Chengdu No.7 Middle School 20 13 Foreign Students' Entrance Exam Mathematics Examination Questions
First, multiple-choice questions (this big question is a 10 small question, with 6 points for each small question and 60 points for * * *, and each small question has only one correct option).
1. If there is a diamond with an angle of 60 degrees and a side length of 2, the area of its inscribed circle is a..
A: 3? 3? 3? b、C、D、4242
5x？ 6y？ 8z？ 12? 2, if the equation? x？ 4y？ The solution of z 1 is (a, b, c), then a+b+c = b.
2x？ 3y？ 4z？ 5?
a 、- 1 B、0 C、 1 D、2
3. The radii of circle O 1 and circle O2 are 4 and 1 respectively, and the center distance is 2. As the tangent of the circle O2, the longest chord length of the circle O 1 is c.
a、 10 B、8 C、2 D、25
4. As shown below, in trapezoidal ABCD, the areas where AD∑BC, AC and BD intersect at 0, △AOD, △ABO and △BOC are S 1, S2 and S3 respectively, so the size relationship between S 1+S3 and 2S2 is D.
A, unable to determine b, S 1? S3？ 2S2 C、S 1？ S3？ 2S2 D、S 1？ S3？ 2S2
C9 5, the fractional equation about x 2k? 4? k？ 1k？ 5 has only one real number root, so the value of real number k is *** C? xx？ 2
a， 1 b，2 c，3 d，4
6. There are two different Chinese books, two different math books and an English book on the shelf. If books of the same kind are not adjacent and English books are not placed at the far left, the arrangement type is C.
A, B, C, D, 44
a(a？ 1)a3( 1？ a3)a9( 1？ A9)37。 If a? The integer part of the value of is 39274 1? a 1？ a 1？ a
a、 1 B、2 C、3 D、4
8. As shown in the following figure, in the quadrilateral ABCD inscribed in a circle, the bisectors of angles ∠A and ∠D intersect at point E, the straight line MN passing through E is parallel to BC, and intersects AB and CD at m and n, so there is always Mn = D..
a、BM+DN B、AM+CN C、BM+CN D、AM+DN
9. A space geometry is composed of several small squares with a side length of 1 (small cubes can be suspended). The three views are as follows, so there should be at least c such small cubes.
a，8 B， 10 C， 12 D， 14。
Left facade
planform
10, the side length of square ABCD is 1, point e is on the side of AB, and point f is on the side of BC, BE? 1 1，BF？ , move point p from E 47.
Starting from a straight line to f, it bounces whenever it touches the edge of a square, reflects the incident angle when it bounces, and bounces along the incident path when it touches the vertex of a square line. When point P returns to point E for the first time, the distance moved by point P is
a、65 B、3655 C、2 D、22
2. Fill in the blanks (8 small questions in this big question, 6 points for each small question, ***48 points)
1 1, for any real number k, straight line y? kx？ (2k？ 1) passes through a point with the coordinate of _ _ _ _ (-2,1) _ _ _ _ _ _ y? k(x？ 2)? 1 Obviously when x=-2 and y= 1.
12, as shown in the figure below, the length of the conical bus is 2 and the radius of the bottom surface is.
___________
2, ∠ AOB = 135, the shortest distance from a to b through the side of the cone is
three
A
What is the length of arc AB? Fan out along SA, and it's easy to find the angle.
ASB is 45 degrees 2.
It's easy to ask
AB=
13, set (3x? 2)? a0？ a 1x？ a2x？ a3x？ a4x？ a5x？ a6x，
So a 1? a2？ a3？ a4？ a5？ a6？ ___ 623456
a0？ 26? 32; a0？ a 1？ a2？ a3？ a4？ a5？ a6？ 1
The original formula =1-32 =-31;
14. As shown in the figure below, if the points are evenly thrown into the regular pentagonal ABCDE area, the probability of falling into the pentagonal FGHJK area is _ _ _ _ _ _ _.
exist
Obviously HCDE is a parallelogram, so he =CD is HJ=x, AE=a is JE = A-X.
It is easy to know that triangle HAB is similar to triangle Abe.
And then a? Xa solving xax
(a？ x)？ (a？
x)
7? The area ratio 2 is the square of the side length ratio, so the probability is
15, function y? kx？ 1 and y? The image of x intersects with two points (x 1, y 1) and (x2, y2). If 2y2y 1 18, then K = _ _ _ _ X 1x2.
kx？ 1? X2 So x 1？ x2？ k； x 1x2？ 1
You can get the value of k as 18 y2y 1x2y2? x 1y 1x2(kx2？ 1)? x 1(kx 1？ 1)? x 1x2x 1x2x 1x2
16. When △ABC, ∠ C = 90, D and E are points on BC, CA and CA respectively, BD = points on CA, BD = AC, AE = DC. Let AD and BE intersect at point P, then ∠ BPD =
_______
E
B
Extend the connection between AD and F, BF is perpendicular to AF, perpendicular to F PL, BC is perpendicular to L, BD is A, AC=a, CD=b, AE=b, EC = A-B.
Obviously, a triangular ADC is similar to a triangle.
BDF
2baBF？
So DF? DFBF if DL=x, then PL? ax b
Triangle BPL is similar to triangle BEC.
ax2？ Answer? X solves x? An a? Ba? Ba? b
It is easy to find PD
Bring the police? DM？ Bachelor of medicine
The DPB angle is 45 degrees.
17, function y? 2x？ 1? 2? The maximum value of x is _ _ _
Do x? 1? Obviously, k ranges from 0 to 0.