Mathematical paper

note:

1, full mark 150, test time 120 minutes. Use a calculator in the exam.

2. Before answering the questions, candidates should write their name, admission ticket number and seat number in the designated position.

After that, the answers for each question in the multiple-choice questions should be blacked out with 2B pencil labels, and the corresponding answers should be written on the answer sheet with a clean eraser. Non-multiple choice questions that cannot be answered in the questionnaire must be written on the answer sheet with a 0.5mm black pen, with neat font and clear handwriting.

The four multiple-choice questions must be answered in the order of the answers to the questions and questions on the answer sheet. , beyond the answering machine or other problems that are invalid in the title area. Answer waste paper, invalid questionnaire.

5. Draw the first picture with 2B pencil to describe the black decision. You must use a 0.5mm black pen.

6. After the exam, submit the test paper and answer sheet.

Multiple-choice questions (big questions 10, 4 points for each small question, 40 points for each small question) have only one topic option that meets the requirements of the topic.

(20 12, Urumqi, Xinjiang, 1, 4) 8th root ()

A, 2, -2 C 2 D,

one

(20 12, Urumqi, Xinjiang, 2,4 points) The digits and patterns of data 8,7,6,5,7,8,8 are ().

A, 5, answer] 7 B, 5, 8 C, 7, 7 D, 7, 8

[answer] d

3(20 12, Urumqi, Xinjiang, 3,4) as a geometric figure, its lateral area ()

a，8 B，C，D，2 4

Answer b

4, (20 12, Urumqi, Xinjiang, 4,4 points) In an opaque bag, there are black balls, white balls and a group of experimental balls: balls, which are randomly recorded in the color of the bag after stirring. On the right side of the repeating table is a set of activity data, and then the probability of clicking on the white ball is probably ()

A 0.4 B 0.5 C 0.6 D 0.7

[Answer] C p>5, (Urumqi, Xinjiang, 20 12, 5, 4) is the square of the side length (a+b) of (1), and the shape of the chart (2) composed of the shaded parts in the graph (1) can be verified.

A(A + B)(A-B)= A2-B2 B，(A+B)2-(A2+B2)= 2AB & lt； / C，(A + B)2 - (AB)2 = 4AB D，(AB)，2 +2 AB = A2 + B2

Answer] B

The image of (20 12 Urumqi, Xinjiang, 6,4 points) function (k is constant) passes through the volume (y2) of (2, y 1) point, then the relationship between y 1 and y2 is ().

a，Y 1 Y2，y 1 >； Y2 D is related to the value of k.

Answer a

7, (20 12, Urumqi, Xinjiang, 7, 4) In order to make the city "bluer and warmer", the government decided to carry out the renovation project, heating by coal and gas in winter. At present, two engineering teams A and B are excavating two 600-meter-long pipelines at the same time, respectively, and the excavation length Y(M) and the excavation time x (2) will be excavated by team B two days later.

a， 1 B，2 C，3 D，4

[answer] d

8(20 12, Urumqi, Xinjiang, August 4) Then, in the flat ABCD, there is a rectangular paper long enough to be folded with a straight crease at point A, so that point B falls on edge AD, and the intersection of the crease and edge BC is at point E; Then the straight crease of point E makes point A fall on the edge BC, and ∠AFE crease EF passes through the edge of dimension () of point F.

22.50 lbs, 450 degrees, 600 degrees, 67.50 degrees.

[answer] d

(Urumqi, Xinjiang, 20 12, 9,4 points) Ancient Greek mathematicians 1, 3,6, 10, 15, ... are all called trigonometric numbers, but the difference is 16 triangle,10.

A，30 B，3 1 C，32 D，33 A，B

10( 20 12, Urumqi, Xinjiang 10.4) AD∥BC, ∠D = 900, AD = 2, BC = 5, DC = DC, P is slightly better than △PAD, △PBC, so it is like this.

A 1 B 2 C 3 D，4 A. C

2. Fill in the blanks (4 points for each small question, 20 points for * * *) and fill in the answers directly in the corresponding positions on the answer sheet.

1 1, (20 12, Urumqi, Xinjiang, 1 1, 4 points) as shown in the figure, straight line A∨B, ∞ =

[Answer] 153

12, (20 12, Urumqi, Xinjiang, 12,4) decomposition factor X3-X =

[answer] X(X+1)(x- 1)

13, (20 12 Urumqi, Xinjiang, 13, 4 points) at the periphery of 20□ABCD, AB.

[Answer] 10

14(20 12, Urumqi, Xinjiang, 14, 4 points) function Y = X2+MX-4, when x

[Answer] M≤-4

15(20 12, Urumqi, Xinjiang, 15,4) isosceles △ABC is inscribed with the length of point O on the side of BC and AB within a distance of 5 ⊙ O.

