Ninth grade math final exam questions
Seat number
First, multiple-choice questions: this big question * * 10 small questions, 3 points for each small question, * * 30 points.
1, in the rectangular coordinate system, the coordinates of point p (-2,3) with respect to the origin symmetry point q are
A.(2，-3)b .(2，3)c .(3，-2)d .(2，-2，-3)
The hour hand of the clock keeps turning, from 6 am to 9 am.
The rotation angle is
A, B, C, D and IX
3, the root of the equation is
A. BC, BC,
4. A bird flies freely in the air and then lands on the picture at will.
In one of the squares shown (every square is exactly the same except the color), and then
The probability of a bird stopping in a black square is.
A.B. C. D。
In an opaque plastic bag, there are red and white balls ***40, all of which are the same except the color. After touching the ball many times, Xiao Ming found that the frequency of touching the red ball was stable at around 15%.
Then the red ball in the pocket may have
a，4 B，6 C，34 D，36。
6. A chemical fertilizer plant produced M fertilizer in the first quarter, and then produced X% more than the previous quarter.
If the fertilizer produced in the third quarter is N, the equation can be listed as follows
Answer. m( 1+x)？ =n B. m( 1+x%)？ =n
c。 ( 1+x%)？ =n D. a+a (x%)？ =n
7. The following statement is true.
A, =+= 3+4 b, the root of equation 2x2=x is x =
C, the arcs of equal chords are equal to d, and it will rain tomorrow is a random event.
8. The radii of two circles are known, which are two equations and two circles respectively.
If the center distance is 1, the positional relationship between two circles is
A. Externalization B. Insectization C. Intersection D. Externalization
9. If the radius ⊙o is 13, the chord AB∑CD, AB = 24, and CD = 10, the distance between AB and CD is
A, 7 B, 17 C, 7 or 17 D, 34
10. As shown in the figure, a semicircle O with the waist CD of right-angled trapezoid ABCD as the diameter is known.
Tangent to the upper bottom AD, the lower bottom BC and the waist AB of the trapezoid, and the tangent points are respectively
Is d, c, e. If the radius of semicircle O is 2 and the waist AB of trapezoid is 5,
So the perimeter of the trapezoid is
10
Fill in the blanks: this big question is ***8 small questions, each with 3 points ***24 points.
1 1.2-=
12. For a circle with a diameter of 12cm, the chord length that bisects the radius vertically is cm.
13. If the algebraic expression is meaningful, the value range of m is.
14. One side of the triangle is 10, and the other two sides are X of a quadratic equation. -14x+48 = 0, then this triangle is a triangle.
15. Given that point A (a, 2) and point B (-1, b) are symmetrical about the origin o, the value of is _.
16. As shown in the figure, AB is the diameter of circle O, point C is on the extension line of AB, and CD is tangent to points O and D of circle.
If ∠ c = 18, ∠CDA=.
(Question 16) (Question 17)
17. As shown in the figure, in circle O, ∠ AOB = 60, AB = 3 ㎝, then the length of the lower arc AB is.
18. If real numbers A and B are satisfied, the value of a+b is _ _ _ _ _ _.
Third, the solution: this big question is ***7 small questions, with ***66 points. Write the necessary words to prove the process or calculus steps when answering.
19, (8 points) calculation: 3 ÷+(- 1) 2
20.(8 points) Simplify before evaluating: (-), where x =+ 1,
y=- 1，
2 1, (8 o'clock) As shown in the figure, AB is the diameter ⊙ O, and C is a point on ⊙ O. If AC=8㎝, AB= 10㎝, and OD⊥BC is at point D, what is the length of BD?
22.( 12 points) The opaque pocket is filled with red, yellow and blue balls (everything else is the same), including two red balls and one blue ball 1 piece. The probability of finding the red ball now is.
(1). Find out the number of yellow balls in the bag;
2. Touch a ball for the first time (don't put it back). Touch the ball for the second time. Please use tree diagram or list method to find the probability that all balls are red.
23.(8 o'clock) As shown in the figure, in the plane rectangular coordinate system, the quadrilateral ABCD is called "basic figure", and the coordinates of each point are A (4 4,4), B (1, 3), C (3 3,3) and D (3 3,0/) respectively.
(1) Draw a quadrilateral a 1 b 1 c 1 d 1, and find A1,B1,C1,D/kloc.
A 1(，)，B 1(，)，C 1(，)，D 1(，)；
(2) Draw the symmetrical figure a2b2d2 of the "basic figure" about the X axis.
(3) Draw the quadrilateral A3b3c3d3, so that the figure composed of the quadrilateral A3B3C3D3 and the first three figures is both central symmetric and axisymmetric.
24.( 10) A certain district left an open space of 1798 square meters during the construction of the district, preparing to build a rectangular open-air swimming pool. As shown in the design, the length of the swimming pool is twice as wide, with a 5-meter-wide open space in front of the swimming pool and a 2-meter-wide road and a 1 meter-wide green belt on the other three sides.
Please calculate the length and width of swimming pool.
(2) If the swimming pool is 3 meters deep, you need to stick tiles on the bottom floor and wall (***5 faces). Please calculate the total area to be tiled.
25.( 12 points)
As shown in figure 15, in Rt△ABC, ∠ B = 90 bisector, ∠A intersects BC at D, E is a point on AB, and DE=DC, with D as the center and the length of DB as the radius, draw a circle.
It is proved that (1)AC is the tangent of ⊙D; (2)AB+EB=AC .
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