mathematics

1. Multiple choice questions (only one alternative answer to the following questions is correct, with 3 points for each small question and 24 points for * * *).

1. The picture in the lower left corner shows a geometric figure composed of six identical cubes. The top view of this geometry is

2. In response to the national call of "developing a low-carbon economy and living a low-carbon life", there are 60,000 residents in Shenyang.

The court has established a "low-carbon energy-saving and emission-reduction family file", so the figure of 60000 is expressed by scientific notation as (A) 60? 104

(B) 6？ 105 (C) 6？ 104 (D) 0.6？ 106 。

3. Which of the following operations is correct (A) x2? x3=x5 (B) x8？ x2=x4 (C) 3x？ 2x= 1 (D) (x2)3=x6 .

4. The following events are inevitable: (a) The shooter hit the bull's-eye with one shot; (b) buying movie tickets at will,

The seat number is even. (c) Take out a ball from a bag with only a red ball. Throw a ball with even texture.

The coin landed face up.

5. As shown in the figure, in the plane rectangular coordinate system established on the square paper, press Rt△ABC around point C..

Turn 90 clockwise? , get Rt△FEC, then the coordinates of point A corresponding to point F are

(1) (? 1， 1) (B)(？ 1，2) (C) ( 1，2) (D) (2， 1).

6. Inverse proportional function y=? The image is located in (a) the first and second quadrants, and (b) the second and third quadrants.

(c) first and third quadrants (d) second and fourth quadrants.

7. In the radius 12? o，60？ The arc length of the central angle is (A) 6? (B) 4？

(C) 2？ (D)？ . .

8. As shown in the figure, in equilateral △ABC, D is a point on the side of BC, E is a point on the side of AC, and

? ADE=60？ , BD=3, CE=2, then the side length of △ABC is (A) 9 (B) 12.

(C) 15 (D) 18 .

Fill in the blanks (4 points for each small question, 32 points for * * *)

9. A set of data 3, 4, 4, 6, the range of this set of data is.

10. Calculation: () 0=.

1 1. Decomposition factor: x2? 2xy？ y2= .

12. linear function y=? 3x？ In 6, the value of y increases with the value of x.

13. The solution set of the inequality group is.

14. As shown in the figure, in □ ABCD, point E is on the side of BC, be: EC = 1: 2,

Connect AE and BD at point F, and then sum the area of △BFE and the area of △DFA.

Than.

15. In the plane rectangular coordinate system, points A 1( 1, 1), A2 (2 2,4), A3 (3 3,9), A4 (4 4,0/6), ...

Determine the coordinates of point A9 as.

16. If the sum of the upper and lower bottoms of the isosceles trapezoid ABCD is 2, the acute angle formed by the two diagonals is 60? , isosceles trapezoid

The area of ABCD is.

Iii. Solving problems (sub-items 17 and 18 8, 19, 10, * * 26).

17. Simplify before evaluating:? , where x=? 1。

18. Xiao Wu visited the World Expo in Shanghai during the holiday. According to the tourist flow, Xiao Wu decided to go to China Pavilion (Hall A) and Japan on the first day.

Randomly choose one of the pavilions in (b) and (c) to visit, and the pavilions from France (d), Saudi Arabia (e) and Finland will be visited the next day.

(f) Choose a museum to visit at random. Please use list method or draw a tree diagram (tree diagram) to invite Xiao Wu to visit on the first day.

Probability of visiting the China Pavilion (A) and the Finland Pavilion (F) the next day. (The National Pavilion can be represented by corresponding letters)

19. As shown in the figure, the diagonal lines AC and BD of rhombic ABCD intersect at point O, and points E and F are edges respectively.

The midpoint OF AB and AD connects EF, OE and of. It is proved that the quadrilateral AEOF is a diamond.

Iv. (For each small question 10, ***20)

On 20.201April 14, domestic refined oil prices rose for the first time this year, and the price of No.93 gasoline in a city was raised from 6.25.

Yuan/liter rose to 6.52 yuan/liter. An investigator in a newspaper asked the question "the impact of rising gasoline prices on car use"

Private car owners who own motor vehicles conducted a questionnaire survey and made some statistical charts as follows:

Percentage of car owners

A. no 4% impact

B. it has little impact and can accept p.

C.yes, the number of cars used has decreased by 52%.

D. it has a great impact and needs to give up using the car m.

E. Don't care about this problem 10%

(1) Combined with the above statistics, we can get: p=, m =；;

(2) According to the above information, please fill in the bar chart directly in the answer sheet;

(3) At the end of April, 2065438+00, if there are about 200,000 private car owners in this city, please estimate according to the above information.