A.2 or 4

Answer the questions in words (questions, big questions and 9 small questions, including IV, ***90 points), and the answers should be written in the corresponding positions on the answer sheet to prove or calculate the process.

Me (15, 7th minute, 16,17,8)

16(20 12, Urumqi, Xinjiang, 16, 7 points):

A.] solution: the original formula = 1 +3.

= 1

17, (20 12, Urumqi, Xinjiang, 17, 8 points) to solve inequalities:

[Answer] Solution: Solve the problem of x ≥ 1 2x- 1

Therefore, the original solution inequality 1 ≤ x

Two (the full score of this question is 32, the 8 o'clock question 18, 19 12, 12, 20 questions).

18(20 12, Urumqi, Xinjiang, 18,8), confirmation of diagonal AC and BE∑DF at point E and point F □ABCD: BF = DE.

[Answer] Proof: ∵ABCD is a parallelogram.

∴AD = CB，ad∑CB，

∴∠BCE =∠DAF

∫∫DF again,

∴∠BEC =∠DFA

At CEB and △AFD,

∠BCE =∠DAF∠BEC =∠DFA，BC = DA

∴△CEB?△AFD

∴BE = DF

So the parallelogram of BFED. ∴BF = Germany

19(20 12 Urumqi, Xinjiang, 19, 12) first bought a certain kind of fruit with 500 yuan, and the sales performance was good. The fruit of the same variety of shops and fruit shops is 1650 yuan, and the number of people who buy it is three times, but the purchase price is 0.5 per kilogram.

(1) The quantity of fruit purchased for the first time is USD per kilogram.

(2) For every kilogram of these fruits sold by fruit shops in 8 yuan, the first 5% of the fruits purchased are discounted, and the fruit shops with a loss of 2% are profitable in selling these fruits?

[Answer] Solution: (1) The first set share purchase price is $ X per kilogram of fruit, per question.

Solution, after testing, x = 5, when x = 5, it is the solution of the original equation.

The price of purchasing 5 yuan for the first time;

(2) First purchase: 500÷5 = 100 kg, second purchase: 3× 100 = 300 kg,

Profit: [100× (1-5 )× 8-500]+[300× (1-2 )× 8-1650 = 962.

A: The first purchase price of fruit is five yuan per kilogram, and the fruit shop sells these fruits at a profit of 962 yuan.

20, Wang (20 12, Urumqi, Xinjiang, 20, 12) said that the score (full score 100) of the campus safety knowledge contest of this course was divided into five groups, 1 group: 50 ≤ X.

(1) Please fill in the frequency distribution table and frequency distribution histogram;

(2) From the students in group 1 and group 5, Wang randomly selects two students to speak, and at least the students who can get the probability are in group 1;

(3) From 1 group and 5 groups, students randomly select the probability and events that score m and n respectively.

[Answer] (1) The frequency distribution table needs to be filled in (upper and lower 2, 0. 16, 20, 50 frequency distribution histogram complete numbers, omitted.

(2) 1, and group 2 is marked as A 1, a2; There are three people in five groups, namely b 1, B2, B3, random A 1, A2, A 1, B 1, B2, A 1, B3, A2, B 1. A2, B3, B 1, B2, B 1, B3, B2, B3, characterized in that at least one student pump in the first group is A 1, A2, A 1, B 1, B2. A2, B2, A2, B3, so at least one student is a group, if they can get the probability.

(3) Being able to get the first group, their lowest score is 50 points, and the scores of the top two students are both lower than 60 points, so it meets the question; I can get five groups of two students, with the lowest score of 90 and the highest score of 100. So the meaning of conformity does not conform to the meaning of the question, that is, the question of A 1 can get two students from the first group and one student from the fifth group, so 30

Three (out of 2 1, 2 1 question, the topic is 1 1 minute, and the 22nd question is1minute).

(20 12, Urumqi, Xinjiang, 2 1,1rest) From B to A, it's 48km away from the bus station, and from B to A, it's northeast, and the speed of trucks is 40km per hour. It takes two hours to drive due north, and the two cars just meet.

(1) Find the speed; BR/>； (2) the value of sin

& ltBR/A.( 1) According to the meaning of the question, two cars meet at BM intersection, intersection C./> From point ⊥CA B to point E, we can see that ∠BAE = 600 is at RT △ AEBAE = ABCOS ∠ BAE = 24km = ABS in ∠ BAE = 40× 2 = 80km.

24km ÷ AC = ∴ CE = AC+AE =104km

∴ speed 1 12km

∴ passenger RT△CEB, BC = =112 ÷ 2 = 56km/h;

(2) As can be seen from the meaning of the question, =∠C, ∴ SINC =

22, (20 12, Urumqi, Xinjiang, 22. 10) as shown in the figure, AB⊙? Diameter, c is a point on the circumference, and the straight line MN passing through point c satisfies ∠MCA =∠CBA.

