Zhejiang education printing plate ninth grade mathematics volume one final examination questions
First, multiple-choice questions * * * This big question * * 10 small questions, 4 points for each small question, ***40 points. Give four points for each small question.
Only one option meets the requirements of the topic. Please fill in the answers in the brackets after the question * *
1. If □+2=0, then the real number in□ is * * * *.
A.-2 B- c . d . 2
2. In ⊿ABC, if the length of each side is enlarged by 2 times at the same time, the sine and cosine values of acute angle A are * * * * * *.
A. both of them have been expanded by 2 times. B. both are reduced by 2 times. C. Both remain the same. D. The sine value is enlarged by 2 times, and the cosine value is reduced by 2 times.
3. The approximate images of distance s and time t are shown in the left figure below, and the approximate images of speed v and time t are * * * * * *.
o
A.B. C. D。
Xiao Ming plays table tennis with two classmates, and uses the game of "palm of hand and back of hand" to decide the order of appearance.
People have the same possibility every time, hitting the heart and the back of the hand with their hands. If one person is different from the other two, this person will be the last one.
Field. Three people push at the same time, and the probability that Xiao Ming finally pushes in the game is * * * * * *
A.B. C. D。
5. As shown in the figure, in ABCD, AB= 10, AD=6, E is the midpoint of AD, and take a little F on AB as.
△CBF∽△CDE, then the length of BF is * * * * * *
? A.5？ B.8.2？ C.***？ D. 1.8
6. What is the probability that any of the 9 natural numbers from1to 9 is a multiple of 2 or a multiple of 3?
A.B. C. D。
7. As shown in the figure, the sides of the small squares are all L, so the shaded part of the triangle in the figure below is * * * * similar to △ABC.
A B C D
8. As shown in the figure, △ABC is known. Take any point o, even AO, BO and CO, and take the middle point.
D, e, f, get △DEF, then the number of the following statements is * * * * * *
①△ABC and△△△ def are similar graphs; ②△ABC and△△△ def are similar graphs;
③ The perimeter ratio of △ ABC to △DEF is1:2; ④ The area ratio of △ ABC to △DEF is 4: 1.
A. 1
9. The image of known quadratic function passes through points A * * 1, 2***, B***3, 2***, C***5, 7***. If the points M * *-2, Y 1 * *, N * *.
A.y 1
10. In a match of 1500m, there are the following judgments: A said: C is the first, and I am the third; B said: I am the first, and Ding is the fourth; C said, secondly,
I won the third place. As a result, everyone only got one sentence right, so it can be judged that the first place is * * * * * *.
Antidepressants.
Two. Fill in the blanks * * * This big question * * 6 small questions, with 5 points for each small question and 30 points for * * *. Please fill in the answer on the line * * *
1 1. It is known that the * * section of a flat roof is the width of an isosceles triangle * * and the design inclination of the top of the slope * * * as shown in Figure * * *.
The design height is _ _ _ _ _ _ _.
* * * No.65438 +0 1 map * * * No.65438 +04 map * * * * No.65438 +05 map * * *
12. If there is a right-angled trapezoidal part, the length of the inclined waist is, then the length of the other waist of the part is _ _ _ _ _ _ _ _. * * * The result is not approximate * * *
13. On a photocopied piece of paper, the length of the base of the isosceles triangle is changed from 3 cm in the original picture to 6 cm, and the length of the waist is changed from 6 cm in the original picture.
2 centimeters became centimeters.
14. The images of quadratic function and linear function are as shown in the figure, then
The value range of is _ _ _ _ _.
15. As shown in the figure, the quadrilateral ABCD is a rectangle, and there is only one intersection point between the semicircle with BC diameter and the AD side, and AB=x, then the shaded part.
The area of is _ _ _ _ _ _.
16. there is a Rt△ABC, ∠A=, ∠B=, AB= 1. Put it in a plane rectangular coordinate system so that the hypotenuse BC is on the X axis.
The right vertex A is on the inverse proportional function y=, so the coordinate of point C is _ _ _ _ _ _ _.
