Huanggang city 20 10 autumn final exam ninth grade mathematical simulation test questions
(Proposer: Huang Sheng from Zhudian Middle School in Xishui County)
1. Multiple choice questions: (3 points for each of the 6 small questions in this question, *** 18 points)
1. The following four playing card patterns belong to central symmetry ().
2. If the whole newspaper is similar to half a newspaper, the aspect ratio of this newspaper is ()
a . 2∶ 1 b .∶ 1 c . 4∶ 1d .∶ 1
3. A store holds a prize-winning sales activity in the following ways: every purchase of goods over 10 yuan will be given a lottery ticket, and every 1000 lottery tickets will be a lottery unit, with a grand prize of 1, 40 first prizes and 60 second prizes. Then 10 yuan's commodity lottery winning probability is
A B C D
4. If the sum of the inner angles of a regular polygon with a side length of 2 is twice the sum of its outer angles, the radius of the regular polygon is ().
A.2 B.3 C. 1 D. 12
5. The following statement is incorrect ()
(1) the arcs of equal central angles are equal; ② The diameter of the bisector is perpendicular to the chord; ③ The circle is an axisymmetric figure; Any diameter is its axis of symmetry; (4) two equal-length arcs are equal-length arcs.
1。
6. Square, square and square positions are shown in Figure 4. If the point is on the line segment and the side length of the square is 4, the area is: ()
a、 10 B、 12 C、 14 D、 16
Fill in the blanks (***8 small questions, each with 3 points. * * * 24 points)
7. If x:y:z=2:3:4, then _ _ _ _ _
8. It is known that the radii of two circles are 2 and 6 respectively, and the center distance is 5, so the positional relationship between the two circles is _ _ _ _ _ _ _ _ _ _ _ _ _.
9. If known, the value of the algebraic expression is _ _ _ _ _ _ _ _ _
10. A chord divides a circle into two parts: 2:3, so the degree of the circumferential angle subtended by this chord is _ _ _ _ _ _ _ _ _ _ _.
1 1. Move the factors other than the root number in the quadratic root into the root number, and the result is _ _ _ _ _ _ _ _ _ _.
12. The equation x2+kx+ 1= 0 about x If two x 1 and x2 satisfy the condition: x 1- x2 = 1, then k =.
13. Given that the generatrix length of the cone is 5cm, the diameter of the bottom surface is 6cm, and the surface area of the cone is (the result is still π).
14. Xiao Min did well in this year's school sports meeting. The function H = 3.5t-4.9T2 can describe the change of the height of the center of gravity when he takes off. So the time for him to reach the highest center of gravity after jumping is
Iii. Answering questions (out of 78)
15.( 12 minutes) Solve the equation: (1). (2).
16.(8 points) Find the value of the known decimal part.
17 .( 10) "Five? In order to attract readers, a bookstore has set up a turntable that can rotate freely (as shown in the figure, the turntable is divided into 12 copies), which stipulates that readers can get a chance to rotate the turntable every time they buy a book with a price of 100 yuan. If the turntable stops and the pointer is just aimed at the red, yellow and green areas, then the reader can get 45 yuan, 30 yuan and green respectively.
(1) Write the probability that the turntable rotates once to get the 45 yuan book coupon;
(2) Which way do you think is more cost-effective for readers, the turntable or the book coupon? Please explain the reason.
18.( 12 minutes) As shown in the figure, a point is a point inside an equilateral. Rotate the point clockwise and connect.
(1) Verification: it is an equilateral triangle;
(2) When, try to judge the shape and explain the reasons;
(3) Inquiry: When it is how many degrees, is it an isosceles triangle?
19.( 12 minutes) As shown in the figure, in the isosceles trapezoid ABCD, AD ‖ BC. O is the midpoint of CD edge, with O as the center, OC length as the radius as the circle, BC edge passing point E ⊥ E as EH⊥AB, and vertical foot as H. O and AB edges are known.
(1) Verification: OE ‖ AB; (2) verification: EH = AB；; (3) If, the value of.
