Traditional Culture Encyclopedia - Weather forecast - Send me the exam questions of Chengdu Mathematics, too ~ Hehe, good-hearted person

Send me the exam questions of Chengdu Mathematics, too ~ Hehe, good-hearted person

I don't know if you can see the pictures. If not, you can send me your email, and then I will send it directly to you in Word.

In 2009, Chengdu, Sichuan Province, took the senior high school entrance examination in mathematics.

(Including Chengdu Grade Three Graduation Examination)

The whole volume is divided into volume A and volume B, with volume A scoring 100 and volume B scoring 50; Examination time 120 minutes. Volume A is divided into Volume I and Volume II, with Volume I being multiple-choice questions and Volume II being other types of questions.

1. Multiple choice questions: (3 points for each small question, * * * 30 points)

1. The result of calculating 2×) is

(a)- 1 (b) l (c)-2 (D) 2

2. In the function, the range of independent variables is

(A) (B) (C) (D)

3. As shown in the figure, a geometric figure has three views, so the shape of the geometric figure is

(a) cuboid (b) triangular prism (c) cone (d) cube

The following statement is correct.

(1) "The probability of rain tomorrow is 75%" In a city, it means that it will rain 75% of the time tomorrow.

(b) Throw a uniform coin at random, and the face must face up after landing.

(3) In the lucky draw, "winning probability is" means winning the prize after 100 times.

(d) On the plane, the two diagonals of the parallelogram must intersect.

5. If △ABC∽△DEF is known and AB: DE = 1: 2, the ratio of △ABC's area to △DEF's area.

(A) 1:2(B) 1:4(C)2: 1(D)4: 1

6. In the plane rectangular coordinate system xOy, the point A (2 2,3) is known. If OA rotates180 counterclockwise around the origin o to get 0A',

Then the position of point a' in the plane rectangular coordinate system is

(a) first quadrant (b) second quadrant (c) third quadrant (d) fourth quadrant

7. If a quadratic equation with one variable has two unequal real roots, the value range of is

(A) (B) and (c) (D) and

8. If the circumference of the cone bottom circle is 4πcm and the length of the bus is 6cm, the center angle of the cone side development diagram is

(A)40(B)80(C) 120(D) 150

9. An airline stipulates that the weight (kg) of luggage carried by passengers and their freight (yuan) are determined by the linear function image as shown in the figure, so the maximum weight of free luggage that passengers can carry is

(A)20 kg (B)25 kg

28 kg (D)30 kg

10. In order to know the daily electricity consumption of residents in a residential area, a classmate living in the residential area randomly selected the daily electricity consumption of l5 households, and the results are as follows:

Daily electricity consumption

(unit: degrees) 5 6 7 8 10

Number of families

Then the following statement about the daily electricity consumption of l5 households is wrong.

(a) The mode is 6 degrees; The average is 6.8 degrees.

Fill in the blanks: (4 points for each small question, *** 16 points)

Write the answer directly on the horizontal line of the topic.

1 1. The solution of the fractional equation is _ _ _ _ _ _ _

12. As shown in the figure, fold the rectangular ABCD along BE, if ∠ CBA ′ = 30, ∠ BEA ′ = _ _ _ _.

13. Since the reform and opening up 30 years ago, the urbanization of Chengdu has maintained a rapid and stable development trend. According to statistics, by the end of 2008, the permanent population of five urban areas (excluding high-tech zones) in the central city of Chengdu reached 44 1 10,000, and the following statements were made for this permanent population: 2 people; (3) people. Among them, the serial number expressed by scientific notation is _ _ _ _ _ _ _.

14. As shown in the figure, △ABC is inscribed in ⊙O, AB=BC, ∠ ABC = 120, AD is the diameter of ⊙O, and AD = 6, then BD = _ _ _ _ _ _

Three. (15 is 6 points for each small question, 16 is 6 points, *** 18 points)

15. Answer the following questions:

(1) calculation:

(2) Simplify first, then evaluate:, where.

16. Solve the inequality group and express its solution set on the given number axis.

Iv. (8 points for each small question, *** 16 points)

17. Linear function and inverse proportional function are known, in which the image of linear function passes through point p (,5).

