mathematics
This paper is divided into two parts: test paper and answer sheet. Test paper ***8 pages, answer sheet ***6 pages. The perfect score is 150. Examination time 120 minutes.
Precautions:
1. When answering questions, candidates must fill in their names and test numbers on the answer sheet with 0.5mm black ink pen, and carefully check the names and test numbers on the bar code.
2. Choose 2B pencil to fill in multiple-choice questions in the corresponding position of the title label on the answer sheet, and write non-multiple-choice questions in the box corresponding to the answer sheet with 0.5mm black ink pen. The answer written beyond the answer area is invalid; Draft paper and test paper are invalid.
3. After the exam, return the test paper and the answer sheet together.
The first volume (multiple choice questions, ***36 points)
1. Multiple-choice questions: This big question consists of 12 small questions, with 3 points for each small question and 36 points for * * *. Of the four options given in each question, only one meets the requirements of the topic.
1, calculation:-1-2 =
a 、- 1 B、 1 C 、-3 D、3
2. The following operations are correct.
a、a+a2=a3 B、2a+3b=5ab
c 、( a3)2=a9 D、a3÷a2=a
3. Throw a cube dice with even texture and six points engraved with 1 respectively, as shown in the figure. Observe the number of points upward. The following are inevitable events.
A, the number of occurrences is 7 B, and the number of occurrences will not be 0.
C, the number of occurrences is 2 D, and the number of occurrences is odd.
4, make the function y = 1-2x meaningful independent variable x value range is
a、x≤ 12 B、x≠ 12 C、x≥ 12 D、x< 12
5. Place a pair of conventional triangular rulers as shown in the figure, and the degree of ∠AOB in the figure is
a、75 B、95 C、 105 D、 120
6. Master Wang nailed four boards into a quadrilateral wooden frame, as shown in the figure. In order to prevent the wooden frame from deforming, he must nail at least a few more sticks.
A, 0 B, 1 C, 2 D and 3.
7. The following statements about rectangles are correct.
A, the quadrilateral with equal diagonal lines is rectangle B, and the quadrilateral with diagonal lines bisecting each other is rectangle.
C, the diagonal lines of the rectangle are perpendicular to each other and divided into two; The diagonals of a rectangle are equal and are divided in two.
8. A building block consists of four identical cubes, the three views of which are shown in the figure, so this building block may be
9. After the disaster, Sichuan moved from tragic to heroic. The victims carried forward the great spirit of earthquake relief, and Guihua Village sent 15 male and female villagers up the mountain to purchase the cement needed for building houses. It is known that a male villager chooses two bags and two female villagers choose one bag, and * * * buys back 15 bags. How many male and female villagers are there in this purchase?
A, 3 male villagers, female villagers 12 b, 5 male villagers, female villagers 10.
C, 6 male villagers, 9 female villagers D, 7 male villagers and 8 female villagers.
On the weekend of 10, Xiao Fang and Xiao Li, who are both 1.6m in height, came to Xijiang Park to calculate the height of the South Tower with their own knowledge, as shown in the figure. Xiao Fang stood at A and measured the elevation angle α of her tower top at 45, while Xiaoli stood at B and measured the elevation angle β of her tower top at 30. They also measured that the distance between point A and point B was 30 meters. Assuming that their eyes are above their heads 10cm, we can calculate the height of the tower (the result is accurate to 0.0 1, and the reference data is 2 ≈1.414,3 ≈1.732).
a，36.2 1m b，37.7 1m c，40.98m d，42.48m。
1 1, as shown in the figure, in the isosceles trapezoid abcd, ABCD, diagonal AC and BD intersect at O, ∠ Abd = 30, AB = 8 cm, then the area of △COD is
A, 433cm2 b, 43cm2 c, 233cm2 d, 23cm2.
12, if x 1 and X2 (x 1 < x2) are two roots of the equation (X-A) (X-B) = 1 (A < B), then the real number x 1, x2, x2.
a、x 1 < x2 < a < b
c、x 1 < a < b < x2 D、a < x 1 < b < x2
Volume 2 (multiple choice questions, *** 1 14)
2. Fill in the blanks: This big question has 6 small questions, each with 4 points and * * * 24 points. Fill in the answers on the horizontal line in the corresponding positions on the answer sheet.
13, decomposition factor: a3-a =.
14, as shown in the figure, AB∨CD, CP cross AB at o, AO = PO, if ∠ C = 50, then ∠ A = degrees.
