Mathematics examination questions for the final exam of senior one 1. Multiple choice questions: (5 points for each small question, ***60 points)

1, the straight line equation that passes through the point (-1, 3) and is perpendicular to the straight line x-2y+3=0 is ().

a、x-2y+7=0 B、2x+y- 1=0

c、x-2y-5=0 D、2x+y-5=0

2. As shown in the figure, the front view and the left view of space geometry are equilateral squares.

The top view is circular, so this geometry is ().

A, prism B, cylinder C, frustum D, cone

3. straight line: ax+3y+ 1 = 0,: 2x+(a+ 1) y+ 1 = 0, if ∨, then a= ().

A, -3 B, 2 C, -3 or 2 D, 3 or -2

4. Given circle C 1: (x-3) 2+y2 = 1, circle C2: x2+(y+4) 2 = 16, the positional relationship between circle C 1 and C2 is ().

A, intersection b, phase separation c, inscribed d, circumscribed

5. In the arithmetic series {an}, the tolerance takes the maximum value of the sum of the previous items ().

A, 5 B, 6 C, 5 or 6 D, 6 or 7

6, if it is a geometric series, and the first n terms, then ()

A, B,

7. If the variables x and y satisfy the constraints y 1, x+y0 and x-y-20, the maximum value of z=x-2y is ().

a、4 B、3

c、2 D、 1

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8. When a is an arbitrary real number and the straight line (a- 1)x-y+a+ 1=0 passes through the fixed point c, the equation of a circle with the center of c and the radius of 5 is ().

a、x2+y2-2x+4y=0 B、x2+y2+2x+4y=0

c、x2+y2+2x-4y=0 D、x2+y2-2x-4y=0

9. The curve expressed by the equation is ()

A, a circle B, two semicircles C, two circles D, semicircles

10, in △ABC, a is an acute angle, lgb+lg( )=lgsinA=-lg, then △ABC is ().

A, isosceles triangle b, equilateral triangle c, right triangle d, isosceles right triangle

1 1, let p be the moving point on a straight line, the intersection point p is two tangents of circle c, and the tangents are a and b respectively, then the minimum area of quadrilateral PACB is ().

a、 1 B、C、D、

12. Let the equations of two straight lines be x+y+a=0 and x+y+b=0 respectively. It is known that A and B are two real roots of the equation x2+x+c=0.

And 0 18, the maximum and minimum values of the distance between these two straight lines are () respectively,

A, B, C, D,

Volume 2 (non-multiple choice questions ***90 points)

Fill in the blanks: (5 points for each small question, * * * 20 points)

13, and the coordinates of point A and point B in the spatial rectangular coordinate system are (1, 1, 2) and (2, 3, 4) respectively, then _ _ _ _

14, Equation _ of a straight line that crosses the point (1 2) and has the same intercept on two coordinate axes.

15, if the real number satisfies the following value range

16, acute triangle, if, then the following statement is correct.

① ② ③ ④

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Three. Problem solving: (where 17 is 10, and each is 12, ***70).

17, the ratio of the distances from point P(2, -5) to point A(3, -2) and point B(- 1, 6) is 1: 2, and the equation of straight line l is found.

18. In △ABC, A, B and C are opposite sides of A, B and C respectively, 2sin A=3cos A,

(1) If a2-c2=b2-mbc, find the value of m;

(2) If a=3, find the maximum value of △ABC area,

19. The investor invested 720,000 yuan to build a vegetable processing factory in a development zone, and invested1200,000 yuan in the first year, with an annual increase of 40,000 yuan thereafter. Since the first year, the annual vegetable sales revenue is 500,000 yuan, assuming that the total net profit in the first n years (f(n)= the total income in the first n years, the total expenditure in the first n years, and an investment amount),

(1) In what year did the factory start to make profits?

(2) A few years later, in order to develop new projects, investors have two treatment plans for the factory: ① When the annual average net profit reaches the maximum, they will sell the factory for 480,000 yuan; ② When the total net profit reaches the maximum, the factory will be sold for 654.38+10,000 yuan. Which scheme is more cost-effective?

20. There is a circular village with a radius of 3. A and B start from the center of the village at the same time. B always goes north, and A always goes east first. Shortly after leaving the village, they changed direction and went along a straight line tangent to the perimeter of the village. Later, they happened to meet B. We assume that A and B have a certain speed, and the speed ratio is 3: 1. Where did they meet?

2 1, let the sum of the first n items in the series be, if there is any positive integer n,

(1) Assume and verify that the sequence is a geometric series, and find the general term formula.

(2) Find the sum of the first n items in the sequence,

22. The known curve C: x2+y2-2x-4y+m = 0.

(1) When m is a value, curve c represents a circle;

(2) If curve C and straight line x+2y-4=0 intersect at two points M and N, and OMON(O is the origin of coordinates), find the value of M. ..