Mathematics Test
Note: 1. The whole volume is divided into Volume I and Volume II, with a total of 8 pages. The first volume is multiple choice, and the second volume is non-multiple choice.
90 minutes, full mark 100.
2. Before answering the question, please fill in the name, candidate number, subject code, examination room number and seat number on the answer sheet; Write the examination room, room number, seat number, examinee number and name on the sealed line of Book II. Do not make any marks on the answer sheet and test paper.
3. The first volume of multiple-choice questions (1- 10), after choosing the answer to each question, write the corresponding question on the answer sheet with 2B pencil.
The answer label is blacked out. If you need to change it, clean it with an eraser and choose another answer. If the answer is written in the first volume, no extra points will be given. The answer (1 1-22) to the non-multiple choice questions in volume 2 must be written in the designated position of the topic in volume 2.
After the exam, please return the test paper and the answer sheet together.
The first volume (multiple choice questions, ***30 points)
First, multiple-choice questions (this big question * * 10 small questions, 3 points for each small question, 30 points for * * *)
Each question gives four answers, only one of which is correct. Please use 2B pencil to erase the corresponding answer label on the answer sheet.
The absolute value of 1 -3 equals
A. the third century BC.
2. As shown in figure 1, the top view of the cylinder is
Figure 1 A B C D
3. During the period of1-May this year, the accumulated local general budget revenue of Shenzhen is 216.58 million yuan, and the data is accurate to 216.58 million yuan.
A. Billion quantile
4. In the following figure, the axis symmetry is
A B C D
5. The solution set of the following inequality groups is represented on the number axis, as shown in Figure 2.
A.B.
Figure 2
6. In order to know the students' study at home on Saturday and Sunday, the head teacher visited six students in the class and got to know their situation.
The study time at home is shown in the following table. The learning styles and average learning time of these six students are as follows
A.4 hours and 4.5 hours
Student name Xiaoli Xiaoming Xiaoying Xiaohua Xiaole Shawn
Study time (hours) 4 6 3 4 5 8
B.4.5 hours and 4 hours
C.4 hours and 3.5 hours
D.3.5 hours and 4 hours
7. The image of this function is shown in Figure 3, so the image of this function is roughly as follows.
Figure 3 A B C D
8. Several students from Grade Three took a group photo as a souvenir. It is understood that it costs 0.80 yuan to develop a negative and 0.35 yuan to develop a photo. On the premise that each student gets a photo and uses a negative, the average money is less than that of 0.5 yuan. What about the number of students taking a group photo?
A.b. At least 6 people C. At most 5 people D. At least 5 people
9. As shown in Figure 4, when Wang Hua walked from B to C under the street lamp A at night, she measured
The length of the shadow disc is 1 m. Go straight ahead for 3 meters and measure it when you get to E.
The length of the shadow EF is 2 meters, and it is known that the height of Wang Hua is 1.5 meters, then
Height AB of street lamp a is equal to
4.5 m B.6 m
C.7.2 D.8m
Figure 4
10. as shown in figure 5, in □ABCD, AB: AD = 3:2, ∠ ADB = 60,
Then the value of cosA is equal to
A.B.
C.D.
Figure 5
Academic Examination of Shenzhen Junior High School Graduates in 2006
Math test
Title 23
1 1~ 15 16 17 18 19 20 2 1 22
score
The second volume (multiple choice questions, ***70 points)
Scoring reviewer
II. Fill in the blanks (5 small questions in this big question, 3 points for each small question, *** 15 points)
Please fill in the answer under the corresponding question number in the answer sheet 1, otherwise you will not get extra points.
Answer sheet 1
The title is112131415.
Answer a question.
1 1. A shopping mall launched a lucky draw during May Day. There are two red and white table tennis balls in the lucky draw box, except for the color. When customers draw prizes, they draw two balls at a time. If the two balls are the same color, he wins, but if the colors are different, he wins. Then the probability of winning the prize is that the customer touched the prize once.
12. Simplify:
13. As shown in Figure 6, in the quadrilateral ABCD,
Diagonal AC and BD intersect at O-point. If no letters and auxiliary words are added,
Help lines need to be added in order to make the quadrilateral ABCD square.
On one condition. Figure 6
14. There are 9 steps at the side door of People's Park, and Can Cong only climbs 1 or 2 steps at a time. Xiao Cong found that when the number of steps is 1, 2, 3, 4, 5, 6, 7, ... gradually increases, and the number of different ways of climbing stairs is 65438+.