How many cars host the attitude of "little impact, acceptable"?

2 1. As shown in the figure, what is AB? The diameter of O, the point C is on the extension line of BA, and the straight line CD and

? O is tangent to point d, and the chord DF? AB is at point E, and the line segment CD= 10 is connected to BD;

(1) Verification:? CDE=2？ b；

(2) What if BD: AB =: 2? The radius of o and the length of DF.

V. (This question 10)

22. Read the following materials to solve the following problems:

★ Reading materials:

(1) Contour concept: On the map, we call it a closed curve connected by points with the same altitude on the ground contour.

For example, as shown in figure 1, connecting points with altitudes of 50m, 100m and 150m respectively forms 50.

M, 100 m and 150 m.

(2) The steps of using contour topographic map to find the slope are as follows (as shown in Figure 2).

Step 1: Read out the heights of points A and B respectively according to the contour topographic map where points A and B are located; A and B.

Vertical distance = height difference between point A and point B;

Step 2: Measure the distance of AB in units of D on the contour topographic map. If the scale of the contour topographic map is

1: n, then the horizontal distance between point A and point B = DN.

Step 3: AB = = slope;

Please fill in the blanks according to the following problem-solving process and write the results directly on the answer sheet.

Xiaoming and Xiaoding are students in a middle school. They live in a mountain city. As shown in figure 3 (schematic diagram), Xiao Ming goes to school from home A to home B every day.

AB and BP learn P on the road, and Xiaoding learns P. Mountain contour topographic map from home C along CP road every day.

The ratio is 1: 50000. On the contour topographic map, AB =1.8cm, BP = 3.6cm, CP = 4.2cm ..

(1) Calculate the slopes of AB, BP and CP respectively (the slight change of the slope in the middle of the same section is ignored);

(2) If they leave home on foot at 7 o'clock in the morning without stopping, who will get to school first? (Assume that when the slope is between and.

The average walking speed of Xiaoming and Xiaoding is about1.3m/s; When the slope is between and, Xiaoming and Xiao.

The average walking speed is about 1 m/s)

Solution: Horizontal distance of (1) AB = 1.8? 50000=90000 (cm) =900 (m), and the slope of AB = =;

Horizontal distance of BP =3.6? 50000 =180000 (cm) =1800 (m), and the slope of BP = =;

Horizontal distance of CP =4.2? 50000=2 10000 (cm) =2 100 (m), and the slope of CP =? ;

(2) Because

Because? So what is the average walking speed of Xiaoding on CP? M/s, slope

The distance of AB =? 906 (m), the distance of slope BP =? 18 1 1 (m), oblique

Slope distance CP =? 2 12 1 (m), so the time from home to school for Xiaoming =

=2090 (seconds). How long does Xiaoding spend from home to school? Seconds. So? Get to school first.

Six, (this question 12 points)

23. Company A has two green agricultural products planting bases, A and B, and some agricultural products are harvested on the same day in the harvest period.

Part of it is stored in the warehouse, and the other part is shipped to other places for sale. According to experience, this agricultural product is harvested in two planting bases.

Cumulative total output y (ton) and harvest days x (days) satisfy the functional relationship y=2x? 3 ( 1? x？ 10 and x is an integer). Agricultural products are on the market

During the harvest period, the cumulative output of base A and base B accounts for the percentage of the total output of the two bases and the cumulative output of base A and base B respectively.

In the cumulative output of the two bases A and B, the percentage of the quantity stored in the warehouse is as follows:

The cumulative output of the project accounts for the proportion of the base.

Percentage of the cumulative total output of the two bases, and the cumulative storage volume of the bases accounts for.

Percentage of base cumulative output

per cent

Planting base

60% 85%

B 40% 22.5%

(1) Please use an algebraic expression containing y to express the cumulative warehousing quantity of two cardinals at harvest;

(2) The total amount of agricultural products stored in the warehouse by Base A and Base B during harvesting is P (ton), so P (ton) is requested.

Functional relationship with harvest days x (days);

(3) On the basis of (2), if there are 42.6 tons of this agricultural product in the warehouse, the harvest period will start to meet the local market demand.

At the same time, some of these agricultural products are transferred from the warehouse and put into the local market every day. If farmers sell in the local market

The total product m (ton) and the harvest days x (days) satisfy the functional relationship m=? x2？ 13.2x？ 1.6 ( 1? x？ 10 and x is an integer).

Q: How many days have agricultural products been sold continuously in this harvest period, and the inventory of this agricultural product has reached the lowest value? What is the minimum inventory?

