2012 Urumqi High School Entrance Examination Questions and Answers for All Subjects

2012 Urumqi Junior High School Graduates Academic Proficiency Test

Mathematics Paper

Note:

1, the full score of the paper is 150 points, The exam time is 120 minutes. Use a calculator on the exam.

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

Afterwards, use a 2B pencil to mark the answer to each question in the multiple-choice question. Write the corresponding answer on the answer sheet. Use a clean eraser to mark the changes in other answer marks. If you cannot answer the question again, you can't answer the question. The non-multiple-choice questions must be written on the answer sheet with a 0.5 mm black pen, with neat fonts and clear handwriting.

The 4 non-multiple choice questions must be answered in the order in which the answers appear on the answer sheet. , written responses beyond the clicker or other questions in the title area are not valid. Answer waste paper, invalid questionnaire.

5. Draw the first picture with a 2B pencil to describe the black decision. A 0.5mm black writing pen must be used.

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

Multiple-choice questions (10 major questions, 4 points each, 40 points). Only one topic option matches the question Requirements

(2012, Urumqi, Xinjiang, 1,4) 8 cubic roots ()

A, 2, -2 C±2 D,

A

(2012, Urumqi City, Xinjiang, 2,4 points) The data 8, 7, 6, 5, 7, 8, 8 digits and the mode are ()

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

[Answer] D

3 (2012, Urumqi, Xinjiang, 3, 4) As a geometric shape, side area ()

A, 8 B, C, D, 2 4

Answer B

4, ( 2012, Urumqi, Xinjiang, 4,4 points) In an opaque bag, equipped with black balls and white balls of different colors, a set of experimental balls were touched: the balls, after stirring, were randomly recorded in the color of the bag, repeated on the right side of the table is a set of active data, and the probability of clicking the white ball is approximately ()

A 0.4 B, 0.5 C, 0.6 D, 0.7

[Answer] C p> 5, ( 2012 Xinjiang Urumqi, 5,4) is the square of the length of the side (a + b) of (1), the shaded part in figure (1) consists of the shape of the graph (2), and from this the equation can be verified ()

A (A + B) (A-B) = A2-B2 B, (A + B) 2 - (A2 + B2) = 2AB

Answer] B

(2012 Urumqi, Xinjiang, 6,4 points) Function (k is a constant) image passing through the body (y2) of point (2, y1), then the size relationship between y1 and y2 is ()

A, Y1 Y2, Y1> Y2 D, is related to the value of k< /p>

Answer A

7, (2012, Urumqi, Xinjiang, 7,4) In order to make the city "bluer skies and warmer rooms", the government decided to implement the renovation project , coal and gas heating in winter, now two engineering teams A and B are excavating two 600-meter-long pipes at the same time. As shown in the figure, the digging pipeline length Y (M) and the excavation time x (days) are as follows Statement: 1 A team digs 100 meters for a whole day; ② Team B excavates two days later and digs 50 meters per day; ③ When x = 4, the length of the pipe dug by teams A and B; (4) Group A is better than B The team completed the task two days ahead of schedule.

Correct ()

A, 1 B, 2 C, 3 D, 4

[Answer] D

8 (2012, Urumqi, Xinjiang, 8 , 4) Then flatten ABCD, have a rectangular piece of paper long enough to make a straight crease at point A, fold the piece of paper so that point B falls on side AD, and the intersection of the crease and edge BC is at point E; , then make a straight crease at point E so that point A falls on edge BC, ∠AFE crease EF intersects AD at the edge of the size () of point F

A, 22.50 B, 450 C, 600 D , 67.50

[Answer] D

(Urumqi, Xinjiang, 2012, 9,4 points) Ancient Greek mathematicians 1,3,6,10,15,.... .. .... is called a triangle number, and the difference between the 16 triangles and the 14 triangle numbers is ()

A, 30 B, 31 C, 32 D, 33 A, B

10 (2012 Urumqi, Xinjiang, 10.4 points) AD∥BC, ∠D = 900, AD = 2, BC = 5, DC = DC, P is slightly better. The similarity between △PAD and △PBC is like this A point P ()

A 1 B 2 C 3 D, 4 A. C

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

11. (2012, Urumqi, Xinjiang, 11.4 points) As shown in the figure, straight line A∥B, ∠=°

[Answer] 153

12, (2012, Urumqi, Xinjiang, 12,4) Decomposed factors X3-X =

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

13. (2012 Urumqi, Xinjiang, 13.4 points) In the periphery 20□ABCD, AB

[Answer] 10

14 (2012, Urumqi, Xinjiang, 14,4 points) Function Y = X2 + MX-4, when x <2, Y and x subtract Small, meters

[Answer] M≤-4

15 (2012, Urumqi, Xinjiang, 15,4) Isosceles △ABC is inscribed at a distance of radius 5⊙O Within the range, point O is on the length of sides BC and AB.

