A.24 to B.30 to C.48 to D.60
9. If the minimum value of the function is 3, the value of the real number is ().
A.5 or 8 B. or 5 C. or D. or 8
10. In the plane rectangular coordinate system, the known vector points satisfy. Curve, region zxxk. If it is two independent curves, then ().
A.B. C. D。
Volume (non-multiple choice questions * * 100)
2. Multiple-choice question: This big question has five small questions, each with 5 points and * * 25 points.
1 1. If the image of the function is moved to the right by units, the image obtained is symmetrical, then the minimum positive value of is _ _ _ _ _ _ _ _.
12. This series is arithmetic progression. If,, constitutes the geometric series of the topic network, then
________.
(13) Let be be a natural number greater than 1, and the expansion of is. If the location of the point is as shown, then
(14) Let it be the left focus and the right focus of the ellipse, and the straight line passing through this point intersects the ellipse at two points. If it is an axis, the equation of the ellipse is _ _ _ _ _ _ _ _.
(15) It is known that the vector sums of two groups of non-zero vectors are arranged in two and three. Remember that the topic network represents the smallest of all possible values. Then the following proposition is _ _ _ _ _ _ (write the numbers of all correct propositions).
① There are five different values.
② If there is, it has nothing to do with it.
(3) if there is, it has nothing to do with it.
4 if, then. Theme network
⑤ If yes, the included angle with is
3. Solution: This big question is ***6 small questions with a score of ***75. The solution should be written with Wen Zi's explanation and proof of the course network or calculation steps. The answer should be written in the designated area on the answer sheet.
16. Let the length of the opposite side of the inner corner be, and
( 1);
(2) the value.
17 (the full score of this small question is 12)
Party A and Party B play Weiqi, and it is agreed that the party who wins two games in a row will win directly. If the winning game does not appear after five games, it is determined that the player with more winning games wins the game. Assume that the winning probability of each game is 0, the winning probability of Party B is 0, and the results of each game are independent.
(1) Find the probability that A will win the game in 4 innings (including 4 innings);
(2) Write down the figures of the General Administration when the competition is decided, the distribution table of the results and (mathematical expectations).
18 (the full mark of this small question is 12)
In which a function is set.
(1) discusses the monotonicity of its domain;
(2) When, the value when finding the value and the minimum value.
(19) (the full score of this small question is 13)
As shown in the figure, it is known that the sum of two parabolas, the sum of two straight lines passing through the origin, and intersect at two points respectively.
(1) Proof:
(2) Make a straight line through the origin (different from,) and intersect at two points respectively. Remember the area of the topic network and the values of and respectively.
(20) (The full mark of this question is 13)
As shown in the figure, in a quadrilateral, the bottom quadrilateral is a trapezoid, the plane passing through three points is marked as, and the intersection point with is.
(1) Proof: Yes, the midpoint;
(2) Find the ratio of the volume of the upper and lower parts divided by the plane;
(3) If the area of the trapezoidal theme net is 6, find the dihedral angle formed by the plane and the bottom.
(2 1) (the full score of this small question is 13)
Let's say a real number, an integer.
Evidence: if and when;
(2) The sequence is satisfied, which is proved as: topic network.