Find the math test questions and answers of Wuhan 20 10 senior high school entrance examination.

20 10 Mathematics Examination Paper for Senior High School Entrance Examination in Wuhan, Hubei Province

Name: _ _ _ _ _ _ Score: _ _ _ _ _ _ _

The first volume (multiple choice questions, ***36 points)

1. Multiple choice questions (* * 12 questions, 3 points for each question, ***36 points) There are four alternative answers to the following questions, of which one and only one is correct. Please black out the code of the correct answer on the answer sheet.

1. The reciprocal of rational number 2 is

Article 2 (2) (3) (4)

2. The value range of the independent variable X in the function y= is

x 1(B)x 1(C)x 1(D)x 1

3. As shown in the figure, the solution set of an inequality group is expressed on the number axis, so this inequality group may be

(A)x & gt； 1，x & gt2(B)x & gt； 1，x & lt2(C)x & lt； 1，x & lt2(D)x & lt； 1，x & gt2

4. The following statement: "To throw a coin with uniform texture, you must face up"; "Randomly drawn from a deck of ordinary playing cards.

First, the number of points must be 6 ";

Everyone is right.

5. In the first month of the opening of Expo 20 10, 6.64 million tickets were sold, and 6.64 million tickets were expressed by scientific counting method.

664 104(B)66.4 105(C)6.64 106(D)0.664 107

6. As shown in the figure, there is a point d in △ABC, and DA=DB=DC. If DAB=20 and DAC=30, the size of BDC is

100 80 70 50

7. If x 1 and x2 are two roots of the formula x2=4, the value of x 1x2 is

8 (B) 4 (C) 2 (D) 0 .

As the picture shows, there is a cylindrical tea box and a cubic ink box on Miss Li's desk. When Xiao Fang looks from above, the figure he sees is

9. As shown in the figure, the centers of all squares are at the origin of coordinates, and each side is parallel to the X axis or the Y axis. From the inside out, their side lengths are 2, 4, 6, 8, ... and their vertices are A 1, A2, A3, A4, ..., so the coordinates of vertex A55 are

(A) ( 13， 13) (B) ( 13， 13) (C) ( 14， 14) (D) ( 14， 14)。

10. As shown in the figure, the diameter AB of the circle O is 10, the chord AC is 6, and the ACB is flat.

If the bisector intersects the circle O in D, the length of CD is (A) 7 (B) 7 (C) 8 (D) 9.

1 1. With the development of economy, people's living standards are constantly improving. The figure below shows the statistics of the total number of tourists and the annual growth rate of tourism revenue in a scenic spot from 2007 to 2009. It is understood that the tourist income of this scenic spot in 2008 was 45 million yuan. The following statement:

Among the three years, the income of tourists in this scenic spot was the highest in 2009; Compared with 2007, the tourism revenue of this scenic spot increased by [4500 (129%) 4500 (133%)] ten thousand yuan in 2009. According to the annual growth rate of tourists in 2009, the total number of tourists in this scenic spot will reach 2.8 million in 20 10. Where is the correct number?

(A) 0 (B) 1 (C) 2 (D) 3

12. As shown in the figure, in the right-angled trapezoidal ABCD, AD//BC, ABC = 90, BDDC, BD=DC, CE bisects BCD, AB intersects at point E, BD intersects at point H, and EN//DC intersects at point N BD .. The following conclusions: BH = DHCH = (1. =; The correct answer is

Only (a), (b), (c) and (d).

Volume 2 (multiple choice questions, ***84 points)

Fill in the blanks (***4 small questions, each with 3 points, *** 12 points)

13. calculation: sin30=, (3a2)2=, =.

14. The weights (unit: kg) of four girls in Class 2, Grade 8 in a school are 35, 36, 38 and 40 respectively. The median of this set of data is.

15. As shown in the figure, if the straight line y 1=kxb intersects with point A (0 0,2) and the straight line y2=mx intersects with point P (1, m), it is not equal.

The solution set of type group mx & gtkxb & gtmx2 is.

16. As shown in the figure, the straight line y= xb intersects with the Y axis at point A, and the hyperbola y= is in the first picture.

If the intersection is limited to b and c, and AB AC = 4, then k=.

Third, answer questions (***9 small questions, ***72 points)

17. (The full mark of this question is 6) Solve the equation: x2x 1=0.

18. (The full mark of this question is 6) Simplify first and then evaluate: (x2), where x=3.