(1) Try to determine the expression of the inverse proportional function;

(2) If the Q point is the intersection of the linear function and the inverse proportional function image in the third quadrant, find the coordinates of the Q point.

18. The ninth grade students in a middle school carried out practical activities to measure the height of an object while learning the chapter "Angular relationship of right triangle". They want to measure the height of the school building. As shown in the figure, they first measured the elevation angle of vertex A of teaching building AB at point C as 30, and then advanced 60 meters to the teaching building to reach point D, and measured the elevation angle of point A as 45. Please calculate the height of this teaching building according to these data.

Verb (abbreviation of verb) (for each small question 10, ***20)

19. There is a uniform regular tetrahedron with four faces marked with numbers L, 2, 3 and 4 respectively. Xiaohong throws it at random once, and records the number on the landing side as X; There are also three cards with the same back, and the numbers 1 2 and 1 L, 1 are written on the front respectively. After mixing, Xiao Liang put them face down on the table, and randomly selected a card from them, and recorded the number on the front of the card as Y; Then they calculate the value of s = x+y.

(1) Use tree diagram or list method to represent all possible situations of S;

(2) when S=0 and s

20. It is known that A and D are two points on the arc. On the same side of a straight line, the vertical lines passing through these two points respectively are B and C, E is the moving point on BC, connecting AD, AE and de, and AED = 90°.

(1) as shown in figure ①, if AB=6, BC= 16, BE:CE= 1:3, find the length of AD.

(2) As shown in Figure ②, if point E happens to be the center of this arc, what is the equivalent relationship between line segments AB, BC and CD? Please write your conclusion and prove it. Further exploration: When A and D are on both sides of a straight line, and AB≠CD, and other conditions remain unchanged, what is the equivalent relationship between line segments AB, BC and CD? Please write the conclusion directly, without proof.

Volume B (***50 points

1. Fill in the blanks: (4 points for each small question, * * * 20 points)

Write the answer directly on the horizontal line of the topic.

2 1. Simplified: = _ _ _ _ _ _

22. As shown in the figure, A, B and C are three points on ⊙0. Take BC as one side, let ∠CBD=∠ABC, pass BC as a point, let PE ∠ AB pass BD at point E, if ∠ AOC = 60, BE=3, then point P.

23. If we know, remember that the expression of,,,, and calculation inference is = _ _ _ _ _.

(expressed by algebraic expression with n)

24. As shown in the figure, the area of the square OABC is 4, and the point B is on the image of the inverse proportional function. If point R is any point different from point B on the inverse proportional function image, the intersection point R is perpendicular to the X axis and the Y axis respectively, and the vertical feet are M and N. Subtract the area of the overlapping part with the square OABC from the area of the right angle OMRN, and record the remaining area as S.

When S=m (m is a constant, 0

(represented by an algebraic expression containing m)

25. It is known that M(a, b) is a point in the plane rectangular coordinate system xOy, where A is any one of three numbers L, 2, 3 and B is any one of four numbers L, 2, 3, 4. Define "point M(a, b) on straight line x+y=n" as an event (2≤n≤7 n).

Second, (**8 points)

26. A college graduate responded to the call of "starting his own business" and invested in a jewelry store. This shop bought a new ornament that went on sale this year and sold it for 30 days. After sale, it was learned that there was the following relationship between daily sales volume P (pieces) and sales time X (days): p =-2x+80 (1). It is also known that the sales price (yuan/piece) in the first 20 days has the following relationship with the sales time x (day): (1≤x≤20, where x is an integer), and the sales price (yuan/piece) in the last 10 day has the following relationship with the sales time x (day): = 45 (.

(1) Try to write the functional relationship between the daily sales profit (yuan) in the first 20 days and the daily sales profit (yuan) in the next 10 days and the sales time x (days);

(2) In the 30-day trial sale, which day has the largest daily sales profit? Find out this maximum profit.

Note: Sales profit = sales revenue-purchase cost.

Three. (*** 10 point)

27. As shown in the figure, the bisector AD of Rt△ABC is inscribed in ⊙O, AC=BC, ∠BAC intersects with ⊙0 at point D, BC intersects with point E, extends BD, intersects with AC at point F, connects CD, and G is the midpoint of CD, and connects 0g.