20.( 12 points) There is a kind of crab that can only survive for two days at most when caught from the sea. If kept in a pond, the survival time can be prolonged, but a certain number of crabs die every day. Assuming that the individual quality of crabs is basically unchanged during the stocking period, an existing dealer buys 1000 kg of live crabs at the market price and raises them in the pond. At this time, the market price is 30 yuan per kg. Thereafter, the market price per kilogram of live crabs can be increased by 1 yuan per day. However, all kinds of fees need to be paid for stocking for one day, with an average of 10 kg of crabs dying every day. Assuming that all the dead crabs are sold on the same day, the price is 20 yuan per kilogram.
(1) Let the market price per kilogram of live crabs after X days be P yuan, and write the functional relationship between P and X;
(2) If live crabs are sold once after X days, the total sales of 1000 kg crabs is Q yuan, and write the functional relationship between Q and X. 。
(3) How many days after the dealer hoards the crabs and sells them, can he get the maximum profit (profit = Q- total purchase)?
2 1.( 12 minutes) As shown in the figure, in the plane rectangular coordinate system, translate the parabola to the left by 1 unit, and then translate it down by 4 units to get a parabola. The obtained parabola intersects the axis at two points (the point is to the left of the point), intersects the axis at one point, and the vertex is.
( 1);
(2) the judgment of shape, and explain the reasons;
(3) Whether there is a point on the line segment to make it similar. If yes, find out the coordinates of the point; If it does not exist, explain why.
Reference answer
1-6 BBDADD
7.
8. Intersection
9.289
10.72 or 108.
1 1.
12.
13.24πcm2
14.s
15.( 1) , ; (2) , .
16.2
17.
18.( 1) Proof:
According to the meaning of the question: △ APB△ ADC
So AP = ad, ∠ BAP = ∠ CAD,
So ∠ BAP+∠ cap = ∠ CAD+∠ cap.
So ∠ BAC = ∠ pad
Because ABC is an equilateral triangle
So ∠ BAC = 60
So ∠ pad = 60
So △ADP is an equilateral triangle.
(2) ∠ODC=60 from (1) and ∠ADC=BOC= 150,
So ∠ADO= 150-60=90.
So △AOD is a right triangle.
(3) Solution:
1) when DP = DC
Because DP = AP and DC = BP.
So pa = Pb
And because PC = PC, AC = BC.
So △ ACP△ BCP
So ∠ ACP = ∠ BCP = 60/2 = 30
Because ∠ BPC = 1 10.
So APC = 1 10.
So ∠ APB = 360-110 * 2 =140.
X = 140。
2) when DP = CP
Because DP = AP
So pa = PC
And because Pb = Pb and AB = BC.
So △ ABP △ CBP
So ∠ APB = ∠ CPB = 1 10.
X = 1 10。
3) when CP = CD
Because CD = BP
So CP = BP
Because AP = AP, AB = AC.
So △ ABP △ ACP
So ∠ APB = ∠ APC
So ∠ APB = (360-110)/2 =125.
X = 125。
To sum up, when x = 140 or x = 1 10 or x = 125.
△DPC is an isosceles triangle
19.
20.( 1) from the meaning of the question: p=30+x,
(2) Understand from the meaning of the problem
The sales volume of live crabs is (1000- 10x) (30+x) yuan.
The sales of dead crabs is 200x yuan.
∴q=( 1000- 10x)(30+x)+200x=- 10x2+900x+30000.
(3) Let the total profit be
l = Q-30000-400 x =- 10 x2+500 x
=- 10(x2-50x)=- 10(x-25)2+6250。
When x=25, the total profit is the largest, and the maximum profit is 6250 yuan.
2 1. Solution: The vertex coordinate of (1) is (0,0).
Vertex coordinates,
.3 points
(2) Derived from (1).
When,
.
.
.4 points
When,,
Point coordinates are.
Vertex coordinates again, 5 points
Make the symmetry axis of parabola intersect with this point.
Make an axis at this point.
In,;
In,;
In,;
,
This is a right triangle. 7 points
(3) existence.
According to (2), it is an isosceles right triangle,
Connect, pass through the point, do it at the point,
.
(1) If, then
, that is.
,
.
,
.
The point is in the third quadrant,
. 10 point
(2) if, then
, that is.
,
.
The point is in the third quadrant,
.
To sum up, there are two points similar to those in ① and ②, and the coordinates are. 12 respectively.