A. 2 or 4

Answer the question (question, 9 small questions of the big question, including IV, ***90 points) text description, the answer should be written in Use the corresponding position on the answer sheet to prove or calculate the process.

Me (15 points for this question, 7 minutes, 16 questions, 17 questions, 8 points)

16 (2012, Urumqi, Xinjiang, 16,7 points):

p>

A.] Solution: original formula = 1 +3

= 1

17, (2012, Urumqi, Xinjiang, 17,8 points) Solve the inequality :

[Answer] Solution: Solve for x≥1 2X-1 <3, solve for p>

II (the full score for this question is 32 points, 8 points for questions 18, questions 19 for 12 points, 20 questions for 12 minutes)

18 (2012, Urumqi, Xinjiang, 18,8), E, Confirmation of the diagonal AC and BE∥DF of two points □ABCD in F: BF = DE.

[Answer] Prove: ∵ABCD is a parallelogram

∴AD = CB, AD∥CB,

∴∠BCE =∠DAF

Again ∵ ∥DF,

∴∠BEC = ∠DFA

In △CEB and △AFD,

∠BCE =∠ DAF∠BEC =∠DFA, BC = DA

∴ △CEB≌△AFD

∴BE = DF

Thus the parallelogram of BFED. / The quantity is 3 times the number of people, but the purchase price is 0.5 per kilogram.

(1) First purchase quantity and purchase price of fruits in USD per kilogram?

(2) These fruits sold in fruit shops are 8 yuan per kilogram. The first 5% of the fruit purchased is lost in sales. The fruit shop that purchased the fruit at a loss of 2% sells these fruits profitably. ?

[Answer]Solution: (1) First set the purchase price of the shares to x$ per kilogram of fruit, each problem is solved

After checking, it is x = 5, x = 5 is the solution of the original equation.

The price of the first purchase is 5 yuan;

(2) The first batch of purchase: 500÷5 = 100 kilograms, the second purchase: 3×100 = 300 kilograms, < /p>

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

A: The purchase price of a single purchase of fruits is five yuan per kilogram, and the fruit shop makes a profit of 962 yuan by selling these fruits

20, Wang (2012, Urumqi City, Xinjiang, 20th, 12 points) The results (scores, full score of 100 points) of the campus safety knowledge competition of this course are divided into 5 groups, Group 1: 50≤X <60, Group 2: 60≤X <70,... . ,5:90≤X<100. Draw the frequency distribution table and frequency distribution histogram as shown in the figure (incomplete)

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

(2) Wang From the students in Group 1 and Group 5, two students are randomly selected to speak, and at least the probability of the students in Group 1 can be obtained;

(3) From Groups 1 and 5, Students randomly draw the probabilities that the scores are M, N, and "event".

[Answer] (1) The frequency distribution table needs to be filled in (top and bottom 2, 0.16, 20, 50 frequency distribution histogram completed Numbers, slightly

(2) Groups 1 and 2 are denoted as A1, A2; 3 people in 5 groups are denoted as b1, B2, B3, random A1, A2, A1, B1, A1, B2, A1, B3, A2, B1, A2, B2; A2, B3, B1, B2, B1, B3, B2, B3, characterized in that at least one student in the first group pumps A1, A2, A1, B1, A1, B2, A1, B3, A2, B1; A2, B2, A2 B3, so at least one student in a group, if they can get the probability

(3) can get the first group, their lowest score is 50, and the two highest scores are lower than 60, therefore, it is in line with the meaning of the question; two students can be obtained from five groups, the lowest score is 90, and the highest score is more than 100, therefore, the meaning is not consistent It is in line with the meaning of the question, that is, two students are drawn in the same group, that is, the question A1 can get two students from the first group, and the other one from the 5th group, so 30 < , A2, B1, B2, B1, and b3, B2, B3, therefore, can be used for the probability of the event.

III (Full score of 21 points, 21 questions, and title in 11 minutes, 22nd question in 10 minutes)

(2012, Urumqi, Xinjiang, 21,11 break) is located 48 kilometers in the west-south direction of 600, away from the bus station from B at A, it is along the northeast direction from B, and the truck speed is 40 kilometers per hour A start, two hours of driving along the north direction, the two cars just got to know each other

(1) Find the speed of the car; BR />(2) The value of crime

⊥CA From point B to point E, we can see that ∠BAE = 600 at RT△AEB AE = ABcos ∠BAE = 24 km = ABsin ∠BAE = 40×2 = 80 km

24 km ∵AC = ∴CE = AC + AE = 104 km

∴ Speed ??112 Kilometers

∴ Passenger RT△CEB, BC == 112÷2 =56 kilometers/hour;

(2), we can see from the meaning of the question, =∠C, ∴ Sin SINC =

22, (2012, Urumqi, Xinjiang, 22.10 points) 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) Prove: Straight line MN is tangent line ⊙O;

(2) Pass through point A AD⊥MN to point D, cross ⊙O point E, it is known that AB = BC = 3, find the shaded area.

