First, multiple-choice questions: This big question is a small question of *** 10, with 5 points for each small question and 50 points for * * *. Of the four options given in each question, only one meets the requirements of the topic.
1. If,,, then ()
A.B. C. D。
1.b Propositional Intention This small topic mainly examines the knowledge of complementary sets and intersections in sets, the understanding and mastery of sets in set operations, and of course the basic properties of inequalities.
Therefore, analysis.
2. ""Yes ""()
A. Sufficient and unnecessary conditions B. Necessary and insufficient conditions
C. sufficient and necessary conditions D. neither sufficient nor necessary conditions
2. The small topic of the intention of a proposition mainly examines the basic relationship of the proposition, and the question type in the topic examines the concept of the proposition and the understanding degree of the proposition concept through the analysis of inequality.
Resolve for''''; The opposite is not necessarily true, so ""is a necessary and sufficient condition for "".
3. If (is an imaginary unit), then ()
A.B. C. D。
3. The small topic of D proposition intention mainly examines the operation and concept of complex numbers, and directly examines the understanding of the concept and properties of complex numbers with the operation of complex numbers as the carrier.
analyse
4. Let it be two different planes and a straight line, and the following statement is true ()
A. If, then B. If, then
C. If, then D. If, then
4.c Proposition Intention This topic mainly examines the positional relationship between straight lines and surfaces in solid geometry. By investigating parallelism and verticality, the basic element relationship in solid geometry is fully mobilized.
Analysis may occur for A, B and D, but it is correct for C. 。
5. Known vectors,. If the vector satisfies, then ()
A.B. C. D。
5.d Proposition Intention This topic mainly examines the coordinate operation of plane vectors. Through the investigation of the parallel and vertical relationship of plane vectors, the application of coordinate operation of plane vectors in solving specific problems is well reflected.
Analyze possible settings, and then, have; Again, yes, yes.
6. It is known that the left focus of the ellipse is, the right vertex is, the point is on the ellipse, and the axis intersects the straight line at this point. If so, the eccentricity of the ellipse is ().
A.B. C. D。
6. The examination of the combination of geometry and plane vector in the D proposition not only reflects the intersection of geometry and vector, but also reflects the clever use of the combination of numbers and shapes.
Ellipse analysis, because, then.
7. A program block diagram as shown in the figure, the output value after the program runs is ().
A.B.
C.D.
7. A Proposition Intention This topic examines the concept and basic application of programming languages. Through the investigation of programming language, it fully embodies the key of circular language in mathematical programming language.
Analyze for, and for, and then output when the conditions are not met.
8. If the function is established, the following conclusion is correct ()
A. In the world, it is playing an increasingly important role.
B, it is a decreasing function on.
C. is an even function.
D., this is a strange function
8.c Proposition Intention This topic mainly examines the concepts and basic knowledge of full-name quantifiers and existential quantifiers. By examining quantifiers and combining the nature of functions, it makes an intersection problem.
Analysis is sometimes a balanced function.
9. It is known that the lengths of three sides of a triangle are respectively, so the greatest common divisor between its sides and a circle with radius is ().
A.B. C. D。
9.c Proposition Intention This question examines the knowledge of plane geometry well and is comprehensive and flexible. The above examination methods require simplicity and agility, both the position of tangent and circle and the movement of circle.
Analytically, for a circle with a radius of 1, there is a position that is exactly the inscribed circle of a triangle, and there are only three intersections at this time. For a circle that is slightly shifted to the right or has other changes, four intersections can be realized, but more than five intersections cannot be realized.
10. Known as a real number, the image of the function cannot be ().
10.d Proposition Intention This question is a question to examine trigonometric function images, but because it contains parameters, the knowledge points examined are rich. Combined with graphic examination, the questions examined are vivid and rich in depth.
Analytically, when the amplitude is greater than 1, the period of trigonometric function is 0, and d does not meet the requirements. Its amplitude is greater than 1, but its period is greater than.
Non-multiple choice questions (* * 100)
Precautions:
1. Write the answers on the answer sheet with a black pen or signature pen, not on the test paper.
2. To draw on the answer sheet, you can use 2B pencil first, and after confirmation, you must use a signature pen or a pen-and-ink drawing with black handwriting.
Fill in the blanks: There are 7 small questions in this big question, each with 4 points and * * * 28 points.
1 1. Let the common ratio of geometric series and the sum of the first few terms be, then.
1 1. 15 Proposition Intention This topic mainly examines the general term and summation formula of geometric series in the series, and fully reflects the knowledge connection between the general term formula and the summation of the previous items through the investigation of the knowledge points of the series.
analyse
12. If the three views (unit:) of a geometric figure are shown in the figure, the volume of the geometric figure is.
12. 18 Proposition Intention This topic mainly examines three views of geometry, which fully embodies the intuitive requirements of geometry and the combination of surface area and volume.
Geometry consists of two cuboids, the lower volume is and the upper volume is, so the volume of geometry is 18.
13. If the real number satisfies this set of inequalities, the minimum value is.
13.4 Proposition Intention This topic mainly examines the maximum problem in linear programming. The examination of this question not only embodies the requirement of drawing the linear region correctly, but also embodies the requirement of solving the maximum value of the linear objective function.