(1) proves that the straight line MN is tangent ⊙ o;

(2) From the points A, AD⊥MN, D and E, we can know that AB = BC = 3, and find the shadow area.

The answer proves that: (1) connecting oc: ab is ⊙? C is the point on the circumference, ∴∠ACB = 900, that is ∠ACO +∠OCB = 900∵OC = OB, ∴∠OCB =∠OBC, and ∠ MCA. Tangent line;

(2) connection, CE, OE( 1)OC⊥AD⊥MN, MN, oc∑AE

In Rt△ACB, Cosb =∴∠B = 600, so OC = OB = BC = 3, ∴OC = AE quadrilateral AOCE parallelogram, so S△EAC = S△EOC.

So Yin, S = S△ADC-S△ fan EOC.

RT△ACB，BC = 3，AB = 6∴AC = 3

RT△ ADC，AC = 3∠DCA =∠B = 600,∴DC =，AD =

∴ s△ ADC = ad DC = s△ fan EOC =

So S Yin = S△△△fan EOC ADC-S =

Iv. (Full score for this question 10)

23(20 12, Urumqi, Xinjiang, 23. 10 min) The schematic diagram of the parabolic arch FE bridge in the column spans AB 100 m, and the equidistant column supports the bridge, and the horizontal distance between adjacent columns is 10 m (regardless of the column thickness), with the characteristic of/kloc-0.

(1) Find the oc height of the central column;

(2) Whether there is a row of owners' corporations whose height is exactly half, please explain the reasons. BR p> Answer (1) According to the meaning of the question, list the midpoint O of AB after OC.

Figure, the origin of point O, straight line AB, where the X axis is established in a rectangular coordinate system.

The problem is transformed into a ordinate point C = OA-FA = 40 (m), so (50 50,0), E (-40,3.6).

The analytical formula of set parabola is y = ax2+c.

∴ Solution:

When X = 0 and Y = 10, ∴y =-X2+10.

That is, the middle of the column with the height OC is10 (m);

(2) Assuming that there are pillars half the height of a corporation, the operating height of the legislature is 5 meters. ..

5 = 10 inch -x2 solution: = 25

The distance between adjacent columns of ∵ is 10 m, which is a multiple of the meaning of the question on each middle column. According to a point on the Y axis in the column of abscissa OC 10,

∴ = 25, and the meaning of not matching,

The height of the non-existent column OC is exactly half of the height.

BR/>； Five, (this question 12 points)

24(20 12, Urumqi, Xinjiang, 24, 12) For example, point A (-12,0) and point B (3,0) are known in the figure, and the positive half axis of the Y axis of the angular bisector CD of Rt and ∞△ACB is found.

(1) Find the coordinates of point C;

(2) the position of the analytical formula of the straight line L at point C;

(3), meet the requirements for L S△PBC = S△ABC.

(4) It is known that the quadrilateral of points N, O, C, M and N on the plane at points L and M is a rhombus. If it exists, directly write the coordinates of n points; Please indicate the reason. ..

∵

[Answer] Solution: (1)△AOC∽ △COB, with OC2 = OA×OB = 36∴= 6.

Point C on the other Y axis rotates on the axis, so the coordinate of point C is (0,6);

(2) Through point D, DE⊥BC DB, which is 5 meters long.

RT△DEB DE = DB，SINB = M = M = DB cosB = M

In RT△DEC, ∠DEC = 450, so ce = de = m.

Let CE+BE = BC, that is, when m+m = 3, m = 5.

From the known point D, OA = 3 and so = 2, so point D (-2,0);

Let the straight line L analyze the formula: when y = KX+b, when C (0,6) and D (-2,0) are substituted into Y = KX+B.

It is obtained in solution, so the analytical formula of linear rise is: y = 3× 6;

(3) The midpoint f (-4.5,0) taken by1passes through the intersection line L of BC at point F and the AB CF of the connection point P 1.

It is easy to know the meaning of S△P 1BC = S△FBC = S△ACB, ∴ point P 1. BR/>； The straight line P 1F moves one unit to the left from the straight line BC (7.5 units to the left).

The analytical formula of BC line is y =-2X +6,

The linear P 1F solution is y = -2(7.5)6, i.e. >: Y =-2x -9, from point P 1(-3, -3).

② line l, and take P2 C P2 = P 1, where S△P2BC = S△P 1BC is the general meaning of in = S△ACB∴ symbol P2.

C P2 = C, we can get that the coordinates of point P 1 P2 are (3, 15) ∴ point p (-3,3) or P (-3, 15) allows S△PBC = S△APBC.

(4) point N( 1, 3), (), (); .