15,2011April, Mianyang announced the results of the sixth national census. According to the census, the resident population of Mianyang is about 46 1 000, which should be expressed by scientific notation.
16, as shown in the figure, put the regular hexagon ABCDEF in the rectangular coordinate system, and the center of the circle coincides with the origin of the coordinate. If the coordinate of point A is (-1, 0), the coordinate of point C is.
17. As shown in the figure, fold the rectangular paper ABCD with a length of 8cm and a width of 4cm in half, so that the points A and C coincide, and the length of the crease EF is cm.
18. Observe the numbers above. They are arranged according to certain rules. According to this rule, the first number * * * has 120 ★.
Third, the answer: this big question ***7 small questions, ***90 points. The solution should be written in words, proof process or calculation steps.
19, (2 small questions in this question, 8 points for each small question, *** 16 points)
(1) calculation: (12)-2-| 22-3 |+3 18
(2) Solve the equation: 2x2x-5-22x+5 = 1.
20. (The full mark of this question is 12)
Luban Zhuang Jie Company designed the Zhuang Jie for Furong Community, and the investigator designed the following questionnaire to conduct a special investigation on Zhuang Jie style.
Through a random sampling survey of 50 households, the following data are obtained:
A: A: A: A: A: A: A: A: A: A: A: A.
B A A D B A B A B A A C A C B A A D A A A
A: A: A: A: A: A: A: A: A: A: A: A.
(1) Please complete the following statistics on home improvement style:
Percentage of families with decoration style
A. Chinese wind right right 25.50%
B. European style
C. Korean 10%
D. others plus 5 10%
Total 50 100%
(2) Please describe the statistical data in the table (1) with a fan-shaped statistical chart; (Note: Please indicate the degree of the central angle of each part)
(3) If the company wants to recruit 10 decoration designers, how many do you think designers with various decoration styles should recruit respectively?
2 1, (the full mark of this question is 12)
As shown in the figure, the curve is a branch of the image with inverse proportional function y = n+7x.
(1) In which quadrant is the other branch of the inverse proportional function located? What is the range of the constant n?
(2) If the image of the linear function y =-23x+43 intersects with the image of the inverse proportional function at point A, intersects with the X axis at point B, and the area of △AOB is 2, find the value of n. ..
22. (The full mark of this question is 12)
As shown in the figure, in trapezoidal ABCD, ABCD, ∠ bad = 90, and the semicircle O with the diameter of ad is tangent to BC.
(1) verification: ob ⊥ oc;
(2) If AD = 12, ∠ BCD = 60, ⊙O 1 circumscribes a semicircle O and is tangent to BC and CD, find the area of ⊙O 1.
23. (The full mark of this question is 12)
Wang Wei is going to use a 30-meter-long fence to form a triangle to raise rabbits. It is known that the length of the first side is one meter, but due to the terrain limitation, the length of the second side can only be twice the length of the first side, more than 2 meters.
(1) Please use a to indicate the length of the third side;
(2) Can the length of the first side be 7 meters? Why? Please explain the reason and find the range of a.
(3) Can the enclosed small circle be in the shape of a right triangle, and all sides are integers? If yes, explain your enclosure method; If not, please explain why.
24. (The full mark of this question is 12)
It is known that the parabola y = x2-2x+m- 1 has only one intersection with the X axis, and it intersects with point A on the Y axis, as shown in the figure, and its vertex is B. ..
(1) Find the value of m;
(2) It is proved that △ABC is an isosceles right triangle by taking a parallel line with X axis and passing through a parabola at point C;
(3) After the parabola is translated down by 4 units, the parabola C' is obtained, which intersects with the left semi-axis of the X axis at point E, and intersects with the Y axis at point F ... As shown in the figure, the point P on the parabola C' is requested to make △EFP a right triangle with EF as the right.
25. (The full mark of this question is 14)
It is known that △ABC is an isosceles right triangle, ∠ A = 90, D is the moving point on the waist AC, C is the extension line of BD or BD, and the vertical foot is E, as shown in figure 1.
(1) If BD is the center line of AC, as shown in Figure 2, find the value of BDCE;
(2) If BD is the bisector of ∠ABC, as shown in Figure 3, find the value of BDCE;
(3) Combining (1) and (2), please infer the range of BDCE (write a conclusion directly without proof) and explore whether the energy value of BDCE is less than 43. If yes, find the position of point D that meets the conditions; If not, please explain why.
Mianyang Yanting Zouzhou Editing and Finishing
20 1 1 June 28th, 2008