Reference answers and grading standards of science mathematics test questions
1. Multiple choice questions: * * 12 small questions, with 5 points for each small question and * * 60 points.
Title number
1
2
three
four
five
six
seven
eight
nine
10
1 1
12
election
D
C
A
A
D
A
B
B
C
B
D
B
1. Select D. Analyze OR, from, from.
2. choose C. analysis, and the plural number of its * * * yoke is so.
3. choose a. analysis; On the other hand, it cannot be launched.
4. Select the domain analyzed by A. as the record, and then
, so it's odd function.
5. Choose D. The zero point of the analytic function is the root of the equation, and make
Image, observe its intersection with a straight line, and know when,
Sometimes there is an intersection, that is, the function has zero.
6. choose a. Analyze the basis, and then based on:
, the solution.
7. choose B. analysis, so, that is, so,
Through this point, that is,
The solution is this function,
Solution, so the monotone increasing interval of the function is.
8. choose B. according to the meaning of the question, there is, so.
9. Choose C. Analysis (omitted)
10. Choose B. The asymptote of analytic hyperbola is, and the directrix of parabola is, if, when the straight line passes through the point,
1 1. Choose D. The equation of analytic easy-to-know straight line is, and the equation of straight line is
, available at the same time, again,
∴ , ,
∵ is an obtuse angle ∴, that is to say,
Simplify, therefore, that is, or, and therefore.
12. Select B. Parse settings, that is, the right side, respectively.
get
Chapter 7.
That is,
∴ .
Fill in the blanks: **4 small questions, each with 5 points and ***20 points.
13. Fill in and analyze the data on the cover page.
drift along
Therefore, ∴.
14. Fill in. Analytic plane ∑ plane, the distance from ∴ to the plane is equal to the distance between planes, equal to, and,
∴ The volume of a triangular pyramid is.
15. Fill in. Analysis, the point rotates once every second, so the second rotates,,, and then.
16. Fill in. Let the equation of the straight line be, then the equation of the straight line is,
Then the point is satisfied,
By the same token,
therefore
∫ (If and only if, take the equal sign)
Therefore, the minimum value is.
Third, the answer: **6 small questions, ***70 points.
17. (I) Let the common ratio and the tolerance be, depending on the meaning of the question.
Solve, or (give up) ∴; ... 6 points
(2) Derived from (1),
Because,
So, that is to say, the minimum value of ∴ is 6... 12 points.
18.(I) Obey hypergeometric distribution according to conditions: where the possible value is, and its distribution list is:.
... 6 points
(2) According to the meaning of the question, the probability of air quality reaching Grade I every day in a year is,
Then, the number of days in a year when the air quality reaches Grade I is ∴ (days).
So on average, one day in a year, the air quality reaches Grade 1 ... 12.
19. Let the center of a square be, the midpoint be, and the midpoint be, and take the straight lines of,, as the axis, axis, axis respectively, as shown in the figure to establish a spatial rectangular coordinate system.
In, available,
Then,
.
therefore
.
(Ⅰ)∵ ,
∴, that's ⊥; ... 6 points
(ii) Let the normal vector of the plane be, which is obtained by the following formula
Therefore, in the same way, the normal vector of the plane can be obtained as,
Let the plane angle of dihedral angle be, then ... 12 points.
20. (i) The radius ⊙ is, and the equation ⊙ is,
If the axis is ⊥, then, that is, then (the vertical line passes through the vertical line), then the trajectory of the point is a parabola with the focus as the alignment.
The trajectory equation of point ∴ is: ... 6 points.
(ii) When it is not perpendicular to the axis, the linear equation is obtained by the following formula
, set, and then
∴ ,
When perpendicular to the axis, it can also be obtained,
To sum up, there are ... 12 points.
2 1.(Ⅰ)∵ ,
∴ The tangent slope of the curve at this point is,
Therefore, according to the meaning of the question,
When, the function monotonically increases; When, the function monotonically decreases; Therefore, the monotonic increasing interval of the function is 0, and the decreasing interval is 0; ... 6 points
(2) If, because everything exists, it conflicts with the meaning of the question at this time, so it is, by, by, by.
When, the function monotonically increases; When, the function monotonically decreases; Therefore, the maximum value is obtained at, so it holds if and only if it is correct.
Orders.
Then, when, the function monotonically decreases; When, the function monotonically increases; Therefore, the minimum value is obtained at, so it holds if and only if, that is, if.
So this set of values is ... 12 points.
22. (Ⅰ) Connection, ∵ is the diameter of ∴.
∴
∵ ,∴ ,
∵ is a chord, and the sum of straight lines is tangent to the point.
∴
∴, that is, equal share; ... five points
(ii) learned from (i) ∴.
∫∴, so,
So the size is ... 10 minute.
23. (Ⅰ) Let any point on the curve be, then on the circle,
Here it is.
The polar coordinate equation of a straight line is, written as,
Let any point on the straight line be there, then this point is on it.
So, that is:
So the equation of the straight line is …5 points.
(ii) Let any point on the curve be,
Its distance from the straight line is,
Among them, it is satisfactory that:
Timely ∴, ... 10 o'clock
24.(Ⅰ) ...5 points
(Ⅱ)∵ ,
The establishment of ∴ is necessary and only necessary.
That is, or, or, solution, or
Therefore, the range of values is ... 10 minute.