1. Fill in the blanks 1. Let the set A={- 1, 1, 3}, B={a+2, a2+4}, AB={3}, then the real number A = _ _ _ _ _ _ _ _ _ _ _ _
2. Let the complex number Z satisfy z(2-3i)=6+4i (where I is an imaginary unit), then the modulus of Z is _ _ _ _ _ _ _ _ _ _ _ _.
There are three small balls of the same size and 1 black balls in the box. If two balls are randomly drawn, the probability that the colors of the two balls are different is _ ▲ _ _
4. In order to know the quality of a batch of cotton, a cotton mill randomly selected 100 cotton fibers (the length of cotton fibers is an important indicator of cotton quality), and the obtained data are all in the interval, and the frequency distribution histogram is shown in the figure. In the sampling of 65,438+000 cotton fibers, the length of _ _ _ _ _ is less than 20mm.
5. Let the function f (x) = x (ex+AE-x) and xr be an even function, then the real number A = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
6. In the plane rectangular coordinate system xOy, if there is a point M on the hyperbola, and the abscissa of the point M is 3, then the distance from M to the right focus of the hyperbola is _ _ _ _ _ _ _ _ _.
7. The figure on the right is the flow chart of an algorithm, so the value of the output S is _ _ _ ▲ _ _ starts1n1SS+2ns33 nn+1nnoutput s end yes.
8. Function y = x2(x >；; 0) The abscissa of the intersection of the tangent at point (ak, ak2) and the X axis is ak+ 1, k is a positive integer, and a 1= 16, then a1+A3+A5 = _ _ _ _ _ ▲
9. In the plane rectangular coordinate system xOy, it is known that there are only four points on the circle, and the distance from the straight line 12x-5y+c=0 is 1, so the value range of the real number c is _ _ _ _ _ _ _ _.
10, the image of function y=6cosx intersects with the image of y=5tanx defined on the interval as p, the passing point p is PP 1x, the axis is at point P 1, and the straight line PP 1 intersects with the image of y=sinx at point P2, then the line segment p/kloc-0.
1 1, given the function, the range where x satisfies the inequality is _ _ _ _ ▲ _ _
12, let the real numbers x and y satisfy 38,49, then the maximum value of is _ _ _ _ _ _ _.
13, acute triangle ABC, where the opposite sides of A, B and C are A, B and C respectively, then _ _ ▲
14. Cut a regular triangular thin plate with a side length of 1 into two pieces along a straight line parallel to the bottom, one of which is trapezoidal. Note that S=, then the minimum value of s is _ _ _ _ _ _ _ _ _ _ _ _.
Second, answer the question.
15, (14 point) In the plane rectangular coordinate system xOy, find points A (- 1, -2), B (2 2,3), C (-2,-1) (1).
16, (14 minutes) As shown in the figure, in a quadrilateral P-ABCD, the PD plane ABCD, PD=DC=BC= 1, AB=2, AB‖DC, BCD=900( 1).
17, (14) An interest group measured the height h (unit m) of the AE of the TV tower, as shown in the schematic diagram. The height of the vertically placed reference BC is h=4m, the elevation angle ABE=α, and the ADE=β( 1). The team measured a set of α and β values, Tan α = 65438. Please calculate the value of h accordingly. (2) After analyzing some measurement data, the team found that properly adjusting the distance d (unit m) from the pole to the TV tower can improve the measurement accuracy. If the actual height of the TV tower is 125m, and ask what D is, α-β is the maximum.
18.( 16 minutes) In the plane rectangular coordinate system, as shown in the figure, the left and right vertices of the ellipse are known as A and B, and the right vertex is F. The straight lines Ta and TB passing through point T () intersect the ellipse at point M, where M >；; 0, ① Let the fixed point P satisfy, set the trajectory of point P and set the coordinates of point T.. It is proved that the straight line MN must pass through a point on the X axis (its coordinates have nothing to do with m) ABOF.
19.( 16 points) Let the sum of the first n items of a series be all positive numbers, and it is known that the series is a arithmetic progression with tolerance. ① The general formula for finding series (expressed by) ② is set as a real number, and the inequality holds for any positive integer. Validation: The maximum value of is.
20.( 16 points) Set a function defined on the interval, and its derivative function is. If there are real numbers and functions, there is >: 0, so a function is said to have properties. (1) Set a function, here is the real number ① proof: the function has properties ② Find the monotone interval of the function (2) The given function has properties, and if |||
Science additional question 2 1 (choose two answers from the following four questions, each question 10 points) (1) Geometry proof is selected. AB is the diameter of ⊙O, D is the upper point of ⊙O, and the tangent of ⊙O passes through point D and extends to C. If DA=DC, 1), let k0, kR, M=, N=, A, B, C be transformed into point A/kloc- △ A 1b 1c 1 circle ρ=2cosθ is tangent to the straight line 3ρcosθ+4ρsinθ+a=0, and the value of real number A (4) is proved by choosing known real numbers A and A, b0, and the verification is 22. (10) One factory produces two kinds of products, namely, 80% of first-class products and 20% of second-class products. Production of B-class products, 90% of first-class products and 10% of second-class products. When producing a product, the first-class product can earn 40 thousand yuan, and the second-class product can lose 6.5438+0 million yuan; When producing a product B, the first-class product can earn 60,000 yuan, and the second-class product can lose 20,000 yuan. Let the production of various products be independent of each other (1). Let x (unit: 10,000 yuan) be the total profit obtained by cosnA from the production of 1 A products and B products. Find the distribution table of X. (2) Find the probability that the profit obtained from the production of 4 A products is not less than 100,000 yuan. (10)