Seven, (this question 12 points)

24. As shown in figure 1, in △ABC, point P is the midpoint of BC side, and straight line A rotates around vertex A. If B and P are on opposite sides of straight line A,

BM？ Line a is at point m, CN? Line a is at point n, connecting PM and pn;

(1) Extend MP to point E (as shown in Figure 2). ? Proof: △BPM? △CPE； ? Verification: PM = PN；;

(2) If the straight line A rotates around the point A to the position in Figure 3, the points B and P are on the same side of the straight line A, and other conditions remain unchanged. now

Is PM=PN still valid? If yes, please give proof; If not, please explain the reasons;

(3) If the straight line A rotates around the point A to a position parallel to the BC side, other conditions remain unchanged. Please judge the quadrilateral MBCN directly.

Is the shape and PM=PN still valid at this time? There is no need to explain why.

Eight, (this question 14 points)

25. as shown in figure 1, in the plane rectangular coordinate system, the parabola y=ax2? C intersects with the positive semi-axis of X axis at point F (16,0) and with the positive semi-axis of Y axis.

The axis intersects with the point E (0, 16), and the vertex D of the square ABCD with the side length of 16 coincides with the origin O, and the vertex A is heavier than the point E.

Closed, vertex c coincides with point f;

(1) Find the function expression of parabola;

(2) As shown in Figure 2, if the square ABCD moves in the plane and the BC side is always perpendicular to the straight line of the X axis, it is a parabola.

The line always intersects with AB edge at point P, and intersects with CD edge at point Q (when moving, point P does not coincide with points A and B,

Point q does not coincide with points c and d). The coordinate of point a is (m, n) (m >; 0)。

? When PO=PF, the coordinates of point p and point q are obtained respectively;

? Are you online? On the basis of, when the square ABCD is translated left and right, please write the value range of m directly;

? When n=7, is there an m value that makes point P the midpoint of AB edge? If yes, request the value of m; If it doesn't exist

Yes, please explain why.

Shenyang 20 10 unified entrance examination for secondary schools

Answer math questions

I. Multiple-choice questions: (3 points for each small question, ***24 points)

1.A 2。 C 3。 D 4。 C 5。 B 6。 D 7。 B 8。 A

Fill in the blanks (4 points for each small question, 32 points for * * *)

9.3 10.？ 1 1 1.(x？ Y)2 12。 Decrease 13. 1? x？ 114.1:915. (9,81)16. Or

Iii. Solving problems (8 points will be deducted for each item 17, 18, 19 and 10, and 26 points will be deducted for * * *).

17. [Solution] Original formula =? =, when x=? 1, the original formula = =.

18.[ Solution] By drawing a tree (shape) diagram; Or list:

Christian era

English (A, E)

Female (ah, female)

begin

B

D(B，D)

English (b, e)

F(B，F)

C

D(C，D)

English (Chinese, English)

Female (middle and female)

the next day

first day

A (a, d) (a, e) (a, f)

B (B，D) (B，E) (B，F)

C (C, D) (C, E) (C, F)

From the table (or tree diagram/tree diagram), we can see that * * * has 9 possible results, and the possibility of each result is similar.

At the same time, Xiao Wu happened to visit A on the first day and F on the second day, and got the result (A, F).

P (Xiao Wu happened to visit A on the first day and F on the second day) =.

19. [Proof] ∫ Points E and F are the midpoint of AB and AD respectively, ∴AE= AB and AF= AD.

∵ quadrilateral ABCD is diamond, ∴AB=AD, ∴AE=AF,

Similarly, the diagonal AC of diamond ABCD intersects BD at point O,

∴O is the midpoint OF BD, ∴OE and of are the midline of △ABD.

∴ Quadrilateral AEOF is a parallelogram, ae = af, and∴ Quadrilateral AEOF is a diamond.

Iv. (For each small question 10, ***20)

20.( 1) 24%, 10%;

(2) B: 960 people, D: 400 people;

(3) 200000? 24% = 48,000 people, so it can be estimated that it is a car with an attitude of "little impact and acceptable".

There are about forty-eight thousand people in the Lord.

2 1.( 1) [Proof] Connect OD, ∫ straight CD and? O is tangent to point d, ∴OD? CD，

∴? CDO=90？ ,∴? CDEODE=90？ And ∵DF? AB，

∴? DEO=？ DEC=90？ ,∴? EODODE=90？ ,

∴? CDE=？ EOD again? EOD=2？ B,∴？ CDE=2？ B.

