Mathematics problems in senior high school entrance examination (big questions)

Xining senior high school entrance examination in 2007

Math test

(Full score of the test paper 120, test time 120 minutes)

1. Fill in the blanks (this question is * *12 15 empty, with 2 points for each empty space and 30 points for * * *).

1. If the income 15 yuan is recorded as+15 yuan, then the expenditure 20 yuan is recorded as _ _ _ _ _ _.

2. The reciprocal of is _ _ _ _ _ _ _ _ _ _ _ _; Decomposition factor: _ _ _ _ _ _ _ _ _ _ _.

On the morning of April 6th+May 6th, 2007, BOCOG held a press conference in Beijing on the sale of tickets for the Beijing 2008 Olympic Games, and more than 7 million tickets for the Beijing Olympic Games began to be accepted by the public. This data can be expressed in scientific symbols as _ _ _ _ _ _ _ _ _ _ _.

4. Find the pattern and fill in the numbers: 20 13, 4 102, 30 14, 5 103, 40 15, _ _ _ _ _ _ _ _.

Calculation: _ _ _ _ _ _ _ _ _ _.

5. As shown in figure 1, a, c and b are three points on the circle O. If ∠ AOC = 40, the degree of ∠ABC is _ _ _ _ _ _ _ _ _ _ _ _.

Figure 1

6. As shown in Figure 2, if the pattern is densely paved with isosceles trapezoid with the same shape and size, the bottom angle (acute angle) of the isosceles trapezoid in the pattern is _ _ _ _ _ _ _ _ _ _ _ _ _.

Figure 2

7. Grade 9 (1) class physical education graduation examination results of a school are shown in the following table:

The probability of randomly selecting a student who gets exactly 30 points is _ _ _ _ _ _ _ _ _ _ _; The information that can be obtained from the table is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _. (Just write one)

8. It is known that in the linear function (A and B are constants), some corresponding values of X and Y are as follows, so the solution of the equation about X is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

9. As shown in Figure 3, reduce △DEF to half of its initial value. The operation method is as follows: take any point P, connect DP, take the midpoint A of DP, then connect EP and FP, and take their midpoints B and C to get △ABC, then the area ratio of △ABC to △DEF is _ _ _ _ _ _ _ _ _ _ _ _ _.

Figure 3

10. As shown in Figure 4, rotate △ ABC 25 counterclockwise around point C to get △ dec. When ∠ AFD = 50 and ∠ ACE = 80, ∠ B = _ _ _ _ _ _ _ _ _ _ _ _

Figure 4

1 1. As shown in Figure 5, point P is on the image of inverse proportional function, and the area of △OAP is 5, then k = _ _ _ _ _ _ _ _

Figure 5

12. As shown in Figure 6, suppose two rectangles with a length of 12 and a width of 8 overlap, and it is known that the length of AB is 7, then the shadow area of the overlap of the two rectangles is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

Figure 6

Second, the multiple-choice question (this question ***8 small questions, each small question 3 points, ***24 points. Of the four options given in each question, only one meets the requirements. Please fill in the brackets of the corresponding question number below with the option number you think is correct)

13. The following calculation is correct ()

A.B.

C.D.

14. A train runs from Xining to Lhasa at a constant speed. In fig. 7, the image that can roughly reflect the relationship between the distance S(km) and the travel time t(h) of the train from Lhasa is ().

Figure 7

15. In less than a year, in order to hedge the problem of excess economic liquidity in China, the People's Bank of China has raised the deposit reserve ratio five times, and commercial banks have implemented the deposit reserve ratio of 7.5% before July 5, 2006. Since February 25th, 2007, the deposit reserve ratio has been raised to 10.0%, with an increase rate of ().

A.B. 25.0% C. 20.0% D. 10.0%

16. "In order to treat the sewage in our city, it is necessary to lay a 960m-long pipeline. In order to minimize the impact of construction on traffic, in actual construction, ◆◆◆◆◆◆◆◆ ◆. Assuming that the original plan is to lay the pipeline x meters every day, the equation can be obtained. " According to this scenario, the missing condition indicated by "◆◆◆◆" in the question should be increased to ().