19. (The full mark of this question is 6) As shown in the figure. Points b, f, c and e are on the same straight line, and points a and d.

On both sides of the straight line are BE, AB//DE, AC//DF, BF=CE. Proof: AC=DF.

20. (The full mark of this question is 7) Xiao Wei and Xiaoxin play a card-drawing game: the back is exactly the same, and the front is written with 1, 2, 3 respectively.

After mixing four 4 cards, Xiao Wei randomly chooses one card from them. Write down the numbers and put them back. After mixing, Xiao Xin randomly chooses one.

Zhang, write down these numbers. If the sum of the two recorded numbers is greater than 4, there will be little students; If the sum of the two recorded numbers is not greater than 4,

Then Xiao Xinsheng.

(1) Please use the list or draw a tree diagram. Calculate the winning probabilities of Xiao Wei and Xiao Xin respectively;

(2) If the card number drawn by Xiao Wei is 1, who is more likely to win the prize? Why?

2 1. (The full mark of this question is 7)

(1) In the plane rectangular coordinate system, translate point A (3 3,4) to the right by 5 units to point A 1, and then rotate point A 1 clockwise by 90 degrees around the coordinate origin to point A2. Write the coordinates of points A 1 and A2 directly;

(2) In the plane rectangular coordinate system, translate the point B(a, b) in the second quadrant to the right by m units to the point B 1 in the first quadrant, then rotate the point B 1 clockwise by 90 degrees to the point B2 near the coordinate origin, and directly write out the coordinates of the point B 1, b2;

(3) In the plane rectangular coordinate system. Translate the point P(c, d) horizontally by n units to the point P 1, and then rotate the point P 1 around the coordinate.

Rotate the origin clockwise by 90 degrees to point P2, and write the coordinates of P2 directly.

22. (The full mark of this question is 8 points) As shown in the figure, point O is equally divided on APB, and circles O and PA are tangent to point C;

(1) Verification: The straight line PB is tangent to the circle O;

(2) The extension line of 2)PO intersects with circle O at point E ... If the radius of circle O is 3, PC=4. Find the chord length CE.

23. (The full mark of this question is 10) A hotel has 50 rooms for tourists to stay in. When the price of each room is 180 yuan per day, all rooms will be occupied. If the daily price of each room increases by 10 yuan, one room will be free. For every room that tourists stay in, the hotel needs to pay all kinds of expenses in 20 yuan. According to the regulations, the daily house price cannot be higher than that in 340 yuan. Let's assume that the price of each room increases by X yuan per day (X is a positive integer multiple of 10).

(1) Let the number of rooms scheduled for one day be y, and directly write the functional relationship between y and x and the range of the independent variable x;

(2) Let the daily profit of the hotel be W yuan, and find the functional relationship between W and X;

(3) How many rooms are booked a day, and what is the maximum profit of the hotel? What is the maximum profit?

24. (Full score of this question 10) Known line segment OAOB, point C is the midpoint of OB, and point D is a point on line segment OA. Connect AC and BD at point p.

(1) as shown in figure 1, when OA=OB and d is the midpoint of OA, the required value;

(2) As shown in Figure 2, when OA=OB and =, find the value of tanBPC;

(3) As shown in Figure 3, when AD: AO: OB = 1: N: 2, write the value of tanBPC directly.

25. (Full score of this question 12) As shown in the figure, the parabola y 1=ax22axb passes through two points, A (1 0) and C(2,), and intersects with the X axis at another point, B;

(1) Find the analytical expression of this parabola;

(2) If the vertex of parabola is m, point P is the moving point on line segment OB (not coincident with point B), point Q moves on line segment MB, MPQ = 45°, let line segment OP=x, MQ=y2, find the functional relationship between y2 and X, and directly write the value range of independent variable X;

(3) In the same plane rectangular coordinate system, two straight lines x=m and x=n intersect with parabola at points E and G respectively, and the function image in (2) intersects with points F and H respectively. Can quadrilateral EFHG be a parallelogram? If yes, find the quantitative relationship between m and n; If not, please explain why.

20 10 mathematical solutions for the senior high school entrance examination in Wuhan, Hubei province

First, multiple-choice questions:

1. Answer, 2. Answer 3. b，4。 d，5。 c，6。 Answer, 7. d，8。 Answer, 9. c， 10。 b， 1 1。 c， 12。 b，

Second, fill in the blanks

13.，9a4，5， 14。 37, 15. 1 & lt； x & lt2, 16.,

Third, answer questions.

