Junior high school mathematics simulation test paper has the answer.

Simulated test questions for senior high school entrance examination 4 2009.5

First, multiple choice questions

1. Among the following real numbers, the irrational number is ().

A.B. C. D。

2. As shown in the figure, there is a cubic paper box with triangles, squares and circles drawn on three sides. Now use a pair of scissors to cut along its edge to form a plane figure. The expanded figure can be ().

3. If is, the value of is equal to ().

University of California, Los Angeles or

4, in the following equation, there is a real root is ()

A.B.

C.D.

Xiaohua saw the clock on the wall behind him in the mirror. What time do you think is the closest to 8 o'clock ()?

6. As shown in figure AD⊥CD, AB = 13, BC = 12, CD = 3, AD = 4, then sinB= ().

A, B, C, D,

7. The two triangles in Figure 2 are similar figures, and their similar centers are ().

A.b., c.d.

8. In a square ABCD, e and f are the midpoint of AB and BC respectively, and AF and DE intersect at point O, then = ()

A.B. C. D。

9. As shown in the figure, the side length of an equilateral triangle is equal to the circumference of the circle circumscribed by one side. When the circle rotates from a certain position along the three sides of an equilateral triangle in the direction of the arrow until it returns to its original starting position, the circle rotates.

A.4 laps B.3 laps C.5 laps D.3.5 laps

10, in memory of the victims of the Wenchuan earthquake in Sichuan, on the first day of the national mourning day, the national flag rose to the top of the flagpole at a uniform speed in a school, and then dropped to the middle of the flagpole at a uniform speed after a pause of 3 seconds. The approximate image that can correctly reflect the functional relationship between China flag height H (m) and flag-raising time T (s) in this process is as follows.

1 1, the image of quadratic function is shown in the figure, then the following relationship is incorrect ().

a 、< 0 B 、> 0 C 、> 0 D 、> 0

12, as shown in the figure, the straight line AB is tangent to the point C with a radius of 2 ⊙O, D is the point above ⊙O, and ∠ EDC = 30, and the chord EF‖AB, then the length of EF is ().

The second century BC.

fill (up) a vacancy

13, calculation: =

14, decomposition factor:.

15. As shown in Figure 5, D is the midpoint of the AB side and will be folded along a straight line passing through D,

Let point A fall at f on BC, and if so, then _ _ _ _ _ _ _ degrees.

16, given that A, B and C are on the same straight line, M and N are the midpoint of line segments AB and BC respectively, AB = 60 and BC = 40, then the length of MN is.

17, about the quadratic equation of one variable is known. If the two real roots of this equation are and satisfy, the value of is.

Third, answer questions.

Eating zongzi on Dragon Boat Festival is a traditional custom of the Chinese nation. On the morning of the fifth day of May, my mother prepared four zongzi for Yang Yang: one with sausage stuffing, one with red dates stuffing and two with assorted stuffing. The four zongzi are all the same except the inner stuffing. Yang Yang likes to eat zongzi with various fillings.

(1) Please use the tree diagram or list method to predict the probability that eating two zongzi is just assorted stuffing for Yang Yang;

(2) Before eating zongzi, Yang Yang is going to use the turntable as shown in the figure to carry out the simulation test of eating zongzi (this turntable is divided into four sectors on average, and the position of the pointer is fixed. After rotating the turntable, it is allowed to stop freely, and one of the sectors will just stop at the position pointed by the pointer. If the pointer points to the intersection of two sectors, rotate the turntable again). It is stipulated that the turntable rotates twice in a row to eat two zongzi at random, so it is estimated that eating two zongzi is just mixing stuffing. Try to explain why.

19, as shown in the figure, in △ABC, D is a point above AC, CD=2DA, ∠ BAC = 45, ∠ BDC = 60, CE⊥BD, E is vertical foot, and AE is connected.

(1) Write all the equal line segments in the graph and prove them.

(2) Is there a similar triangle in the diagram? If yes, please write a pair; If not, please explain why.

(3) Find the area ratio of △BEC and △BEA.

20. A table tennis training hall is going to buy a brand 10 table tennis bat, each with a table tennis bat. It is understood that both supermarkets sell this brand of table tennis rackets and table tennis. The price of each racket is 20 yuan, and the price of each table tennis is 1 yuan. At present, both supermarkets are promoting sales. All the goods in the supermarket are 10% off (10% off the original price), and the supermarket buys 65438.