15. In △ABC, AB = 3, AB=6, BC+AC=8, and the median line CD=3, then the area of △ABC is.
Iii. Answering questions (There are 7 questions in this big question, of which 16 and 17 have 6 points; 18 7 points; 19 and 20 questions 8 points; 2 1, 22 questions each 10, ***55 points)
Scoring reviewer
16.(6 points) Calculation:
Solution: Original formula =
Scoring reviewer
17.(6 points) Solve the equation:
Solution:
Scoring reviewer
18.(7 points) As shown in Figure 7, in trapezoidal ABCD, AD‖BC,
. (1) (3 points) Verification:
Prove:
(2)(4 points) If yes, find the area of trapezoidal ABCD.
Solution:
Scoring reviewer
19.(8 points) A middle school library divides books into four categories: natural science, literature and art, social encyclopedia and mathematics. In the "Shenzhen Reading Month" activity, in order to know the borrowing situation of books, the librarian made statistics on the borrowing amount of various books this month. Figure 8- 1 and Figure 8-2 are two incomplete frequency distributions drawn by librarians after collecting data.
frequency table
Book category frequency
Natural science 400 0.20
Literature and art 1000 0.50
Social Encyclopedia 500 0.25
mathematics
(1)(2 points) Fill in the blanks in the frequency distribution table in Figure 8- 1.
(2)(2 points) In Figure 8-2, the part representing "natural science" is completed.
(3)(2 points) If the school intends to buy 10000 books, please estimate how many books on Mathematics should be purchased.
Solution:
(4)(2 points) According to the information provided in the chart, please make reasonable suggestions.
Scoring reviewer
20.(8 points) When a craft shop sells a craft at a marked price, each piece can make a profit in 45 yuan; Selling 8 pieces of this handicraft at a 15% discount on the list price is equivalent to the profit of selling 12 pieces of this handicraft in 35 yuan by lowering the list price.
(1)(4 points) What is the purchase price and list price of each piece of this handicraft?
(2)(4 points) If each handicraft is purchased according to the purchase price obtained in (1) and sold at the marked price, the handicraft shop can sell 100 pieces of this handicraft every day. If the price of each handicraft is reduced by 1 yuan, four more such handicrafts can be sold every day. How much is the price reduction of each handicraft for sale, and the maximum profit can be obtained every day? What is the maximum profit?
Scoring reviewer
2 1.( 10 minute) As shown in Figure 9, the parabola intersects the axis at two points (the point is on the left side of the point), and the other point on the parabola is in the first quadrant, which satisfies that ∠ is a right angle, just making △ ∽△.
(1)(3 points) Find the length of the line segment.
Solution:
(2)(3) Find the functional relationship of parabola.
Solution:
(3)(4 points) Is there a point on the axis that makes △ an isosceles triangle? If yes, find out the coordinates of all qualified points; If it does not exist, please explain why.
Solution:
Scoring reviewer
22.( 10 points) As shown in figure 10- 1, in the plane rectangular coordinate system, the point is on the positive semi-axis of the shaft, and ⊙ two points intersect with the shaft, which is the midpoint of the intersection of the point and the shaft. If the coordinate of the point is (-2,0),
(1)(3 points) Find the coordinates of this point.
Solution:
(2)(3 points) Link verification: ‖.
Prove:
(3)(4 o'clock) As shown in Figure 10-2, the tangent passing through this point is ⊙, and the intersection axis is at this point. When the moving point moves on the circumference of ⊙, whether the ratio of ⊙ has changed, and if not, the ratio is found; If so, explain the law of change.
Solution:
Reference answers to the academic examination of Shenzhen junior high school graduates in 2006
First, multiple-choice questions (this big question * * 10 small questions, 3 points for each small question, 30 points for * * *)
The title is 1 23455 6789 10.
Answer B C C D D A C B B A
II. Fill in the blanks (5 small questions in this big question, 3 points for each small question, *** 15 points)
The title is112131415.
Answer1/31/(m-3) AC = BD 55 7
Iii. Answering questions (There are 7 questions in this big question, of which 16 and 17 have 6 points; 18 7 points; 19 and 20 questions 8 points; 2 1, 22 questions each 10, ***55 points)
16、-3/2
17、2
18, (1) omitted; (2)
19、( 1) 100,0.05; (2) ellipsis; (3)500; (4) Omission
20、( 1) 155,200; (2) 10,4900。
2 1、( 1) ; (2) ; (3) Four points:
22、( 1)(0,4); (2) Prompt, find the length of OG, and get og: oc = om: ob; (3)3/5