Three. Answer * * * This big question * * 8 small questions, ***80 points, the answer should be written in words, and the proof process or calculus process * * *
17.*** The full mark of this question is 8 * * *
At Christmas, Xiaoming himself made a conical Santa Claus hat out of cardboard. The diameter of the conical cap bottom is 18 cm, and the bus length is 36 cm. Please accurately calculate the cardboard area needed to make such a conical hat.
18.*** The full mark of this question is 8 * * *
Class 9 * * 1 * * will elect1monitor and 65438 monitor respectively. At present, there will be two boys A and B and two girls C and D running for office. Please find out the probability of two girls being elected monitor and monitor at the same time by listing or drawing a tree diagram.
19.*** The full mark of this question is 8 * * *
In class, teachers and students explore together, and the inner diameter of cylindrical pipeline can be measured with a ball with known radius. After Xiao Ming came home, he put a small ball with a radius of 5 cm on the mouth of the thermos cup. After thinking, he found a measurement method and drew a sketch, as shown in figure * * *. Please provide help according to the information in the picture.
Xiao Ming calculates the inner diameter of the thermos cup.
20.*** The full mark of this question is 8 * * *
A sealed container with variable volume is filled with a certain amount of carbon dioxide. When the volume of the container changes, the density of the gas will also change. The unit of density * * * is the inverse proportional function of the unit of volume * * * *: m3 * *, and its image is as shown in the figure.
* * *1* * find the functional relationship between them, and write the range of independent variables;
***2*** Find the current gas density.
2 1.*** The full mark of this question is 10 * * *
As shown in the figure, in the diamond ABCD, point E is on the CD, connecting AE, and extending the extension line with BC.
This line intersects at point F.
* * *1* * Write all similar triangles in the diagram * * No need to prove * * *;
* * * 2 * * If the side length of rhombic ABCD is 6 and DE: AB = 3: 5, try to find the length of CF. 。
22.*** The full mark of this question is 12 * * *
As shown in the figure, AB is the diameter of ⊙O, and the point P is the moving point * * P on ⊙O, which is not connected with A and B * * *, connecting AP and PB, and the intersection point O is OE⊥AP in E and OF⊥BP in F respectively.
* * *1* * If AB= 12, will the length of line segment EF change when point P moves on ⊙O? If yes, please explain why. If it will not change, request the length of EF;
* * * 2 * * If AP=BP, it is proved that the quadrilateral OEPF is a square.
23.*** The full mark of this question is 12 * * *
In class, Miss Zhou raised the following questions. Xiao Ming and Xiao Cong perform on the blackboard respectively. Please also answer this question:
On a rectangular ABCD paper, AD=25cm, AB=20cm. Now fold this paper as shown in the figure below, and find out the length of the crease separately.
* * * 1 * * as shown in figure1,the crease is AE;
* * * 2 * * As shown in Figure 2, P and Q are the midpoint of AB and CD respectively, and the crease is AE;
* * * 3 * * As shown in Figure 3, the crease is EF.
24.*** The full mark of this question is 14 * * *
As shown in the figure, in △ABC, AC=BC, ∠ A = 30, AB =. Now let's make a triangle.
The vertex D of the 30-degree angle in the plate moves on the side of AB, so that the two sides of this 30-degree angle intersect with the sides AC and BC of △ABC at points E and F, and connect de, d F and EF, so that DE is always perpendicular to AB. Let the area of △DEF be.
*** 1*** Draw a graph that meets the requirements, write a triangle that must be similar to △ADE * * * Does not include this triangle * * *, and explain the reasons;
* * * 2 * * * Can EF and AB be parallel? If yes, request the length of AD at this time; If not, please explain the reasons;
***3*** Find out the functional relationship between independent variables and write the range of independent variables. What is the maximum value? What is the maximum value?
answer
First, multiple-choice questions * * * This big question * * 10 small questions, each small question is 4 points, ***40 points * * *
1.A 2。 C 3。 A 4。 C 5。 D
6.C 7。 B 8。 C 9。 B 10。 B
II. Fill in the blanks * * * This big question * * 6 small questions, with 5 points for each small question and ***30 points for * * *
1 1. 12.5 13.4 14.
