1. (Hubei Volume 2) Translate the image according to vector a=, and the analytical formula of the translated image is
A.B.
C.D.
Answer: Look at the data "symbol" of vector a=, instruct the image to move down to the left, and deny B, C and D according to the formula of "subtraction on the same side and addition on the other side". The answer is A. 。
Explain that the formula is a summary of experience. It is unreasonable to use the formula directly. The result of moving the image of y=f(x) along the vector a=(m, n) is
Y-n=f(x-m) (ipsilateral subtraction)
Or y=f(x-m)+n (addition of different sides)
2. (Question 4 of Beijing Volume) It is known that O is a point on the plane where △ABC is located, D is the midpoint of BC, and =0, then
A.B.
C.D.
A: a.
3. (Question 4 of Hunan Volume) Let it be a non-zero vector, if the function f(x)=(xa+b)? If the image of (a-xb) is a straight line, there must be ().
A.B. C. D。
Answer: If the image of f(x) is a straight line, then f(x) is a linear form of X. After f(x) is expanded, is there a quadratic form of x -x2a? B so -a? B=0 a⊥b, so choose A.
4. (National Volume 1, Question 3) Known vectors,, and ()
A. vertical B. neither vertical nor parallel C. parallel and in the same direction D. parallel and reverse
A: that is, a? B=0。 The answer is a.
5. (Zhejiang Volume No.7) If the zero vector is satisfied, then ()
A.B.
C.D.
Answer: ∴|a+b|2=|b|2, that is, (a+b)2=b2, which sort is A? b=- |a|2。
∴(|a+2b|-|2b|)2=a2+4a？ b =-| a | 2 & lt； 0,∴|a+2b|<； |2b|。 The answer is C.
6. (National Volume II, Question 5) Where? In ABC, it is known that D is a point on the side of AB. If =2, =, then? =
(A) (B) (C) - (D)
A: therefore, choose a.
It shows that there is basically no error in this problem under normal operation, unless the sign changes accidentally in the process of vector "shifting term".
7. (Question 9 of National Volume II) According to the vector A = (2,3), translate the image of function y=ex to get the image of y=f(x), then f(x)= 1
ex-3+2(B)ex+3-2(C)ex-2+3(D)ex+2-3
Answer: according to the law of "left plus right minus, up plus down minus" and the given quantity, the answer is C.
It shows that if the rules are not well related to the vector translation problem, it is easy to choose a, b or d.
8. (Tianjin Volume No.65438 +00) Set the sum of two vectors, where is the real number. If so, the value range of is ().
A.
Answer: λ+2=2m, ①.
, ②
Get from (1)
Get from ① ②
∴-6≤4m2-9m≤-2.
∴ ≤m≤2。
∴
The answer is a.
Explain that the ratio of two parameters is only converted into one parameter, and then find its value range.
9. (Chongqing VolumeNo. 10) As shown in Figure (10), in a quadrilateral,
,
,
The value of is ()
A.B. C. D。
Answer: by
get
∴
The answer is C.
Explain the simple application of cross product.
10. (Liaoning Volume No.3) If vectors A and B are not * * * lines, a? B≠0, the included angle between vectors A and C is ()
0 BC
Answer:.
So the angle between a and c is.
The answer is D.
1 1. (Liaoning Volume No.6) If the image of function y=f(x) is translated according to vector a, the image of function y=f(x+ 1)-2 is obtained, and vector a= ().
A.(- 1，-2) B.( 1，-2)c .( 1，2) D.( 1，2)
Answer: from y=f(x+ 1)-2, we get y+2=f(x+ 1), which is obtained by moving the image of function y=f(x) to the left by one unit and then to the lower by two units, so the vector a=(- 1).
The answer is a.
12. (Fujian Volume No.4) For vectors and real numbers, the correct proposition in the following propositions is ().
A. if a? B=0, then or B. If, then or
C.If, then or D. If A? b=a？ So, c
Answer: For A, a counterexample can be given: when a⊥b and a b=0.
For C, a2=b2 can only be deduced as |a|=|b|, while A = B cannot be deduced.
For D, a b= a c can be transferred to a⊥(b-c).
The answer is B.
(7) Mathematical elites solve the problem of "equation of straight line and circle"
1. (Hubei VolumeNo. 10) It is known that a straight line (a and b are nonzero constants) and a circle x2+y2= 100 have a common point, and the abscissa and ordinate of the common point are integers, so such a straight line * * exists.
60 years
Answer: Find the whole point, namely: (10,0), (8,6), (6,8), (0,10), (-6,8), (-8,6), (-10).
There are two types of straight lines passing through hours:
One is the secant of a circle, and every two points passing through this 12 point can be regarded as a straight line, among which six diameters and eight straight lines parallel to the coordinate axis are unqualified, that is, there are 66-6-8=52 secants;
One is that eight tangents passing through points that are not on the coordinate axis can make a circle.
So there are 52+8=60 such straight lines.
The answer is a.
Explain that a straight line is an intercept, so you should remove the straight line that passes through the origin and is parallel to the coordinate axis, and don't forget the tangent of the circle.
2. (Question 6 of Beijing Volume) If the plane area represented by the inequality group is a triangle, the range of a is
A.B.
C.D.
Solution: The area of a triangle has been determined by the first three conditions of the inequality group.
So x+y=a can only be in the interval between the two dotted lines in the figure.
In addition, therefore, a has two ranges.
The answer is D.
Explain that as long as the diagram is made, the problem will be clear at a glance.
3. (National Volume 1, Question 6) Of the four points given below, the point whose distance to the straight line is, and which lies in the indicated plane area is ().
A.B. C. D。
Answer: Look at the point that satisfies the first condition,1-1=1,-1+1.
1-(-1)+1= 3, excluding D. If x-y+ 1 is>0, we can rule out that B and A are dissatisfied.
x+y- 1 & lt； 0, so there is only C.
Explain the exclusion method, the first condition is related to the second condition, and you can kill two birds with one stone by listing all the items.
4. (Zhejiang Volume No.3) The equation about a straight line with symmetry is ()
A.B.
C.D.
Solution: according to the choice, which answer is added to the known straight line and divided by 2 to get x= 1, and only D can eliminate Y.
The answer is D.
Explain that because it is a multiple-choice question, you don't need to get points. When two straight lines are added and divided by 2, it is the axis of symmetry.
5. (Su JuanNo. 10) In the plane rectangular coordinate system, if the plane area is known, the area of the plane area is ().
A.B. C. D。
Solution: Let x+y = x, x-y = t, and we can get the plane area b = {(x, t) | s ≤ 1, s+t ≥ 0, s-t ≥ 0} from the meaning of the question.
And the answer is B.
6. (Tianjin Volume No.2) If the variables meet the constraints, the maximum value of the objective function is ().
a . 4 b . 1 1c . 12d . 14
Answer: Just draw a linear planning area, as shown below.
It can be seen that z=4x+y reaches the maximum at a (2 2,3) 1 1.
The answer is B.
Explain how to speak with pictures.
7. (Liaoning Volume No.8) The range of known variables X and Y that meet the constraint conditions is ().
A.b . c . d .[3，6]
A: The area represented by the constraint is as shown in the figure:
The geometric meaning of is the slope of the connecting line between the midpoint and the origin in the region.
∴ ∈ .
The answer is a.
Explain that this topic examines linear programming problems and the idea of combining numbers and shapes.