I. Multiple choice questions
Set a set, and the number of sets satisfied by B is
1 (B)3 (C)4 (D)8
(2) Let it be an arbitrary function on r, then the following statement is correct.
(a) odd function; (b) odd function.
Is an even function.
(3) Give the following four propositions:
① Two straight lines perpendicular to the same straight line are parallel to each other.
② Two planes perpendicular to the same plane are parallel to each other.
Straight lines are parallel to each other if the angles they make with the same plane are equal.
(4) If a straight line is a non-planar straight line, then the two straight lines intersecting the two are non-planar straight lines.
Where the number of false propositions is
1 (B)2 (C)3 (D)4
(4) The two asymptotes of hyperbola and straight line enclose a triangular region, and the inequality group representing this region is
(A) (B) (C) (D)
(5) Let it be an operation on R, and A is a nonempty subset of R. If there is, it is said that A is closed to the operation, and the following number sets are closed to the four operations of addition, subtraction, multiplication and division (divisor is not equal to zero).
(1) natural number set (2) Integer set (3) Rational number set (4) Irrational number set.
(6) The lengths of the opposite sides of the three internal angles are set vectors respectively. If, the size of the angles is
(A) (B) (C) (D)
(7) The equation about the straight line is symmetrical to the curve.
(A) (B)
(C) (D)
(8) Curves and curves
(a) Equal focal length (b) Equal eccentricity (c) Same focal length (d) Same alignment.
(9) In a geometric series, the sum of the preceding items is, and if the series is also a geometric series, it is equal to.
(A) (B) (C) (D)
(10) The common points of lines and curves are
1 (B)2 (C)3 (D)4
(1 1) If the function is known, the range of is
(A) (B) (C) (D)
(12) Let,, and the point be a moving point on the line segment. If, then the range of real numbers is
(A) (B) (C) (D)
Step 2 fill in the blanks
(13) Rule _ _ _ _ _ _ _ _
( 14) _____________
(15) Among the five table tennis players, there are two veteran players and three new players. Now, three players have been selected to participate in the team competition held in the second stadium. 1, No.2 and No.3, so at least one old player should be selected. At least 1 new players in No.2 are arranged in _ _ _
(16) If the angles formed by a straight line and the face of a regular quadrangular prism are all, then = _ _ _ _ _ _
Three. solve problems
(17) (the full score of this small question is 12)
Known function,. Find:
(i) the maximum value of the function and a set of independent variables to obtain the maximum value;
(II) The monotone increasing interval of the function.
(18) (the full mark of this small question is 12)]
It is known that the midpoint of the square, and will be folded along, as shown in the figure, and the size of the dihedral angle is.
(i) the plane of evidence;
(2) If it is a regular triangle, try to judge whether the projection of the point on the plane is on a straight line, prove your conclusion and find the cosine of the angle.
(19) (the full score of this small question is 12)
At present, there are two projects, A and B. For every100000 yuan invested, the profit probability after one year is 6.5438+0.2 million yuan, 6.5438+0.654.38+0.8 million yuan and 6.5438+0.654.38+0.7 million yuan respectively. It is known that the profit of project B is related to the adjustment of product price. In each adjustment, the probability of price decline is that the product price of project B will be adjusted independently twice in one year. Keep in mind that the number of times that the product price of Project B falls within one year is: for every input of Project B 1 00000 yuan, take 0, 1 2, and the corresponding profit after one year is 13000 yuan,1.
(i) Probability distribution and mathematical expectation;
(II) When and the range of values to be obtained.
(20) (The full score of this small question is 14)
Known points are two moving points on a parabola, coordinate origin, vector, and satisfy. Let the equation of a circle be
(i) Prove that the line segment is the diameter of a circle;
(2) When the minimum value of the distance from the center of the circle C to the straight line X-2Y =0, find the value of p. ..
2 1. (The full score of this small question is 12)
The function f(x)= is known, where a, b and c are arithmetic progression with a tolerance of d, a > 0 and d > 0. Let [1-] be 0, and put a, b, c.
(i) Seek
(II) If ⊿ABC has one side parallel to the X axis and the area is, find the values of A and D.
22. (The full score of this short question is 12)
Known, where, hypothetically,
(i) Writing;
(2) proof: for anyone, there is always.
Look at/April/April/shijuan/shijuan.htm again.