20 1 1 National Unified Examination for Enrollment of Ordinary Colleges and Universities

Science Mathematics (Compulsory+Elective 2)

This paper is divided into two parts: the first volume (multiple choice questions) and the second volume (non-multiple choice questions). Volume I 1 to 2 pages, and volume II, 3 to 4 pages. After the exam, return this paper together with the answer sheet.

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 for each 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. The answer on the test question is invalid.

3. Volume I *** 12 questions, with 5 points for each question and 60 points for each question. Only one of the four options given in each question meets the requirements of the topic.

(1) Complex number = 1+, which is the complex number of * * * yoke, then-1 =

(A)-2 (B)- (C) (D)2

(2) The inverse function of function = (≥ 0) is

(A) = ( ∈R) (B) = ( ≥0)

(C) = ( ∈R) (D) = ( ≥0)

(3) Among the following four conditions, set >; The necessary and sufficient conditions for the establishment are

(A)>+ 1 (B)>- 1 (C)>(D)>

(4) Let it be the sum of the first n items of arithmetic progression. If the tolerance d = 2, then k =

(A ) 8 (B) 7 (C) 6 (D) 5

(5) Set a function. After moving the image to the right by one unit length, the obtained image coincides with the original image, and the minimum value of is equal to.

Article 3 (C)6 (D)9

(6) It is known that dihedral angle α–ι-β, points A∈α, AC ⊥ ι, C are vertical feet, B ∈ι, BD⊥ ι, D is vertical feet, if AB=2, AC = BD = 65438+.

(A) (B) (C) (D) 1

(7) A middle school has two identical stamp albums and three identical stamp albums, and four of them are given to four friends, each of whom has 1 book, so the different ways of giving are * * * ().

(1) Four species (2) 10 species (3) 18 species (4) and 20 species.

(8) The area of the triangle formed by the sum of the tangent and the straight line of the curve at point (0,2) is

(A) (B) (C) (D) 1

(9) Let it be a odd function with a period of 2, if, then.

(A) (B) (C) (D)

(10) It is known that the focus of parabola C: =4x is f, and the straight line y=2x-4 intersects with c at points A and B, then cos.

(A) (B) (C)。 — (D)

(1 1) It is known that the circle m of the plane α tangent sphere passes through the center m to form a 60? The plane β of dihedral angle cuts the sphere to get n. If the radius of the sphere is 4 and the area of the circle M is 4л, the area of the circle N is ().

(A) .7л (B)。 9л (C)。 1 1л (D)。 13л

(12) If the vector is satisfied, the maximum value of is equal to ().

(A)2 (B) (C) (D) 1

Precautions:

1. Before answering questions, candidates should fill in their mortal names and admission ticket numbers clearly on the answer sheet with a black ink pen with a diameter of 0.5 mm, and then stick a bar code. Please carefully check the mortal 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 * * *.

2. Fill in the blanks: 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)

In the binomial expansion of (13)( 1- )20, the difference between the coefficient of x and the coefficient of x9 is _ _ _ _ _ _ _ _ _ _ _.

(14) given sin =, then tan 2 = _ _ _ _ _ _ _ _ _ _ _

(15) If F 1 and F2 are known as the left and right focal points, the coordinates of point and point M are (2,0), and AM is the bisector of ∠F 1AF2, then _ _ _ _ _ _ _ _ _ _

(16) It is known that E and F are on the square ABCD, a1b1d1lengbb1,CC 1, b1.

Third, the solution: this big question is ***6 small questions, with ***70 points. 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)

The opposite sides of the internal angles A, B and C of △ ABC are A, B and C respectively. Given A-C = 90, a+c=, find c.

(18) (The full mark of this small question is 12) (Note: the answer on the test paper is invalid)

According to the previous statistics, the probability of the owner buying an insurance is 0.5, and the probability of buying an insurance but not buying an insurance is 0.3.

(1) Ask the local area 1 car owners to buy at least two insurances, A and B1;

(ii) X represents the number of car owners who have not bought two insurance policies among the 65,438+000 car owners in this area. Find the 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 pyramid, ∨, ⊥, the sides are equilateral triangles, = =2, = = 1.

(i) Evidence: ⊥ Aircraft;

(2) Find the angle with the plane.

(20) (The full mark of this small question is 12) (Note: the answer on the test paper is invalid)

Let the sequence satisfy the sum.

(i) General formula for searching;

(ii) Establishment, documentation and certification:

(2 1) (The full mark of this small question is 12) (Note: the answer on the test paper is invalid)

It is known that O is the coordinate origin, F is the focal point on the positive and semi-axis of ellipse C: axis, and a straight line passing through F and having a slope of-intersects with C at points A and B, and point P satisfies.

(I) prove that point p is on c;

(Ⅱ) Let the symmetry point of point P with respect to point O be Q, and prove that four points A, P, B and Q are on the same circle.

(22) (The full mark of this small question is 12) (Note: the answer on the test paper is invalid)

(i) Set a function to prove that when > 0, > 0;

(2) Randomly draw one card at a time from 1 to 100, and then put it back in its original place, so as to draw 20 times in a row, assuming that the probability of drawing 20 numbers is the same. Prove: