Mathematics problems in senior two.

Senior two last semester math final examination questions.

First, multiple-choice questions (this big question * * 12 small questions, 5 points for each small question, ***60 points)

1. Let the set be equal to ()

A.B. C. D。

2. If the solution set of inequality is (-1, 2), then the real number A is equal to ().

A.8 B.2 C.-4 D.-8

3. If point (a, b) is the moving point on the straight line x +2y+ 1=0, the maximum value of ab is ().

A.B. C. D。

4. Find the linear equation () which intersects the intersection of 2x-y- 10 = 0 and is parallel to the straight line of 3x-2y+4 = 0.

A.2x+3y+6 = 0 b . 3x-2y- 17 = 0 c . 2x-3y- 18 = 0d . 3x-2y- 1 = 0

5. The distance from the center of the circle to the straight line is ()

A.B. C. D。

6. If the real semi-axis length of hyperbola is 2 and the focal length is 6, then the eccentricity of hyperbola is ().

A. 7th century BC

7. The chord length of the straight line L passing through the focus of the ellipse and perpendicular to the X axis cut by the ellipse is ()

A. 3 D BC

8. The focal coordinate of the ellipse is ().

A.(0，0)，(0，-8)B.(0，0)，(-8，0)C.(0，0)，(0，8)D.(0，0)，(8，0)

9. The shortest distance from point to point on the curve (including parameters) is ().

A.B. C. D。

10. The vertex of the parabola is at the origin, the axis of symmetry is the coordinate axis, and the focus is on the straight line, then the equation of the parabola is ().

None of the above is true.

1 1. In the same coordinate system, the curve of the equation is roughly ().

12. In the Cartesian coordinate system xOy, it is known that the equations of straight lines on three sides of △AOB are respectively, so the total number of integral points (that is, points with integer abscissa and ordinate) inside and on both sides of △AOB is ().

A.95 B.9 1 C.88 D.75

II. Fill in the blanks (4 small questions in this big question, 4 points for each small question, *** 16 points)

13. One focus of the ellipse is.

14. Known straight line x = a(a >；; 0) is tangent to the circle (x-1) 2+y 2 = 4, so the value of a is

15. As shown in the figure, F 1, F2 is the left and right focus of the ellipse, point P is on the ellipse, and △POF2 is a regular triangle with area, so the value of b2 is.

16. The domain of the function is _ _.

Third, answer the question (this big question * * 6 small questions, ***74 points)

17. Solve the inequality about x:. (12)

18. Let it be two fixed points, and the ratio of the distance from the moving point P to the point A to the point B is constant. Find the trajectory of the point P, (12).

19. A factory uses two kinds of raw materials A and B to produce two kinds of products A and B. It is known that the quantity of raw materials needed to produce 1t A and 1t B respectively, the profit that can be obtained and the existing raw materials of the factory are shown in the following table. Q: Under the existing raw materials, how much can products A and B be produced separately to maximize the total profit? The relationship between products and raw materials is as follows:

A product

(1t) product b

(1t) Total raw materials

(ton)

A raw material (t) 2 5 10

Raw material B (t) 5 3 18

Profit (ten thousand yuan) 4 3

(12)

20. It is known that the vertex of a parabola is at the origin, and its directrix passes through the right focus of the curve and is perpendicular to the X axis.

Parabola and hyperbola intersect at point (), and find the equation of parabola and hyperbola. (12)

2 1. Given the ratio of a point to two fixed points, the distance from a point to a straight line is 1. Find the equation of the straight line. (12)

22. It is known that the focus of an ellipse is, and the intersection of a straight line passing through point F2 and perpendicular to the X axis and the ellipse is B, and two different points on the ellipse satisfy the conditions that,, and form a arithmetic progression.

(i) solving the equation of the ellipse;

(II) Find the abscissa of the AC midpoint of the chord. (14)

Reference answer

First, multiple-choice questions (this big question * * 12 small questions, 5 points for each small question, ***60 points)

The title is123455678911112.

Answer A C C B A C C D B C D B c d b c d b

2. Fill in the blanks (this big question has four small questions, each with 4 points, *** 16 points)

13. 1 14.3 15. 16.(- 1,0)

Three. Answer the question (this big question is ***6 small questions, ***74 points)

17. Solution: The original inequality can be simplified as

When a> 1 sometimes exists (an inequality in the middle can be omitted)

When 0

∴ When a> is 1, the solution set of inequality is: When 0

18. Solution: Let the coordinates of the fixed point p be (x, y).

simplify

When, in order.

When a= 1, it is simplified to x = 0.

So when, the trajectory of point P is a circle with center and radius;

When a= 1, the trajectory of point p is the y axis.

19. solution: assume that products a and b are xt and yt respectively, and the total profit is z million yuan.

Depending on the meaning of the question, the available constraints are as follows

Make a feasible region as shown in the figure: the objective function z=4x+3y,

Make a straight line l0: 4x+3y = 0, and then make a set of straight lines parallel to l0.

L: 4x+3y = z, when the straight line L passes through point P, z=4x+3y gets the maximum value.

From, the intersection p is obtained.

So there is

Therefore, when producing 2.5 t A products and 1t B products, the total profit is the largest, which is 1.3 million yuan.

20. Solution: According to the meaning of the question, the distance from the focus of parabola to the directrix is 2C (that is, the focal length of hyperbola).

Let the equation of parabola be ∵ parabola passing point ①.

It can also be seen from ① ② that ② is available.

The equation of parabola is, and the equation of hyperbola is

2 1. Solution: The coordinate of the set point is, which is set by the question.

End ... ① Because the distance from point to point is 1,

So ∞, the equation that the slope of a straight line is a straight line is ... (2).

Substitute Formula ② into Formula ① for solution, and the coordinates of points substituted into Formula ② are as follows

Or; or

The equation of a straight line is or.

22. Solution: (1) Starting from the definition and conditions of ellipse.

Yes, again, so.

So the elliptic equation is