(1) Judge the relationship between 0G and CD, write your conclusion and prove it;

(2) Verification: AE = BF

(3) If, find the area of ⊙ o.

Four. (*** 12)

28. In the plane rectangular coordinate system xOy, it is known that the parabola y= intersects with the X axis at two points A and B (point A is on the left side of point B) and intersects with the Y axis at point C, and its vertex is m. If the functional expression of the straight line MC is, the intersection point with the X axis is n, and COS∠BCO= =.

(1) Find the function expression of this parabola;

(2) Is there a point P on this parabola that is different from point C, so that a triangle with N, P and C as its vertices is a right triangle with NC as its right side? If it exists, find the coordinates of point P; If it does not exist, please explain the reason;

(3) The intersection point A is perpendicular to the X axis and the intersection line MC is at the Q point. If the parabola moves up and down along its symmetry axis, there is always a common point between the parabola and the line segment NQ. How many unit lengths can the parabola move up at most? How many unit lengths can you translate downward at most?

In 2008, Chengdu, Sichuan Province, took the senior high school entrance examination in mathematics.

(Including Chengdu Grade Three Graduation Examination)

Volume 1 (*** 100)

The first volume (multiple choice questions, ***30 points)

Precautions:

1. Volume I ***2 pages. Before answering the first volume, candidates must scribble their names, admission ticket numbers and exam subjects on the test paper and answer sheet. At the end of the exam, the invigilator will take back the test paper and the answer sheet together.

The first volume is full of multiple-choice questions. There are four options for each question, and only one of them meets the requirements of the question. After selecting the answer for each question, black the answer label of the corresponding question on the answer sheet with 2B pencil; If you need to change it, clean it with an eraser and choose another answer. The answers to multiple-choice questions cannot be answered on the test paper. Please pay attention to the format of machine-readable answer sheet.

1. Multiple choice questions: (3 points for each small question, * * * 30 points)

The value of 1. 2cos45 is equal to

(A) (B) (C) (D)

2. Simplify (-3x2)? The result of 2x3 is

(A)- 6x5 (B)- 3x5 (C)2x5 (D)6x5

3. The torch relay of Beijing Olympic Games takes "harmonious journey" as the theme and "ignite passion and pass on dreams" as the slogan.

The total distance is about 1370000 km, which is expressed by scientific calculation method as follows.

(a)13.7×104km (b)13.7×105km.

4. Build a geometric model with several small cubes with the same size and side length of 1. Three views as shown in the figure, and then build this.

The number of small cubes used in the geometric model is

(A)4 (B)5 (C)6 (D)7

5. The following events are inevitable.

(a) Turn on the TV and select a channel. The weather forecast is playing on the screen.

(b) Go to the cinema and buy a movie ticket at will. The seat number is odd.

(d) Even dice are thrown, and even points face upwards after the dice stop rotating.

6. In the function y=, the range of the independent variable x is

(A)x≥ - 3 (B)x≤ - 3 (C)x≥ 3 (D )x≤ 3

7. As shown in the figure, in △ABC and △DEF, the existing condition AB=DE, and two conditions need to be added to make △ ABC △ def. A set of conditions that cannot be added are

(A)∠B=∠E，BC=EF (B)BC=EF，AC=DF

(C)A =∠D，B =∠E(D)A =∠D，BC=EF

8. A traffic controller counted the number of people who ran a red light at the intersection in the city center on Sunday. According to the number of people who ran the red light in each time period from 7: 00 am to 12: 00 am (taking 1 hour as a time period), he made a histogram as shown in the figure, and the mode and median of the number of people who ran the red light in each time period were as follows

15，20 (D) 10，20

9. As shown in the picture, Xiaohong wants to make a conical funnel model with a height of 4cm and a bottom circumference of 6πcm with cardboard. If seams and wear are not counted, the cardboard area she needs is

(A) 12πcm2(B) 15πcm2(C) 18πcm2(D)24πcm2

10. It has the following functions: ① y =-3x; ②y = x– 1:③y =-(x & lt； 0); ④y = x2+2x+ 1。 Among them, when X is in the range of independent variables, the function of Y increasing with the increase of X is as follows

(A)①② (B)①④ (C)②③ (D)③④

Volume 2 (multiple choice questions, ***70 points)

Precautions:

Volume two and volume two of 1 A *** 10 page, answer directly on the test paper with a blue-black pen or ballpoint pen.