17. solution: ∫a = 1, b= 1, c= 1, ∴ = b24ac =141(/kloc-0

18. solution: the original formula = =2 (x3), and when x=3, the original formula =2.

19. proof: ∫ab//de, ∴ABC=DEF, ∫AC//df, ∴ACB=DFE, bf = ec, ∴BC=EF,

∴△ABC△DEF,∴AC=DF。

20. Solution: (1) has 16 possible results, in which the sum of numbers of 10 is greater than 4 and the sum of numbers of 6 is less than 4.

P (small students) = =, P (small freshmen) = =;

(2) P (small students) =, p (small freshmen) =, small freshmen may win.

2 1. Solution: (1) The coordinate of point A 1 is (2,4), and the coordinate of A2 is (4,2);

(2) the coordinate of point B 1 is (am, b), and the coordinate of B2 is (b, am);

(3) The coordinate of 3)P2 is (d, cn) or (d, cn).

22.( 1) It is proved that the intersection o is ODPB at point D, which is connected with OC. * tangent circle o at point c of pa, ∴OCPA. Point o is on the bisector of ∴oc=od. APB ∴PB is tangent to circle o.

(2) Solution: do CFOP at point F after crossing point C. In Rt△PCO, PC=4, OC=3, OP=5, =5, ∫ocpc = opcf = 2s△pco, ∴CF=. In Rt△COF, OF==. ∴EF=EOOF=,∴CE==。

23. Solution: (1) y=50x (0x 160, where x is an integer multiple of 10).

(2)W =(50x)( 180 x20)= x234x 8000；

(3) w = x234x8000 = (x170) 210890, when x

When x= 160, the maximum value is w = 10880, while when x= 160, y=50x=34. Answer: If you book 34 rooms a day, the hotel will make the biggest profit every day, with a maximum profit of 10880 yuan.

24. solution: (1) extend AC to point e, make CE=CA, connect BE, and ∵C is the midpoint of OB.

∴△BCE△OCA,∴BE=OA,E=OAC,∴BE//OA，

∴△APD~△EPB,∴=。 And ∵D is the midpoint of OA,

OA=OB,∴==。 ∴==,∴=2。

(2) extend AC to point h so that CH=CA, and connect BH and ∵C as the midpoint of OB,

∴△BCH△OCA,∴CBH=O=90,BH=OA。 By =,

Let AD=t and OD=3t, then BH=OA=OB=4t. In Rt△BOD,

BD==5t,∵OA//BH,∴△HBP~△ADP，

∴===4。 ∴BP=4PD=BD=4t,∴BH=BP。

∴tanBPC=tanH===。

(3) tanBPC= .

25. solution: (1) ∵ parabola y 1=ax22axb passes through two points, a (1, 0) and C(0), ∴, ∴a=

The analytical formula of b=, ∴ parabola is y 1= x2x.

(2) MNAB, whose vertical foot is n. M (1, 2) is easily obtained from y 1= x2x,

n( 1,0),a( 1,0),b(3,0),∴ab=4,mn=bn=2,mb=2，

MBN=45. According to Pythagorean theorem, there is BM 2BN 2=PM 2PN 2.

∴(2)222=PM2 (1x)2…, while MPQ=45=MBP,

∴△MPQ~△MBP,∴PM2=MQMB=y22…。

Y2=x2x is obtained by and. ∵0x & lt； 3. ∴ The functional relationship between Y2 and X is y2 = x2x (0x

(3) the quadrilateral EFHG can be a parallelogram, and the quantitative relationship between m and n is

Mn=2(0m2 and m 1). Point E and point G are parabolas y 1= x2x.

The intersections with straight lines x=m and x=n, respectively, and the coordinates of points e and g are

E(m, m2m), G(n, n2n). Similarly, the coordinates of point F and point H.

Is F(m, m2m), H(n, n2n).

∴ef=m2m(m2m)=m22m 1,gh=n2n(n2n)=n22n 1。

∵ quadrilateral EFHG is a parallelogram, EF=GH. ∴m22m 1=n22n 1,∴(mn2)(mn)=0。

Manganese, ∴mn=2 (0m2 and m 1).

So the quadrilateral EFHG can be a parallelogram, and the quantitative relationship between m and n is mn=2 (0m2 and m 1).