First, multiple-choice questions (this big question * * 10 small question, 3 points for each question, 30 points for * * *)

The range of 1. real number is meaningful, so the value range of x is ().

a . x > 1 b . x≥l c . x < 1d . x≤ 1

2. Among the following traffic signs, the one with both central symmetry and axial symmetry is ().

3.(08 Guangzhou) The following statement is true ()

A "80% probability of rain tomorrow" means that it will rain 80% of the time tomorrow.

B "The probability of flipping a coin is 0.5" means that every time a coin is flipped twice, 1 coin faces up.

C "Lottery winning probability is 1%" means that buying 100 lottery tickets will definitely win.

D "The probability of throwing cube dice with odd faces is 0.5" means that if the dice are thrown many times, the average number of points is odd, that is, every two times 1 time.

4. It is known that the radius of the cone bottom is 1cm, the length of the bus is 3cm, and its total area is ().

aπb 3πc 4πd 7π

5. If known, the value of is ().

A.- 1。

6.(08 Dezhou) If the constant term of the unary quadratic equation about X is 0, the value of m is equal to.

A. 1

C. 1 or 2 d.0

7. If the quadratic equation of x has two real roots, the range of k is ().

A.B. - 1 C. D

8. As shown in the figure, it is the diameter, the point is at the top, it is the midpoint, it is the moving point on the diameter, and the minimum value is ().

A.B. C. D。

9. (Guang 'an Curriculum Reform in 2008) As shown in Figure 9- 1 Put four cards on the table, one of which is rotated 180o, and poker is placed as shown in Figure 9-2, so the rotated cards start from the left.

Figure 9- 1 Figure 9-2

A. the first b, the second c, the third d and the fourth

10. (Dezhou, 08) As shown in the figure, AB is the diameter ⊙O, AD = DE, AE and BD intersect at point C, then the angle equal to ∠BCE in the figure is

A.2 B.3 C.4 D.5

Fill in the blanks (this big question has ***8 small questions, 4 for each small question, ***32 points)

1 1. If established, the condition is.

12. The arc arch bridge has a span of 12m and an arch height of 4m. Then the diameter of the circle where the bridge arch is located is.

13. (Double cypress in 2008) is ⊙O in diameter, ⊙O in cut, ⊙O in cross, and connected. If, the degree is.

14. It is called a real number and its value is.

15. As shown in the figure, in quadrilateral ABCD, ∠BAD=∠C=90? 0? 2, AB=AD, AE⊥BC in E, if AE=5, then S quadrilateral ABCD= =.

16. (Guang 'an Curriculum Reform in 2008) Fifty Fuwa cards, the mascots of Beijing Olympic Games, are the same in size, texture and back pattern, and placed face down on the desktop. Randomly select one of them, put the Fuwa's name drawn on the front of the card back to its original place as it is, wash it and draw it again, and repeat the above process. Finally, it was recorded that the frequency of pumping Huanhuan was 20%, so the Huanhuan in these cards was probably _ _.

17. (Adapted) For any real number, the specified meaning is, then when,

18. In rectangular ABCD, AB=5, CD= 12. If two circles centered on A and C are tangent, then point D is within ⊙C, and point B is outside ⊙ C ... Then the range of radius R of ⊙A is _ _ _ _ _ _ _ _.

Third, solve the problem (this big question is 8 small questions, out of 58 points)

19. Calculation (***8 points)

① ; ②

20. Solve equations (***8 points)

(Formula solution) ②

21.(* * * 6 points) (Fuzhou, 2008) As shown in the figure, in the middle, the coordinates of the point are (4,2).

(1) Draw 3 units and then pan down;

(2) Draw a counterclockwise rotation around this point, and find the route length from this point to this point (the result is reserved).

22. (* * * 6 points) (Yiwu, 08) "If one party is in trouble, all parties will support it". The Wenchuan earthquake in Sichuan touched the hearts of people all over the country. A hospital in our city is going to choose a doctor and a nurse from three doctors A, B and C and two nurses A and B to support Wenchuan.

(1) If a doctor and a nurse are randomly selected, all possible results are represented by tree diagram (or list method);

(2) Find the probability of choosing doctor A and nurse A accurately.

23.(8 points) As shown in the figure, a naval base is located at A, with an important target B at 200 nautical miles due south, and an important target C at 200 nautical miles due east. Island D is located at the midpoint of AC, and there is a supply dock on the island: Island F is located on BC, just south of Island D, and a warship sails from A to C at a constant speed. Generally, supply ships depart from D at the same time, along the southwest.

