Ninth grade mathematics last semester final review training questions

(This training question is divided into three major questions, full score 120, training time *** 120 minutes. )

First, multiple-choice questions (this big question 10, ***30 points):

1. Known =, where a≥0, then the condition that B meets is ()

A.b<0 b.b ≧ 0 c.b must be equal to zero D. Not sure.

2. The analytical formula of a given parabola is y= -(x-3)2+ 1, and its fixed-point coordinate is ().

A.(3， 1) B.(-3， 1) C.(3，- 1) D.( 1，3)

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

4. Given (1-x)2+=0, the value of x+y is ().

A. 1

5. In the school sports meeting, Xiao Ming's shot put made a hole with a diameter of 10cm and a depth of 2cm, and the diameter of the shot put was about ().

A.10cm B.14.5cm C.19.5cm D.20cm.

6. At the New Year's party, the class committee of Class 9 (1) designed a game to give winners A and B one of two different prizes. Now the names of the prizes are written on the same cards, with the back arranged neatly, as shown in the figure. If the card with the second prize written on it is placed in the shadow, the probability that the winner Xiaogang will win the second prize is ().

A.B. C. D。

By the end of 2007, a city had afforested 300 hectares. After two years of afforestation, the afforestation area has increased year by year, reaching 363 hectares by the end of 2009. Let the average annual growth rate of afforestation area be x, and the listed equation is correct ().

a . 300( 1+x)= 363 b . 300( 1+x)2 = 363

c . 300( 1+2x)= 363d . 300( 1-x)2 = 363

8. It is known that the unary quadratic equation x2 +mx+4=0 about x has two positive integer roots, so the possible value of m is ().

Morning & gt0b.m > 4 c-4，-5 D.4，5

9. As shown in the figure, in order to save the handling effort, Xiao Ming rolled a cubic wooden box with a side length of 1m on the ground along the straight line L from the initial position without sliding. After rolling for one week, the curved surface ABCD, which was originally in contact with the ground, falls back to the ground, so the length of the path taken by point A 1 is ().

A.()m B.( )m

C. Doctor of Medicine

10. As shown in the figure, it is known that the straight line BC cuts ⊙O at point C, PD is the diameter of ⊙O, the extension line of BP and CD intersects at point A, ∠ A = 28, ∠ B = 26, then ∠PDC is equal to ().

34 BC to 36 BC

II. Fill in the blanks (this big topic is 6 small questions, *** 18 points):

1 1. Known = 1.45438+04, then (keep two significant figures).

12. If the radii of two circles are two in the equation x2-3x+2=0, and two

If two circles intersect, the range of the distance d between the two circles is.

13. If the function y=ax2+3x+ 1 has only one intersection with the X axis, the value of a is.

14. As shown in the figure, it is known that the large semicircle O 1 is inscribed with the small semicircle O2 at point B, and the chord MN of the large semicircle is tangent to the small semicircle at point D. If MN∑AB, when MN=4, the area of the shaded part in this figure is.

15. In order to encourage consumers to ask for invoices from merchants, the state has formulated certain incentives. Among them, there are four kinds of invoices for 100 yuan (the appearance is the same, and the reward amount is sealed with a sealed label): 5 yuan, 50 yuan and thank you. Now a merchant has 1000 100. The reward of this 1000 invoice is shown in the following table. If a consumer spends 100 yuan and asks the merchant for an invoice, the winning probability of 10 yuan is.

5 yuan150 yuan, 0 yuan Thank you for asking.

Quantity: 50, 20, 10, and the rest.

16. As shown in the figure, AB is the diameter ⊙O, CD is the chord, and CD⊥AB is in E. If CD=6 and OE=4, the length of AC is.

Three. Solution (8 questions in this big question, ***72 points):

17.(6 points) Calculation:.

18.(6 points) Solve the equation: x2-6x+9=(5-2x)2.

19.(8 points) Simplify before evaluating:

Where a is the solution of equation 2x2-x-3=0.

20.(8 points) As shown in the figure, it is known that there are three concentric circles, and the three vertices of the equilateral triangle ABC are on three circles respectively. Please rotate this triangle clockwise around point O 120 and draw △A/B/C/. Draw with a ruler, don't draw, leave a mark.

2 1.( 10) There are only two different colors of red balls and yellow balls in the sealed pocket. If you randomly take a ball out of your pocket, the probability is.

(1) Find the functional relationship between y and x;

(2) If you take six red balls out of your pocket, and the probability that one of them is a red ball is zero, how many red balls and yellow balls are there in your pocket?

22.( 10) In order to measure the accuracy of a circular part, two right-angle triangular rulers with the same size and an angle of 30 degrees were designed on the processing line, and the measurement was carried out according to the schematic diagram.

(1) If ⊙O is tangent to AE and AF at points B and C respectively,

Where the edges of DA and GA are on the same straight line. Verification:

oa⊥dg；

(2) In the case of (1), if AC= AF, and

AF=3, find the length BC of the arc.