Answer proof: (1) Connecting OC∵ AB is ⊙? The diameter of , C is a point on the circumference, ∴∠ACB = 900, that is, ∠ACO + ∠OCB = 900 ∵OC = OB, ∴∠OCB = ∠OBC, and ∠MCA = ∠’s CBA, so ∠’s MCA = ∠ OCB∴∠ACO +∠MCA = 900, that is, OC⊥MN, MN line point C ∴ straight line MN⊙? Tangent;

(2) Connection, CE, OE (1) OC⊥AD⊥MN, MN, OC∥AE

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

So Yin, S = S△ADC-S△Fan EOC

p>

RT△ACB, BC = 3, AB = 6∴AC = 3

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

p>

∴S△ADC = AD·DC = S△Fan EOC =

So S Yin = S△△Fan EOC ADC-S =

Four, (this question Full score 10 points)

23 (2012, Urumqi, Xinjiang, 23.10 points) Schematic diagram of the FE Bridge with parabolic arches in columns. The bridge spans AB for 100 meters, the columns supporting the bridge are equidistant, and the adjacent columns are 10 meters apart. The horizontal distance of the column (regardless of the thickness of the column) is characterized by, 10 meters, and the distance from point A in height is 3.6 meters.

(1) Find the OC height of the middle column;

(2) Is there a column whose height is exactly half the OC, please explain the reason. BR p>Answer (1) According to the meaning of the question, the midpoint O of AB after the middle column OC.

In the figure, the origin of point O, the straight line AB, and the X axis, establish a rectangular coordinate system.

The problem is transformed into a vertical coordinate point C = OA-FA = 40 (meters), so (50,0), E (-40, 3.6)

Analysis of set parabola The formula is y = AX2 + C

∴Solution:

∴y =-X2 +10, when X = 0, Y = 10

That is the height The middle of the OC column is 10 (m);

(2) Assuming that there is a column with half the height of the OC, the height of the root legislative operation is 5 m.

5 =-x2 in 10 solution: =±25

The distance between adjacent columns of ∵ is 10 meters, and the middlemost column on each column means a multiple of the problem , according to the abscissa coordinate of a point in the y-axis of column OC 10,

∴=±25, and the problem of mismatched meaning,

The height of ∴ does not exist in column OC Exactly half the height

BR />Five, (12 points for this question)

24 (2012 Urumqi, Xinjiang, 24, 12 o'clock), for example, in the figure, the known point A ( -12,0), B (3,0), find the angular bisector of Rt △ACB, the positive half-axis of the y-axis of CD and ∠ACB = 900

(1) Find the point C Coordinates;

Point C on (2), analytical formula of line l in it;

(3), satisfying L S△PBC = S△ABC

< p>(4) It is known that there are points N, O, C, M on the plane at points L and M. The quadrilateral with N as the vertex is a rhombus. If it exists, directly write the coordinates of point N; if so, please indicate the reason..

∵

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

The other point C on the y-axis is rotating on the wheel axis, so, the coordinates of point C (0,6);

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

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

In RT△DEC, ∠DEC = 450, so, CE = DE = meters

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

From the well-known line segment of point D, OA = 3, so = 2, So point D (-2,0);

Let the analytical formula of straight line l: be y = KX + b, C (0,6) and D (-2,0) are substituted into Y = KX + b,

What is obtained is what is obtained in the solution, so the straight-line analytical formula is: y = 3×6;

(3) The midpoint F taken by 1 ( -4.5,0) The cross line l connecting AB CF of point P1 through point F BC is easy to know, S△P1BC = S△FBC = S△ACB, ∴The meaning of point P1 point. BR />The straight line P1F is shifted left by one unit from the straight line BC (7.5 units left)

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

The solution style of this straight line P1F For y = -2 (7.5) 6 i.e. > Y = -2x of -9, from point P1 (-3, -3)

② line l, and take P2 C P2 = P1, at this time S△P2BC = S△P1BC in = S△ACB∴The general meaning of rune P2.

C P2 = C, it can be obtained that the coordinates of the P1 P2 point are (3,15) ∴ point P (-3, -3) or P (3, 15) allowing S△PBC = S△ APBC

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