Mathematics Examination Paper of Shanghai Senior High School Entrance Examination in 2007

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Unified academic examination for junior high school graduates in Shanghai in 2007

Math test

Note to candidates:

1. This volume contains four major questions, ***25 questions;

2. Except for the first and second questions, unless otherwise specified, the main steps of proof or calculation should be written.

1. Fill in the blanks: (This title is *** 12, with a full score of 36) [Only write the results directly, and fill in 3 points correctly in each blank, otherwise it will be zero].

1. Calculation:.

2. Decomposition factor:.

3. simplify.

4. If the function is known, then.

5. The domain of the function is.

6. If both real roots of the equation are 0, then.

7. The root of the equation is.

8. As shown in figure 1, the image of the proportional function passes through this point, and the resolution function is.

9. As shown in Figure 2, a point on the extension line of the parallelogram is connected with and intersects with this point. Please write a pair of similar triangles in the picture without auxiliary lines.

10. If the length of one tangent of two circles is equal to 5 and the length of the other tangent is equal to 0, then.

1 1. As shown in Figure 3, in the rectangular coordinate plane, the line segment is perpendicular to the axis and the vertical foot is. If the line segment is folded along the axis and the point falls on the point, the abscissa of the point is.

12. Figure 4 is a square grid. Please choose a white unit square and color it black, so that the black part in Figure 4 is a figure with a symmetrical center.

Second, multiple-choice questions: (this big question ***4 questions, full score 16 points)

Of the four conclusions of the following questions, one and only one is correct. Write the code of the correct conclusion in parentheses after the question, and choose the right one to get 4 points; If you don't choose, choose wrong or choose more than one, you will get zero point.

13. Among the following quadratic roots, the one with the same quadratic root is ().

A.B. C. D。

14. If the image of the linear function passes through the first quadrant and intersects the negative semi-axis of the shaft, then ()

A.、b、c、d、

15. If a condition is added to a known quadrilateral, it can be concluded that the quadrilateral is a square, then this condition can be ().

A.B. C. D。

16. Xiaoming accidentally broke the round glass at home. There are four in Figure 5. In order to match the round glass with the same size as before, a piece of glass that Xiao Ming got in the shop should be ().

A. Block ① B. Block ②

C. block ③ D block ④

Three. (There are ***5 questions in this big question, out of 48 points)

17. (The full mark of this question is 9)

Solve the inequality group: and express the solution set on the number axis.

18. (The full mark of this question is 9)

Solve the equation:

19. (The full score of this question is 10, (1) is 6, and (2) is 4. )

As shown in Figure 6, on the rectangular coordinate plane, it is the origin, the coordinate of the point is, the point is in the first quadrant,,.

Find the coordinates of point (1); The value of (2).

20. (The full score of this question is 10, the full score of (1) is 4, and the full score of (2) and (3) is 3)

Xiao Li and Xiao Jie, junior three students, conducted a sample survey in our school to find out the weekly online time of junior two students. Xiao Li investigated the weekly online time of 40 computer enthusiasts in Grade Two students, and calculated that the average weekly online time of these students was 2.5 hours. Xiaojie randomly selected 40 students from the list of all junior two students and investigated their weekly online time. According to calculation, the average online time of these students is 65,438+0.2 hours per week. Xiaoli and Xiaojie compiled their own data, as shown in Table 1. Please answer the following questions based on the above information:

(1) Which student's sample do you think is representative? A:;

It is estimated that the average online time of all junior two students in this school is hours per week;

(2) According to specific representative samples, the frequency distribution histogram in Figure 7 is supplemented;

(3) In the representative sample, the median time period is hours/week.

a period of time

(hour/week) Xiaoli sampling

Sampling number of little heroes

number of people

0~ 1 6 22

1~2 10 10

2~3 16 6

3~4 8 2

(Each group can contain the lowest value, but not the highest value)

Table 1

2 1. (The full mark of this question is 10)

Since 200 1, China has implemented drug price reduction five times, with a total amount of 26.9 billion yuan. The years of five drug price reductions and the corresponding price reductions are shown in Table 2, and the relevant data of 2003 and 2007 are lacking. It is known that the price reduction of drugs in 2007 was six times that of drugs in 2003. Combined with the information in the table, we can find the amount of drug price reduction in 2003 and 2007.

200 1 2003 2004 2005 2007

Price reduction amount (100 million yuan) 54 35 40

Table 2

Four, (this big topic ***4 questions, out of 50 points)

22. (The full score of this question is 12, and the full score of each small question is 6.)

In the rectangular coordinate plane, the vertex of the quadratic function image is and passes through this point.

(1) Find the analytic expression of quadratic function;

(2) Translate the quadratic function image by several units to the right, so that the translated image can pass through the coordinate origin. And directly write the coordinates of another intersection point between the translation image and the axis.

23. (The full score of this question is 12, and the full score of each small question is 6.)

As shown in Figure 8, in the trapezoid, the extension line of the intersection of, and is at the point.