2. Fill in the items in the sealed line clearly before answering the questions.

Fill in the blanks: (4 points for each small question, *** 16 points)

Write the answer directly on the horizontal line of the topic.

1 1. At present, there are two volleyball teams, A and B. The average height of players in each team is 1.85 m, and the variance is =0.32 and =0.26 respectively. So the team with neat height is the team.

12. It is known that x = 1 is the root of the unary quadratic equation 2x2+kx–1= 0, then the value of the real number k is.

13. As shown in the figure, given that PA is the tangent of ⊙O, the tangent point is A, PA = 3, ∠ Apo = 30, then OP =.

14. As shown in the figure, in the plane rectangular coordinate system, △PQR is a graph obtained by some transformation of △ABC. Observe the coordinate relationship between point A and point P, point B and point Q, and point C and point R. Under this transformation, if the coordinate of any point M in △ABC is (x, y), the coordinate of their corresponding point N is.

Three. (15 is 6 points for each small question, 16 is 6 points, *** 18 points)

15. Answer the following questions:

(1) calculation:.

(2) Simplify:

16. Solve the inequality group and write the maximum algebraic expression solution of the inequality group.

Iv. (8 points for each small question, *** 16 points)

17. As shown in the figure, the math extracurricular activity group of Class 1, Grade 9 in a middle school uses weekends to carry out extracurricular practical activities. They want to measure the distance between two small islands C and D in the lake on Mount AB next to the artificial lake in the park. The depression angle of the island C in the lake is 60 from the top of the mountain A, and the depression angle of the island D in the lake is 45. It is known that the height of hill AB is180m.

18. As shown in the figure, it is known that the image of inverse proportional function y = passes through point A (1, -3), and the image of linear function y = kx+b passes through point A and point C (0, -4), and intersects with the image of inverse proportional function at another point B. 。

(1) Try to determine the expressions of these two functions;

(2) Find the coordinates of point B. 。

Verb (abbreviation of verb) (for each small question 10, ***20)

19. An opaque carton contains four balls with the same shape, size and texture, which are marked with the numbers 1, 2, 3 and 4 respectively.

(1) Take out two balls at a time from the carton, and find the probability that one of the numbers marked on the two balls is odd and the other is even;

(2) First, randomly take out a small ball from the carton, and use the number marked on the ball as the tenth digit; Put the ball back, take out a ball at random, and take the number marked on the ball as a digit. What is the probability that the two digits can be divisible by 3? Try to use tree diagram or list method to explain.

20. It is known that in trapezoidal ABCD, AD‖BC, AB = DC, E and F are points on the sides of AB and BC respectively.

(1) As shown in Figure ①, fold the trapezoidal ABCD with EF as the symmetry axis, so that point B coincides with point D, DF⊥BC. If AD =4 and BC=8, find the area value of trapezoidal ABCD;

(2) As shown in Figure ②, connect EF and extend the extension line to point G with DC. If FG=k? What is the quantitative relationship BEtween EF(k is a positive number), be and CG? Write your conclusion and prove it.

Volume B (***50 points)

1. Fill in the blanks: (4 points for each small question, * * * 20 points)

Write the answer directly on the horizontal line of the topic.

2 1. Given that y = x–1,the value of x2–2xy+3y2–2 is.

22. A farmer rented a seeder to sow wheat. Two days after the first seeder sowed, it transferred the second seeder to participate in sowing until it completed the sowing task of 800 mu. The functional relationship between the number of acres sown and the number of days is as shown in the figure, so the number of days that the second seeder participates in sowing is.

23. As shown in the figure, it is known that point A is within the acute angle ∠MON. Try to determine points B and C ON OM and ON respectively to minimize the perimeter of △ABC. Write down the main steps of your drawing and mark the points you have determined.

(It is required to draw a sketch and keep the trace)

24. If m is 0, any number in 1, 2, 3, and n is any number in 1, 2, then the probability that the quadratic equation x2–2mx+N2 = 0 has real roots is.

25. As shown in the figure, it is known that A, B and C are three points on ⊙O, AB= 15cm, AC=3 cm, ∠ BOC = 60. If D is a point on BC line and the distance from D to straight line AC is 2, BD= cm.