23.( 12 point) As shown in the figure, the intersection of parabola y=-x2+bx+c and X axis is A, and the intersection with Y axis is B, OA and OB (OA

(1) Find the coordinates of point A and point B;

(2) Find the analytical expression of this parabola and the coordinates of vertex d;

(3) Find the coordinates of another intersection point c between this parabola and the X axis;

(4) Is there a point P on the straight line BC, which makes the quadrilateral PDCO trapezoid? If it exists, find the coordinates of point P; If it does not exist, explain why.

24.( 12 minutes) As shown in the figure, in the rectangular coordinate system xoy, point A (2,0) and point B are in the first quadrant and △OAB is an equilateral triangle. The positive semi-axis of the circumscribed circle of △OAB intersects with the Y axis at point C, and the tangent of the circle passing through point C intersects with the X axis at point D. 。

(1) Determine whether point C is the midpoint of arc OB? And explain the reasons;

(2) Find the coordinates of point B and point C;

(3) Find the resolution function of straight CD;

(4) Point P is on the line segment OB, and the quadrilateral OPCD is equal.

Waist trapezoid, find the coordinates of point p.

Reference answer:

First, multiple-choice questions: BADCB, BBCCB.

Second, fill in the blanks:

1 1.0. 17; 12. 1 & lt； d & lt3; 13.a= or 0;

14.2 ; 15.； 16.3 .

Third, answer questions:

17. solution: the original formula =1-(2-1)+2 =1-1+2-=+2.

18. Solution: x2-6x+9=(5-2x)2, (x-3)2=(5-2x)2,

[(x-3)+(5-2x)][(x-3)-(5-2x)]=0

∴x 1=2,x2=。

19. solution: original formula =()(a+ 1)= 1

= ,

From the equation 2x2-x-3=0: x 1=, x2=- 1,

But when a=x2=- 1, the score is meaningless; When a=x 1=, the original formula =2.

20. Omit.

2 1.( 1) from the meaning of the question:, arranged as: y =；;

(2) Judging from the meaning of the question, the solution: x= 12, y=9, a: omitted.

22. solution: (1) proof: connect OB, oc, ∵AE, AF is the tangent of ⊙O, BC is the tangent point,

∴∠ oba =∠ OCA = 90, which is easy to prove ∠ bao =∠ cao;

∠EAD=∠FAG，∴∠dao=∠gao； ;

∠ Dag = 180, ∴∠ Dao = 90, ∴OA⊥DG.

(2) Because ∠ OCA = ∠ OBA = 90 and ∠ EAD = ∠ FAG = 30, ∠ BAC =120;

And AC= AF= 1, ∠ OAC = 60, so OC=, the length of the arc BC is.

23. Solution: (1)∵x2-6x+5=0, and the two real roots are OA and OB (OA

∴oa= 1,ob=5,∴a( 1,0),b(0,5).

(2) ∵ parabola y=-x2+bx+c, the intersection with the x axis is a, and the intersection with the y axis is b,

The solution is,

∴ The analytic formula of quadratic function is y=-x2-4x+5,

Vertex coordinates are: d (-2,9).

(3) The coordinate (-5,0) of another intersection point c of this parabola and the X axis.

(4) The analytical formula of linear CD is y=3x+ 15,

The analytical formula of BC line is: y = x+5;

① If CD is taken as the cardinal number, the analytical formula of OP∑CD and straight line OP is y=3x.

So there is,

Solution:

The coordinate of point p is (5/2, 15/2).

② If OC is the cardinal number, DP∨CO,

The analytical formula of straight line DP is: y=9,

So there is,

Solution:

∴ The coordinate of point P is (4,9),

There is a point p on the straight line BC,

The quadrilateral PDCO is made into a trapezoid,

And the coordinates of point p are (5/2, 15/2) or (4,9).

24. solution: (1)C is the midpoint of arc OB, connecting AC,

∴ac ∵oc⊥oa is the diameter of a circle,

∴∠abc=90；

△ OAB is an equilateral triangle,

∴∠ABO=∠AOB=∠BAO=60，

∠∠ACB =∠AOB = 60，

∴∠COB=∠OBC=30，

∴ arc OC= arc BC,

That is, c is the midpoint of arc OB.

(2) Let B BE⊥OA be at point E, ∫ A (2,0), ∴OA=2, OE= 1, BE=,

∴ The coordinate of point B is (1,);

∫C is the midpoint of the arc OB, CD is the tangent of the circle, and AC is the diameter of the circle.

∴AC⊥CD,AC⊥OB,∴∠CAO=∠OCD=30，

∴OC= ,∴C(0)。

(3) In △COD, ∠ COD = 90, OC=,

∴OD=, ∴D (,0), ∴ The analytical formula of linear CD is: y= x+.

(4)∵ Quadrilateral OPCD is an isosceles trapezoid,

∴∠CDO=∠DCP=60，

∴∠OCP=∠COB=30 ,∴PC=PO.

The crossing point p is PF⊥OC in f,

And then ∴PF=

The coordinates of point p are: (,).