Laying 20 meters less than originally planned every day, resulting in completing the task four days ahead of schedule.

B. laying 20 meters more than originally planned every day, resulting in completing the task four days ahead of schedule.

C laying 20 meters more than planned every day, resulting in a delay of 4 days to complete the task.

D laying 20 meters less than planned every day, resulting in a 4-day delay in completing the task.

17. According to the information in the grid in Figure 8, after estimation, the following values are closest to the value of ().

A.0.6246 b 0.8 12 1

C. 1.6582d 2. 1809

Figure 8

18. The following survey is applicable to the general survey ().

A may 1 investigate the air quality in Xining.

Investigate the height of all the students in your class.

C. investigate the weekly pocket money of all middle school students in Xining.

D Investigate whether the bacterial content of milk in bags of Tianlu supermarket in Xining exceeds the standard.

19. If the sum of the internal angles of an N-polygon does not exceed 2007, then the maximum number of sides of an N-polygon is ().

A. 1 1 b . 12 c . 13d . 14

20. As shown in Figure 9, when Xiao Ming was playing on the swing, he found that the rope on the swing was 2 meters long. At rest, the pedal is 0.5m off the ground, and the swing steps on the board at the highest point1.5m (symmetrical left and right), so the length of the arc swung by the swing is ().

A.B. C. D。

Figure 9

Third, answer the question (there are 3 small questions in this question, 7 points for each small question, ***2 1 point)

2 1. Calculation:

22. As shown in figure 10, the quadrilateral ABCD is a diamond, e is a point on the BD extension line, f is a point on the DB extension line, and DE=BF. Please take f as the endpoint and connect it to a point marked with letters in the picture. Guess and prove that it is equal to an existing line segment in the graph (only prove that a group of line segments are equal).

(1) Link _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _;

(2) Guess: _ _ _ _ _ _ _ _ _ _ = _ _ _ _ _ _ _ _ _ _;

(3) prove that:

Figure 10

23. Form an isosceles triangle with a thin iron wire with a length of 16cm. If the base length is ycm, the waist length is xcm.

(1) Write the functional relationship between base length y and waist length x;

(2) Find the range of independent variable x;

(3) Draw the image of this function in the grid diagram 1 1.

Figure 1 1

Four, (this question ***3 small questions, each small question 8 points, ***24 points)

According to the research of biologists, many characteristics of human body are controlled by genes. Some people have single eyelids, while others have double eyelids, which is controlled by a pair of human genes. The gene f controlling single eyelid is recessive, and the gene f controlling double eyelid is dominant, so a pair of genes controlling eyelid may be ff, Ff or FF. People with ff gene have single eyelids, and people with Ff or FF gene have double eyelids. Genetically, it is also possible for parents to pass on a gene they carry to their children. For example, if both parents have double eyelids and their genes are ff, then their children have only three possibilities: Ff, Ff or FF, which can be expressed in the following table:

(1) Can you calculate the probability that all their children have double eyelids?

(2) If the father's gene is ff and the mother's gene is Ff, please use the tree diagram to find out the probability that their children are double eyelids.

25. as shown in figure 12, in circle o, AB is the diameter, AD is the chord, and the tangent passing through point b intersects with the extension line of AD at point c, and AD=DC, so find the degree of ∠ABD.

Figure 12

26. A middle school in Xining decided to recommend one of the three classes of Grade 9 (2), (3) and (6) as the municipal advanced collective candidate class after a preliminary comparison of the graduating classes of junior high school. Now make a comprehensive quality evaluation of these three classes. The following table shows their scores of three quality evaluations (full marks for each item are 10).

(1) Please complete the above table;

(2) Excuse me, among the three evaluation scores of each class, can the statistics of the average reflect the differences in the evaluation results of the three classes? If possible, please recommend a class as a candidate class for the municipal advanced collective; If not, please set the proportion of each evaluation content according to the importance of the three projects, recalculate the score of each class, and recommend a class with the highest score as the candidate class of the municipal advanced collective. (The proportion you set must meet the following requirements: ① All are integers; ② Total 10).

