Mathematics examination for science students
First, multiple choice questions
(1) setting function
, the real number.
=
(A)-4 or -2
(B)-4 or 2
(C)-2 or 4
(D)-2 or 2
(2) put the plural
The plural of * * * yoke is written as
I is an imaginary unit if
(A)3-i
(B)3+ 1
1+3i
(D)3
(3) If the three views of an aggregate are shown in the figure, the direct view of the aggregate can be
(4) The following proposition is wrong
(a) If the aircraft
And then the plane.
There must be a straight line parallel to the plane.
(b) If the aircraft
Not perpendicular to the plane
And then the plane.
There must be no straight line perpendicular to the plane.
(c) If the aircraft
, plane
, then
(d) If the aircraft
And then the plane.
All straight lines are perpendicular to the plane.
(5) Set a real number
System satisfying inequality
if
Is an integer, then
The minimum value of is
(A) 14
(B) 16
(C) 17
(D) 19
(6) If
, then
(1)
(2)
(3)
(4)
(7) If
Is a real number, then "
"yes.
about
Sufficient and unnecessary conditions
(2) Necessary but insufficient conditions
Sufficient and necessary conditions
Conditions that are neither sufficient nor necessary.
(8) Known ellipse
And hyperbola
Under the public's attention,
Asymptote of sum to
A circle whose long axis is diameter intersects at
At two o'clock,
if
Just put the line segment
So, three equal parts
(1)
(2)
(3)
(4)
(9) Five different books, including two Chinese books, two math books and one physics book 1 book. If they are randomly arranged on the same shelf, the probability that books on the same subject are not adjacent.
(1)
(2)
(3)
D
(10) Let a, b and c be real numbers and f(x).
=(x+a)
Recordset S=
if
The number of elements is set elements S and T respectively, so the following conclusion is impossible.
(1)
= 1 and
=0
(2)
(3)
=2 and
=2
(4)
=2 and
=3
Non-multiple choice part
(*** 100 integral)
Two. Fill-in-the-blank question: This big question has 7 small questions, each with 4 points and * * * 28 points.
(1 1) If the function
Is an even function, then the real number
=
(12) If the program diagram is as shown,
, the value of k output after the program runs is
(13) Let binomial (x-
)n(a & gt； 0), the coefficient of x is a, and the constant term is b,
If B=4A, the value of a is
(14) If the plane vectors α, β satisfy |α|≤ 1, |β|≤ 1, and the areas of parallelograms with adjacent vectors α, β are
The angle between α and β
The value range of is
(15) A graduate attended a job fair and gave a speech to companies A, B and C.
Our company submitted a resume, assuming that the probability of this graduate being interviewed by Company A is
What is the probability of getting an interview with Company B?
And whether these three companies make their interviews independent of each other. Mark X as the number of companies interviewed by the graduate. if
, the mathematical expectation of random variable x.
(16) Settings
Is a real number, if
rule
The maximum value of is
. .
(17) Settings
oval
focus
On an ellipse, if
; Zedian
The coordinates of are
.
Third, answer questions; This big topic ***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
Intermediate angle
Opposite is a, b, c, b, C.
known
and
.
(i) When
Time and demand
The value of;
(2) Ruojiao
For acute angle, find the value range of p;
(19) (the full mark of this question is 14) arithmetic progression whose known tolerance is not 0.
The first item of
Be a (
), let the sum of the first n items in the series be
, and
Geometric series of process
(1) search sequence
General formula of sum
2. Remember
, when?
Try to compare.
and
The size of.
(20) (The full mark of this question is 15) As shown in the figure, it is in a triangular pyramid.
Yes,
D is the midpoint of BC, PO⊥ plane ABC, and the vertical foot O falls on the line segment AD. BC=8, PO=4, AO=3 and OD=2 are known.
Evidence: Associated Press ⊥ BC;
(ii) Whether there is a point m on the line segment AP, so that the dihedral angle A-MC-β is a straight dihedral angle.
Horn? If it exists, find out the length of AM; If it does not exist, please explain why.
(2 1) (full mark of this question 15) Known parabola.
：
=
, round
：
The center of the circle is point m.
(i) Find the point m on the parabola.
precise
Distance of line;
(ii) The known point p is a parabola.
At the last point (different from the origin), make a circle after point P.
Two tangents, intersecting parabolas.
At point A and point B, if you cross a straight line at point M and point P,
perpendicular to
AB, find a straight line.
Equation of
(22) (The full mark of this question is 14)
set function
(i) If
Extreme point of real number
(2) Seeking truth from facts
Value, so for any
, eternity.
Has been established, note:
Is the base of the natural logarithm.