(1) Verification:;

(2) If,, find the side length.

24. (The full score of this question is 12, and the full score of each small question is 4 points.)

As shown in Figure 9, in the rectangular coordinate plane, the image of the function (,is a constant) passes by, where the intersection point is the vertical axis, the vertical foot is, the intersection point is the vertical axis, and the vertical foot is, connected,,.

(1) If the area of is 4, find the coordinates of this point;

(2) Verification:

(3) If, find the resolution function of a straight line.

25. (The full score of this question is 14, (1) is 4, and (2) and (3) are 5)

It is known that this point is on the ray (as shown in figure 10). It is a moving point on a straight line, and its side is an equilateral triangle (the points are arranged clockwise), which is the outer center.

(1) When a point moves on a ray, it is proved that the point is on the bisector;

(2) When a point moves on the ray (points do not coincide with each other) and intersects with the point, set, find the resolution function about it, and write the definition domain of the function;

(3) If the point is on the ray, the circle is inscribed. If the edge of the circle is tangent to the circle, please write the distance from point to point directly.

Unified academic examination for junior high school graduates in Shanghai in 2007

Key points and grading standards of answers in mathematics examination papers

Description:

1. Answers only lists one or more answers to the questions. If the candidates' answers are different from those listed, they can be graded according to the grading standards in the answers.

2. The first big question only requires writing the results directly, and each blank is filled correctly to get 3 points, otherwise it will get 0 points; The second largest question has 4 points for each question, and 0 points for not choosing, wrong choosing or multiple choosing; The scores marked on the right hand side of questions 17 to 25 indicate that candidates should get points for completing this step correctly. When grading, the unit for giving points or deducting points is 1.

Key points of answers and grading standards

A, fill in the blanks (this big question *** 12, out of 36 points)

1.3 2.3.4. 1 5.6.2 7.

8.9. (or, or)

1 0.11.12. See figure1for the answer.

Second, multiple-choice questions (this big question ***4 questions, full score 16 points)

13.C 14。 B 15。 D 16。 B

Three. (There are ***5 questions in this big question, out of 48 points)

17. solution: from, get 0.3 points.

Shit, get 0. 3 points.

The solution set of inequality group is. 1 point.

The solution set is correct on the number axis. Two points.

18. solution: remove the denominator and get 3 points.

Finishing, get 2 points.

0.2 points for solving the equation.

After testing, it is the root of the original equation, and the root of the original equation is .2 points.

19. Solution: (1) As shown in Figure 2, the vertical foot is 1.

In,,,

.2 points

.............................. 1 min.

The coordinates of this point are 2 points.

(2), ...............1min.

At, 1 min.

........................................, two points.

20.( 1) Xiaojie; 1.2.2 points, 2 points

(2) The histogram is correct. 3 points

(3) 0 ~ 1.3.

2 1. Solution: [Solution 1] Let the amount of drug price reduction in 2003 and 2007 be 1 100 million yuan and 1 100 million yuan respectively. 1 min.

According to the meaning of the question, you must

Solve the equation and get

A: The amount of drug price reduction in 2003 and 2007 was 2 billion yuan and 654.38+02 billion yuan respectively. 654.38+0 points.

[Scheme II] Let the amount of drug price reduction in 2003 be 1 100 million yuan, 1 minute.

Then the amount of drug price reduction in 2007 is 1 100 million yuan.

According to the meaning of the question, get .2 points.

Solve the equation and get 0.4 points.

A: The amount of drug price reduction in 2003 and 2007 was 2 billion yuan and 654.38+02 billion yuan respectively. 654.38+0 points.

Four, (this big topic ***4 questions, out of 50 points)

22. Solution: (1) Let the quadratic resolution function be 2 points.

If the image of the quadratic function passes through this point, the score is 0.3.

The second resolution function is. 1.

(2) Work, get, solve the equation, get .2 points.

The coordinates of the two intersections of the quadratic function image and the axis are and respectively.

The quadratic function image moves 1 unit to the right and passes through the coordinate origin. Two points.

The coordinate of another intersection between the translation image and the axis is .2 minutes.

23.( 1) Proof:

. 1 point

Divide equally,

, 1 min

Say it again,

. 1 point

The trapezoid is an isosceles trapezoid, which is .2 points.

(2) solution: as shown in figure 3, left,

The vertical feet are respectively, and then.

At, 1 min.

And, and,

, get ................. 1 minute.

Similarly, we can see that in the middle, .................................................................................................................................................................

, .

Say it again.

,. 1 point

The quadrilateral is a parallelogram, and the score is. 1.

. 1 point

24.( 1) solution: function, constant) image passing,. 1 fraction.

Let's say the intersection point, according to the meaning of the question, the coordinates of the point are, the coordinates of the point are,

The coordinates of the point are 1 point.

, , .

The area multiplied by 4 is 1 point.

Well, the coordinates of the point are. 1 point.

(2) Proof: According to the meaning of the question, the coordinates of the point are,