(1) If you only buy the required rackets and table tennis in one supermarket, is it more cost-effective to go to the supermarket or the supermarket?

(2) If necessary, please design the most economical purchase plan.

Wang Liang is good at improving his study methods. He found it best to review and reflect on the process of solving problems. One day, he spent 30 minutes studying independently. Suppose that the relationship between the time (unit: minutes) he spent solving problems and the amount of learning benefits is shown in Figure A, and the relationship between the time (unit: minutes) he spent reviewing and reflecting and the amount of learning benefits is shown in Figure B (which is part of a parabola and is

(1) Find the functional relationship between Wang Liang's learning income and problem-solving time, and write the range of independent variables;

(2) Find out the functional relationship between the learning gains of Wang Liang's review and the review time;

(3) How does Liang allocate the time for solving problems and reviewing and reflecting, so as to maximize the total learning benefit of these 30 minutes?

(The total amount of learning, the amount of learning to solve problems, and the amount of learning to review and reflect)

22. As shown in the figure, the diameter ⊙ is, the straight line passing through this point is the tangent of ⊙, and ⊙ is two points on ⊙, connecting,, and.

(1) Verification:;

(2) If it is a bisector, find the length.

23. As shown in the figure, in a square with a side length of 4, the points move from top to bottom, and the connecting lines intersect with the points.

(1) proves that no matter where the point moves, there is △△;

(2) When the point moves to what position, the area of △ is square;

(3) If a point moves from one point to another, and then continues to move to another point, delta is only an isosceles triangle when the point moves to what position in the whole moving process.

24. As shown in Figures ① and ②, in the plane rectangular coordinate system, the coordinate of a point is (4,0), a circle with a radius of 4 centered on a point intersects the axis, two points are chords, and the chords are moving points on the axis, and they are connected.

(1);

(2) As shown in Figure 1, when tangent to, find the length;

(3) As shown in Figure ②, when the point is on the diameter, the extension line of intersects with the point. Why an isosceles triangle?

2 1. Solution: (1) Hypothesis, substitute, and get.

The range of independent variables is:.

(2) when, setting,

Substitute, get,.

When was that?

(3) Let Wang Liang spend a few minutes reviewing and reflecting, and the total learning benefit is,

Then the time he spends solving the problem is minutes.

When.

When … increases, it decreases.

To sum up, when, at this time.

In other words, when Wang Lianghua takes 26 minutes to solve the problem and 4 minutes to review and reflect, the total learning benefit is the greatest.

23.( 1) Prove that no matter where a point moves in a square, it has = ∞ =∞△△

(2) Solution 1: When the area of △ is exactly the area of ABCD square,

If you pass a little Q, it means ⊥ yes, ⊥ yes, then =

= = ∴ =

Get the solution from △∞△

When ∴, the area of △ is square.

Solution 2: Establish a rectangular coordinate system as shown in the figure with the origin, and make the ⊥ axis at this point and the ⊥ axis at this point when passing through this point.

= = ∴ =

The point is located on the diagonal of the square ∴. The coordinates of this point are

∴ Intersection point (0,4), (The functional relationship between these two points is:

When the coordinate of point ∴ is (2,0).

When ∴, the area of △ is square.

(3) If △ is an isosceles triangle, then = or = or =

① When the point moves to coincide with the point, it is known that the quadrilateral is a square =

Delta is an isosceles triangle at this point.

(2) When the points overlap, the points also overlap. At this point =, △ is an isosceles triangle.

③ Solution 1: As shown in the figure, when the set point moves to the edge, there is =

∵ ‖ ∴∠ =∠

Once again ∵∞ =∞∞ =∞.

∴∠ =∠ ∴ = =

∵ = = =4

∴

That is, when delta is an isosceles triangle.

Scheme 2: Establish the rectangular coordinate system as shown in the figure with the origin. When a point moves on a plane, if there is an = passing point, the ⊥ axis is at this point, and the ⊥ axis is at this point, it is in δ, and ∞ = 45.

∴ =∴ The coordinates of this point are (,).

∴ Functional relationship between intersection and two points: +4

When =4, the coordinate of point ∴ is (4,8-4).

△ is an isosceles triangle when a point moves on a plane.

24. Solution: (1)∵,

∴: This is an equilateral triangle. ..................................................... (2 points)

(2)CP and tangent, ∴.

Again: (4,0), ∴.

...................... (5 points)

(3) (1) Over-time operation, foothold, delayed delivery,

∫ is the radius,

This is an isosceles triangle.