Ninth grade mathematics volume I final quality test questions
1. Multiple choice questions (L2 is in this big question * * *. Of the four options given in each question, only one is correct. Please select the correct option. For each question, get 3 points for correct answer, 0 points for wrong answer, and do not choose or choose multiple answers. )
1. The following figure is centrosymmetric, but not axisymmetric ().
2. The eye chart is no stranger to us. The picture is a part of the eye chart, in which the transition between two E's with upward openings is ().
A. Translation B. Rotation
C. Symmetry D. Potential similarity
3. calculation: tan45? +sin30？ =( )
Article 2 (2) (3) (iv)
Xiao Ming put 12 pages of the same size in the handout folder, including 4 pages of Chinese, 2 pages of mathematics and 6 pages of English. He randomly selected 1 page from the lecture folder, and the probability that the selected paper happens to be a math paper is ().
A.B. C. D。
5. As shown in the figure, in the square grid of, rotate around a certain point, and the center of rotation can be ().
A.e point b point f point
C. point g, point d and point h.
6. Move the parabola to the left by 1 unit, and then move it up by 3 units, then the analytical formula of the parabola after translation is
A.B.
C.D.
7. As shown in the figure, the vertices of △ABC are all lattice points in a square grid, so cos? ABC equals ()
A, B, C, D,
8. The image of quadratic function y=ax2+bx+c is shown in the figure. If point A (1, y 1) and point B (-6, y2) are two points on the image, then the size relationship between y 1 and y2 is ().
A.y 1y2 D. Not sure.
9. As shown in the figure, AC is the diameter of ⊙O, BD is the chord of ⊙O, and EC∨AB intersects with ⊙O in E, then the graph and? BOC equiangular * * * has ()
A.2 B. 3 C. 4 D.5
10. As shown in the figure, the side length of each small square is 1, so the triangle (shaded part) in the following figure is similar to that in the left figure ().
1 1. As shown in the figure, ⊙ is the inscribed circle of △ABC, and the tangents are,, and known respectively. And then what? The degree is ()
.35 caliber? B.40？
C.45？ D.70？
12. As shown in the figure, the diameter of the semicircle, the small circle inscribed with the semicircle, and the tangent point, if the radius ⊙ is, the functional relationship is ().
A.B.
C.D.
One, two, three total scores
19 20 2 1 22 23 24 25 26
2. Fill in the blanks (this big question ***5 small questions, ***20 points, only the final result is needed. Get 4 points for each small question. )
13. Take any 9 natural numbers from 1 to 9, and the probability that this number can be divisible by 2 is.
14 As shown in the figure, steel balls are often used in engineering to measure the diameter of holes in parts. Suppose the diameter of the steel ball is 10mm, and the distance from the top of the steel ball to the surface of the part is 8mm, as shown in the figure, the diameter of this hole is mm. 。
15. Given that the generatrix length of a cone is 5, the bottom radius is 3, and its side area is.
16, as shown in the figure, Xiao Ming measures the shadow length of a tree as 2m at a time and 8m at a time. If two beams of sunlight are perpendicular to each other, the height of the tree is _ _ _ _ meters.
17, the image of the quadratic function is shown in the figure, so in the three formulas ①, ② and ③, _ _ _ _ _ _ _ _ _ (serial number) has a positive value.
Third, answer questions (this big question is ***7 small questions. ***64 points. The solution is to write the necessary text description, proof process or calculation steps. )
18, ((1) 4 points, (2) 5 points, ***9 points)
(1) calculation:+
(2) Part of the parabola is shown in the figure.
(1) Find the resolution function;
(2) Write two correct conclusions related to images:
, .
(Symmetry axis equation, except the coordinates of the intersection of the image with the positive and negative X axis and the Y axis)
19. (The full mark of this question is 7) As shown in the figure, the detector of the hot air balloon shows that the elevation angle of the top B of a tall building is 45 degrees with the hot air balloon. Look at the depression angle of C at the bottom of this tall building. Is it 60? The horizontal distance between the hot air balloon and the tall building is 50 meters. Find the height of this building (take 1.45438+04 and 1.732).
(1) Please write down all possible situations of the two teams in the first game in an appropriate way (represented by codes A, B, C, D, E and F);
(2) Find the probability that both teams are military art troupes in the first game, P.
2 1. (The full mark of this question is 9 points) As shown in the figure, AB is known as the diameter ⊙O, and the straight line CD is tangent to ⊙O at point C, and AC is equally divided. DAB。
(1) verification: AD? CD；
(2) If AD=2 and AC=, find the length of AB.
22. (full mark of this question 10) As shown in the figure, in the parallelogram ABCD, point A is AE? BC, the vertical foot is E, the connecting line DE, and F is a point on the line segment DE, and? AFE=？ B.
(1) Verification: △ ADF ∽△ dec;
(2) If AB=4, AD=3 and AE=3, find the length of AF.
