The first volume (multiple choice questions ***30 points)
First, multiple-choice questions (this big question has * * 10 small questions. 3 points for each small question, 30 points for * * *. Only one of the four options given in each small question meets the requirements of the topic)
The arithmetic square root of 1 Yes ()
A.B. C. D。
2. According to the statistics of Jining Tourism Bureau, about 359,525 people came to visit China during the Spring Festival of 20 12. This number of tourists (with three significant figures) is expressed as () by scientific counting method.
A.3.59× B.3.60× C.3.5 × D.3.6 ×
3. The following operation is correct ()
A.B.
C.D.
4. As shown in the figure, the left view of a three-dimensional figure composed of several small cubes is ()
5. The following events determine the event is ()
A. toss a coin, face up. B. Buy a welfare lottery ticket and you win the prize.
Put four balls in three drawers, one of which has at least four balls.
D. Throw an even cube dice, with six faces marked with,,, and respectively, and the odd points face up after the dice stops rotating.
6. If the formula makes sense, the value range of X is ()
A.x≥2 B.x≠3 C.x≥2 or x≠3 D.x≥2 and x≠3.
7. If and are known, the value range of is ().
A.B. C. D。
8. The image of the quadratic function is the same as the image in the shape and opening direction, but the position is different, so the vertex coordinate of the quadratic function is ().
A.()B.() C.() D .()
9. As shown in the figure, P 1 is a point of the inverse proportional function on the first quadrant image, and the coordinates of point A 1 are
(2,0). If △P 1O A 1 and △P2 A 1 A2 are equilateral triangles, then the coordinate of point A2 is ().
A.2 B.2- 1
C.2 D.2- 1
10. In the plane coordinate system, the location of the square ABCD is shown in the figure, and the coordinates are point A (1 0) and point D (0,2). Extend the X axis of CB to point A 1 to form a square A1b1c.
The area of square 20 12 is ()
A.B.
C.D.
Precautions:
1. Volume II, page ***6. Use 0.5mm black ink pen to answer the answer sheet.
2. Fill in the items in the sealed line clearly before answering the questions. Calculators are not allowed to be used during the exam.
Volume 2 (70 points for non-multiple choice questions * *)
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2. Fill in the blanks (This big question has five small questions. 3 points for each small question, *** 15 points. Fill in the answers on the lines in the questions)
1 1. Decomposition factor: 22+4+2 =.
12. When one side of a ruler with a width of 75px is tangent to the circle,
The reading of the intersection of the other side and the circle is as shown in the figure (unit: cm), so the radius of the circle is cm.
13. The result of simplification is _ _ _ _ _ _ _ _.
14. As shown in the figure, in right-angle ABCD, AB=3, AD=4, point P is on AD, PE⊥AC is on E, and PF⊥BD is on F, then PE+PF is equal to.
15. Scroll (not slide) the straight line L of four sides of a square ABCD with a side length of 200px to the right. When the square rolls twice, the length of the route that the vertex A of the square passes is cm.
Third, the solution (this big problem ***8 small problems. * * * 55 points. The solution should be written in words, proof process or calculus steps)
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16.(4 points) Calculation:
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17.(4 points) Solve the equation:.
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18. (The full mark of this question is 6)
(1) (3 points) If a person climbs from the foot of the mountain to the top of the mountain, he needs to climb the hillside first and then find the height of the mountain (as a result, the root mark can be kept).
(2) (3 points) As shown in the figure, among △ABC and △ABD, AD and BC intersect at point O, ∠ 1=∠2. Please add a condition (no more line segments, no more labels or other letters) to make AC=BD, and give proof.
The condition you added is:.
Prove:
[Source: Xue Ke # Net]
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19. (The full mark of this question is 6)
A real estate is going to be sold at an average price of 6000 yuan per square meter. Since the introduction of the new real estate policy in the State Council, property buyers have been holding money to wait and see. In order to speed up the capital turnover, the developers decided to start selling at an average price of 4,860 yuan per square meter after two price reductions.
(1) Find the average percentage of each downward adjustment;
(2) Someone is going to buy a house with an average opening price of 100 square meter, and the developer gives the following two preferential schemes to choose from: ① 9.8% discount for sales; (2) No discount, one-time delivery, decoration cost per square meter of 80 yuan. Which scheme is more favorable?
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20. (The full mark of this question is 7 points)
During the May Day holiday, a company organized some employees to travel to A, B, C and D respectively, and the company purchased air tickets to various places according to the quota. The following figure is a histogram of the types and quantities of unfinished tickets, according to which the following questions are answered:
(1) If the number of tickets to D accounts for 10% of all tickets, request the number of votes to D to complete the statistical chart;
(2) If the company distributes tickets by random lottery, and each person draws one ticket (all tickets are identical in shape, size and texture, and have been fully washed), what is the probability that employee Xiao Hu will be drawn to A?
(3) If both Xiao Wang and Xiao Li want a ticket, they decide to throw a regular tetrahedron dice with 1, 2, 3, 4 on each side. The specific rule is: "Everyone throws it once. If the number of landing sides cast by Xiao Wang is less than that of Xiao Li, the ticket will be given to Xiao Wang, otherwise it will be given to Xiao Li. "
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2 1. (The full mark of this question is 9)
As shown in the figure, the image of inverse proportional function (x > 0) passes through the endpoint A of line segment OA, with O as the origin, AB⊥x axis at point B, and the coordinate of point B is (2,0), and tan∠AOB=.
(1) Find the value of k;
(2) Move the line segment AB to the position of the line segment DC along the positive direction of the X-axis, and the image of the inverse proportional function (x > 0) just passes through the midpoint e of DC, so as to obtain the functional expression of the straight line AE;
(3) If the straight line AE intersects with the X axis at point M, and intersects with the Y axis at point N, please explore the size relationship between the line segment AN and the line segment ME, write your conclusion and explain the reasons.
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22. (The full mark of this question is 9 points)
As shown in figure 1, △ABC is an isosceles right triangle, quadrilateral ADEF is a square, and d and f are on the sides of AB and AC respectively. At this time, BD=CF and BD⊥CF are established.
(1) When the square ADEF rotates counterclockwise around point A θ(0