C) (D)
(8) Rules
(A) (B) (C) (D)
(9) If the left and right focal points of hyperbola are known, and the point is above 60, the distance to the axis is
(A) (B) (C) (D)
(10) The range of values of the known functions, if, and, is
(A) (B) (C) (D)
(1 1) It is known that the radius of a circle is 1, where is the two tangents of the circle and the sum is the two tangents, so? The minimum value of is
(A)-4+ (B)-3+ (C)-4+2 (D)-3+2
(12) It is known that there are four points A, B, C and D on the sphere with radius 2. If AB=CD=2, the volume of tetrahedral ABCD is the largest.
20 10 National Unified Examination for Enrollment of Ordinary Colleges and Universities
Science Mathematics (Compulsory+Elective Ⅱ)
Volume II
Precautions:
1. Before answering questions, candidates should clearly fill in their name and admission ticket number with a black ink pen with a diameter of 0.5 mm on the answer sheet, and then stick a bar code. Please carefully approve the admission ticket number, name and subject on the bar code.
2. On page ***2 of Volume 2, please use a black ink pen with a diameter of 0.5mm to answer the questions on the answer sheet. The answer on the test paper is invalid.
3. Volume II *** 10, 90 points * * *.
Fill-in-the-blank question: This big question has four small questions, each with 5 points and ***20 points. Fill in the answers on the lines of the questions.
(Note: the answer on the test paper is invalid)
The solution set of (13) inequality ≤ 1 is.
(14) is known as the angle of the third quadrant, then.
(15) If the straight line = 1 has four intersections with the curve, the value range of is.
(16) It is known that F is a focus of ellipse C, B is an endpoint of short axis, and the extension line of line segment BF intersects with point D, then the eccentricity of C is 0.
3. Solution: This big question is ***6 small questions, with a score of ***70. The solution should be written in proof process or calculus steps.
(17) (The full mark of this small question is 10) (Note: the answer on the test paper is invalid)
Given that the internal angles A and B of △ABC and their opposite sides A and B satisfy, find the internal angle C..
(18) (The full mark of this small question is 12) (Note: the answer on the test paper is invalid)
The manuscript submitted to the magazine will be reviewed by two experts first, and if it can pass the review of two preliminary evaluation experts, it will be hired; If both experts are unqualified, they will not be hired; If it can pass the preliminary expert's evaluation, it will be reviewed by a third expert. If you can pass the evaluation of the evaluation experts, you will be hired, otherwise you will not be hired. Suppose that the probability that the manuscript can pass the examination of the preliminary examination experts is 0.5, and the probability that the manuscript can pass the examination is 0.3. Independent evaluation by experts.
(i) Find out the probability that 1 articles submitted to the magazine will be hired;
(II) Remember that X represents the number of articles hired out of the four articles submitted to the magazine, and find the distribution list and expectation of X..
(19) (The full mark of this small question is 12) (Note: the answer on the test paper is invalid)
As shown in the figure, in the S-ABCD of a quadrangular pyramid, the bottom surface of SD is ABCD, AB DC, AD DC, AB=AD= 1, DC=SD=2, E is a point on the side SB, and the plane EDC is SBC.
(1) Proof: SE=2EB
(ii) find the dihedral angle a-de-c. ..
(20) (The full mark of this small question is 12) (Note: the answer on the test paper is invalid)
The function f (x) = (x+1) inx-x+1is known.
(i) If (x)≤ +ax+ 1, find the range of a;
(2) Proof: (x- 1)f(x)≥0.
(2 1) (The full mark of this small question is 12) (Note: the answer on the test paper is invalid)
It is known that the focus of parabola C =4x is f, the straight line L(- 1, 0) passing through point K intersects with point A and point B, and the symmetrical point of point A about the X axis is d. 。
(i) prove that the point f is on the straight line BD;
(Ⅱ) Let = and find the equation of inscribed circle m of △BDK.
(22) (Full score for this small question 12) (Note: the answer on the test paper is invalid)
In the known sequence
(i) Let c= and find the general term formula of the sequence;
(Ⅱ) Find the value range of c that makes the inequality hold.