Exquisite Compilation of College Entrance Examination Simulation Questions in Provinces and Cities of China (New Curriculum Standard Volume III) 20 12 Mathematical Answers

20 12 National Unified Entrance Examination for Colleges and Universities (Shandong Volume)

Liberal arts mathematics

The first volume (***60 points)

1. Multiple-choice question: This topic is entitled *** 12, with 5 points for each question and 60 points for each question. Only one of the four options given in each small question meets the requirements of the topic.

(1) If the complex number z satisfies the imaginary unit), otherwise,

(A)3+5i (B)3-5i (C)-3+5i (D)-3-5i

(2) The known complete works, sets and positive sums

(A){ 1，2，4} (B){2，3，4} (C){0，2，4} (D){0，2，3，4}

(3) The domain of the function is

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

(4) A sample data obtained from a certain measurement are as follows: 82, 84, 84, 86, 86, 88, 88, 88. If the B sample data happens to be the data obtained by adding 2 to the A sample data, then the following numerical characteristics of the A and B samples are the same.

(a) Mode (b) Mean (c) Median (d) Standard deviation

(5) Let the proposition p: the minimum positive period of the function is; Proposition Q: The image of a function is symmetrical about a straight line. Then the following judgment is correct.

(A)p is true (b) false (c) false (d) true.

(6) If the variables meet the constraints, the value range of the objective function is

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

(7) Execute the program block diagram on the right. If the input is 4, the output value of n is

2 (B)3 (C)4 (D)5

(8) The sum of the maximum and minimum values of the function is

(A) (B)0 (C)- 1 (D)

(9) The positional relationship between circles is as follows

(a) inscribed (b) intersected (c) circumscribed (d) separated.

The image of the (10) function is roughly as follows

(1 1) It is known that the eccentricity of hyperbola is 2. If the distance from the focus of the parabola to the hyperbolic asymptote is 2, the equation of the parabola is

(A)(B)(C)(D)[ Source: Z_xx_k.Com]

(12) Setting function. If there are only two different similarities between the image and the image, then the following judgment is correct.

(A) (B)

Volume II (***90 points)

Fill-in-the-blank question: This big question has four small questions, each with 4 points, *** 16 points.

(13) As shown in the figure, the side length of the cube is 1, and e is a point on the line segment, so the volume of the triangular pyramid is _ _ _ _ _.

(14) The figure on the right is a histogram of sample frequency distribution based on the average temperature (unit:℃) data of some cities in June of a certain year, in which the average temperature ranges from [20.5 to 26.5], the sample data are grouped into,,,,,, and the number of cities whose average temperature is lower than 22.5℃ in the known sample is 165438+.

(15) If the maximum value of the function on [- 1 2] is 4, the minimum value is m, and the function is a increasing function on, then a = _ _ _ _.

(16) As shown in the figure, in the plane rectangular coordinate system, the initial position of the center of the unit circle is (0, 1), the position of a point P on the circle is (0,0), and the circle rolls forward on the X axis. When the circle rolls to the center of (2, 1), its coordinate is _.

Third, answer: This big question is ***6 small questions, ***74 points.

(17) (the full score of this small question is 12)

In △ABC, the opposite sides of the inner angle are known respectively.

(1) Verification: geometric series;

(ii) If, find the area s of δ.

(18) (the full score of this small question is 12)

There are five cards in the bag, including three red cards, numbered 1, 2 and 3 respectively; Two blue cards, numbered 1 and 2 respectively.

(i) Choose two cards from the above five cards, and find the probability that the two cards are different in color and the sum of the labels is less than 4;

(2) Put another green card with a label of 0 into the current bag, and choose two cards randomly from these six cards to find the probability that the colors of the two cards are different and the sum of the labels is less than 4.

(19) (the full score of this small question is 12)

As shown in the figure, geometry is a quadrangular pyramid, and delta is a regular triangle.

(i) Verification:

(ii) If ∞, m is the midpoint of AE,

Proof: ∑ plane.

(20) (The full score of this small question is 12)

It is known that the sum of the first five items in arithmetic progression is 105, and.

(i) Find the general term formula of the sequence;

(ii) For any, no more than the number of items in the series is recorded as. Find the sum of the first m items in a sequence.

(2 1) (the full score of this small question is 13)

As shown in the figure, the eccentricity of the ellipse is, and the area of the rectangular ABCD surrounded by straight lines is 8.

(i) Find the standard equation of ellipse m;

(ii) Let a straight line and an ellipse m have two different intersections, and a rectangle ABCD has two different intersections. The maximum value and the value of m when finding the maximum value.

(22) (The full score of this small question is 13)

It is known that the function is constant, e=2.7 1828… is the base of natural logarithm), and the tangent of the curve at this point is parallel to the X axis.

(i) find the value of k;

(ii) Monotone interval of the solution;

(iii) Let, where is the derivative function. Proof: for any. [Source: Subject Network ZXXK]

Reference answer:

First, choose a topic:

( 1)A(2)C(3)B(4)D(5)C(6)A(7)B(8)A(9)B( 10)D( 1 1)D( 12)B

(12) solution: If, then the equation has the same solution, so it has only two different zeros. If, then, it is necessary and only necessary or, because, therefore, there must be this. Then, it is best to set. Therefore, compare the coefficients, so. Therefore, the answer is B.

Second, fill in the blanks

(13) With △ as the bottom surface, it is easy to know that the height of the triangular pyramid is 1, so. [Source: Zxxk.Com]

(14)9 The sum of the two leftmost rectangles is 0.10×1+0.12×1= 0.22, and the total number of cities is11ò

(15) When, when, at this time, this time is a decreasing function, not the meaning of the question. If, then, therefore, the test results meet the meaning of the question.

( 16)

Third, answer questions.

(17)(I) by the known:

According to sine theorem,

So geometric series.

(ii) If so,

∴ ,

∴△ area.

(18) (1) There are the following 10 possibilities for choosing two cards from five cards: red 1 red 2, red 1 red 3, red 1 blue 1 and red/kloc-.

(II) After adding a green card with the number 0, select two cards from the six cards. In addition to the above situation of 10, there are five situations: red 1 green 0, red 2 green 0, red 3 green 0, blue 1 green 0, blue 2 green 0, that is, there are five kinds of * *.

(19)(I) Let the midpoint be O, connecting OC and OE, then we can know that,

Also know, so the plane OCE.

So, OE is the perpendicular bisector of BD.

So ...

(II) Take point n in AB and connect it,

∵ M is the midpoint of AE, ∴∥,

Delta is an equilateral triangle.

From ∠ BCD = 120 and ∠ CBD = 30, so ∠ ABC = 60+30 = 90, that is,

So ND∑BC,

So plane MND∨ plane BEC, so DM∨ plane BEC.

(20)(I) Known from:

Solve,