(2) [Solution] Connect AD, ∫ab is the diameter o of the circle, ∴? ADB=90？ ,

∫BD:ab =:2, ∴△ADB in Rt, cosB= =,

∴? B=30？ ,∴? AOD=2？ B=60？ In Rt△CDO, CD= 10,

∴OD= 10tan30？ =, that is? The radius of o is, in Rt△CDE, CD= 10,? C=30？ ,

∴DE=CDsin30？ =5, ∫ chord DF? The diameter AB is at point E, ∴DE=EF= DF, ∴DF=2DE= 10.

V. (This question 10)

22.？ ? & lt& lt？ 1 ? 2 12 1 ? Xiao Ming (2 points in each space, * * * 10)

Six, (this question 12 points)

23. [Solution] (1)? Cumulative storage capacity of warehouse A in Base: 85%? 60%y=0.5 1y (ton),

? Accumulated storage in warehouse B of Base: 22.5%? 40%y=0.09y (ton),

(2) p=0.5 1y？ 0.09y=0.6y，∫y = 2x？ 3、∴p=0.6(2x？ 3)= 1.2x？ 1.8;

(3) that warehouse set up in this harvest period has t ton of this agricultural product,

T=42.6？ p？ m=42.6？ 1.2x？ 1.8? (? x2？ 13.2x？ 1.6)=x2？ 12x？ 46=(x？ 6)2? 10,

∵ 1 & gt； 0, the opening of ∴ parabola is upward, and ∵ 1? x？ 10, x is an integer,

When x=6, the minimum value of t is 10.

∴ After 6 days of continuous sales in this harvest period, the inventory of agricultural products reached the lowest value, and the lowest inventory was 10 ton.

Seven, (this question 12 points)

24.( 1)[ proof]? As shown in figure 2, ∫BM? Line a is at point m, CN? The straight line a is at point n,

∴? BMN=？ CNM=90？ ,∴BM//CN,∴？ MBP=？ ECP，

And ∵P is the midpoint between ∴BP=CP and ∵ BC? BPM=？ CPE,∴△BPM？ △CPE，

? ∵△BPM？ △CPE, ∴PM=PE, ∴PM= ME, ∴△MNE in Rt, PN= ME.

∴pm=pn；

(2) It holds, as shown in Figure 3.

【 Prove 】 The extension lines of extension MP and NC intersect at point E, ∫BM? Line a is at point m, CN? The straight line a is at point n,

∴? BMN=？ CNM=90？ ,∴? BMNCNM= 180？ ,∴BM//CN,∴？ MBP=？ ECP，

∵P is the midpoint of BC province, ∴BP=CP and ∵? BPM=？ CPE,∴△BPM？ △CPE,∴PM=PE，

∴PM= me, and then in Rt△MNE, PN= me, ∴PM=PN.

(3) The quadrilateral MBCN is a rectangle, and PM=PN holds.

Eight, (this question 14 points)

25. [Solution] (1) is composed of parabola y=ax2? C passes through points E (F( 16) and F( 16,0) to get:, and a=? ，c= 16，

∴y=？ x2？ 16;

(2) ? PG, some p? The x axis is at the g point, po = pf, ∴OG=FG, ∫ f (16,0), ∴OF= 16,

∴og= =? 16=8, that is, the abscissa of point P is 8 and point P is on a parabola.

∴y= 82？ 16= 12, that is, the ordinate of point p is 12, ∴ P (8, 12).

The ordinate of point ∵P is 12, the side length of square ABCD is 16, and the ordinate of point ∴Q is? 4,

∵Q is on a parabola, ∴? 4= ? x2？ 16,∴x 1=8，x2=？ 8 ,

∵m & gt； 0,∴x2=？ 8 (give up), ∴x=8, ∴Q(8,? 4);

? 8 ? 16 & lt； m & lt8;

? Does not exist;

Reason: When n=7, the ordinate of point P is 7, ∫ point P is on a parabola, ∴7=? x2？ 16,

∴x 1= 12,x2=？ 12，∵m & gt； 0,∴x2=？ 12 (omitted), ∴x= 12, ∴P point coordinates are (12,7),

∵P is the midpoint of AB, ∴AP= AB=8, ∴ The coordinates of point A are (4,7), ∴m=4,

The side length of square ABCD is 16, and the coordinate of point B is (20,7).

The coordinates of point C are (20,? 9) What is the ordinate of point Q? 9, ∫Q is on a parabola,

∴ ? 9= ? x2？ 16,∴x 1=20,x2=？ 20，∵m & gt； 0,∴x2=？ 20 (truncated), x=20,

Q point coordinates (20,? 9), ∴ point Q coincides with point C, which contradicts that point Q does not coincide with point C.

When n=7, there is no such value of m, that is, p is the midpoint of the AB side.