Verb (abbreviation of verb) (this question * * *, question 27, 9 points, question 28 12 points, ***2 1 minute)

27. In a mathematical inquiry activity, Xiao Qiang only used a straight line to divide the rectangular ABCD into two parts with equal area, as shown in figure 13:

Figure 13

For the three rectangles in (1) Figure 14, please boldly try to draw a straight line that conforms to the above segmentation method (note: ① The special points through which the drawn straight line passes must be clearly marked; ② Only one rectangle is drawn);

Figure 14

(2) According to the division method of Youhe, a rectangle can be divided into two parts with equal area by only one straight line. Do you think there is _ _ _ _ _ _ _ _ _ _?

(3) From the above experimental operation, what rules do you find in the straight line you drew in the rectangle?

________________________________________________________________________。

(4) Can the irregular figure 15 below be divided into two parts with equal area by a straight line according to the above division method?

Figure 15

28. as shown in figure 16, it is known that the image of quadratic function intersects the x axis at point c and point c, and the vertex is p. ..

(1) Find the analytical expression of this parabola;

(2) Find the line segment length PC;

(3) Let D be a point on the line segment OC, and ∠DPC=∠BAC, and find the coordinates of point D. ..

Figure 16

Test answer

Xining senior high school entrance examination in 2007

Reference answers and grading opinions of mathematics test papers

1. Fill in the blanks (this question is * *12 15 empty, with 2 points for each empty space and 30 points for * * *).

1.2.

3.； 4.6 104, 1

5.20 6.60

7.24~26 points are the most (the answer is not unique).

8.9. 1:4

10.50 1 1. 10

12.42

Second, multiple-choice questions (this question ***8 small questions, 3 points for each small question, ***24 points)

CBAB·CBCD

Three. (There are 3 small questions in this question, 7 points for each small question, ***2 1 point)

2 1. Solution: 3 points for the original formula.

4 points

6 points

= 0.7 points

22. (The answer is not unique)

Solution: link AF 1.

Guess: AF=AE 3 points

Proof: link AC, pay BD at O 4.

∫ The quadrilateral ABCD is a diamond.

∴AC⊥BD in O, OD=OB.

∫ Germany =BF, ∴OF=OE 5 points.

∴AC perpendicular bisector EF 6 o'clock

∴AF=AE (the distance from the point on the middle vertical line to both ends of the line segment is equal) 7 points.

23. Solution: (1) 3 points.

(2) According to the meaning of the question:

that is

Solution: 5 points

(3) (see grid diagram) 7 points

Four, (this question ***3 small questions, each small question 8 points, ***24 points)

A: (1)P (their children have double eyelids) = 3 points.

(2) See the tree diagram for 6 points.

P (their children have double eyelids) 8 points.

25. Solution: ∫BC tangent circle O is at point B and AB is the diameter.

∴AB⊥BC 2 points

* AD =DC

∴BD=AD=CD (the median line on the hypotenuse of a right triangle is equal to half of the hypotenuse) 4 points.

∴∠Abd =∞∠dab (equiangular) 5 points.

∫AB is the diameter of the circle o.

∴∠BDA = 90° (the circumference angle of the diameter is a right angle) 7 points.

∴∠ Abd = 45 8 points

26. Solution: (1) Average value: 7; Music, body and beauty award: 8.2 points

(2) It can't reflect the difference of three kinds of evaluation results; Three points

(The answer is not unique. As long as ① the proportional design meets the requirements, ② the calculation is accurate, and ③ the recommended results are obtained, you can score. )

Example: Let the score be 4: 5: 1, and get 4 points according to the topic.

Class 2, Grade 9: 5 points

Class 3, Grade 9: 6 points

Class 6, Grade 9: 7 points

It is recommended that Grade 9 (2) class be the municipal advanced collective candidate class. 8 points

Verb (abbreviation of verb) (this question * * *, question 27, 9 points, question 28 12 points, ***2 1 minute)

27.( 1) (The answer is not unique, and the following answers are for reference only) Draw the correct 3 points.

(2) Countless 5 points

(3) Any straight line passing through the symmetrical center of a rectangle can divide the rectangle into two parts with equal areas.

7 points

(4) (The answer is not unique, and the following answers are for reference only) Draw the correct 9 points.

28. Solution: (1)∵ Parabolic passing point