(1) How many nautical miles are there between Island D and Island F?

(2) It is known that the speed of warships is twice that of supply ships. On the way from B to C, the warship met the supply ship at point E, so how many nautical miles did the supply ship sail when they met? (The result is accurate to 0. 1 nautical mile)

24. (6 points in this question) As shown in the figure, ⊙I is the inscribed circle of △ABC, AB=9, BC=8, CA= 10, points D and E are points on AB and AC respectively, and d E is the tangent of ⊙I,

Find the perimeter of △ADE.

25. (Self-made questions) (8 points) Explore the mysteries in the table below, fill in the blanks and complete the following questions.

Factorization of quadratic trinomial with two roots of quadratic equation in one variable

(1). If the unary quadratic equation () has a solution, please factorize the quadratic trinomial.

(2) Using the above conclusions, factorize the quadratic trinomial.

26. (* * * 8 points) (Guang 'an Curriculum Reform in 2008) As shown in Figure 26- 1, in equilateral △ABC, AD⊥BC is at point D, and the circle with the same diameter as AD is tangent to BC at point E, tangent to AB at point F and connected to EF.

(1) Judge the positional relationship between EF and AC (no need to explain the reason);

(2) As shown in Figure 26-2, the horizontal E is the vertical line of BC, which intersects G and meets AC, so as to judge the shape of the quadrilateral ADEG and explain the reasons.

(3) Determine the position of the center O and explain the reasons.

Nine grades first volume comprehensive examination questions

First, multiple-choice questions (this big question * * 10 small question, 3 points for each question, 30 points for * * *)

1.B 2。 D 3。 D 4。 C 5。 A six. B 7。 D 8。 B 9。 B 10。 D

Fill in the blanks (this big question has ***8 small questions, 4 for each small question, ***32 points)

1 1.

12. 13m

13.

Solution: Tangent ⊙O is the diameter of ⊙O,

∴ .

,∴ .

∴ .

14. 13

Solution: according to the meaning of the question, it is so, so.

That's why. So ...

At this time, from the conditional equation, we can get,

therefore

15.25

16. 10

17.2

18. 1∠r∠8， 18∠r∠25。

Third, solve the problem (this big question is 8 small questions, out of 58 points)

19. Solution: (1) Original formula =

(2) Original formula =

20.20、① ②

2 1. solution: (1) sketch;

(2) sketch. The route length from point A to point A2 is =

22. Solution: (1) Use tabular method or tree diagram to represent all possible results as follows.

(1) list method: (2) tree diagram:

A b

A (A, A) (A, B)

B (B, A) (B, B)

C (C, A) (C, B)

(2) (Just choose doctor A and nurse A)=

What is the probability of choosing doctors and nurses?

23. solution: (1) connect DF, and then connect DF⊥BC.

∵AB⊥BC, AB=BC=200 nautical miles.

∴AC= AB=200 nautical miles, ∠ C = 45 degrees.

∴CD= AC= 100 nautical mile

DF=CF，DF=CD

∴ df = cf = CD =×100 =100 (nautical mile)

Therefore, the distance between Island D and Island F is 100 nautical mile.

(2) Assuming that the supply ship sailed X nautical miles when they met, then DE=x nautical miles, AB+BE=2x nautical miles,

EF=AB+BC-(AB+BE)-CF=(300-2x) nautical miles

In Rt△DEF, the equation can be obtained according to Pythagorean theorem.

x2= 1002+(300-2x)2

Finishing, 3x2-1200x+100000 = 0.

Solving this equation, we get: x1= 200-≈118.4.

24. From the tangent length theorem, it can be concluded that the circumference of △ADE is 9.

25. Solution:

(2) Solving equations

So =

26. Solution: (1)EF//AC.

(2) The quadrilateral ADEG is a rectangle.

Reason: ∵EG⊥BC, ∴AD//EG, that is, the quadrilateral Adeg is a rectangle.

(3) The center O is the intersection of AC and EG.

Reason: connecting FG, it can be known from (2) that EG is the diameter, ∴FG⊥EF,

It is also known from (1) that EF//AC, ∴AC⊥FG,

If the quadrilateral ADEG is a rectangle, if the quadrilateral adeg is a rectangle, then AG is the tangent of the known circle.

And AB is also the tangent of the known circle, AF=AG,

AC is the perpendicular bisector of FG, so AC must pass through the center of the circle.

Therefore, the center o is the intersection of AC and eg.

Note: it can also be demonstrated according to △ ago △ AFO.