23. (Full score for this question 10) There is a kind of grape: it can only be kept for a week at most when it is picked from the tree. If stored in the cold storage, the fresh-keeping time can be extended, but a certain number of grapes go bad every day. Assuming that the weight is basically unchanged during the fresh-keeping period, an individual businessman has bought 200 kilograms of this grape at the market price and put it in the cold storage. At this time, the market price is 2 yuan per kilogram. It is estimated that after that, every year,
(1) Fresh grapes are sold once after X days of storage. Assuming that the sales amount of fresh grapes is Y yuan, write the functional relationship between Y and X;
(2) In order to make the sales amount of fresh grapes reach 760 yuan and empty the cold storage as soon as possible, it needs to be sold out in a few days;
(3) Ask the self-employed, how many days will they store these grapes and sell them at one time to get the maximum profit. What is the maximum profit? (This question does not require writing the range of independent variable X)
24. (Subject 12 points) As shown in the figure, in the plane rectangular coordinate system, point A (10,0), with OA as the diameter, makes a semicircle C in the first quadrant, and point B is the moving point on the semicircle, connecting OB and AB, extending AB to point D, so that DB=AB and intersection D are the vertical lines of the X axis respectively.
(1) When? AOB=30？ When, find the length of arc ab;
(2) When DE=8, find the length of the line segment EF;
(3) When the intersection point E is between O and C during the movement of point B,
Is there a triangle with vertices e, c and f in phase with △AOB?
If yes, request the coordinates of point E at this time; If it doesn't exist,
Please explain the reason.
The answer to the final quality examination paper of the first volume of ninth grade mathematics
1.B 2。 D 3.c 4。 C 5。 C 6。 C 7。 B 8。 A nine. C 10。 B 1 1。 A 12。 B
13. 14.8 15. 16.4 17.① ②
18、 + .
= =
19、
Solution: Because the parabola passes through (1, 0) (0,3), the solution is:
20. Solution: (1) Draw a tree diagram from the meaning of the question as follows:
B.C.
D E F D E F D E F
All possible situations are: (a, d), (a, e), (a, f), (b, d), (b, e), (b, f), (c, d), (c, e), (c, F).4 points.
(2) There are 9 possible equal possibility results, among which there are 3 results in which both teams are Army Art Troupe in the first game, so P (both teams are Army Art Troupe) = .7 points.
2 1, answer: (1) proof: link BC. 1.
The straight line CD is tangent to o at point c,
DCA=？ B. 2 points
∫ communication split? DAB，DAC=？ Taxi. ADC=？ ACB.3 points
∵AB is the diameter ⊙ O, ACB=90? . ADC=90？ , that is, AD? CD.5 points
(2) Solution: ∵? DCA=？ b，？ DAC=？ Taxi? △ADC∽△ACB.6 points
AC2 = AD? AB。
AD = 2，AC=，？ AB= .9 points.
22.( 1) Prove that the ∵ quadrilateral ABCD is a parallelogram.
? AD∨BC，AB∨CD，
ADF=？ CED？ B+？ C= 180？ .
∵? AFE+？ AFD= 180，？ AFE=？ b，
AFD=？ C.
? △ADF∽△DEC.6 point
(2) Solution: ∵ Quadrilateral ABCD is a parallelogram,
? AD∨BC CD = AB = 4。
∵AE？ BC，？ AE？ Advertising.
In Rt△ADE, DE=
∫△ADF∽△DEC，？ . ? . AF=. 10 point
23. Solution: (1) Fresh grapes are sold once after X days. If the total sales amount of fresh grapes is Y yuan, there are three points.
A: A few minutes.
(3) If this batch of grapes is stored for X days for sale, there are
Therefore, this batch of grapes can be sold after being stored for 45 days, and the maximum profit can be 405 yuan 1 minute.
24.( 1) link BC,
∫A( 10，0)，？ OA= 10，CA=5，
∵? AOB=30？ ,
ACB=2？ AOB=60？ ,
? The length of arc AB =；; 4 points
(2) connecting OD,
∵OA is⊙ C diameter, OBA=90? ,
AB = BD，
? OB is perpendicular bisector of AD,
? OD=OA= 10，
In Rt△ODE,
OE=，
? AE=AO-OE= 10-6=4，
By who? AOB=？ ADE=90？ -? OAB？ OEF=？ Drug control bureau,
Get △OEF∽△DEA,
? , that is,? EF = 3； 4 points
(3) Let OE=x, and when the intersection point E is between O and C, it is defined by points E, C and F..
A triangle with vertices is similar to delta △AOB,
what's up ECF=？ Bao Er or? ECF=？ OAB，
1 When? ECF=？ In BOA, at this time △OCF is an isosceles triangle, and point E is OC.
Midpoint, ie OE=,? E 1(，0)； (2 points)
2 When? ECF=？ At OAB, CE=5-x, AE= 10-x,
? CF∨AB, where CF=,
∫△ECF∽△EAD，
? That is, the solution is,
? E2(，0)； (2 points)