2. Let the equation of the straight line L be (m+2) x+3y = m, and calculate the value of m according to the following conditions. The intercept of (1)L on the x axis is -2 (2) and the slope is-1.
3. Given that a straight line L passes through point (-2,2) and forms a triangle with two coordinate axes, find the equation of the straight line.
4. It is known that the straight line L 1: X+ay-2A-2 = 0, L2: AX+Y- 1-A = 0. (1) if L 1‖L2, try to find the value of a (2) if L 1⊥L2, try to find the value of a. ..
5. Two parallel straight lines L 1 and L2 pass through points P 1( 1, 0) and P2 (0,5) respectively. (1) If the distance from L 1 to L2 is 5, let L 1 and L2 be the equation (2) for finding two straight lines.
6. circle x? +y？ +2x+4y-3 = 0 Distance from line L: x+y+ 1 = 0 is the coordinate of the point under root 2.
7. known cycle c 1: x? +y？ +2x+8y-8 = 0, circle C2: x? +y？ +4x-4y-2 = 0。 Try to judge the relationship between circle C 1 and circle C2.
8. Find the straight line x-y-5 = 0 and cross the circle X? +y？ -4x+4y+6 = 0。
9. On the way back to Hong Kong in a straight line, a ship received a typhoon rainstorm from the Meteorological Observatory: the typhoon center was located 70 kilometers west of the ship, and the affected area was a circular area with a radius of 30 kilometers. It is known that the port is located 40 kilometers north of the typhoon center. If the ship does not change course, will it be affected by the typhoon?
10. straight line y = x and circle x? +(y- 1)？ =r？ Tangent line, find the value of R.
1 1. Find the equation of the circle according to the following conditions. (1) The center of the circle is a point with a radius of 2 (0, 1). C(-2) is centered at point C (-2,-1) and tangent to the straight line 3x-4y-6 = 0. (3) The intersection points (0, 1) and (2, 1) have a radius of 5.
12. The arch span of circular arch bridge with holes is 20 m and the arch height is 4 m. The arch circle equation of this circular arch.
13. The standard equation of a circle whose center is at point (8, -3) when the circle passes through point P(5, 1).
14. Find the equation of a circle with C( 1 3) as the center and tangent to the straight line 3x-4y-7 = 0.
15. It is known that the center of the circle is on the straight line 2x+y = 0, and it is tangent to the straight line x+y- 1 = 0 at point (2,-1), so as to find the standard equation of the circle.
16. Find the equation of a circle with three points A (0,0) B (1,1) C (4,2), and find the radius length and center coordinates of the circle.
17. Given that the diameter endpoint of a circle is A(x 1, y 1)B(x2, y2), try to find the equation of this circle.
18. find two circles C 1: x? +y？ -4x+2y = 0, circle C2: x? +y？ Equation of a circle whose center is on the straight line L: 2x+4y- 1 = 0.
① given set A={y|y=x+ 1/x-1, x∈R, and x≠0}, b = {x | x > 0}, the largest element of A∩(B's complement to r) is
A.-2b 2c-3d 3
(2) A batch of goods traveled from City A to City B at a constant speed with the speed of V km/h on the 17 train. It is known that two subway lines are 400km long. For safety reasons, the distance between two trucks should not be less than (v/20)? Km, how soon can all these goods be shipped to B city? (I don't remember the conductor)
③ Let y=f(x) be the odd function on R, and f(x+2)=-f(x). F(x)=x when-1≤x≤ 1? .
(1) Try to prove that the straight line x= 1 is the symmetry axis of the image of function y=f(x).
(2) when trying to find x∈, the analytical formula of f(x)
(3) if a = {x || f (x) | > a, x ∈ r}, and A≦? , the range of the real number A.
④ The following five relationships:? ∈{0},{? },0∈? ,{? }? {0}, where the correct number is ()
A. 1
⑤ known set a = {x | x? -4mx+2m+6=0, x∈R}, b = {x | x < 0, x ∈ r}, if A∩B≦? , the range of the real number m
6. The known function f(x)=2sin(x/4)cos(x/4)-2√3sin? (x/4)+√3
1. Find the minimum positive period and maximum value of function f(x)
2. Let g(x)=f(x+π/3) judge the parity of the function and explain the reasons.
First, multiple-choice questions (* * 12 small questions, 4 points for each small question, ***48 points)
(1) Set,,, and then CU.
(A) (B) (C) (D)
(2) The domain of the function is
(A) (B) (C) (D)
(3)
(A) (B) (C) (D)
(4) Yes, if, then
(A) (B) (C) or (d) or
(5) The following functions are power functions.
(A) (B) (C) (D)
(6) If the function is known, the value of is
1 (C) (D) 2
(7) move the image of the function to the left in parallel by one unit length, and then move it upward in parallel by 1 unit length to obtain
What is the arrival analytic function?
(A) (B)
(C) (D)
(8) The size relationship between and is
(A) (B) (C) (D) Not sure.
(9) If,, and,, then the size relationship is
(A) (B) (C) (D)
(10) If the real number is full, then three known vertices and one point in the plane satisfy:
Feet:, then the value of is
(A) (B) (C) (D)
The number of zeros of the (1 1) function in the interval is
(A) 3 (B) 5 (C) 7 (D) 9
A fish tank with a height of (12), the axial section of full tank water is as shown in figure 1, and the bottom of the fish tank touches a small hole, from which the full tank water flows out.
If the depth of the fish tank is 0 and the volume of water is 0, the approximate image of the function is
(A) (B) (C) (D)
Fill in the blanks (***4 questions, 4 points for each question, *** 16 points)
(13) If the included angle of the vector is, then.
(14) If, the image of the function always passes through the fixed point.
(15) Let it be an odd function in the world, when,
Then.
(16) draws the following conclusions:
① The function is odd function;
② The minimum positive period of the function is:
③ An axis of symmetry of the function image is:
(4) The function has a single reduced interval at the top.
The serial number of the correct conclusion is (fill in the serial number of all correct conclusions).
Three. Problem solving (***6 small questions, * * 56 points, problem solving should be written in words, proof process or calculus steps)
(17) (full mark for this question)
Known sets, and,
The range of realistic figures.
(18) (full mark for this question)
In rectangular coordinate system, it is known that,,.
(i) If it is an obtuse angle, and, find.
(ii) the value, if any.
(19) (the full mark of this question is 10)
As shown in Figure 2, it is known that it is a sector with radius and central angle, a moving point on the arc of the sector, and the sector is inscribed with a rectangle. Remember, what is the maximum area of a rectangle when taking the corner? Find this maximum area.
Figure 2
(20) (The full mark of this question is 10)
Known functions, (where and).
(i) Find the domain of the function;
(2) Judge the parity of the function and give the proof;
(iii) If yes, the range of the function is the value of a real number.
(2 1) (the full mark of this question is 10)
Known, and it is two equations, try to find out:
The value of (i);
(2) the value.
(22) (The full mark of this question is 10)
Known vector,, where, the maximum value of the function is set to.
(i) Find the analytical formula of the function;
(ii) setting and finding the maximum and minimum values of the function and the corresponding values;
(iii) If it is true for any real number, find the range of the number.