By drawing its linear programming, we can know that when a straight line passes through this point,
14. The frequency distribution histogram of a sample with a capacity of is as follows, so the frequency of data in the interval is.
14.30 proposition intention This topic examines the histogram of frequency distribution. By asking questions, we not only examined the drawing ability, but also examined the level and ability of using charts to solve practical problems.
The value of frequency/interval in the interval is, and the total number is 100, so the frequency is 30.
15. divide the residential electricity consumption in a certain area into two time periods: peak period and low period for time-sharing pricing. The sales price table of power grid in this area is as follows:
Price list of electricity consumption in peak hours and price list of electricity consumption in low hours.
Peak monthly electricity consumption
(kWh) Peak electricity price
Monthly electricity consumption in low valley (unit: Yuan/kWh)
(unit: kWh) Low valley electricity price
(Unit: Yuan/kWh)
50 and below 0.568 50 and below 0.288
The ratio of parts exceeding 50 to 200 is 0.598, and the ratio of parts exceeding 50 to 200 is 0.3 18.
The part exceeding 200 is 0.668, and the part exceeding 200 is 0.388.
If a household's electricity consumption is kWh in the peak period in May and kWh in the low period,
According to this billing method, the electricity bill payable at home this month is yuan (answered by numbers).
15. The topic of proposition intention is a practical problem. Through the calculation of electricity charge in real life, not only the concept of function is investigated, but also the application of piecewise function is emphatically investigated.
The analysis of electricity bill payable should be divided into two parts, the peak part is; For the low peak part, the sum of the two parts is.
16. Let the sum of arithmetic progression's antecedents be, then,, become arithmetic progression. By analogy, the above conclusions are as follows: Let the antecedent product of geometric series be, then,, become geometric series.
16. Propositional Intention This topic is a combination of sequence and analogical reasoning, which not only examines the knowledge of arithmetic progression and geometric sequence in sequence, but also examines the method and ability of analogical reasoning through known conditions.
The analysis of geometric series, and so on, if the product of the previous term of geometric series is, then, becomes geometric series.
17. There is a card, and each card is marked with two consecutive natural numbers, among which.
Take any card from this card and record the event "the sum of two numbers on this card (for example, if you get it)."
If the card is marked, the sum of each of the two numbers on the card is not less than "Yes".
Then.
17. Proposition intention This question is a permutation and combination question, which not only examines the ability to analyze and solve problems, but also pays more attention to the ability and level of students to solve practical difficulties by enumerating problems.
There are five cases, that is, there are 20 basic events, for cases above 14. Therefore,
Third, answer: This big question is ***5 small questions, ***72 points. The solution should be written in words, proof process or calculation steps.
18. (The full mark of this question is 14) In the middle, the opposite sides of the angle are respectively and satisfy,
. (i) Areas to be discovered; (II) If yes, the value obtained.
18. Analysis: (1)
And, and, so, so the area is:
(II) is known from (i), but, therefore,
therefore
19. (The full mark of this question is 14) As shown in the figure, the plane,, and are the midpoint. (1) Proof: aircraft; (II) Find the sine value of the included angle with the plane.
19.(I) Prove that the connection is at the midpoint of, yes, so, again, so, there are plane ACD and DC plane ACD, so the plane ACD.
(2) In the middle, so.
DC plane ABC, so plane ABC
Plane Abel, plane Abel, plane ABC, plane Abel.
According to (i), the quadrangle DCQP is a parallelogram, so
So the plane ABE, so the projection of the straight line AD on the plane ABE is AP,
So the angle between the straight line AD and the plane ABE is
In,,
therefore
20. (The full mark of this question is 14) is set as the sum of the first few items of the series,,, where is a constant.
(i) Seek;
(II) If there is,,, become the value of geometric series.
20. Analysis: (1) When,
( )
Experience, formula () holds,
(ii) Geometric series,
That is, in order,
To determine arbitrariness,
2 1. (The full mark of this question is 15) Known function.
(i) If the image of the function passes through the origin and the tangent slope at the origin is 0, the value to be obtained;
(II) If the function is not monotonic in the interval, then.
Analysis: (1) From the meaning of the question
Again, solve, or
(Ⅱ) The function is not monotonic in the interval, which is equivalent to
Derivative function can get both real numbers greater than 0 and real numbers less than 0.
That is, the function has zero, and according to the existence theorem of zero, there are
, namely:
Tidy up: solve
22. (Full score of this question 15) Known parabola: the distance from the last point to its focus is.
(i) the value of the sum;
(2) Let the abscissa of a point on a parabola be that a straight line passing through it intersects another point, the axis of intersection is at that point, and the vertical line passing through this point intersects another point. If it is tangent, find the minimum value.
22. Analyze (i) the directrix equation obtained from the parabolic equation: according to the definition of parabola.
The distance from the point to the focus is equal to the distance from the directrix, that is, the solution is
The parabolic equation is:, which will be substituted into the parabolic equation to solve.
According to the meaning of the question, the slope of the straight line passing through this point exists and is not 0, so be it.
Then, when
Simultaneous equations, sorted out:
That is, the solution or.
And the slope of the straight line is
simultaneous equation
Tidy up, that is:
, get:, or
,
And that slope of the tangent of the parabola at point n:
MN is the tangent of parabola.
Get (give up), or,