Second, (**8 points)

26. Jin Quan Street Reconstruction Project Headquarters wanted to bid for a bid project, and received bids from two construction teams, A and B. It was learned from the bids that the number of days required for Team A to complete the project alone was the number of days required for Team B to complete the project alone; If Team A works for 10 days first, the remaining works can be completed by Team A and Team B in 30 days.

(1) How many days will it take for Team A and Team B to finish this project alone?

(2) It is known that the daily construction cost of Team A is 8400 yuan, and that of Team B is 5600 yuan. The construction cost of the project budget is 500,000 yuan. In order to shorten the construction period and reduce the impact on residents, team A and team B are planned to cooperate to complete the project. Is the construction cost of the project budget enough? If not, how much extra budget is needed? Please give your judgment and explain the reasons.

Three. (*** 10 point)

27. As shown in the figure, it is known that the radius of ⊙O is 2, the chord AB=2 of ⊙O is ⊙M in diameter, and the point C is the moving point on the optimal arc of ⊙O (not coincident with the points A and B). Connect AC and BC, intersect ⊙M at point D and point E respectively, and connect D E.

(1) The number of times to find ∠C;

(2) Find the length of DE;

(3) If tan∠ABC=y, = x (0

Four. (*** 12)

28. As shown in the figure, in the plane rectangular coordinate system xOy, the coordinate of vertex A of △OAB is (10,0), vertex B is in the first quadrant, and =3, sin∠OAB=.

(1) If point C is the symmetrical point of point B relative to the X axis, find the functional expression of parabola passing through O, C and A;

(2) In (1), is there a point p on the parabola, which makes the quadrilateral with the vertices of p, o, c and a trapezoid? If it exists, find the coordinates of point P; If it does not exist, please explain the reason;

(3) If point O and point A are transformed into point Q( -2k, 0) and point R(5k, 0) (k >; Constant 1), let two points (q and r) be set, the intersection of a parabola with QR's median vertical axis and Y axis is n, its vertex is m, and the area of △QNM is the area of △QNR. The value of:.

In 2008, Chengdu, Sichuan Province, took the senior high school entrance examination in mathematics.

Mathematics Reference Answers and Grading Opinions (including Chengdu Grade Three Graduation Examination)

Volume 1 (*** 100)

The first volume (***30 points)

1. Multiple choice questions: (3 points for each small question, * * * 30 points)

1.b； 2.a； 3.d； 4.b； 5.c；

6.c； 7.d； 8.a； 9.b； 10.C。

Volume II (***70 points)

Fill in the blanks: (4 points for each small question, *** 16 points)

1 1 . b； 12. 13.； 14.。

Three. (15 is 6 points for each small question, 16 is 6 points, *** 18 points)

15.( 1) solution: 4 points for the original formula.

.2 points

(2) Solution: the original formula scored 4 points.

.2 points

16. Solution: 0.2 points for solving inequality.

0.2 points for solving inequality.

The solution set of inequality group is. 1 point.

The largest integer solution of this inequality group is 2. 1 min.

Iv. (8 points for each small question, *** 16 points)

17. solution: as shown in the figure, from known to available, 0.2 points.

Yes,.

In the middle again,

, that is.

.3 points

(m) .2 points

A: The distance between the islands is 0. 1 minute.

18. Solution: (1) Image passing point of inverse proportional function,

, that is.

The expression of the inverse proportional function is 0.3 points.

The image of the linear function passes through the point,

solve

The expression of a linear function is 0.3 points.

(2) By elimination, we get.

Namely.

Or ...

Available or.

So still

The coordinates of this point are,

The coordinates of this point are 0.2 points.

Verb (abbreviation of verb) (for each small question 10, ***20)

19. Solution: (1) Take two balls out of the carton at random. All possible outcomes of these figures are as follows:

***6 kinds;

There are four kinds of tag numbers, one is odd and the other is even. Three points

.2 points

(2) draw a tree diagram:

Or list method:

1 2 3 4

1 ( 1 1) ( 12) ( 13) ( 14)

2 (2 1) (22) (23) (24)

3 (3 1) (32) (33) (34)

4 (4 1) (42) (43) (44)

3 points

There are 16 possible results, 5 of which are divisible by 3.