15. 16.*** ,0***,*** ,0***,*** ,0***,*** ,0***
Three. Answer this big question * * * 8 small questions, ***80 points * * *
17.*** The full mark of this question is 8 * * *
Solution: 2 points.
= material1018cm2 .................................................... 6 points.
18.*** The full mark of this question is 8 * * *
Solution: The tree diagram is analyzed as follows:
Four points.
As can be seen from the tree diagram, the probability of two girls being elected as monitor and vice monitor is =.......................4 points.
* * * Ellipsis list method * * *
19.*** The full mark of this question is 8 * * *
Solution: even OD, ∵ EG = 8, OG = 3, even number.
∴ GD = 4,3 points.
Therefore, the inner diameter of the thermos cup is 8 cm. ..................................................................................................................................................................
20.*** The full mark of this question is 8 * * *
Solution: * * *1* * * ... 4 points.
***2*** When used, = 1kg/m3. .............................................................................................................................................
2 1.*** The full mark of this question is 10 * * *
Solution: * * *1* * △ ECF ∽△ ABF, △ECF∽△EDA, △ ABF ∽△ EDA. ......................................................................................................
* * * 2 * * *∫de:ab = 3:5，∴ DE: EC = 3: 2 ......................................................................................................................
∫△ECF∽△EDA, ∴, ............................................................ 2 points.
∴ .............................................. 3 points.
22.*** The full mark of this question is 12 * * *
Solution: * * *1* * ef has the same length. ...............................................................................................................................................
OE⊥AP in e key, OF⊥BP in f key,
∴ AE=EP, BF=FP, ................................................. 2 points.
∴ ............................................ 2 points.
* * * 2 * * *∫AP = BP, while ∵OE⊥AP is in E, OF⊥BP is in F,
OE = of, 3 points.
∵ AB is the diameter ⊙O, ∴∠ P = 90, ............................... 1 min.
∴ Opf is a square. Two points for ............................................
* * * or use, ap = bp, ∴ OE=OF to prove * * *
23.*** The full mark of this question is 12 * * *
Solution: * * 1 * * * ∵ From the folding, it can be known that △ABE is an isosceles right triangle.
∴ AE = AB = 20cm ............................................... 3 points.
***2*** ∵ According to folding, AG=AB, ∠GAE=∠BAE.
Point p is the midpoint of AB,
∴ AP= AB，
∴ AP= AG，
At Rt△APG, ∠ gap = 60, ∴∠ EAB = 30, .................................................................................................................................
In Rt△EAB, AE = ab = cm .................................................................... 2 points.
* * * 3 * * * point is EH⊥AD at point H, even BF.
According to folding, DE=BE,
af = fg，DF=AB，GD=AB，∴△abf?△GDF，
∫∠GDF =∠CDE，GD=CD，∴ Rt△GDF≌Rt△CDE，
∴ DF=DE=BE，
At Rt△DCE, DC2+CE2=DE2,
CB = 25，CD=20，202 + CE2=***25-CE***2，
∴ CE=4.5，BE=25-4.5=20.5，HF=20.5-4.5= 16， .............................................................................................................
At Rt△EHF,
∫EH2+HF2 = FE2，202 + 162=FE2，
∴ ef = = cm .............................................. 3 points.
24.*** The full mark of this question is 14 * * *
Solution: * * 1 * * * Graphics Example: Deduct 2 points for correct graphics.
△ Ade ∽△BFD
* ∴∠fdb=60 de⊥ab,∠edf=30，
∵∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠873
∴△ ade ∽△ BFD ............................................................................1min.
***2***EF can be connected in parallel with AB, ................ 1 min.
At this time, in the right angle △ADE, DE=,
At right angles △DEF, EF=, ............... 1 min.
△DBF, bd =, ∴ DF=, .............................. 1 min in the right angle.
And DF=2EF, ∴ =,
∴ .................................................. 2 points.
***3***, that is,
Three points
When, the maximum value = ......................................... 2 points.