.2 points

20.( 1) solution: from the meaning of the question, there is.

. 1 point

As shown in the figure, the point is made on the point.

Then a quadrilateral is a rectangle.

In and,

, ,

. (HL)

.2 points

. 1 point

(2) Guess: (or). 1.

Proof: as shown in the figure, after a little work, give it to the point.

Then.

Say it again,

That is.

. That is. Two points.

, .

It is an isosceles trapezoid.

. .

. 1 point

Volume B (***50 points)

1. Fill in the blanks: (4 points for each small question, * * * 20 points)

2 1. 1; 22.4;

23. Do some symmetry points respectively; Links, respectively, at point, point, point is what you want. (2 points) as shown in the figure (2 points);

24.； 25.。

Second, (**8 points)

26. Solution: (1) It takes days for Team B to complete the project alone, but it takes days for Team A to complete the project alone.

According to the meaning of the question, you get.

Solve.

It is proved to be the root of the original equation. 3 points

Answer: It takes 60 days and 90 days for Team A and Team B to complete this project alone. 6438+0 points.

(2) It will take several days for Team A and Team B to cooperate to complete this project.

Get 0.2 points.

Required project cost: (ten thousand yuan). 1 min.

The construction cost of the project budget is not enough, so an additional budget of 4000. 1 yuan is needed.

Three. (*** 10 point)

27. Solution: (1) link.

And then in,

, ,

, .

Link. Then.

.3 points

[or: extend and intersect at a point, link.

Yes, and.

In ..

Say it again,

, .]

(2) In and,

, ,

Link. Then.

Yes,

, .

That is.

.3 points

[or: the point moves on a plane with the same length. When the point moves to the intersection of the extension line and the intersection point, it can be obtained. ]

(3) links.

Yes, the diameter.

By, available,.

Yes,

, ,

;

It can also be seen from (2).

.3 points

Yes,

. 1 point

[Or: From (2), we know that,

It can be seen from (2) that …

Contact. In, from Pythagorean theorem, we get

Again, that is.

but

]

Four. (*** 12)

28. Solution: (1) As shown in the figure, the passing point is on the point.

Yes,

, ,

According to Pythagorean theorem,

Yes

The point is in the first quadrant,

The coordinates of this point are.

The coordinate of a point about an axisymmetric point is .2 minutes.

Let the function expression of parabola passing through three points be

pass by

The function expression of parabola passing through three points is .2 points.

(2) Suppose there is a point on the parabola in (1), so that a quadrilateral with vertices is a trapezoid.

① This point is not the vertex of a parabola,

Parallel lines passing through a point intersect parabola as straight lines at a point.

Then the functional expression of the straight line is.

Be, make or be.

There's still a little ...

Obviously quadrilateral.

A point is a point that meets the requirements. 1 min.

2 if. Let the functional expression of a straight line be.

If you replace these points, you will get.

The functional expression of the straight line is.

Therefore, the function expression of a straight line can be set to.

If you replace these points, you will get.

The functional expression of the straight line is.

That is to say.

There's still a little ...

If the intersection point is the axis of the point, then.

In, from Pythagorean theorem, we get.

And ...

In quadrilateral, but.

A point is a point that meets the requirements. 1 min.

3 if. Let the functional expression of a straight line be.

Substitute in the integral and you get.

The functional expression of the straight line is.

That is to say.

There's still a little ...

If the intersection point is the axis of the point, then.

In, from Pythagorean theorem, we get

And ...

In quadrilateral, but.

A point is a point that meets the requirements. 1 min.

To sum up, there is a point on the parabola in (1).

Make a quadrilateral with a trapezoid vertex. 1 min.

(3) According to the topic, the opening of parabola may be upward or downward.

① When the parabolic opening is upward, the parabola intersects the negative semi-axis of the shaft at the point.

The function expression of parabola can be set to.

Namely.

As shown in the figure, the axis of the intersection is on the point.

.2 points

② When the parabolic opening is downward, the parabola intersects with the positive semi-axis of the shaft at this point.

Similarly, you can get. 1 minute.

To sum up, the value of is. 1.

Previous article:Weather forecast sign
Next article:What month is suitable for Lijiang?